It pays to follow the leader: Metabolic cost of flight is lower for trailing birds in small groups.

Many bird species commonly aggregate in flocks for reasons ranging from predator defense to navigation. Available evidence suggests that certain types of flocks-the V and echelon formations of large birds-may provide a benefit that reduces the aerodynamic cost of flight, whereas cluster flocks typical of smaller birds may increase flight costs. However, metabolic flight costs have not been directly measured in any of these group flight contexts [Zhang and Lauder, J. Exp. Biol. 226, jeb245617 (2023)]. Here, we measured the energetic benefits of flight in small groups of two or three birds and the requirements for realizing those benefits, using metabolic energy expenditure and flight position measurements from European Starlings flying in a wind tunnel. The starlings continuously varied their relative position during flights but adopted a V formation motif on average, with a modal spanwise and streamwise spacing of [0.81, 0.91] wingspans. As measured via CO2 production, flight costs for follower birds were significantly reduced compared to their individual solo flight benchmarks. However, followers with more positional variability with respect to leaders did less well, even increasing their costs above solo flight. Thus, we directly demonstrate energetic costs and benefits for group flight followers in an experimental context amenable to further investigation of the underlying aerodynamics, wake interactions, and bird characteristics that produce these metabolic effects.

Shape-Morphing Dynamics of Soft Compliant Membranes for Drag and Turbulence Modulation.

We study the kinematics and dynamics of a highly compliant membrane disk placed head-on in a uniform flow. With increasing flow velocity, the membrane deforms nonlinearly into increasingly parachutelike shapes. These aerodynamically elongated materials exhibit a modified drag law, which is linked to the elastohydrodynamic interactions. We predict the unsteady structural response of the membranes using a nonlinear, aeroelastic model-in excellent agreement with experimental measurements of deformations and force fluctuations. With simultaneous membrane interface tracking, force measurements and flow tracing, we reveal that a peculiar skewness in the membrane's oscillations triggers turbulence production in the wake, thereby modulating the drag. The present work provides a demonstration of the complex interplay between soft materials and fluid turbulence, leading to new, emergent system properties.

Power requirements for bat-inspired flapping flight with heavy, highly articulated and cambered wings.

Bats fly with highly articulated and heavy wings. To understand their power requirements, we develop a three-dimensional reduced-order model, and apply it to flights of Cynopterus brachyotis, the lesser dog-faced fruit bat. Using previously measured wing kinematics, the model computes aerodynamic forces using blade element momentum theory, and incorporates inertial forces of the flapping wing using the measured mass distribution of the membrane wing and body. The two are combined into a Lagrangian equation of motion, and we performed Monte Carlo simulations to address uncertainties in measurement errors and modelling assumptions. We find that the camber of the armwing decreases with flight speed whereas the handwing camber is more independent of speed. Wing camber disproportionately impacts energetics, mainly during the downstroke, and increases the power requirement from 8% to 22% over flight speed U = 3.2-7.4 m s-1. We separate total power into aerodynamic and inertial components, and aerodynamic power into parasitic, profile and induced power, and find strong agreement with previous theoretical and experimental studies. We find that inertia of wings help to balance aerodynamic forces, alleviating the muscle power required for weight support and thrust generation. Furthermore, the model suggests aerodynamic forces assist in lifting the heavy wing during upstroke.

Bats actively modulate membrane compliance to control camber and reduce drag.

Bat wing skin is exceptionally compliant and cambers significantly during flight. Plagiopatagiales proprii, arrays of small muscles embedded in the armwing membrane, are activated during flight and are hypothesized to modulate membrane tension. We examined the function of these muscles using Jamaican fruit bats, Artibeus jamaicensis. When these muscles were paralyzed using botulinum toxin, the bats preferred flight speed decreased and they were unable to fly at very low speeds. Paralysis of the plagiopatagiales also resulted in increased armwing camber consistent with a hypothesized role of modulating aeroelastic interactions. Other compensatory kinematics included increased downstroke angle and increased wingbeat amplitude. These results are consistent with the bats experiencing increased drag and flight power costs associated with the loss of wing-membrane control. Our results indicate that A. jamaicensis likely always employ their wing membrane muscles during sustained flight to control camber and to enhance flight efficiency over a wide flight envelope.

Aerosol transmission in passenger car cabins: Effects of ventilation configuration and driving speed.

Identifying the potential routes of airborne transmission during transportation is of critical importance to limit the spread of the SARS-CoV-2 virus. Here, we numerically solve the Reynolds-averaged Navier-Stokes equations along with the transport equation for a passive scalar in order to study aerosol transmission inside the passenger cabin of an automobile. Extending the previous work on this topic, we explore several driving scenarios including the effects of having the windows fully open, half-open, and one-quarter open, the effect of opening a moon roof, and the scaling of the aerosol transport as a function of vehicle speed. The flow in the passenger cabin is largely driven by the external surface pressure distribution on the vehicle, and the relative concentration of aerosols in the cabin scales inversely with vehicle speed. For the simplified geometry studied here, we find that the half-open windows configuration has almost the same ventilation effectively as the one with the windows fully open. The utility of the moonroof as an effective exit vent for removing the aerosols generated within the cabin space is discussed. Using our results, we propose a "speed-time" map, which gives guidance regarding the relative risk of transmission between driver and passenger as a function of trip duration and vehicle speed. A few strategies for the removal of airborne contaminants during low-speed driving, or in a situation where the vehicle is stuck in traffic, are suggested.

Effects of confinement on the dynamics and correlation scales in kinesin-microtubule active fluids.

We study the influence of solid boundaries on dynamics and structure of kinesin-driven microtubule active fluids as the height of the container, H, increases from hundreds of micrometers to several millimeters. By three-dimensional tracking of passive tracers dispersed in the active fluid, we observe that the activity level, characterized by velocity fluctuations, increases as system size increases and retains a small-scale isotropy. Concomitantly, as the confinement level decreases, the velocity-velocity temporal correlation develops a strong positive correlation at longer times, suggesting the establishment of a "memory". We estimate the characteristic size of the flow structures from the spatial correlation function and find that, as the confinement becomes weaker, the correlation length, l_{c}, saturates at approximately 400 microns. This saturation suggests an intrinsic length scale which, along with the small-scale isotropy, demonstrates the multiscale nature of this kinesin-driven bundled microtubule active system.

Airflows inside passenger cars and implications for airborne disease transmission.

Transmission of highly infectious respiratory diseases, including SARS-CoV-2, is facilitated by the transport of exhaled droplets and aerosols that can remain suspended in air for extended periods of time. A passenger car cabin represents one such situation with an elevated risk of pathogen transmission. Here, we present results from numerical simulations to assess how the in-cabin microclimate of a car can potentially spread pathogenic species between occupants for a variety of open and closed window configurations. We estimate relative concentrations and residence times of a noninteracting, passive scalar-a proxy for infectious particles-being advected and diffused by turbulent airflows inside the cabin. An airflow pattern that travels across the cabin, farthest from the occupants, can potentially reduce the transmission risk. Our findings reveal the complex fluid dynamics during everyday commutes and nonintuitive ways in which open windows can either increase or suppress airborne transmission.

A bioinspired Separated Flow wing provides turbulence resilience and aerodynamic efficiency for miniature drones.

Small-scale drones have enough sensing and computing power to find use across a growing number of applications. However, flying in the low-Reynolds number regime remains challenging. High sensitivity to atmospheric turbulence compromises vehicle stability and control, and low aerodynamic efficiency limits flight duration. Conventional wing designs have thus far failed to address these two deficiencies simultaneously. Here, we draw inspiration from nature's small flyers to design a wing with lift generation robust to gusts and freestream turbulence without sacrificing aerodynamic efficiency. This performance is achieved by forcing flow separation at the airfoil leading edge. Water and wind tunnel measurements are used to demonstrate the working principle and aerodynamic performance of the wing, showing a substantial reduction in the sensitivity of lift force production to freestream turbulence, as compared with the performance of an Eppler E423 low-Reynolds number wing. The minimum cruise power of a custom-built 104-gram fixed-wing drone equipped with the Separated Flow wing was measured in the wind tunnel indicating an upper limit for the flight time of 170 minutes, which is about four times higher than comparable existing fixed-wing drones. In addition, we present scaling guidelines and outline future design and manufacturing challenges.

Scaling of the performance of insect-inspired passive-pitching flapping wings.

Flapping flight using passive pitch regulation is a commonly used mode of thrust and lift generation in insects and has been widely emulated in flying vehicles because it allows for simple implementation of the complex kinematics associated with flapping wing systems. Although robotic flight employing passive pitching to regulate angle of attack has been previously demonstrated, there does not exist a comprehensive understanding of the effectiveness of this mode of aerodynamic force generation, nor a method to accurately predict its performance over a range of relevant scales. Here, we present such scaling laws, incorporating aerodynamic, inertial and structural elements of the flapping-wing system, validating the theoretical considerations using a mechanical model which is tested for a linear elastic hinge and near-sinusoidal stroke kinematics over a range of scales, hinge stiffnesses and flapping frequencies. We find that suitably defined dimensionless parameters, including the Reynolds number, Re, the Cauchy number, Ch, and a newly defined 'inertial-elastic' number, IE, can reliably predict the kinematic and aerodynamic performance of the system. Our results also reveal a consistent dependency of pitching kinematics on these dimensionless parameters, providing a connection between lift coefficient and kinematic features such as angle of attack and wing rotation.

Wings as inertial appendages: how bats recover from aerial stumbles.

For many animals, movement through complex natural environments necessitates the evolution of mechanisms that enable recovery from unexpected perturbations. Knowledge of how flying animals contend with disruptive forces is limited, however, and is nearly nonexistent for bats, the only mammals capable of powered flight. We investigated perturbation recovery in Carollia perspicillata by administering a well-defined jet of compressed air, equal to 2.5 times bodyweight, which induced two types of disturbances, termed aerial stumbles: pitch-inducing body perturbations and roll-inducing wing perturbations. In both cases, bats responded primarily by adjusting extension of wing joints, and recovered pre-disturbance body orientation and left-right symmetry of wing motions over the course of only one wingbeat cycle. Bats recovered from body perturbations by symmetrically extending their wings cranially and dorsally during upstroke, and from wing perturbations by asymmetrically extending their wings throughout the recovery wingbeat. We used a simplified dynamical model to test the hypothesis that wing extension asymmetry during recovery from roll-inducing perturbations can generate inertial torques that alone are sufficient to produce the observed body reorientation. Results supported the hypothesis, and also suggested that subsequent restoration of symmetrical wing extension help to decelerate recovery rotation via passive aerodynamic mechanisms. During recovery, humeral elevation/depression remained largely unchanged while bats adjusted wing extension at the elbow and wrist, suggesting a proximo-distal gradient in the neuromechanical control of the wing.

The dynamics of hovering flight in hummingbirds, insects and bats with implications for aerial robotics.

We analyze the effects of morphology and wing kinematics on the performance of hovering flight. We present a simplified dynamical model with body translational and rotational degrees of freedom that incorporates the flapping, long-axis wing rotation and folding of the wing. To validate our simulation, we compare our results with direct measurements from hovering insects, hummingbirds and bats. Results show that long-axis wing rotation angle (a proxy for pronation) has a significant effect on energy efficiency. For a given wing rotation amplitude, the hovering system has a power-optimal flapping frequency for each stroke-plane orientation, and that frequency closely corresponds to the wingbeat frequencies observed in a diverse range of hummingbird species. We find that larger animals (with larger total mass and wing size), such as bats, require more power to maintain a stable hovering orbit and that hovering with a constant wingspan becomes increasingly impractical with increasing body size. We show, as an exemplar, that for a system of the size of a hovering bat, e.g. Glossophaga soricina, hovering with constant wingspan is dynamically possible, but is implausible and inefficient. For these conditions, hovering with varying wingspan, retracting the wing on the upstroke, is a more realistic hovering modality.

Changes in the flagellar bundling time account for variations in swimming behavior of flagellated bacteria in viscous media.

Although the motility of the flagellated bacteria, Escherichia coli, has been widely studied, the effect of viscosity on swimming speed remains controversial. The swimming mode of wild-type E. coli is often idealized as a run-and-tumble sequence in which periods of swimming at a constant speed are randomly interrupted by a sudden change of direction at a very low speed. Using a tracking microscope, we follow cells for extended periods of time in Newtonian liquids of varying viscosity and find that the swimming behavior of a single cell can exhibit a variety of behaviors, including run and tumble and "slow random walk" in which the cells move at a relatively low speed. Although the characteristic swimming speed varies between individuals and in different polymer solutions, we find that the skewness of the speed distribution is solely a function of viscosity and can be used, in concert with the measured average swimming speed, to determine the effective running speed of each cell. We hypothesize that differences in the swimming behavior observed in solutions of different viscosity are due to changes in the flagellar bundling time, which increases as the viscosity rises, due to the lower rotation rate of the flagellar motor. A numerical simulation and the use of resistive force theory provide support for this hypothesis.

The influence of aspect ratio and stroke pattern on force generation of a bat-inspired membrane wing.

Aspect ratio (AR) is one parameter used to predict the flight performance of a bat species based on wing shape. Bats with high AR wings are thought to have superior lift-to-drag ratios and are therefore predicted to be able to fly faster or to sustain longer flights. By contrast, bats with lower AR wings are usually thought to exhibit higher manoeuvrability. However, the half-span ARs of most bat wings fall into a narrow range of about 2.5-4.5. Furthermore, these predictions do not take into account the wide variation in flapping motion observed in bats. To examine the influence of different stroke patterns, we measured lift and drag of highly compliant membrane wings with different bat-relevant ARs. A two degrees of freedom shoulder joint allowed for independent control of flapping amplitude and wing sweep. We tested five models with the same variations of stroke patterns, flapping frequencies and wind speed velocities. Our results suggest that within the relatively small AR range of bat wings, AR has no clear effect on force generation. Instead, the generation of lift by our simple model mostly depends on wingbeat frequency, flapping amplitude and freestream velocity; drag is mostly affected by the flapping amplitude.

Speed-dependent modulation of wing muscle recruitment intensity and kinematics in two bat species.

Animals respond to changes in power requirements during locomotion by modulating the intensity of recruitment of their propulsive musculature, but many questions concerning how muscle recruitment varies with speed across modes of locomotion remain unanswered. We measured normalized average burst EMG (aEMG) for pectoralis major and biceps brachii at different flight speeds in two relatively distantly related bat species: the aerial insectivore Eptesicus fuscus, and the primarily fruit-eating Carollia perspicillata These ecologically distinct species employ different flight behaviors but possess similar wing aspect ratio, wing loading and body mass. Because propulsive requirements usually correlate with body size, and aEMG likely reflects force, we hypothesized that these species would deploy similar speed-dependent aEMG modulation. Instead, we found that aEMG was speed independent in E. fuscus and modulated in a U-shaped or linearly increasing relationship with speed in C. perspicillata This interspecific difference may be related to differences in muscle fiber type composition and/or overall patterns of recruitment of the large ensemble of muscles that participate in actuating the highly articulated bat wing. We also found interspecific differences in the speed dependence of 3D wing kinematics: E. fuscus modulates wing flexion during upstroke significantly more than C. perspicillata Overall, we observed two different strategies to increase flight speed: C. perspicillata tends to modulate aEMG, and E. fuscus tends to modulate wing kinematics. These strategies may reflect different requirements for avoiding negative lift and overcoming drag during slow and fast flight, respectively, a subject we suggest merits further study.

Wake structure and kinematics in two insectivorous bats.

We compare kinematics and wake structure over a range of flight speeds (4.0-8.2 m s(-1)) for two bats that pursue insect prey aerially, Tadarida brasiliensis and Myotis velifer Body mass and wingspan are similar in these species, but M. velifer has broader wings and lower wing loading. By using high-speed videography and particle image velocimetry of steady flight in a wind tunnel, we show that three-dimensional kinematics and wake structure are similar in the two species at the higher speeds studied, but differ at lower speeds. At lower speeds, the two species show significant differences in mean angle of attack, body-wingtip distance and sweep angle. The distinct body vortex seen at low speed in T. brasiliensis and other bats studied to date is considerably weaker or absent in M. velifer We suggest that this could be influenced by morphology: (i) the narrower thorax in this species probably reduces the body-induced discontinuity in circulation between the two wings and (ii) the wing loading is lower, hence the lift coefficient required for weight support is lower. As a result, in M. velifer, there may be a decreased disruption in the lift generation between the body and the wing, and the strength of the characteristic root vortex is greatly diminished, both suggesting increased flight efficiency.This article is part of the themed issue 'Moving in a moving medium: new perspectives on flight'.

Simplifying a wing: diversity and functional consequences of digital joint reduction in bat wings.

Bat wings, like other mammalian forelimbs, contain many joints within the digits. These joints collectively affect dynamic three-dimensional (3D) wing shape, thereby affecting the amount of aerodynamic force a wing can generate. Bats are a speciose group, and show substantial variation in the number of wing joints. Additionally, some bat species have joints with extensor but no flexor muscles. While several studies have examined the diversity in number of joints and presence of muscles, musculoskeletal variation in the digits has not been interpreted in phylogenetic, functional or ecological contexts. To provide this context, the number of joints and the presence/absence of muscles are quantified for 44 bat species, and are mapped phylogenetically. It is shown that, relative to the ancestral state, joints and muscles were lost multiple times from different digits and in many lineages. It is also shown that joints lacking flexors undergo cyclical flexion and extension, in a manner similar to that observed in joints with both flexors and extensors. Comparison of species with contrasting feeding ecologies demonstrates that species that feed primarily on non-mobile food (e.g. fruit) have fewer fully active joints than species that catch mobile prey (e.g. insects). It is hypothesized that there is a functional trade-off between energetic savings and maneuverability. Having fewer joints and muscles reduces the mass of the wing, thereby reducing the energetic requirements of flapping flight, and having more joints increases the assortment of possible 3D wing shapes, thereby enhancing the range and fine control of aerodynamic force production and thus maneuverability.

Falling with Style: Bats Perform Complex Aerial Rotations by Adjusting Wing Inertia.

The remarkable maneuverability of flying animals results from precise movements of their highly specialized wings. Bats have evolved an impressive capacity to control their flight, in large part due to their ability to modulate wing shape, area, and angle of attack through many independently controlled joints. Bat wings, however, also contain many bones and relatively large muscles, and thus the ratio of bats' wing mass to their body mass is larger than it is for all other extant flyers. Although the inertia in bat wings would typically be associated with decreased aerial maneuverability, we show that bat maneuvers challenge this notion. We use a model-based tracking algorithm to measure the wing and body kinematics of bats performing complex aerial rotations. Using a minimal model of a bat with only six degrees of kinematic freedom, we show that bats can perform body rolls by selectively retracting one wing during the flapping cycle. We also show that this maneuver does not rely on aerodynamic forces, and furthermore that a fruit fly, with nearly massless wings, would not exhibit this effect. Similar results are shown for a pitching maneuver. Finally, we combine high-resolution kinematics of wing and body movements during landing and falling maneuvers with a 52-degree-of-freedom dynamical model of a bat to show that modulation of wing inertia plays the dominant role in reorienting the bat during landing and falling maneuvers, with minimal contribution from aerodynamic forces. Bats can, therefore, use their wings as multifunctional organs, capable of sophisticated aerodynamic and inertial dynamics not previously observed in other flying animals. This may also have implications for the control of aerial robotic vehicles.

Helical motion of the cell body enhances Caulobacter crescentus motility.

We resolve the 3D trajectory and the orientation of individual cells for extended times, using a digital tracking technique combined with 3D reconstructions. We have used this technique to study the motility of the uniflagellated bacterium Caulobacter crescentus and have found that each cell displays two distinct modes of motility, depending on the sense of rotation of the flagellar motor. In the forward mode, when the flagellum pushes the cell, the cell body is tilted with respect to the direction of motion, and it precesses, tracing out a helical trajectory. In the reverse mode, when the flagellum pulls the cell, the precession is smaller and the cell has a lower translation distance per rotation period and thus a lower motility. Using resistive force theory, we show how the helical motion of the cell body generates thrust and can explain the direction-dependent changes in swimming motility. The source of the cell body precession is believed to be associated with the flexibility of the hook that connects the flagellum to the cell body.

How wing kinematics affect power requirements and aerodynamic force production in a robotic bat wing.

Bats display a wide variety of behaviors that require different amounts of aerodynamic force. To control and modulate aerodynamic force, bats change wing kinematics, which, in turn, may change the power required for wing motion. There are many kinematic mechanisms that bats, and other flapping animals, can use to increase aerodynamic force, e.g. increasing wingbeat frequency or amplitude. However, we do not know if there is a difference in energetic cost between these different kinematic mechanisms. To assess the relationship between mechanical power input and aerodynamic force output across different isolated kinematic parameters, we programmed a robotic bat wing to flap over a range of kinematic parameters and measured aerodynamic force and mechanical power. We systematically varied five kinematic parameters: wingbeat frequency, wingbeat amplitude, stroke plane angle, downstroke ratio, and wing folding. Kinematic values were based on observed values from free flying Cynopterus brachyotis, the species on which the robot was based. We describe how lift, thrust, and power change with increases in each kinematic variable. We compare the power costs associated with generating additional force through the four kinematic mechanisms controlled at the shoulder, and show that all four mechanisms require approximately the same power to generate a given force. This result suggests that no single parameter offers an energetic advantage over the others. Finally, we show that retracting the wing during upstroke reduces power requirements for flapping and increases net lift production, but decreases net thrust production. These results compare well with studies performed on C. brachyotis, offering insight into natural flight kinematics.

Hindlimb motion during steady flight of the lesser dog-faced fruit bat, Cynopterus brachyotis.

In bats, the wing membrane is anchored not only to the body and forelimb, but also to the hindlimb. This attachment configuration gives bats the potential to modulate wing shape by moving the hindlimb, such as by joint movement at the hip or knee. Such movements could modulate lift, drag, or the pitching moment. In this study we address: 1) how the ankle translates through space during the wingbeat cycle; 2) whether amplitude of ankle motion is dependent upon flight speed; 3) how tension in the wing membrane pulls the ankle; and 4) whether wing membrane tension is responsible for driving ankle motion. We flew five individuals of the lesser dog-faced fruit bat, Cynopterus brachyotis (Family: Pteropodidae), in a wind tunnel and documented kinematics of the forelimb, hip, ankle, and trailing edge of the wing membrane. Based on kinematic analysis of hindlimb and forelimb movements, we found that: 1) during downstroke, the ankle moved ventrally and during upstroke the ankle moved dorsally; 2) there was considerable variation in amplitude of ankle motion, but amplitude did not correlate significantly with flight speed; 3) during downstroke, tension generated by the wing membrane acted to pull the ankle dorsally, and during upstroke, the wing membrane pulled laterally when taut and dorsally when relatively slack; and 4) wing membrane tension generally opposed dorsoventral ankle motion. We conclude that during forward flight in C. brachyotis, wing membrane tension does not power hindlimb motion; instead, we propose that hindlimb movements arise from muscle activity and/or inertial effects.