From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> 1. Expressions have been derived for an estimate of the average coefficient of lift, for the variation in bending moment or torque caused by wind forces and by inertia forces, and for the power output during hovering flight on one spot when the wings move according to a horizontal figure-of-eight. 2. In both hummingbirds and Drosophila the flight is consistent with steady-state aerodynamics, the average lift coefficient being 1.8 in the hummingbird and 0.8 in Drosophila. 3. The aerodynamic or hydraulic efficiency is 0.5 in the hummingbird and 0.3 in Drosophila, and in both types the aerodynamic power output is 22-24 cal/g body weight/h. 4. The total mechanical power output is 39 cal g -1 h -1 in the hummingbird because of the extra energy needed to accelerate the wing-mass. It is 24 cal g -1 h -1 in Drosophila in which the inertia term is negligible because the wing-stroke frequency is reduced to the lowest possible value for sustained flight. 5. In both animals the mechanical efficiency of the flight muscles is 0.2. 6. It is argued that the tilt of the stroke plane relative to the horizontal is an adaptation to the geometrically unfavourable induced wind and to the relatively large lift/drag ratio seen in many insects. The vertical movements at the extreme ends may serve to reduce the interaction between the shed ‘stopping’ vortex and the new bound vortex of opposite sense which has to be built up during the early part of the return stroke. 7. Two additional non-steady flow situations may exist at either end of the stroke, delayed stall and delayed build-up of circulation (Wagner effect), but since they have opposite effects it is probable that the resultant force is of about the same magnitude as that estimated for a steady-state situation. 8. Most insects have an effective elastic system to counteract the adverse effect of wing-inertia, but small fast-moving vertebrates have not. It is argued that the only material available for this purpose in this group is elastin and that it is unsuited at the rates of deformation required because recent measurements have shown that the damping is relatively high, probably due to molecular factors. <s> BIB001 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> 1. Introduction.- 1.1 Gliders.- 1.2 Active Flyers.- 1.3 Outline of the Book.- 2. Basic Aerodynamics.- 2.1 Introduction.- 2.2 The Flow Around an Aerofoil.- 2.2.1 Bernoulli's Equation.- 2.2.2 Reynolds Number.- 2.2.3 Boundary Layer.- 2.3 Blade-Element and Momentum Jet Theories.- 2.3.1 Lift and Drag.- 2.3.2 Power Required to Fly.- 2.4 Vortex Theory of Flight.- 2.4.1 Bound, Trailing and Starting Vortices.- 2.4.2 Steady Motion.- 2.4.3 Lifting-Line Theories.- 2.4.4 Quasi-Steady Assumption.- 2.4.5 Unsteady Effects.- 3. Physiology of Flight.- 3.1 Introduction.- 3.2 Energy and Mechanical Efficiency.- 3.3 Metabolic Rates.- 3.4 Oxygen Uptake.- 3.4.1 Respiratory Mechanics.- 3.4.2 Respiratory Gas Exchange.- 3.4.3 Circulation.- 3.4.4 Oxygen Consumption Versus Body Mass.- 3.4.5 Mass Loss.- 3.4.6 Heat Loss and Exchange.- 3.5 Altitudinal Changes.- 3.6 Estimates for Cost of Flight.- 3.6.1 Direct Measurements of O2 Uptake and CO2 Production.- 3.6.2 Mass Loss.- 3.6.3 Doubly Labelled Water Method.- 3.6.4 Radio Telemetry.- 3.7 Flight Duration, Flight Range and Cost of Transport.- 4. Morphological Flight Parameters.- 4.1 Introduction.- 4.2 Lenghts, Areas, Masses.- 4.3 Wing Shape.- 4.4 Weis-Fogh's and Ellington's Shape Parameters.- 5. Gliding Flight.- 5.1 Introduction.- 5.2 Gliding Performance.- 5.3 Effects of Change in Wingspan on Gliding Performance.- 5.4 Lifting Line Theory.- 5.5 Flap-Gliding.- 5.6 Stability and Control of Movements.- 5.6.1 Pitch.- 5.6.2 Roll.- 5.6.3 Yaw.- 6. Soaring.- 6.1 Introduction.- 6.2 Soaring Methods.- 6.2.1 Slope Soaring.- 6.2.2 Thermal Soaring.- 6.2.3 Gust, Frontal and Wave Soaring.- 6.2.4 Dynamic Soaring.- 6.3 Soaring Performance and Flight Morphology.- 6.3.1 Circling Performance.- 6.3.2 Cross-Country Soaring.- 6.3.3 Wing Shape in Soaring Birds.- 6.4 Bats and Pterosaurs.- 7. Migration.- 7.1 Introduction.- 7.2 Orientation and Navigation.- 7.3 Flight Range.- 7.4 Cruising Speed and Flight Time.- 7.5 Effect of Wind.- 7.6 Evolution of Soaring Migration.- 7.7 Formation Flight.- 8. Hovering Flight.- 8.1 Introduction.- 8.2 Kinematics of Hovering.- 8.3 The Rankine-Froude Momentum Theory.- 8.4 Blade-Element Theory.- 8.4.1 Profile, Parasite and Inertial Power.- 8.4.2 Weis-Fogh's Model for Normal Hovering.- 8.4.3 Norberg's Model for Asymmetrical Hovering.- 8.5 Vortex Theory.- 8.5.1 Ellington's Hovering Model.- 8.5.2 Rayner's Hovering Model.- 8.6 Animals with Sustained Hovering.- 8.7 Summary and for Ecologists and Others: Recipes for Power Calculation.- 8.7.1 Induced Power, Normal Hovering.- 8.7.2 Induced Power, Asymmetrical Hovering.- 8.7.3 Profile Power, Normal Hovering.- 8.7.4 Profile Power, Asymmetrical Hovering.- 8.7.5 Inertial Power.- 9. Forward Flight.- 9.1 Introduction.- 9.2 Wing Kinematics.- 9.3 Relative Airspeeds and Forces.- 9.3.1 Downstroke Forces.- 9.3.2 Upstroke Forces.- 9.4 Vorticity Action.- 9.5 Power Requirements for Horizontal Forward Flight.- 9.5.1 Induced Power.- 9.5.2 Profile Power.- 9.5.3 Parasite Power.- 9.5.4 Inertial Power.- 9.5.5 Flapping Flight with Constant Circulation.- 9.5.6 A Method of Calculating Forces with Blade-Element Theory.- 9.5.7 Comparison Between Different Power Models.- 9.6 Take-Off, Climbing and Landing.- 9.6.1 Take-Off and Climbing.- 9.6.2 Landing.- 9.7 Flight Manoeuvres.- 9.7.1 Turning Ability.- 9.7.2 Maximum Roll Acceleration and the Initiation of a Turn.- 9.7.3 Prey Catching and Landing Manoeuvres.- 9.8 Energy-Saving Types of Flight.- 9.8.1 Bounding Flight.- 9.8.2 Undulating Flight.- 9.8.3 Ground Effect.- 9.9 For Ecologists and Others: Recipes for Power Calculation.- 9.9.1 Induced Power.- 9.9.2 Profile Power.- 9.9.3 Parasite Power.- 9.9.4 Power Required for a Climb.- 9.9.5 Power Required for a Descent.- 9.9.6 Power Required for Bounding Flight.- 9.9.7 Power Required for Undulating Flight.- 10. Scaling.- 10.1 Introduction.- 10.2 Geometric Similarity.- 10.3 Estimated Relationships Between Wing Characteristics and Body Mass.- 10.3.1 Wingspan.- 10.3.2 Wing Area.- 10.3.3 Wing Loading.- 10.3.4 Aspect Ratio.- 10.3.5 Flight Speed, Power and Cost of Transport.- 10.3.6 Flight Muscle Masses.- 10.3.7 Wingbeat Frequency.- 10.4 Upper and Lower Size Limits.- 11. Morphological Adaptations for Flight.- 11.1 Introduction.- 11.2 Muscle System.- 11.2.1 Muscle Fibre Structure and Function.- 11.2.2 The Structure of Bird Muscle Fibres.- 11.2.3 The Structure of Bat Muscle Fibres.- 11.2.4 Contraction Rate and Wingbeat Frequency.- 11.2.5 Body Size, Wing Shape and Flight Muscle Fibres - a Summary.- 11.2.6 Flight Muscle Power.- 11.2.7 Flight Muscle Structure.- 11.2.8 Muscle Arrangements.- 11.2.9 The Main Flight Muscles.- 11.3 Skeleton System.- 11.3.1 Trunk Skeleton.- 11.3.2 Pectoral Girdle.- 11.3.3 Wing Skeletal and Membrane Arrangements.- 11.3.4 Were Pterosaurs Quadrupedal or Bipedal?.- 11.4 Feather Structure and Function.- 11.4.1 Main Structure.- 11.4.2 Vane Asymmetry and Feather Curvature.- 11.4.3 Flight Feathers of Archaeopteryx.- 11.4.4 Silent Flight.- 11.5 Wing Adaptations Enhancing Flight Performance.- 11.5.1 Wing Camber.- 11.5.2 Wing Flaps.- 11.5.3 Turbulence Generators.- 11.5.4 Wing Slots.- 11.5.5 Energy-Saving Elastic Systems.- 11.6 Tail and Feet.- 12. Flight and Ecology.- 12.1 Introduction.- 12.2 Predictions on Wing Shape and Flight Behaviour.- 12.3 Wing Design in Birds.- 12.3.1 Continuous Foraging Flights.- 12.3.2 Perching.- 12.3.3 Locomotion Among Vegetation.- 12.3.4 Migratory Species.- 12.3.5 Foraging on Ground or in Water.- 12.4 Wing Shape and Foraging Energetics of Hummingbirds at Different Altitudes.- 12.5 Wing Design of Species in a Pariform Guild.- 12.6 Wing Design in Bats.- 12.7 Wing Design and Echolocation Call Structure in Bats.- 12.8 Evolution of Wing Morphology.- 13. Evolution of Flight.- 13.1 The Major Theories.- 13.1.1 Trees-Down Theory.- 13.1.2 Ground-Up Theory.- 13.2 Transition from Gliding to Flapping Flight, an Aerodynamic Model.- 13.3 The Ground-Running and Jumping Scenario, a Discussion.- 13.4 The Climbing Ability in Proto-Fliers.- 14. Concluding Remarks.- References. <s> BIB002 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> The `umbrella effect', a mechanism of camber generation in the hindwing fans of orthopteroid and dictyopteroid insects, is modelled geometrically and mechanically, treating the fan as a framework whose outer margin describes a truncated logarithmic spiral. Tension in the margin compresses the radial veins, causing them to undergo Euler buckling. The model describes the distribution of compression forces in the veins around the spiral, and predicts conditions which must be met, and departures from the model expected in real wings. Actual insects fit the model and predictions quite well. The functional implications, and those of departure from the model, are discussed. <s> BIB003 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> INSECTS cannot fly, according to the conventional laws of aerodynamics: during flapping flight, their wings produce more lift than during steady motion at the same velocities and angles of attack1–5. Measured instantaneous lift forces also show qualitative and quantitative disagreement with the forces predicted by conventional aerodynamic theories6–9. The importance of high-life aerodynamic mechanisms is now widely recognized but, except for the specialized fling mechanism used by some insect species1,10–13, the source of extra lift remains unknown. We have now visualized the airflow around the wings of the hawkmoth Manduca sexta and a 'hovering' large mechanical model—the flapper. An intense leading-edge vortex was found on the down-stroke, of sufficient strength to explain the high-lift forces. The vortex is created by dynamic stall, and not by the rotational lift mechanisms that have been postulated for insect flight14–16. The vortex spirals out towards the wingtip with a spanwise velocity comparable to the flapping velocity. The three-dimensional flow is similar to the conical leading-edge vortex found on delta wings, with the spanwise flow stabilizing the vortex. <s> BIB004 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Visualization experiments with Manduca sexta have revealed the presence of a leading-edge vortex and a highly three-dimensional flow pattern. To further investigate this important discovery, a scaled-up robotic insect was built (the 'flapper') which could mimic the complex movements of the wings of a hovering hawkmoth. Smoke released from the leading edge of the flapper wing revealed a small but strong leading-edge vortex on the downstroke. This vortex had a high axial flow velocity and was stable, separating from the wing at approximately 75 per cent of the wing length. It connected to a large, tangled tip vortex, extending back to a combining stopping and starting vortex from pronation. At the end of the downstroke, the wake could be approximated as one vortex ring per wing. Based on the size and velocity of the vortex rings, the mean lift force during the downstroke was estimated to be about 1.5 times the body weight of a hawkmoth, confirming that the downstroke is the main provider of lift force. <s> BIB005 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> The aerodynamic mechanisms employed durng the flight of the hawkmoth, Manduca sexta, have been investigated through smoke visualization studies with tethered moths. Details of the flow around the wings and of the overall wake structure were recorded as stereophotographs and high-speed video sequences. The changes in flow which accompanied increases in flight speed from 0.4 to 5.7 m s-1 were analysed. The wake consists of an alternating series of horizontal and vertical vortex rings which are generated by successive down- and upstrokes, respectively. The downstroke produces significantly more lift than the upstroke due to a leading-edge vortex which is stabilized by a radia flow moving out towards the wingtip. The leading-edge vortex grew in size with increasing forward flight velocity. Such a phenomenon is proposed as a likely mechanism for lift enhancement in many insect groups. During supination, vorticity is shed from the leading edge as postulated in the 'flex' mechanism. This vorticity would enhance upstroke lift if it was recaptured diring subsequent translation, but it is not. Instead, the vorticity is left behind and the upstroke circulation builds up slowly. A small jet provides additional thrust as the trailing edges approach at the end of the upstroke. The stereophotographs also suggest that the bound circulation may not be reversed between half strokes at the fastest flight speeds. <s> BIB006 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> The free flapping flight of the dragonfly Sympetrum sanguineum and the damselfly Calopteryx splendens was filmed in a large flight enclosure at 3000 frames s-1. The wingtip kinematics are described for these flights. Despite the two species being similar in size, the damselfly flew with wingbeat frequencies half those of the dragonfly. The damselfly could perform a clap and fling, and the proximity to which the wings approached each other during this manoeuvre correlated with the total force produced during the wingstroke. The dragonfly beat its wings with a set inclination of the stroke planes with respect to the londitudinal body axis; the damselfly, in contrast, showed a greater variation in this angle. Both species aligned their stroke planes to be nearly normal to the direction of the resultant force, the thrust. In order to achieve this, the dragonfly body alignment correlated with the direction of thrust. However, the damselfly body alignment was independent of the thrust direction. Velocities and accelerations were greater for the dragonfly than for the damselfly. However, non-dimensional velocities and accelerations normalised by the wingbeat periods were greater for the damselfly. <s> BIB007 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> The elevated aerodynamic performance of insects has been attributed in part to the generation and maintenance of a stable region of vorticity known as the leading edge vortex (LEV). One explanation for the stability of the LEV is that spiraling axial flow within the vortex core drains energy into the tip vortex, forming a leading-edge spiral vortex analogous to the flow structure generated by delta wing aircraft. However, whereas spiral flow is a conspicuous feature of flapping wings at Reynolds numbers (Re) of 5000, similar experiments at Re=100 failed to identify a comparable structure. We used a dynamically scaled robot to investigate both the forces and the flows created by a wing undergoing identical motion at Re of ~120 and ~1400. In both cases, motion at constant angular velocity and fixed angle of attack generated a stable LEV with no evidence of shedding. At Re=1400, flow visualization indicated an intense narrow region of spanwise flow within the core of the LEV, a feature conspicuously absent at Re=120. The results suggest that the transport of vorticity from the leading edge to the wake that permits prolonged vortex attachment takes different forms at different Re. <s> BIB008 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Despite profound musculoskeletal differences, hummingbirds (Trochilidae) are widely thought to employ aerodynamic mechanisms similar to those used by insects. The kinematic symmetry of the hummingbird upstroke and downstroke has led to the assumption that these halves of the wingbeat cycle contribute equally to weight support during hovering, as exhibited by insects of similar size. This assumption has been applied, either explicitly or implicitly, in widely used aerodynamic models and in a variety of empirical tests. Here we provide measurements of the wake of hovering rufous hummingbirds (Selasphorus rufus) obtained with digital particle image velocimetry that show force asymmetry: hummingbirds produce 75% of their weight support during the downstroke and only 25% during the upstroke. Some of this asymmetry is probably due to inversion of their cambered wings during upstroke. The wake of hummingbird wings also reveals evidence of leading-edge vortices created during the downstroke, indicating that they may operate at Reynolds numbers sufficiently low to exploit a key mechanism typical of insect hovering. Hummingbird hovering approaches that of insects, yet remains distinct because of effects resulting from an inherently dissimilar-avian-body plan. <s> BIB009 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> [Abstract] Hummingbirds fly with their wings almost fully extended during their entire wingbeat. This pattern, associated with having proportionally short humeral bones, long distal wing elements, and assumed to be an adaptation for extended hovering flight, has lead to predictions that the aerodynamic mechanisms exploited by hummingbirds during hovering should be similar to those observed in insects. To test these predictions, we flew rufous hummingbirds (Selasphorus rufus, 3.3 g, n = 6) in a variable–speed wind tunnel (0-12 ms) and measured wake structure and dynamics using digital particle image velocimetry (DPIV). Unlike hovering insects, hummingbirds produced 75% of their weight support during downstroke and only 25% during upstroke, an asymmetry due to the inversion of their cambered wings during upstroke. Further, we have found no evidence of sustained, attached leading edge vorticity (LEV) during up or downstroke, as has been seen in similarly-sized insects although a transient LEV is produced during the rapid change in angle of attack at the end of the downstroke. Finally, although an extended-wing upstroke during forward flight has long been thought to produce lift and negative thrust, we found circulation during downstroke alone to be sufficient to support body weight, and that some positive thrust was produced during upstroke, as evidenced by a vortex pair shed into the wake of all upstrokes at speeds of 4 – 12 m s. <s> BIB010 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> The flapping flight of animals generates an aerodynamic footprint as a time-varying vortex wake in which the rate of momentum change represents the aerodynamic force. We showed that the wakes of a small bat species differ from those of birds in some important respects. In our bats, each wing generated its own vortex loop. Also, at moderate and high flight speeds, the circulation on the outer (hand) wing and the arm wing differed in sign during the upstroke, resulting in negative lift on the hand wing and positive lift on the arm wing. Our interpretations of the unsteady aerodynamic performance and function of membranous-winged, flapping flight should change modeling strategies for the study of equivalent natural and engineered flying devices. <s> BIB011 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Staying aloft when hovering and flying slowly is demanding. According to quasi-steady-state aerodynamic theory, slow-flying vertebrates should not be able to generate enough lift to remain aloft. Therefore, unsteady aerodynamic mechanisms to enhance lift production have been proposed. Using digital particle image velocimetry, we showed that a small nectar-feeding bat is able to increase lift by as much as 40% using attached leading-edge vortices (LEVs) during slow forward flight, resulting in a maximum lift coefficient of 4.8. The airflow passing over the LEV reattaches behind the LEV smoothly to the wing, despite the exceptionally large local angles of attack and wing camber. Our results show that the use of unsteady aerodynamic mechanisms in flapping flight is not limited to insects but is also used by larger and heavier animals. <s> BIB012 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Aerodynamic theory and empirical observations of animals flying at similar Reynolds numbers (Re) predict that airflow over hummingbird wings will be dominated by a stable, attached leading edge vortex (LEV). In insects exhibiting similar kinematics, when the translational movement of the wing ceases (as at the end of the downstroke), the LEV is shed and lift production decreases until the energy of the LEV is re-captured in the subsequent half-cycle translation. We here show that while the hummingbird wing is strongly influenced by similar sharp-leading-edge aerodynamics, leading edge vorticity is inconsistent, varying from 0.7 to 26 per cent (mean 16%) of total lift production, is always generated within 3 mm of the dorsal surface of the wing, showing no retrograde (trailing to leading edge) flow, and does not increase from proximal to distal wing as would be expected with a conical vortex (class III LEV) described for hawkmoths. Further, the bound circulation is not shed as a vortex at the end of translation, but instead remains attached and persists after translation has ceased, augmented by the rotation (pronation, supination) of the wing that occurs between the wing-translation half-cycles. The result is a near-continuous lift production through wing turn-around, previously unknown in vertebrates, able to contribute to weight support as well as stability and control during hovering. Selection for a planform suited to creating this unique flow and nearly-uninterrupted lift production throughout the wingbeat cycle may help explain the relatively narrow hummingbird wing. <s> BIB013 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> The interest in flapping wing MAVs has been rising progressively in the past years. The complex aerodynamic mechanisms responsible for high manoeuvrability and energy efficient lift production have been modelled by multiple techniques. Here we present a comparison of several models from the perspective of flight stability in hover. We estimated the stability derivatives by aerodynamic models of various levels of complexity, ranging from analytical expressions derived from a quasi steady model to CFD results that were taken as a reference. The stability of the complete 6DOF linearized system, split into longitudinal and lateral part, was evaluated in terms of eigenvalues and eigenvectors. While the pole locations and modes of longitudinal system were consistent for all the models (two stable subsidence modes, one unstable oscillatory mode), the lateral dynamics showed that quasi steady models with only translational force are insufficient and revealed the necessity of including the rotational lift to obtain pole locations that are in accordance with the CFD study (one slow divergence mode, one fast subsidence mode and one stable oscillatory mode). <s> BIB014 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Most hovering animals, such as insects and hummingbirds, enhance lift by producing leading edge vortices (LEVs) and by using both the downstroke and upstroke for lift production. By contrast, most hovering passerine birds primarily use the downstroke to generate lift. To compensate for the nearly inactive upstroke, weight support during the downstroke needs to be relatively higher in passerines when compared with, e.g. hummingbirds. Here we show, by capturing the airflow around the wing of a freely flying pied flycatcher, that passerines may use LEVs during the downstroke to increase lift. The LEV contributes up to 49 per cent to weight support, which is three times higher than in hummingbirds, suggesting that avian hoverers compensate for the nearly inactive upstroke by generating stronger LEVs. Contrary to other animals, the LEV strength in the flycatcher is lowest near the wing tip, instead of highest. This is correlated with a spanwise reduction of the wing's angle-of-attack, partly owing to upward bending of primary feathers. We suggest that this helps to delay bursting and shedding of the particularly strong LEV in passerines. <s> BIB015 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Visualization of the vortex wake of a flying animal provides understanding of how wingbeat kinematics are translated into the aerodynamic forces for powering and controlling flight. Two general vortex flow patterns have been proposed for the wake of hovering hummingbirds: (1) The two wings form a single, merged vortex ring during each wing stroke; and (2) the two wings form bilateral vortex loops during each wing stroke. The second pattern was proposed after a study with particle image velocimetry that demonstrated bilateral source flows in a horizontal measurement plane underneath hovering Anna’s hummingbirds (Calypte anna). Proof of this hypothesis requires a clear perspective of bilateral pairs of vortices. Here, we used high-speed image sequences (500 frames per second) of C. anna hover feeding within a white plume to visualize the vortex wake from multiple perspectives. The films revealed two key structural features: (1) Two distinct jets of downwards airflow are present under each wing; and (2) vortex loops around each jet are shed during each upstroke and downstroke. To aid in the interpretation of the flow visualization data, we analyzed high-speed kinematic data (1,000 frames per second) of wing tips and wing roots as C. anna hovered in normal air. These data were used to refine several simplified models of vortex topology. The observed flow patterns can be explained by either a single loop model with an hourglass shape or a bilateral model, with the latter being more likely. When hovering in normal air, hummingbirds used an average stroke amplitude of 153.6° (range 148.9°–164.4°) and a wingbeat frequency of 38.5 Hz (range 38.1–39.1 Hz). When hovering in the white plume, hummingbirds used shallower stroke amplitudes ($$ \bar{x} $$ = 129.8°, range 116.3°–154.1°) and faster wingbeat frequencies ($$ \bar{x} $$ = 41.1 Hz, range 38.5–44.7 Hz), although the bilateral jets and associated vortices were observed across the full kinematic range. The plume did not significantly alter the air density or constrain the sustained muscle contractile frequency. Instead, higher wingbeat frequencies likely incurred a higher metabolic cost with the possible benefit of allowing the birds to more rapidly escape from the visually disruptive plume. <s> BIB016 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> While producing one of the highest sustained mass-specific power outputs of any vertebrate, hovering hummingbirds must also precisely modulate the activity of their primary flight muscles to vary wingbeat kinematics and modulate lift production. Although recent studies have begun to explore how pectoralis (the primary downstroke muscle) neuromuscular activation and wingbeat kinematics are linked in hummingbirds, it is unclear whether different species modulate these features in similar ways, or consistently in response to distinct flight challenges. In addition, little is known about how the antagonist, the supracoracoideus, is modulated to power the symmetrical hovering upstroke. We obtained simultaneous recordings of wingbeat kinematics and electromyograms from the pectoralis and supracoracoideus in ruby-throated hummingbirds (Archilochus colubris) hovering under the following conditions: (1) ambient air, (2) air density reduction trials, (3) submaximal load-lifting trials and (4) maximal load-lifting trials. Increased power output was achieved through increased stroke amplitude during air density reduction and load-lifting trials, but wingbeat frequency only increased at low air densities. Overall, relative electromyographic (EMG) intensity was the best predictor of stroke amplitude and is correlated with angular velocity of the wingtip. The relationship between muscle activation intensity and kinematics was independent of treatment type, indicating that reduced drag on the wings in hypodense air did not lead to high wingtip angular velocities independently of increased muscle work. EMG bursts consistently began and ended before muscle shortening under all conditions. During all sustained hovering, spike number per burst consistently averaged 1.2 in the pectoralis and 2.0 in the supracoracoideus. The number of spikes increased to 2.5-3 in both muscles during maximal load-lifting trials. Despite the relative kinematic symmetry of the hovering downstroke and upstroke, the supracoracoideus was activated ~1 ms earlier, EMG bursts were longer (~0.9 ms) and they exhibited 1.6 times as many spikes per burst. We hypothesize that earlier and more sustained activation of the supracoracoideus fibres is necessary to offset the greater compliance resulting from the presence of the supracoracoid tendon. <s> BIB017 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Hummingbirds are specialized hoverers for which the vortex wake has been described as a series of single vortex rings shed primarily during the downstroke. Recent findings in bats and birds, as well as in a recent study on Anna's hummingbirds, suggest that each wing may shed a discrete vortex ring, yielding a bilaterally paired wake. Here, we describe the presence of two discrete rings in the wake of hovering Anna's hummingbirds, and also infer force production through a wingbeat with contributions to weight support. Using flow visualization, we found separate vortices at the tip and root of each wing, with 15% stronger circulation at the wingtip than at the root during the downstroke. The upstroke wake is more complex, with near-continuous shedding of vorticity, and circulation of approximately equal magnitude at tip and root. Force estimates suggest that the downstroke contributes 66% of required weight support, whereas the upstroke generates 35%. We also identified a secondary vortex structure yielding 8-26% of weight support. Lift production in Anna's hummingbirds is more evenly distributed between the stroke phases than previously estimated for Rufous hummingbirds, in accordance with the generally symmetric down- and upstrokes that characterize hovering in these birds. <s> BIB018 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Animal fliers frequently move through a variety of perturbed flows during their daily aerial routines. However, the extent to which these perturbations influence flight control and energetic expenditure is essentially unknown. Here, we evaluate the kinematic and metabolic consequences of flight within variably sized vortex shedding flows using five Anna's hummingbirds feeding from an artificial flower in steady control flow and within vortex wakes produced behind vertical cylinders. Tests were conducted at three horizontal airspeeds (3, 6 and 9 m s−1) and using three different wake-generating cylinders (with diameters equal to 38, 77 and 173% of birds' wing length). Only minimal effects on wing and body kinematics were demonstrated for flight behind the smallest cylinder, whereas flight behind the medium-sized cylinder resulted in significant increases in the variances of wingbeat frequency, and variances of body orientation, especially at higher airspeeds. Metabolic rate was, however, unchanged relative to that of unperturbed flight. Hummingbirds flying within the vortex street behind the largest cylinder exhibited highest increases in variances of wingbeat frequency, and of body roll, pitch and yaw amplitudes at all measured airspeeds. Impressively, metabolic rate under this last condition increased by up to 25% compared with control flights. Cylinder wakes sufficiently large to interact with both wings can thus strongly affect stability in flight, eliciting compensatory kinematic changes with a consequent increase in flight metabolic costs. Our findings suggest that vortical flows frequently encountered by aerial taxa in diverse environments may impose substantial energetic costs. <s> BIB019 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> Experiments on leading-edge vortex (LEV) growth and detachment from a plunging profile have been conducted in a free-surface water tunnel. Direct-force and velocity-field measurements have been performed at a Reynolds number of Re = 10,000, a reduced frequency of k = 0.25, and a Strouhal number of St = 0.16, for three varying leading-edge geometries. The leading-edge shape is shown to influence the shear layer feeding the LEV, and thus to some extent the development of the LEV and associated flow topology. This effect in turn influences the arrival time of the rear (LEV) stagnation point at the trailing edge, which, once breached, constitutes a detachment of the LEV. It is found that despite minor phase changes in LEV detachment through leading-edge shape, the position of the trailing edge (chord length) should be chosen as the characteristic length scale for the vortex separation process. <s> BIB020 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> More than a million insects and approximately 11,000 vertebrates utilize flapping wings to fly. However, flapping flight has only been studied in a few of these species, so many challenges remain in understanding this form of locomotion. Five key aerodynamic mechanisms have been identified for insect flight. Among these is the leading edge vortex, which is a convergent solution to avoid stall for insects, bats and birds. The roles of the other mechanisms - added mass, clap and fling, rotational circulation and wing-wake interactions - have not yet been thoroughly studied in the context of vertebrate flight. Further challenges to understanding bat and bird flight are posed by the complex, dynamic wing morphologies of these species and the more turbulent airflow generated by their wings compared with that observed during insect flight. Nevertheless, three dimensionless numbers that combine key flow, morphological and kinematic parameters - the Reynolds number, Rossby number and advance ratio - govern flapping wing aerodynamics for both insects and vertebrates. These numbers can thus be used to organize an integrative framework for studying and comparing animal flapping flight. Here, we provide a roadmap for developing such a framework, highlighting the aerodynamic mechanisms that remain to be quantified and compared across species. Ultimately, incorporating complex flight maneuvers, environmental effects and developmental stages into this framework will also be essential to advancing our understanding of the biomechanics, movement ecology and evolution of animal flight. <s> BIB021 </s> From Studying Real Hummingbirds to Designing Hummingbird-Like Robots—A Literature Review <s> IV. AERODYNAMICS OF HUMMINGBIRDS <s> This study describes the design, development, and flight tests of a novel control mechanism to generate yaw control torque of a hovering robotic hummingbird (known as Colibri). The proposed method ... <s> BIB022
Although hummingbirds and insects have evolved for sustaining hovering flight, the distinct phylogenies resulted in their different aerodynamic styles. In modern times, the kinematics of hovering hummingbirds was firstly studied in 1939  and an aerodynamic model of hummingbird flight was developed in 1972 BIB001 . It is observed that the hummingbirds' flight feature is no dissimilar to insect flight, although hummingbirds operated at higher Reynolds number than that of insect. Therefore, it is hypothesized that similar kinematics and aerodynamic mechanisms are used in hummingbirds and insects when hovering BIB002 . In recent years, a number of studies on the kinematics, aerodynamics and flight dynamics of hummingbird are done, which reveals that how the hummingbird achieves its aerobatic feats BIB017 , BIB014 , BIB019 . Hummingbirds are capable of flying in hovering with fully extended wing during the entire wingbeat, which is related to the short humeral bones, long distal wing elements. However, by studying the wake of hummingbird wings, it was found that hovering in hummingbirds approaches that of insects, but remains distinct  . Hummingbirds produce pseudo-symmetrical wingbeat cycle in hovering, whereas insects exhibit an elegant aerodynamic symmetry. By studying Rufous hummingbirds hovering, 75% of the weight support is produced in the period of the downstroke, and only 25% during the upstroke BIB009 . Similarly, it is found that 66% of weight support in Anna's hummingbirds is generated during the downstroke in Wolf's study BIB018 . And the further study reveals that the far-failed wake of the hummingbird is remarkably similar to that produced by the hawkmoths BIB005 . Then the asymmetry is also presented partly due to inversion of the cambered wings during the upstroke. It means that such asymmetry was at least in part due to the positive camber of the hummingbird wings, which results in incomplete reversal during the upstroke. By contrast, the aerodynamic BIB003 and inertial forces  contributed by elastic qualities of insects wings allow their wings to reverse their camber fully, therefore, high lift coefficients can be created during both half-strokes BIB006 . On top of that, the ability producing the symmetrical wingbeat cycle for hovering hummingbird is strongly limited due to the fundamental musculoskeletal and the properties of platform materials, although strong similarities are present in the wing kinematics of hummingbirds consisting with certain insects such as hawkmoth and manducasexta. Compared with insects' flight, the understanding of hummingbirds aerodynamics remains limited due to the highly complex morphology of vertebrate wings and the air flow related to their flight at low Reynolds numbers. However, certain aerodynamic mechanisms have been studied and understand improving lift across both insects and hummingbirds like a leading-edge vortex (LEV) which is a convergent solution to prevent the stall. For a flapping wing, the LEV remains stably attached as was first presented in paper BIB004 and confirmed by  . By the wake study of hummingbird wings, it is found that LEVs may dominate at low Reynolds numbers during the downstroke. However, LEVs is exploited as a key mechanism typical of insect hovering  . The attached LEV contributes to sustaining the high lift generation. Similar LEVs are also produced when hummingbird wings are modelled as flat plates BIB010 . And it is observed that a wide range of flyers or biological wings applies LEVs to control their flight BIB021 . By studying of robotic insects, it is found that such aerodynamic mechanism might improve lift by up to 45% in hovering fruit flies  and support up to two-thirds of the lift during the downstroke in hovering hawkmoths BIB005 , BIB021 , BIB007 . Up to 40% of lift is enhanced by the LEV in slow-flying bats BIB012 . For hummingbirds, it can occur up to 26% of the total lift in hovering BIB013 and about 50% of the lift in some forward flying birds BIB015 . Hummingbirds flap one cycle including downstroke and upstroke. Generally, the hummingbird wing rapidly decelerates at the end of upstroke, and re-accelerates at the beginning of the downstroke when rotating, further to say; the wings may pitch during translation to further enhance lift production. The path of the wingtip is more or less equal for both half strokes. By the wake study for hovering Rufous hummingbird in steady position BIB009 , it is observed that there was sufficient circulation in the tip vortices and adequate separation between vortex cores. Wake structures consist of LEVs produced during the downstroke. The two cores of vortices, both rotating in the same direction, were shed in quick succession during the transition from downstroke to upstroke. The key of using LEVs as lift mechanisms is that they are stable enough to remain attached to the wing during translation, rather than to be shed into the wake, as the lift will be lost when stalling. Birch and Lehmann's study reveals that the persistent LEVs are possibly made by stable flows at low Reynolds number BIB008 , and such mechanism may be only available to small fliers  ,  . Certainly, some insects use wing rotation to produce lift when wing turning-around  , that is to say, the wing rotation contributes to the high lift generation during stoke reversals of some wing kinematics, however, they also use the delayed stall mechanism to sustain the high lift generation during the stoke. And the circulation of the LEVs shed at the end of half-cycle can be re-captured in the subsequent reversing half cycle. Currently, by a theoretical and experimental study of aerodynamics, it is observed that a stable and attached LEV around hummingbird wings is primarily airflow when hovering, which is not dissimilar kinematics of insects. And the LEV is shed when translation ceases at the end of the downstroke, which results in lift decrease (except for next half-cycle translation re-started). Warrick's study shows that LEVs are inconsistent and vary a lot from approximate 0.7 to 26% (16 % on average, for details to see BIB013 ) of the total lift production when the hummingbird wing is strongly influenced by similar sharpleading-edge aerodynamics BIB009 , BIB013 . In addition, LEVs are always generated within 3mm of the dorsal surface of wings, showing no retrograde (trailing to leading edge) flow BIB013 . The bound circulations remain attached and persist, not shed as a vortex at the end of translation, and are augmented by the wing rotation between each half-cycle of the wingtranslation. A near-continuous lift BIB013 can be generated by wing turning-around, which contributes to weight support, stability, and adjustment when hovering. At the same time, the chord length has been widely discussed with regard to the LEV formation and shedding BIB020 . Actually, the wake of a hummingbird in hovering mode is more complex. Different species of hummingbird may have distinct wakes when hovering. The study of Warrick et al. BIB009 suggests that 64% of weight support should be produced during downstroke at the slight differences in kinematics between the stroke phases. While, indeed, 66% (on average) of weight support in Anna's hummingbirds BIB018 . Regarding hovering Anna's hummingbirds, their wings generate individual ring structures in each stroke, and such wake consists of separate vortex loops for each wing. These vortex loops are shed at the end of the downstroke and move ventrally, whereas the shed loops move dorsally during the upstroke. In Wolf's study BIB018 , it is discovered that 66% of weight support in hovering Anna's hummingbirds is generated during the downstroke. On top of that, the identified secondary vortex as a LEV is always shed at the end of the downstroke and varied considerably in strength. The 16% of weight support is produced on average by the secondary vortex, which is similar to Rufous hummingbirds BIB009 . Similarly, 65% of support weight in the hovering hawkmoth is generated as well by the LEV BIB005 . Further study revealed that the strength of the vortex at the wing root is about 15% less than the circulation of the tip vortex but remains quite higher than that of slow-flying bats BIB018 . The root circulation in slow-flying bats was only 42% of that at the tip BIB012 . By wake measurement, it is indicated that a more evenly distributed vertical force of Anna's hummingbirds is produced between the wing strokes than that of hovering Rufous hummingbirds BIB018 . And the bilateral vortex was found in hovering Anna's hummingbirds with comparatively strong root vortices BIB018 . Similarly, a bilaterally symmetric wake with one vortex ring is also generated by each wing for bat BIB011 . Meanwhile, their wings are fully extended in hovering throughout the entire wingbeat cycle and generate lift during one cycle BIB002 . Although the bats produce a bilateral wake too, the span efficiency of the bat is lower than that of slow-flying flycatchers BIB012 . Therefore, it is guessed that the hummingbirds might also have lower span efficiency BIB012 . By contrast, from their visualization study, Pournazeri et al. BIB016 identified neither stop nor started vortices of the wake of hovering Anna's hummingbirds. They discovered separated stop vortices for the downstroke and started vortices for the upstroke, but also a combined start/stop vortex at the end of downstroke and the beginning of upstroke, in agreement with what has previously been identified for Rufous hummingbirds BIB009 . Transitions between stroke phases and wing rotations occur quickly, which can lead to a merge of individual vortex structures and result in complex wake configurations. Meanwhile, they found no bilateral vortex loops, which is different from Wolf's study. Nevertheless, although researchers could obtain different results for different species of hummingbirds when hovering, they have a common point that LEVs are playing essential roles for hovering hummingbirds. To investigate the aerodynamics of hovering natural flyers, the full computational fluid dynamics (CFD) and the quasisteady method have been used for the analysis of flapping wings. The full CFD models can provide more information about 3D flow pattern and force characteristics prediction, which is lack of the quasi-steady method. But the quasisteady method is efficient tool for fast analysis as well as can revise the translation force, rotational force, and acceleration effect to address the unique features of flapping wings  . The study of aerodynamics on hummingbirds is quite important not only understanding on flight principle but also utilizing to control stability of flapping wing MAV. At present, many controllers are designed based on the aerodynamics of hummingbirds. Adaptive robust wing trajectory control was applied on flapping wing MAV BIB020 . A comparison of various aerodynamic models was studied on flapping flight stability in hovering BIB014 . Roshanbin A and Preumont A studied the yaw control torque generation in hovering hummingbird-like MAV BIB022 . And PD controller is applied as well in the hummingbird-like MAV  ,  [51]. 