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.

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.

This paper offers a comprehensive review of traditional and advanced stockpile volume-estimation techniques employed within both outdoor and indoor confined spaces, whether that be a terrestrial- or an aerial-based technique. Traditional methods, such as manual measurement and satellite imagery, exhibit limitations in handling irregular or constantly changing stockpiles. On the other hand, more advanced techniques, such as global navigation satellite system (GNSS), terrestrial laser scanning (TLS), drone photogrammetry, and airborne light detection and ranging (LiDAR), have emerged to address these challenges, providing enhanced accuracy and efficiency. Terrestrial techniques relying on GNSS, TLS, and LiDAR offer accurate solutions; however, to minimize or eliminate occlusions, surveyors must access geometrically constrained places, representing a serious safety hazard. With the speedy rise of drone technologies, it was not unexpected that they found their way to the stockpile volume-estimation application, offering advantages such as ease of use, speed, safety, occlusion elimination, and acceptable accuracy compared to current standard methods, such as TLS and GNSS. For outdoor drone missions, image-based approaches, like drone photogrammetry, surpass airborne LiDAR in cost-effectiveness, ease of deployment, and color information, whereas airborne LiDAR becomes advantageous when mapping complex terrain with vegetation cover, mapping during low-light or dusty conditions, and/or detecting small or narrow objects. Indoor missions, on the other hand, face challenges such as low lighting, obstacles, dust, and limited space. For such applications, most studies applied LiDAR sensors mounted on tripods or integrated on rail platforms, whereas very few utilized drone solutions. In fact, the choice of the most suitable technique/approach depends on factors such as site complexity, required accuracy, project cost, and safety considerations. However, this review puts more focus on the potential of drones for stockpile volume estimation in confined spaces, and explores emerging technologies, such as solid-state LiDAR and indoor localization systems, which hold significant promise for the future. Notably, further research and real-world applications of these technologies will be essential for realizing their full potential and overcoming the challenges of operating robots in confined spaces.

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.

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.