A coupled kinematics-energetics model for predicting energy efficient flapping flight

Effects of tag mass on the physiology and behaviour of common noctule bats

BACKGROUND

External tags, such as transmitters and loggers, are often used to study bat movements. However, physiological and behavioural effects on bats carrying tags have rarely been investigated, and recommendations on the maximum acceptable tag mass are rather based on rules of thumb than on rigorous scientific assessment.

METHODS

We conducted a comprehensive three-step assessment of the potential physiological and behavioural effects of tagging bats, using common noctules Nyctalus noctula as a model. First, we examined seasonal changes in body mass. Second, we predicted and then measured potential changes in flight metabolic rate in a wind tunnel. Third, we conducted a meta-analysis of published data to assess effects of different tag masses on the weight and behaviour of bats.

RESULTS

Individual body mass of common noctules varied seasonally by 7.0 ± 2.6 g (range: 0.5-11.5 g). Aerodynamic theory predicted a 26% increase in flight metabolic rate for a common noctule equipped with a 3.8 g tag, equating to 14% of body mass. In a wind tunnel experiment, we could not confirm the predicted increase for tagged bats. Our meta-analysis revealed a weak correlation between tag mass and emergence time and flight duration in wild bats. Interestingly, relative tag mass (3-19% of bat body mass) was not related to body mass loss, but bats lost more body mass the longer tags were attached. Notably, relatively heavy bats lost more mass than conspecifics with a more average body mass index.

CONCLUSION

Because heavy tags (> 3 g) were generally used for shorter periods of time than lighter tags (~ 1 g), the long-term effects of heavy tags on bats cannot be assessed at this time. Furthermore, the effects of disturbance and resource distribution in the landscape cannot be separated from those of tagging. We recommend that tags weighing 5-10% of a bat's mass should only be applied for a few days. For longer studies, tags weighing less than 5% of a bat's body mass should be used. To avoid adverse effects on bats, researchers should target individuals with average, rather than peak, body mass indices.

Axial propulsion with flapping and rotating wings, a comparison of potential efficiency

Interest in biological locomotion and what advantages the principles governing it might offer in the design of manmade vehicles prompts one to consider the power requirements of flapping relative to rotary propulsion. The amount of work performed on the fluid surrounding a thrusting surface (wing or blade) is reflected in the kinetic energy of the wake. Consideration of the energy in the wake is sufficient to define absolute minimum limitations on the power requirement to generate a particular thrust. This work applies wake solutions to compare the minimum inviscid propulsive power requirement of wings flapping and in rotation at wing loading conditions reflective of hover through a state of lightly-loaded cruise. It is demonstrated that hovering flapping flight is less efficient than rotary wing propulsion except for the most extreme flap amplitude strokes ([Formula: see text]   >  160°) if operating at large wake wavelength. In cruise, a larger range of flap amplitude kinematics ([Formula: see text]  >  140°) can be aerodynamically more energy efficient for wake wavelengths reflective of biological propulsion. These results imply, based on the observed wing kinematics of continuous steady flight, that flapping propulsion in animals is unlikely to be more efficient than rotary propulsion.

On the possibility (or lack thereof) of agreement between experiment and computation of flows over wings at moderate Reynolds number

The flight of many birds and bats, and their robotic counterparts, occurs over a range of chord-based Reynolds numbers from 1 × 10⁴ to 1.5 × 10⁵. It is precisely over this range where the aerodynamics of simple, rigid, fixed wings becomes extraordinarily sensitive to small changes in geometry and the environment, with two sets of consequences. The first is that practical lifting devices at this scale will likely not be simple, rigid, fixed wings. The second is that it becomes non-trivial to make baseline comparisons for experiment and computation, when either one can be wrong. Here we examine one ostensibly simple case of the NACA 0012 aerofoil and make careful comparison between the technical literature, and new experiments and computations. The agreement (or lack thereof) will establish one or more baseline results and some sensitivities around them. The idea is that the diagnostic procedures will help to guide comparisons and predictions in subsequent more complex cases.

Modeling perspectives on echolocation strategies inspired by bats flying in groups

Bats navigating with echolocation - which is a type of active sensing achieved by interpreting echoes resulting from self-generated ultrasonic pulses - exhibit unique behaviors during group flight. While bats may benefit from eavesdropping on their peers׳ echolocation, they also potentially suffer from confusion between their own and peers׳ pulses, caused by an effect called frequency jamming. This hardship of group flight is supported by experimental observations of bats simplifying their sound-scape by shifting their pulse frequencies or suppressing echolocation altogether. Here, we investigate eavesdropping and varying pulse emission rate from a modeling perspective to understand these behaviors׳ potential benefits and detriments. We define an agent-based model of echolocating bats avoiding collisions in a three-dimensional tunnel. Through simulation, we show that bats with reasonably accurate eavesdropping can reduce collisions compared to those neglecting information from peers. In large populations, bats minimize frequency jamming by decreasing pulse emission rate, while collision risk increases; conversely, increasing pulse emission rate minimizes collisions by allowing more sensing information generated per bat. These strategies offer benefits for both biological and engineered systems, since frequency jamming is a concern in systems using active sensing.

Predicting power-optimal kinematics of avian wings

A theoretical model of avian flight is developed which simulates wing motion through a class of methods known as predictive simulation. This approach uses numerical optimization to predict power-optimal kinematics of avian wings in hover, cruise, climb and descent. The wing dynamics capture both aerodynamic and inertial loads. The model is used to simulate the flight of the pigeon, Columba livia, and the results are compared with previous experimental measurements. In cruise, the model unearths a vast range of kinematic modes that are capable of generating the required forces for flight. The most efficient mode uses a near-vertical stroke-plane and a flexed-wing upstroke, similar to kinematics recorded experimentally. In hover, the model predicts that the power-optimal mode uses an extended-wing upstroke, similar to hummingbirds. In flexing their wings, pigeons are predicted to consume 20% more power than if they kept their wings full extended, implying that the typical kinematics used by pigeons in hover are suboptimal. Predictions of climbing flight suggest that the most energy-efficient way to reach a given altitude is to climb as steeply as possible, subjected to the availability of power.

Power of the wingbeat: modelling the effects of flapping wings in vertebrate flight

Animal flight performance has been studied using models developed for man-made aircraft. For an aeroplane with fixed wings, the energetic cost as a function of flight speed can be expressed in terms of weight, wing span, wing area and body area, where more details are included in proportionality coefficients. Flying animals flap their wings to produce thrust. Adopting the fixed wing flight model implicitly incorporates the effects of wing flapping in the coefficients. However, in practice, these effects have been ignored. In this paper, the effects of reciprocating wing motion on the coefficients of the fixed wing aerodynamic power model for forward flight are explicitly formulated in terms of thrust requirement, wingbeat frequency and stroke-plane angle, for optimized wingbeat amplitudes. The expressions are obtained by simulating flights over a large parameter range using an optimal vortex wake method combined with a low-level blade element method. The results imply that previously assumed acceptable values for the induced power factor might be strongly underestimated. The results also show the dependence of profile power on wing kinematics. The expressions introduced in this paper can be used to significantly improve animal flight models.

Bat flight: aerodynamics, kinematics and flight morphology

Bats evolved the ability of powered flight more than 50 million years ago. The modern bat is an efficient flyer and recent research on bat flight has revealed many intriguing facts. By using particle image velocimetry to visualize wake vortices, both the magnitude and time-history of aerodynamic forces can be estimated. At most speeds the downstroke generates both lift and thrust, whereas the function of the upstroke changes with forward flight speed. At hovering and slow speed bats use a leading edge vortex to enhance the lift beyond that allowed by steady aerodynamics and an inverted wing during the upstroke to further aid weight support. The bat wing and its skeleton exhibit many features and control mechanisms that are presumed to improve flight performance. Whereas bats appear aerodynamically less efficient than birds when it comes to cruising flight, they have the edge over birds when it comes to manoeuvring. There is a direct relationship between kinematics and the aerodynamic performance, but there is still a lack of knowledge about how (and if) the bat controls the movements and shape (planform and camber) of the wing. Considering the relatively few bat species whose aerodynamic tracks have been characterized, there is scope for new discoveries and a need to study species representing more extreme positions in the bat morphospace.