Dynamic experimental rigs for investigation of insect wing aerodynamics.

This paper provides a systematic and critical review of dynamic experimental rigs used for insect wing aerodynamics research. The goal is to facilitate meaningful comparison of data from existing rigs and provide insights for designers of new rigs. The scope extends from simple one degree of freedom rotary rigs to multi degrees of freedom rigs allowing various rotation and translation motions. Experimental methods are characterized using a consistent set of parameters that allows objective comparison of different approaches. A comprehensive catalogue is presented for the tested flow conditions (assessed through Reynolds number, Rossby number and advance ratio), wing morphologies (assessed through aspect ratio, planform shape and thickness to mean chord ratio) and kinematics (assessed through motion degrees of freedom). Links are made between the type of aerodynamic characteristics being studied and the type of experimental set-up used. Rig mechanical design considerations are assessed, and the aerodynamic measurements obtained from these rigs are discussed.

Energy and time optimal trajectories in exploratory jumps of the spider Phidippus regius.

Jumping spiders are proficient jumpers that use jumps in a variety of behavioural contexts. We use high speed, high resolution video to measure the kinematics of a single regal jumping spider for a total of 15 different tasks based on a horizontal gap of 2-5 body lengths and vertical gap of +/-2 body lengths. For short range jumps, we show that low angled trajectories are used that minimise flight time. For longer jumps, take-off angles are steeper and closer to the optimum for minimum energy cost of transport. Comparison of jump performance against other arthropods shows that Phidippus regius is firmly in the group of animals that use dynamic muscle contraction for actuation as opposed to a stored energy catapult system. We find that the jump power requirements can be met from the estimated mass of leg muscle; hydraulic augmentation may be present but appears not to be energetically essential.

The role of the leading edge vortex in lift augmentation of steadily revolving wings: a change in perspective.

The presence of a stable leading edge vortex (LEV) on steadily revolving wings increases the maximum lift coefficient that can be generated from the wing and its role is important to understanding natural flyers and flapping wing vehicles. In this paper, the role of LEV in lift augmentation is discussed under two hypotheses referred to as 'additional lift' and 'absence of stall'. The 'additional lift' hypothesis represents the traditional view. It presumes that an additional suction/circulation from the LEV increases the lift above that of a potential flow solution. This behaviour may be represented through either the 'Polhamus leading edge suction' model or the so-called 'trapped vortex' model. The 'absence of stall' hypothesis is a more recent contender that presumes that the LEV prevents stall at high angles of attack where flow separation would normally occur. This behaviour is represented through the so-called 'normal force' model. We show that all three models can be written in the form of the same potential flow kernel with modifiers to account for the presence of a LEV. The modelling is built on previous work on quasi-steady models for hovering wings such that model parameters are determined from first principles, which allows a fair comparison between the models themselves, and the models and experimental data. We show that the two models which directly include the LEV as a lift generating component are built on a physical picture that does not represent the available experimental data. The simpler 'normal force' model, which does not explicitly model the LEV, performs best against data in the literature. We conclude that under steady conditions the LEV as an 'absence of stall' model/mechanism is the most satisfying explanation for observed aerodynamic behaviour.

A signature of tree health? Shifts in the microbiome and the ecological drivers of horse chestnut bleeding canker disease.

Host susceptibility to pathogens can be shaped by genetic, ecological, and evolutionary factors. The ability to predict the spread of disease therefore requires an integrated understanding of these factors, including effects of pests on pathogen growth and competition between pathogens and commensal microbiota for host resources. We examined interactions between the leaf-mining moth Cameraria ohridella, the bacterial causal agent of bleeding canker disease Pseudomonas syringae pv aesculi, and the bark-associated microbiota of horse chestnut (Aesculus hippocastanum) trees. Through surveys of > 900 trees from 60 sites in the UK, we tested for ecological or life history predictors of leaf miner infestation, bleeding canker, or coinfection. Using culture-independent sequencing, we then compared the bark microbiomes from 46 trees to measure the association between microbiome composition and key ecological variables, including the severity of disease. Both pest and pathogen were found to respond to tree characteristics, but neither explained damage inflicted by the other. However, we found a clear loss of microbial diversity and associated shift in microbiome composition of trees as a function of disease. These results show a link between bark-associated microbiota and tree health that introduces the intriguing possibility that tree microbiota play key roles in the spread of disease.

Optimum hovering wing planform.

Theoretical analysis is used to identify the optimum wing planform of a flapping/revolving wing in hover. This solution is of interest as a benchmark to which hovering wing geometries driven by broader multidisciplinary evolutionary or engineering constraints can be compared. Furthermore, useful insights into the aerodynamic performance of untwisted hovering wings are delivered. It is shown that profile power is minimised by using an untwisted elliptical planform whereas induced power is minimised by a more highly tapered planform similar to that of a hummingbird.

Dynamic Electromechanical Coupling of Piezoelectric Bending Actuators.

Electromechanical coupling defines the ratio of electrical and mechanical energy exchanged during a flexure cycle of a piezoelectric actuator. This paper presents an analysis of the dynamic electromechanical coupling factor (dynamic EMCF) for cantilever based piezoelectric actuators and provides for the first time explicit expressions for calculation of dynamic EMCF based on arrangement of passive and active layers, layer geometry, and active and passive materials selection. Three main cantilever layer configurations are considered: unimorph, dual layer bimorph and triple layer bimorph. The actuator is modeled using standard constitutive dynamic equations that relate deflection and charge to force and voltage. A mode shape formulation is used for the cantilever dynamics that allows the generalized mass to be the actual mass at the first resonant frequency, removing the need for numerical integration in the design process. Results are presented in the form of physical insight from the model structure and also numerical evaluations of the model to provide trends in dynamic EMCF with actuator design parameters. For given material properties of the active and passive layers and given system overall damping ratio, the triple layer bimorph topology is the best in terms of theoretically achievable dynamic EMCF, followed by the dual layer bimorph. For a damping ratio of 0.035, the dynamic EMCF for an example dual layer bimorph configuration is 9% better than for a unimorph configuration. For configurations with a passive layer, the ratio of thicknesses for the passive and active layers is the primary geometric design variable. Choice of passive layer stiffness (Young's modulus) relative to the stiffness of the material in the active layer is an important materials related design choice. For unimorph configurations, it is beneficial to use the highest stiffness possible passive material, whereas for triple layer bimorph configurations, the passive material should have a low stiffness. In all cases, increasing the transverse electromechanical coupling coefficient of the active material improves the dynamic EMCF.

Aero-optimum hovering kinematics.

Hovering flight for flapping wing vehicles requires rapid and relatively complex reciprocating movement of a wing relative to a stationary surrounding fluid. This note develops a compact analytical aero-kinematic model that can be used for optimization of flapping wing kinematics against aerodynamic criteria of effectiveness (maximum lift) and efficiency (minimum power for a given amount of lift). It can also be used to make predictions of required flapping frequency for a given geometry and basic aerodynamic parameters. The kinematic treatment is based on a consolidation of an existing formulation that allows explicit derivation of flapping velocity for complex motions whereas the aerodynamic model is based on existing quasi-steady analysis. The combined aero-kinematic model provides novel explicit analytical expressions for both lift and power of a hovering wing in a compact form that enables exploration of a rich kinematic design space. Good agreement is found between model predictions of flapping frequency and observed results for a number of insects and optimal hovering kinematics identified using the model are consistent with results from studies using higher order computational models. For efficient flight, the flapping angle should vary using a triangular profile in time leading to a constant velocity flapping motion, whereas for maximum effectiveness the shape of variation should be sinusoidal. For both cases the wing pitching motion should be rectangular such that pitch change at stroke reversal is as rapid as possible.

On the quasi-steady aerodynamics of normal hovering flight part I: the induced power factor.

An analytical treatment to quantify the losses captured in the induced power factor, k, is provided for flapping wings in normal hover, including the effects of non-uniform downwash, tip losses and finite flapping amplitude. The method is based on a novel combination of actuator disc and lifting line blade theories that also takes into account the effect of advance ratio. The model has been evaluated against experimental results from the literature and qualitative agreement obtained for the effect of advance ratio on the lift coefficient of revolving wings. Comparison with quantitative experimental data for the circulation as a function of span for a fruitfly wing shows that the model is able to correctly predict the circulation shape of variation, including both the magnitude of the peak circulation and the rate of decay in circulation towards zero. An evaluation of the contributions to induced power factor in normal hover for eight insects is provided. It is also shown how Reynolds number can be accounted for in the induced power factor, and good agreement is obtained between predicted span efficiency as a function of Reynolds number and numerical results from the literature. Lastly, it is shown that for a flapping wing in hover k owing to the non-uniform downwash effect can be reduced to 1.02 using an arcsech chord distribution. For morphologically realistic wing shapes based on beta distributions, it is shown that a value of 1.07 can be achieved for a radius of first moment of wing area at 40% of wing length.

On the quasi-steady aerodynamics of normal hovering flight part II: model implementation and evaluation.

This paper introduces a generic, transparent and compact model for the evaluation of the aerodynamic performance of insect-like flapping wings in hovering flight. The model is generic in that it can be applied to wings of arbitrary morphology and kinematics without the use of experimental data, is transparent in that the aerodynamic components of the model are linked directly to morphology and kinematics via physical relationships and is compact in the sense that it can be efficiently evaluated for use within a design optimization environment. An important aspect of the model is the method by which translational force coefficients for the aerodynamic model are obtained from first principles; however important insights are also provided for the morphological and kinematic treatments that improve the clarity and efficiency of the overall model. A thorough analysis of the leading-edge suction analogy model is provided and comparison of the aerodynamic model with results from application of the leading-edge suction analogy shows good agreement. The full model is evaluated against experimental data for revolving wings and good agreement is obtained for lift and drag up to 90° incidence. Comparison of the model output with data from computational fluid dynamics studies on a range of different insect species also shows good agreement with predicted weight support ratio and specific power. The validated model is used to evaluate the relative impact of different contributors to the induced power factor for the hoverfly and fruitfly. It is shown that the assumption of an ideal induced power factor (k = 1) for a normal hovering hoverfly leads to a 23% overestimation of the generated force owing to flapping.

Theoretical modelling of wakes from retractable flapping wings in forward flight.

A free-wake method is used to simulate the wake from retractable, jointed wings. The method serves to complement existing experimental studies that visualise flying animal wakes. Simulated wakes are shown to be numerically convergent for a case study of the Rock Pigeon in minimum power cruising flight. The free-wake model is robust in simulating wakes for a range of wing geometries and dynamics without requiring changes to the numerical method. The method is found to be useful for providing low order predictions of wake geometries. However, it is not well suited to reconstructing 3d flowfields as solutions are sensitive to the numerical mesh node locations.

Simulating avian wingbeat kinematics.

Inverse dynamics methods are used to simulate avian wingbeats in varying flight conditions. A geometrically scalable multi-segment bird model is constructed, and optimisation techniques are employed to determine segment motions that generate desired aerodynamic force coefficients with minimal mechanical power output. The results show that wingbeat kinematics vary gradually with changes in cruise speed, which is consistent with experimental data. Optimised solutions for cruising flight of the pigeon suggest that upstroke wing retraction is used as a method of saving energy. Analysis of the aerodynamic force coefficient variation in high and low speed cruise leads to the proposal that a suitable gait metric should include both thrust and lift generation during each half-stroke.