Wingtip Velocity Research Articles

Scaling the vorticity dynamics in the leading-edge vortices of revolving wings with two directional length scales

In revolving or flapping wings, radial planetary vorticity tilting (PVTr) is a mechanism that contributes to the removal of radial (spanwise) vorticity within the leading-edge vortex (LEV), while vorticity advection increases its strength. Dimensional analysis predicts that the PVTr and advection should scale with the wing aspect-ratio (AR) in identical fashion, assuming a uniform characteristic length is used. However, the authors’ previous work suggests that the vorticity advection decreases more rapidly than the PVTr as AR increases, indicating that separate normalizations should be applied. Here, we aim to develop a comprehensive scaling for the PVTr and vorticity advection based on simulation results using computational fluid dynamics. Two sets of simulations of revolving rectangular wings at an angle of attack of 45° were performed, the first set with the wing-tip velocity maintained constant, so that the Reynolds number (Re) defined at the radius of gyration equals 110, and the second set with the wing angular velocity maintained constant, so that Re defined at one chord length equals 63.5. We proposed two independent length scales based on LEV geometry, i.e., wing-span for the radial and tangential directions and wing chord for the vertical direction. The LEV size in the radial and tangential directions was limited by the wing-span, while the vertical depth remained invariant. The use of two length scales successfully predicted not only the scaling for the PVTr and the vorticity advection but also the relative magnitude of advection in three directions, i.e., tangential advection was strongest, followed by the vertical (downwash) and then the radial that was negligible.

Evaluation of drag force of a thrip wing by using a microcantilever

Tiny flight-capable insects such as thrips utilize a drag-based mechanism to generate a net vertical force to support their weight, owing to the low associated Reynolds number. Evaluating the drag generated by such small wings is of considerable significance to understand the flight of tiny insects. In this study, a self-sensing microcantilever was used to measure the drag force generated by an actual wing of a thrip. The wing of a thrip was attached to the tip of the microcantilever, and the microcantilever along with the wing was affixed perpendicular to a constant airflow at the middle of a bench-top wind tunnel. The drag generated by the wing under airflow velocities in the range of 0–4.8 m/s was obtained. In addition, the drag generated by the wing was verified by performing a three-dimensional computational fluid dynamics analysis. At a biological average wing tip velocity of 0.7 m/s, the difference between the measured drag force (290 nN) and calculated drag force (300 nN) was merely 3.3%. This new approach of evaluating the drag force generated by tiny insects could contribute to enhancing the understanding of microscale flight.

A simulation-based study on longitudinal gust response of flexible flapping wings

Winged animals such as insects are capable of flying and surviving in an unsteady and unpredictable aerial environment. They generate and control aerodynamic forces by flapping their flexible wings. While the dynamic shape changes of their flapping wings are known to enhance the efficiency of their flight, they can also affect the stability of a flapping wing flyer under unpredictable disturbances by responding to the sudden changes of aerodynamic forces on the wing. In order to test the hypothesis, the gust response of flexible flapping wings is investigated numerically with a specific focus on the passive maintenance of aerodynamic forces by the wing flexibility. The computational model is based on a dynamic flight simulator that can incorporate the realistic morphology, the kinematics, the structural dynamics, the aerodynamics and the fluid–structure interactions of a hovering hawkmoth. The longitudinal gusts are imposed against the tethered model of a hovering hawkmoth with flexible flapping wings. It is found that the aerodynamic forces on the flapping wings are affected by the gust, because of the increase or decrease in relative wingtip velocity or kinematic angle of attack. The passive shape change of flexible wings can, however, reduce the changes in the magnitude and direction of aerodynamic forces by the gusts from various directions, except for the downward gust. Such adaptive response of the flexible structure to stabilise the attitude can be classified into the mechanical feedback, which works passively with minimal delay, and is of great importance to the design of bio-inspired flapping wings for micro-air vehicles.

Effects of flexibility and aspect ratio on the aerodynamic performance of flapping wings

In the current study, we experimentally investigated the flexibility effects on the aerodynamic performance of flapping wings and the correlation with aspect ratio at angle of attack α = 45°. The Reynolds number based on the chord length and the wing tip velocity is maintained at Re = 5.3 × 103. Our result for compliant wings with an aspect ratio of 4 shows that wing flexibility can offer improved aerodynamic performance compared to that of a rigid wing. Flexible wings are found to offer higher lift-to-drag ratios; in particular, there is significant reduction in drag with little compromise in lift. The mechanism of the flexibility effects on the aerodynamic performance is addressed by quantifying the aerodynamic lift and drag forces, the transverse displacement on the wings and the flow field around the wings. The regime of the effective stiffness that offers improved aerodynamic performance is quantified in a range of about 0.5–10 and it matches the stiffness of insect wings with similar aspect ratios. Furthermore, we find that the aspect ratio of the wing is the predominant parameter determining the flexibility effects of compliant wings. Compliant wings with an aspect ratio of two do not demonstrate improved performance compared to their rigid counterparts throughout the entire stiffness regime investigated. The correlation between wing flexibility effects and the aspect ratio is supported by the stiffness of real insect wings.

Kinematic control of male Allen's Hummingbird wing trill over a range of flight speeds

Wing trills are pulsed sounds produced by modified wing feathers at one or more specific points in time during a wingbeat. Male Allen's hummingbirds (Selasphorus sasin) produce a sexually dimorphic 9 kHz wing trill in flight. Here, we investigated the kinematic basis for trill production. The wingtip velocity hypothesis posits that trill production is modulated by the airspeed of the wingtip at some point during the wingbeat, whereas the wing rotation hypothesis posits that trill production is instead modulated by wing rotation kinematics. To test these hypotheses, we flew six male Allen's hummingbirds in an open-jet wind tunnel at flight speeds of 0, 3, 6, 9, 12 and 14 m s-1, and recorded their flight with two 'acoustic cameras' placed below and behind, or below and lateral to the flying bird. The acoustic cameras are phased arrays of 40 microphones that used beamforming to spatially locate sound sources within a camera image. Trill sound pressure level (SPL) exhibited a U-shaped relationship with flight speed in all three camera positions. SPL was greatest perpendicular to the stroke plane. Acoustic camera videos suggest that the trill is produced during supination. The trill was up to 20 dB louder during maneuvers than it was during steady-state flight in the wind tunnel, across all airspeeds tested. These data provide partial support for the wing rotation hypothesis. Altered wing rotation kinematics could allow male Allen's hummingbirds to modulate trill production in social contexts such as courtship displays.

Hovering flight in the honeybee Apis mellifera: kinematic mechanisms for varying aerodynamic forces.

During hovering flight, animals can increase the wing velocity and therefore the net aerodynamic force per stroke by increasing wingbeat frequency, wing stroke amplitude, or both. The magnitude and orientation of aerodynamic forces are also influenced by the geometric angle of attack, timing of wing rotation, wing contact, and pattern of deviation from the primary stroke plane. Most of the kinematic data available for flying animals are average values for wing stroke amplitude and wingbeat frequency because these features are relatively easy to measure, but it is frequently suggested that the more subtle and difficult-to-measure features of wing kinematics can explain variation in force production for different flight behaviors. Here, we test this hypothesis with multicamera high-speed recording and digitization of wing kinematics of honeybees (Apis mellifera) hovering and ascending in air and hovering in a hypodense gas (heliox: 21% O2, 79% He). Bees employed low stroke amplitudes (86.7° ± 7.9°) and high wingbeat frequencies (226.8 ± 12.8 Hz) when hovering in air. When ascending in air or hovering in heliox, bees increased stroke amplitude by 30%-45%, which yielded a much higher wing tip velocity relative to that during simple hovering in air. Across the three flight conditions, there were no statistical differences in the amplitude of wing stroke deviation, minimum and stroke-averaged geometric angle of attack, maximum wing rotation velocity, or even wingbeat frequency. We employed a quasi-steady aerodynamic model to estimate the effects of wing tip velocity and geometric angle of attack on lift and drag. Lift forces were sensitive to variation in wing tip velocity, whereas drag was sensitive to both variation in wing tip velocity and angle of attack. Bees utilized kinematic patterns that did not maximize lift production but rather maintained lift-to-drag ratio. Thus, our data indicate that, at least for honeybees, the overall time course of wing angles is generally preserved and modulation of wing tip velocity is sufficient to perform a diverse set of vertical flight behaviors.

The effects of artificial wing wear on the flight capacity of the honey bee Apis mellifera

The wings of bees and other insects accumulate permanent wear, which increases the rate of mortality and impacts foraging behavior, presumably due to effects on flight performance. In this study, we investigated how experimental wing wear affects flight performance in honey bees. Variable density gases and high-speed videography were used to determine the maximum hovering flight capacity and wing kinematics of bees from three treatment groups: no wing wear, symmetric and asymmetric wing wear. Wing wear was simulated by clipping the distal-trailing edge of one or both of the wings. Across all bees from treatment groups combined, wingbeat frequency was inversely related to wing area. During hovering in air, bees with symmetric and asymmetric wing wear responded kinematically so as to produce wingtip velocities similar to those bees with no wing wear. However, maximal hovering flight capacity (revealed during flight in hypodense gases) decreased in direct proportion to wing area and inversely to wing asymmetry. Bees with reduced wing area and high asymmetry produced lower maximum wingtip velocity than bees with intact or symmetric wings, which caused a greater impairment in maximal flight capacity. These results demonstrate that the magnitude and type of wing wear affects maximal aerodynamic power production and, likely, the control of hovering flight. Wing wear reduces aerodynamic reserve capacity and, subsequently, the capacity for flight behaviors such as load carriage, maneuverability, and evading predators.

Measurements of Aerodynamic Coefficients for Flapping Wings at 0-90 Angles of Attack

This paper addresses the aerodynamics ofmembrane flappingwings. In a series ofwind-tunnel experiments on the 25 and 74-cm-wingspan models, the stroke-averaged lift and horizontal force were measured at an angle of attack that varied from 0 deg (horizontal) to 90 deg (hovering position). The flapping frequency was held constant, and freestream velocity was varied with the advance ratio range 0–1.2. For high angles of attack, flapping wings do not exhibit a typical abrupt stall seen with fixed wings. This feature in flapping wings allows a smooth transition from a level flight to hovering and back. The angle of attack, corresponding to a balance of forces in the horizontal direction, decreases exponentially with advance ratio. Aerodynamic coefficients are defined using a reference velocity as a vector sum of a freestream velocity and a stroke-averaged wing-tip flapping velocity. The lift and drag coefficients obtained using this procedure collapse well for the studied advance ratios, especially at lower angles of attack. Polynomial approximations for aerodynamic coefficients are proposed that can be used in flight-performance analysis.

Wingbeat kinematics and motor control of yaw turns in Anna's hummingbirds (Calypte anna)

The biomechanical and neuromuscular mechanisms used by different animals to generate turns in flight are highly variable. Body size and body plan exert some influence, e.g. birds typically roll their body to orient forces generated by the wings whereas insects are capable of turning via left-right wingbeat asymmetries. Turns are also relatively brief and have low repeatability, with almost every wingbeat serving a different function throughout the change in heading. Here we present an analysis of Anna's hummingbirds (Calypte anna) as they fed continuously from an artificial feeder revolving around the outside of the animal. This setup allowed for examination of sustained changes in yaw without requiring any corresponding changes in pitch, roll or body position. Hummingbirds sustained yaw turns by expanding the wing stroke amplitude of the outer wing during the downstroke and by altering the deviation of the wingtip path during both downstroke and upstroke. The latter led to a shift in the inner-outer stroke plane angle during the upstroke and shifts in the elevation of the stroke plane and in the deviation of the wingtip path during both strokes. These features are generally more similar to how insects, as opposed to birds, turn. However, time series analysis also revealed considerable stroke-to-stroke variation. Changes in the stroke amplitude and the wingtip velocity were highly cross-correlated, as were changes in the stroke deviation and the elevation of the stroke plane. As was the case for wingbeat kinematics, electromyogram recordings from pectoral and wing muscles were highly variable, but no correlations were found between these two features of motor control. The high variability of both kinematic and muscle activation features indicates a high level of wingbeat-to-wingbeat adjustments during sustained yaw. The activation timing of the muscles was more repeatable than the activation intensity, which suggests that the former may be constrained by harmonic motion and that the latter may play a large role in kinematic adjustments. Comparing the revolution frequency of the feeder with measurements of free flight yaws reveals that feeder tracking, even at one revolution every 2 s, is well below the maximum yaw capacity of the hummingbirds.

Climbing flight performance and load carrying in lesser dog-faced fruit bats (Cynopterus brachyotis)

The metabolic cost of flight increases with mass, so animals that fly tend to exhibit morphological traits that reduce body weight. However, all flying animals must sometimes fly while carrying loads. Load carrying is especially relevant for bats, which experience nightly and seasonal fluctuations in body mass of 40% or more. In this study, we examined how the climbing flight performance of fruit bats (Cynopterus brachyotis; N=4) was affected by added loads. The body weights of animals were experimentally increased by 0, 7, 14 or 21% by means of intra-peritoneal injections of saline solution, and flights were recorded as animals flew upwards in a small enclosure. Using a model based on actuator disk theory, we estimated the mechanical power expended by the bats as they flew and separated that cost into different components, including the estimated costs of hovering, climbing and increasing kinetic energy. We found that even our most heavily loaded bats were capable of upward flight, but as the magnitude of the load increased, flight performance diminished. Although the cost of flight increased with loading, bats did not vary total induced power across loading treatment. This resulted in a diminished vertical velocity and thus shallower climbing angle with increased loads. Among trials there was considerable variation in power production, and those with greater power production tended to exhibit higher wingbeat frequencies and lower wing stroke amplitudes than trials with lower power production. Changes in stroke plane angle, downstroke wingtip velocity and wing extension did not correlate significantly with changes in power output. We thus observed the manner in which bats modulated power output through changes in kinematics and conclude that the bats in our study did not respond to increases in loading with increased power output because their typical kinematics already resulted in sufficient aerodynamic power to accommodate even a 21% increase in body weight.

Bioengineering. The Wing Apparatus and Flapping Behavior of Hymenoptera.

The wing apparatus of Hymenoptera was observed with a scanning electron microscope, and the structure and function of insect wings were studied. The measurements of displacement of extrinsic skeleton vibration produced by wing flapping of a wasp were made by an optical displacement detector system. The free flight of the wasp was analyzed by a three dimensional motion analysis system. The results of a series of measurements revealed the flight characteristics of Hymenoptera, such as the wing tip velocity, wing path, wave form of extrinsic skeleton vibration, and so forth.

Theory of air flow generation by a resonant type PVF2 bimorph cantilever vibrator

A theory is presented for the air flow generation caused by centrifugal forces acting in a vibrating PVF2 multimorph fan in the resonant condition. The vibration system is approximated by a mass acting at the center of inertial force against an elastic plate (the cantilever wing arm). The effect of air was represented by a non-linear dissipative load in the oscillating system. The relevant parameters of this system are then determinable, particularly the vibration amplitude and the wing tip velocity. These parameters determine the generated air flow velocity and volume flow rate. Air flow velocity is predicted to vary inversely as wing length, and the air volume flow rate to remain constant. These predictions agree well with experiment, particularly for larger wing lengths of the fan. Useful design information was obtained.