Leading-edge curvature effect on aerodynamic performance of flapping wings in hover and forward flight.

This study investigates the role of leading-edge (LE) curvature in flapping wing aerodynamics considering hovering and forward flight conditions. A scaled-up robotic model is towed along its longitudinal axis by a rack gear carriage system. The forward velocity of the robotic model is changed by varying the advance ratioJfrom 0 (hovering) to 1.0. The study reveals that the LE curvature has insignificant influence on the cycle-average aerodynamic lift and drag. However, the time-history lift coefficient shows that the curvature can enhance the lift around the middle of downstroke. This enhanced lift is reduced from 5% to 1.2% asJchanged from 0 to 1.0. Further flow examinations reveal that the LE curvature is beneficial by enhancing circulation only at the outboard wing sections. The enhanced outboard circulation is found to emanate from the less stretched leading-edge vortices (LEVs), weakened trailing-edge vortices (TEVs), and the coherent merging of the tip vortices (TVs) with the minor LEVs as observed from the phase-lock planar digital particle image velocimetry measurements. The far-wake observation shows that the LE curvature enhances the vorticity within the TV, helping to reduce the overall flow fluctuations in the far field. These findings can be extended to explain the predominantly straight LE wing shape with a small amount of curvature only observed near the wing tip for flapping fliers with Re from 103to 104.

Enhancing Energy Harvesting Efficiency of Flapping Wings with Leading-Edge Magnus Effect Cylinder.

According to the Magnus principle, a rotating cylinder experiences a lateral force perpendicular to the incoming flow direction. This phenomenon can be harnessed to boost the lift of an airfoil by positioning a rotating cylinder at the leading edge. In this study, we simulate flapping-wing motion using the sliding mesh technique in a heaving coordinate system to investigate the energy harvesting capabilities of Magnus effect flapping wings (MEFWs) featuring a leading-edge rotating cylinder. Through analysis of the flow field vortex structure and pressure distribution, we explore how control parameters such as gap width, rotational speed ratio, and phase difference of the leading-edge rotating cylinder impact the energy harvesting characteristics of the flapping wing. The results demonstrate that MEFWs effectively mitigate the formation of leading-edge vortices during wing motion. Consequently, this enhances both lift generation and energy harvesting capability. MEFWs with smaller gap widths are less prone to induce the detachment of leading-edge vortices during motion, ensuring a higher peak lift force and an increase in the energy harvesting efficiency. Moreover, higher rotational speed ratios and phase differences, synchronized with wing motion, can prevent leading-edge vortex generation during wing motion. All three control parameters contribute to enhancing the energy harvesting capability of MEFWs within a certain range. At the examined Reynolds number, the optimal parameter values are determined to be a∗ = 0.0005, R = 3, and ϕ0 = 0°.

Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics.

Research into how fish and other aquatic organisms propel themselves offers valuable natural references for enhancing technology related to underwater devices like vehicles, propellers, and biomimetic robotics. Additionally, such research provides insights into fish evolution and ecological dynamics. This work carried out a numerical investigation of the most relevant dimensionless parameters in a fish swimming environment (Reynolds Re, Strouhal St, and Slip numbers) to provide valuable knowledge in terms of biomechanics behavior. Thus, a three-dimensional numerical study of the fish-like lambari, a BCF swimmer with carangiform kinematics, was conducted using the URANS approach with the k-ω-SST transition turbulence closure model in the OpenFOAM software. In this study, we initially reported the equilibrium Strouhal number, which is represented by St∗, and its dependence on the Reynolds number, denoted as Re. This was performed following a power-law relationship of St∝Re(-α). We also conducted a comprehensive analysis of the hydrodynamic forces and the effect of body undulation in fish on the production of swimming drag and thrust. Additionally, we computed propulsive and quasi-propulsive efficiencies, as well as examined the influence of the Reynolds number and Slip number on fish performance. Finally, we performed a vortex dynamics analysis, in which different wake configurations were revealed under variations of the dimensionless parameters St, Re, and Slip. Furthermore, we explored the relationship between the generation of a leading-edge vortex via the caudal fin and the peak thrust production within the motion cycle.

Flow development and leading edge vorticity in bristled insect wings.

Small flying insects such as the tiny thrip Gynaikothrips ficorum have wings with bristles attached to a solid shaft instead of solid membranes. Air passing through the bristle fringe, however, makes bristled insect wings less effective for aerodynamic force production. In this study, we quantified the ability of bristled wings to generate a leading edge vortex (LEV) for lift support during wing flapping, scored its circulation during wing translation, and investigated its behaviour at the stroke reversals. The data were measured in robotic model wings flapping with a generic kinematic pattern at Reynolds number of ~ 3.4, while applying two-dimensional particle image velocimetry. We found that aerodynamic performance due to LEV circulation linearly decreases with increasing bristle spacing. The wings of Gynaikothrips ficorum might thus produce approximately 9% less aerodynamic force for flight than a solid membranous wing. At the stroke reversals, leading and trailing edge vortices dissipate quickly within no more than ~ 2% of the stroke cycle duration. This elevated dissipation makes vortex shedding obsolete during the reversals and allows a quick build-up of counter-vorticity when the wing reverses flapping direction. In sum, our findings highlight the flow conditions associated with bristled wing design in insects and are thus significant for assessing biological fitness and dispersal of insects flying in a viscosity-dominated fluid regime.

Improved swimming performance in schooling fish via leading-edge vortex enhancement.

The hydrodynamics of schooling fish has been the subject of continued investigation over the last 50 years; fish schools exhibit a variety of arrangements and several distinct mechanisms have been proposed to explain the hydrodynamic benefits of schooling. In the current study, we use direct numerical simulations to show that a caudal fin swimmer trailing another similar swimmer can significantly improve its swimming performance by positioning itself such that the wake-induced flow of the leading fish, enhances the leading-edge vortex (LEV) on the fin of the trailing fish. Improvements of up to 12% in both the thrust and efficiency of the trailing fish are possible with this mechanism. The mechanisms underlying these interactional effects are quantitatively analyzed by applying the force partitioning method, a powerful data-driven method that partitions the pressure forces on the fish into mechanistically distinct components. The analysis reveals that the LEV on the fin dominates the overall thrust production for these swimmers and its enhancement therefore provides an effective and robust means for harnessing fish-fish hydrodynamic interactions in a school. In addition to confirming the potential energetic benefits of schooling, the LEV enhancement mechanism could be exploited in coordinated swimming of bioinspired multi-vehicle or multi-foil flapping foil propulsion systems.

The leading-edge vortex over a swift-like high-aspect-ratio wing with nonlinear swept-back geometry.

The leading-edge vortex (LEV) is a common flow structure that forms over wings at high angles of attack. Over the years, LEVs were exploited for augmenting the lift of man-made slender delta wings aircraft. However, recent observations suggested that natural flyers with high-aspect-ratio (high-AR) wings, such as the common swift (Apus apus), can also generate LEVs while gliding. We hypothesize that the planform shape and nonlinear sweep (increasing towards the wingtip) enable the formation and control of such LEVs. In this paper, we investigate whether a stationary LEV can form over a nonlinear swept-back high-AR wing inspired by the swift's wing shape and evaluate its characteristics and potential aerodynamic benefit. Particle image velocimetry (PIV) measurements were performed in a water flume on a high-AR swept-back wing inspired by the swift wing. Experiments were performed at four spanwise sections and a range of angles of attack for a chord-based Reynolds number of20000. Stationary LEV structures were identified across the wingspan by utilizing the proper orthogonal decomposition (POD) method for angles of attack of 5∘-15∘. The size and circulation of the stationary LEV were found to grow towards the wingtip in a nonlinear manner due to shear layer feeding and spanwise transport of mass and vorticity within the LEV, thus confirming that nonlinear high-AR swept-back wings can generate stationary LEVs. Our results suggest that the common swift can generate stationary LEVs over its swept-back wings to glide slower and at a higher rate of descent, with the LEVs potentially supporting up to 60% of its weight.

The Aerodynamic Effect of an Alula-like Vortex Generator on a Revolving Wing.

An alula is a small structure of feathers that prevents birds from stalling. In this study, the aerodynamic effect of an alula-like vortex generator (alula-VG) on a revolving wing was investigated using the PIV technique in a water tank. The alula-VG was mounted on a rectangular wing model at two spanwise positions. The wing model with a revolving motion was installed at different angles of attack, which included pre-stall and post-stall conditions. The velocity fields around the wing model with/without an alula-VG were measured and analyzed, including the vorticity contour, the circulation of vortex structures, and the corresponding sectional lift coefficient, which are used to explain the aerodynamic effect induced by an alula-VG. The lift-off and bursting of the leading-edge vortex (LEV) affect the magnitude of the chordwise circulation and the section lift coefficient. The results show that compared to an alula-VG mounted fixed wing model, the flow interactions among the alula-VG induced spanwise flow, the inertial force caused by the revolving motion, and the wing-tip vortex play important roles in the vortex bursting and the resultant aerodynamic performance. The effect of an alula-VG on a revolving wing depends on its spanwise position and the angle of attack of a wing model, which need to be properly matched.

Hydrodynamic interaction of dorsal fin and caudal fin in swimming tuna.

Tuna, which are known for high-performance swimming, possess a large crescent dorsal fin (DF) and a caudal fin (CF) that differ from those of other fishes. The hydrodynamic interaction between the DF and CF in tuna, which are represented by two tandem 3D flapping plates, is numerically explored in the present study. Hydrodynamic properties and wake structures of the models with and without a DF are compared to investigate the effects of the DF. The thrust on the CF is substantially enhanced by the DF, whereas the force on the DF is not affected by the CF. The constructive interaction between the leading-edge vortex (LEV) on the CF and the vortices shed from the dorsal fin (DFVs) is identified from 3D wake topology and 2D vorticity distributions. The circulation of spanwise vorticity quantitatively reveals that the LEV on the CF is strengthened by the same-signed DFV. The effect of the flapping phase of the CF is examined. The DF-CF interaction is sensitive to the flapping phase at a short spacing, whereas a long spacing between the two fins enables a robust constructive interaction in tuna swimming. A systematic study is carried out to explore the effects of the Strouhal number (St) and the Reynolds number (Re) on the interaction of the fins. The enhancement of thrust due to the DF is diminished at St = 0.63, whereas the Re does not substantially influence the constructive DF-CF interaction.

Wing Planform Effect on the Aerodynamics of Insect Wings.

This study investigates the effect of wing planform shape on the aerodynamic performance of insect wings by numerically solving the incompressible Navier-Stokes equations. We define the wing planforms using a beta-function distribution and employ kinematics representative of normal hovering flight. In particular, we use three primary parameters to describe the planform geometry: aspect ratio, radial centroid location, and wing root offset. The force coefficients, flow structures, and aerodynamic efficiency for different wing planforms at a Reynolds number of 100 are evaluated. It is found that the wing with the lowest aspect ratio of 1.5 results in the highest peaks of lift and drag coefficients during stroke reversals, whereas the higher aspect ratio wings produce higher lift and drag coefficients during mid half-stroke translation. For the wings considered, the leading-edge vortex detachment is found to be approximately at a location that is 3.5-5 mean chord lengths from the wing center of rotation for all aspect ratios and root offsets investigated. Consequently, the detachment area increases with the increase of aspect ratio and root offset, resulting in reduced aerodynamic coefficients. The radial centroid location is found to influence the local flow evolution time, and this results in earlier formation/detachment of the leading-edge vortex for wings with a smaller radial centroid location. Overall, the best performance, when considering both average lift coefficient and efficiency, is found at the intermediate aspect ratios of 4.5-6; increasing the centroid location mainly increases efficiency; and increasing the root offset leads to a decreased average lift coefficient whilst leading to relatively small variations in aerodynamic efficiency for most aspect ratios.

Fin-fin interactions during locomotion in a simplified biomimetic fish model.

Fish median fins are extremely diverse, but their function is not yet fully understood. Various biological studies on fish and engineering studies on flapping foils have revealed that there are hydrodynamic interactions between fins arranged in tandem and that these interactions can lead to improved performance by the posterior fin. This performance improvement is often driven by the augmentation of a leading-edge vortex on the trailing fin. Past experimental studies have necessarily simplified fish anatomy to enable more detailed engineering analyses, but such simplifications then do not capture the complexities of an undulating fish-like body with fins attached. We present a flexible fish-like robotic model that better represents the kinematics of swimming fishes while still being simple enough to examine a range of morphologies and motion patterns. We then create statistical models that predict the individual effects of each kinematic and morphological variable. Our results demonstrate that having fins arranged in tandem on an undulating body can lead to more steady production of thrust forces determined by the distance between the fins and their relative motion. We find that these same variables also affect swimming speed. Specifically, when swimming at high frequencies, self-propelled speed decreases by 12%-26% due to out of phase fin motion. Flow visualization reveals that variation within this range is caused in part by fin-fin flow interactions that affect leading edge vortices. Our results indicate that undulatory swimmers should optimize both the positioning and relative motion of their median fins in order to reduce force oscillations and improve overall performance while swimming.

Phenomenology and scaling of optimal flapping wing kinematics.

Biological flapping wing fliers operate efficiently and robustly in a wide range of flight conditions and are a great source of inspiration to engineers. The unsteady aerodynamics of flapping wing flight are dominated by large-scale vortical structures that augment the aerodynamic performance but are sensitive to minor changes in the wing actuation. We experimentally optimise the pitch angle kinematics of a flapping wing system in hover to maximise the stroke average lift and hovering efficiency with the help of an evolutionary algorithm andin situforce and torque measurements at the wing root. Additional flow field measurements are conducted to link the vortical flow structures to the aerodynamic performance for the Pareto-optimal kinematics. The optimised pitch angle profiles yielding maximum stroke-average lift coefficients have trapezoidal shapes and high average angles of attack. These kinematics create strong leading-edge vortices early in the cycle which enhance the force production on the wing. The most efficient pitch angle kinematics resemble sinusoidal evolutions and have lower average angles of attack. The leading-edge vortex grows slower and stays close-bound to the wing throughout the majority of the stroke-cycle. This requires less aerodynamic power and increases the hovering efficiency by 93% but sacrifices 43% of the maximum lift in the process. In all cases, a leading-edge vortex is fed by vorticity through the leading edge shear layer which makes the shear layer velocity a good indicator for the growth of the vortex and its impact on the aerodynamic forces. We estimate the shear layer velocity at the leading edge solely from the input kinematics and use it to scale the average and the time-resolved evolution of the circulation and the aerodynamic forces. The experimental data agree well with the shear layer velocity prediction, making it a promising metric to quantify and predict the aerodynamic performance of the flapping wing hovering motion.

A novel cylindrical overlap-and-fling mechanism used by sea butterflies.

The clap-and-fling mechanism is a well-studied, unsteady lift generation mechanism widely used by flying insects and is considered obligatory for tiny insects flying at low to intermediate Reynolds numbers, Re However, some aquatic zooplankters including some pteropod (i.e. sea butterfly) and heteropod species swimming at low to intermediate Re also use the clap-and-fling mechanism. These marine snails have extremely flexible, actively deformed, muscular wings which they flap reciprocally to create propulsive force, and these wings may enable novel lift generation mechanisms not available to insects, which have less flexible, passively deformed wings. Using high-speed stereophotogrammetry and micro-particle image velocimetry, we describe a novel cylindrical overlap-and-fling mechanism used by the pteropod species Cuvierina atlantica In this maneuver, the pteropod's wingtips overlap at the end of each half-stroke to sequentially form a downward-opening cone, a cylinder and an upward-opening cone. The transition from downward-opening cone to cylinder produces a downward-directed jet at the trailing edges. Similarly, the transition from cylinder to upward-opening cone produces downward flow into the gap between the wings, a leading edge vortex ring and a corresponding sharp increase in swimming speed. The ability of this pteropod species to perform the cylindrical overlap-and-fling maneuver twice during each stroke is enabled by its slender body and highly flexible wings. The cylindrical overlap-and-fling mechanism observed here may inspire the design of new soft robotic aquatic vehicles incorporating highly flexible propulsors to take advantage of this novel lift generation technique.

Leading-edge vortices over swept-back wings with varying sweep geometries.

Micro air vehicles are used in a myriad of applications, such as transportation and surveying. Their performance can be improved through the study of wing designs and lift generation techniques including leading-edge vortices (LEVs). Observation of natural fliers, e.g. birds and bats, has shown that LEVs are a major contributor to lift during flapping flight, and the common swift (Apus apus) has been observed to generate LEVs during gliding flight. We hypothesize that nonlinear swept-back wings generate a vortex in the leading-edge region, which can augment the lift in a similar manner to linear swept-back wings (i.e. delta wing) during gliding flight. Particle image velocimetry experiments were performed in a water flume to compare flow over two wing geometries: one with a nonlinear sweep (swift-like wing) and one with a linear sweep (delta wing). Experiments were performed at three spanwise planes and three angles of attack at a chord-based Reynolds number of 26 000. Streamlines, vorticity, swirling strength, and Q-criterion were used to identify LEVs. The results show similar LEV characteristics for delta and swift-like wing geometries. These similarities suggest that sweep geometries other than a linear sweep (i.e. delta wing) are capable of creating LEVs during gliding flight.

Hawkmoth flight in the unsteady wakes of flowers.

Flying animals maneuver and hover through environments where wind gusts and flower wakes produce unsteady flow. Although both flight maneuvers and aerodynamic mechanisms have been studied independently, little is known about how these interact in an environment where flow is already unsteady. Moths forage from flowers by hovering in the flower's wake. We investigated hawkmoths tracking a 3D-printed robotic flower in a wind tunnel. We visualized the flow in the wake and around the wings and compared tracking performance with previous experiments in a still-air flight chamber. As in still air, moths flying in the flower wake exhibit near-perfect tracking at the low frequencies at which natural flowers move. However, tracking in the flower wake results in a larger overshoot between 2 and 5 Hz. System identification of flower tracking reveals that moths also display reduced-order dynamics in wind compared with still air. Smoke visualization of the flower wake shows that the dominant vortex shedding corresponds to the same frequency band as the increased overshoot. Despite these large effects on tracking dynamics in wind, the leading edge vortex (LEV) remains bound to the wing throughout the wingstroke and does not burst. The LEV also maintains the same qualitative structure seen in steady air. Persistence of a stable LEV during decreased flower tracking demonstrates the interplay between hovering and maneuvering.

Aerodynamic characteristics along the wing span of a dragonfly Pantala flavescens.

We investigated the characteristics of interwing aerodynamic interactions across the span of the high aspect ratio, flexible wings of dragonflies under tethered and free-flying conditions. This revealed that the effects of the interactions on the hindwings vary across four spanwise regions. (i) Close to the wing root, a trailing-edge vortex (TEV) is formed by each stroke, while the formation of a leading-edge vortex (LEV) is limited by the short translational distance of the hindwing and suppressed by the forewing-induced flow. (ii) In the region away from the wing root but not quite up to midspan, the formation of the hindwing LEV is influenced by that of the forewing LEV. This vortex synergy can increase the circulation of the hindwing LEV in the corresponding cross-section by 22% versus that of the hindwing in isolation. (iii) In the region about half-way between the wing root and wing tip there is a transition dominated by downwash from the forewing resulting in flow attached to the hindwing. (iv) A LEV is developed in the remaining, outer region of the wing at the end of a stroke when the hindwing captures the vortex shed by the forewing. The interaction effects depend not only on the wing phasing but also on the flapping offset and flight direction. The aerodynamics of the hindwings vary substantially from the wing root to the wing tip. For a given phasing, this spanwise variation in the aerodynamics can be exploited in the design of artificial wings to achieve greater agility and higher efficiency.

Flying in reverse: kinematics and aerodynamics of a dragonfly in backward free flight.

In this study, we investigated the backward free flight of a dragonfly, accelerating in a flight path inclined to the horizontal. The wing and body kinematics were reconstructed from the output of three high-speed cameras using a template-based subdivision surface reconstruction method, and numerical simulations using an immersed boundary flow solver were conducted to compute the forces and visualize the flow features. During backward flight, the dragonfly maintained an upright body posture of approximately 90° relative to the horizon. The upright body posture was used to reorient the stroke plane and the flight force in the global frame; a mechanism known as 'force vectoring' which was previously observed in manoeuvres of other flying animals. In addition to force vectoring, we found that while flying backward, the dragonfly flaps its wings with larger angles of attack in the upstroke (US) when compared with forward flight. Also, the backward velocity of the body in the upright position enhances the wings' net velocity in the US. The combined effect of the angle of attack and wing net velocity yields large aerodynamic force generation in the US, with the average magnitude of the force reaching values as high as two to three times the body weight. Corresponding to these large forces was the presence of a strong leading edge vortex (LEV) at the onset of US which remained attached up until wing reversal. Finally, wing-wing interaction was found to enhance the aerodynamic performance of the hindwings (HW) during backward flight. Vorticity from the forewings' trailing edge fed directly into the HW LEV to increase its circulation and enhance force production.

Analysis of a swimmer's hand and forearm in impulsive start from rest using computational fluid dynamics in unsteady flow conditions.

The propulsive forces generated by the hands and arms of swimmers have so far been determined essentially by quasi-steady approaches. This study aims to quantify the temporal dependence of the hydrodynamic forces for a simple translation movement: an impulsive start from rest. The study, carried out in unsteady numerical simulation, couples the calculation of the lift and the drag on an expert swimmer hand-forearm model with visualizations of the flow and flow vortex structure analysis. The results of these simulations show that the hand and forearm hydrodynamic forces should be studied from an unsteady approach because the quasi-steady model is inadequate. It also appears that the delayed stall effect generates higher circulatory forces during a short translation at high angle of attack than forces calculated under steady state conditions. During this phase the hand force coefficients are approximately twice as large as those of the forearm. The total force coefficients are highest for angles of attack between 40° and 60°. For the same angle of attack, the forces produced when the leading edge is the thumb side are slightly greater than those produced when the leading edge is the little finger side.

The leading-edge vortex of swift wing-shaped delta wings.

Recent investigations on the aerodynamics of natural fliers have illuminated the significance of the leading-edge vortex (LEV) for lift generation in a variety of flight conditions. A well-documented example of an LEV is that generated by aircraft with highly swept, delta-shaped wings. While the wing aerodynamics of a manoeuvring aircraft, a bird gliding and a bird in flapping flight vary significantly, it is believed that this existing knowledge can serve to add understanding to the complex aerodynamics of natural fliers. In this investigation, a model non-slender delta-shaped wing with a sharp leading edge is tested at low Reynolds number, along with a delta wing of the same design, but with a modified trailing edge inspired by the wing of a common swift Apus apus. The effect of the tapering swift wing on LEV development and stability is compared with the flow structure over the unmodified delta wing model through particle image velocimetry. For the first time, a leading-edge vortex system consisting of a dual or triple LEV is recorded on a swift wing-shaped delta wing, where such a system is found across all tested conditions. It is shown that the spanwise location of LEV breakdown is governed by the local chord rather than Reynolds number or angle of attack. These findings suggest that the trailing-edge geometry of the swift wing alone does not prevent the common swift from generating an LEV system comparable with that of a delta-shaped wing.

Hovering hummingbird wing aerodynamics during the annual cycle. I. Complete wing.

The diverse hummingbird family (Trochilidae) has unique adaptations for nectarivory, among which is the ability to sustain hover-feeding. As hummingbirds mainly feed while hovering, it is crucial to maintain this ability throughout the annual cycle-especially during flight-feather moult, in which wing area is reduced. To quantify the aerodynamic characteristics and flow mechanisms of a hummingbird wing throughout the annual cycle, time-accurate aerodynamic loads and flow field measurements were correlated over a dynamically scaled wing model of Anna's hummingbird (Calypte anna). We present measurements recorded over a model of a complete wing to evaluate the baseline aerodynamic characteristics and flow mechanisms. We found that the vorticity concentration that had developed from the wing's leading-edge differs from the attached vorticity structure that was typically found over insects' wings; firstly, it is more elongated along the wing chord, and secondly, it encounters high levels of fluctuations rather than a steady vortex. Lift characteristics resemble those of insects; however, a 20% increase in the lift-to-torque ratio was obtained for the hummingbird wing model. Time-accurate aerodynamic loads were also used to evaluate the time-evolution of the specific power required from the flight muscles, and the overall wingbeat power requirements nicely matched previous studies.

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.