Wing and body kinematics of forward flight in drone-flies

Wing kinematics measurement and aerodynamics of hovering droneflies with wing damage

In this study, we performed successive unilateral and bilateral wing shearing to simulate wing damage in droneflies (Eristalis tenax) and measured the wing kinematics using high-speed photography technology. Two different shearing types were considered in the artificial wing damage. The aerodynamic force and power consumption were obtained by numerical method. Our major findings are the following. Different shearing methods have little influence on the kinematics, forces and energy consumption of insects. Following wing damage, among the potential strategies to adjust the three Euler angles of the wing, adjusting stroke angle (φ) in isolation, or combing the adjustment of stroke angle (φ) with pitch angle (ψ), contributed most to the change in vertical force. The balance of horizontal thrust can be restored by the adjustment of deviation angle (θ) under the condition of unilateral wing damage. Considering zero elastic energy storage, the mass-specific power (P₁) increases significantly following wing damage. However, the increase in mass-specific power with 100% elastic energy storage (P₂) is very small. The extra cost of the unilateral wing damage is that the energy consumption of the damaged wing and intact wing is highly asymmetrical when zero elastic energy storage is considered. The insects may alleviate the problems of increasing power consumption and asymmetric power distribution by storage and reuse of the negative inertial work of the wing.

Aerodynamic Effects of Ceiling and Ground Vicinity on Flapping Wings

The combined ceiling and ground effect on the aerodynamics of a hovering flapping wing is investigated using numerical simulations. In the simulations, the wing was located between the ceiling and the ground. Simulations were carried out for different wall clearances at two Reynolds numbers (Re = 10 and 100). Special efforts were paid to whether there exists aerodynamic coupling between the ceiling effect and the ground effect. At Re = 10, the combined ceiling and ground effect increases the aerodynamic forces monotonically through two effects, namely the narrow-channel effect and the downwash-reducing effect. Additionally, there exists a coupling effect of the ceiling and the ground for the combined case at Re = 10, where the force enhancement of the combined effect is much more significant than the sum of the ceiling-only effect and the ground-only effect. At Re = 100, the combined effect of ceiling and ground causes three non-monotonic force regimes (force enhancement, reduction and recovery) with increasing wall clearance. The narrow-channel effect at Re = 100 leads to a monotonic force trend, while the downwash-reducing effect results in a non-monotonic force trend. The two effects eventually lead to the three force regimes at Re = 100. Unlike the Re = 10 case, the coupling effect at Re = 100 is small.

Fully-printed metamaterial-type flexible wings with controllable flight characteristics

Insect wings are an outstanding example of how a proper interplay of rigid and flexible materials enables an intricate flapping flight accompanied by sound. The understanding of the aerodynamics and acoustics of insect wings has enabled the development of man-made flying robotic vehicles and explained basic mechanisms of sound generation by natural flyers. This work proposes the concept of artificial wings with a periodic pattern, inspired by metamaterials, and explores how the pattern geometry can be used to control the aerodynamic and acoustic characteristics of a wing. For this, we analyzed bio-inspired wings with anisotropic honeycomb patterns flapping at a low frequency and developed a multi-parameter optimization procedure to tune the pattern design in order to increase lift and simultaneously to manipulate the produced sound. Our analysis is based on the finite-element solution to a transient three-dimensional fluid-structure interactions problem. The two-way coupling is described by incompressible Navier-Stokes equations for viscous air and structural equations of motion for a wing undergoing large deformations. We 3D-printed three wing samples and validated their robustness and dynamics experimentally. Importantly, we showed that the proposed wings can sustain long-term resonance excitation that opens a possibility to implement resonance-type flights inherent to certain natural flyers. Our results confirm the feasibility of metamaterial patterns to control the flapping flight dynamics and can open new perspectives for applications of 3D-printed patterned wings, e.g. in the design of drones with target sound.

Aerodynamic investigation on shifted-back vertical stroke plane of flapping wing in forward flight

In order to properly understand aerodynamic characteristics in a flapping wing in forward flight, additional aerodynamic parameters apart from those in hover-an inclined stroke plane, a shifted-back stroke plane, and an advance ratio-must be comprehended in advance. This paper deals with the aerodynamic characteristics of a flapping wing in a shifted-back vertical stroke plane in freestream. A scaled-up robotic arm in a water towing tank was used to collect time-varying forces of a model flapping wing, and a semi-empirical quasi-steady aerodynamic model, which can decompose the forces into steady, quasi-steady, and unsteady components, was used to estimate the forces of the model flapping wing. It was found that the shifted-back stroke plane left a part of freestream as a non-perpendicular component, giving rise to a time-course change in the aerodynamic forces during the stroke. This also brought out two quasi-steady components (rotational and added-mass forces) apart from the steady one, even the wing moved with a constant stroke velocity. The aerodynamic model underestimated the actual forces of the model flapping wing even it can cover the increasingly distributed angle of attack of the vertical stroke plane with a blade element theory. The locations of the centers of pressure suggested a greater pressure gradient and an elongated leading-edge vortex along a wingspan than that of the estimation, which may explain the higher actual force in forward flight.

Very low Reynolds number causes a monotonic force enhancement trend for a three-dimensional hovering wing in ground effect

This research reports the numerical results of the ground effect trend for a three-dimensional flapping insect wing at a very low Reynolds number (Re = 10). It demonstrates that the ground effect trend at this Re has a 'single force regime,' i.e. the forces only enhance as the ground distance decreases. This phenomenon is unlike the widely expected non-monotonic trend publicized in previous studies for higher Reynolds numbers, that shows 'three force regimes,' i.e. the forces reduce, recover, and also enhance as the ground distance decreases. The force trend in the ground effect correlates to a similar trend in wing-wake interaction or the downwash strength on the wing's head. At very low Re (10), the very large viscosity causes diffused vortices and less advected vortex wake, while at relatively high Re, the vortices are easily separated from the wing and then advected downwards. This different development of the vortex wake caused different force trends for the flapping wing in the ground effect. Furthermore, by examining only the first stroke when there is no vortex wake, we found that the 'ramming effect' enhances the forces on the wing. This effect increases the pressure of the lower wing surface due to the squeezed air between the wing and the ground. The 'ramming effect', combined with the reduced downwash (or wing-wake interaction) effect, causes the force enhancement of the wing near the ground's vicinity. It is further comprehended that the trend is dependent on Re. As the Re is increased, the trend becomes non-monotonic. The effect of varying angles of attack, flapping amplitude and wing planform at very low Re does not change this trend. This ground effect might help insects by enhancing their lift while they hover above the surface. This finding might prove beneficial for developing micro air vehicles.

A semi-empirical model of the aerodynamics of manoeuvring insect flight

Blade element modelling provides a quick analytical method for estimating the aerodynamic forces produced during insect flight, but such models have yet to be tested rigorously using kinematic data recorded from free-flying insects. This is largely because of the paucity of detailed free-flight kinematic data, but also because analytical limitations in existing blade element models mean that they cannot incorporate the complex three-dimensional movements of the wings and body that occur during insect flight. Here, we present a blade element model with empirically fitted aerodynamic force coefficients that incorporates the full three-dimensional wing kinematics of manoeuvring Eristalis hoverflies, including torsional deformation of their wings. The two free parameters were fitted to a large free-flight dataset comprising N = 26 541 wingbeats, and the fitted model captured approximately 80% of the variation in the stroke-averaged forces in the sagittal plane. We tested the robustness of the model by subsampling the data, and found little variation in the parameter estimates across subsamples comprising 10% of the flight sequences. The simplicity and generality of the model that we present is such that it can be readily applied to kinematic datasets from other insects, and also used for the study of insect flight dynamics.

Kinematics Measurement and Power Requirements of Fruitflies at Various Flight Speeds

Energy expenditure is a critical characteristic in evaluating the flight performance of flying insects. To investigate how the energy cost of small-sized insects varies with flight speed, we measured the detailed wing and body kinematics in the full speed range of fruitflies and computed the aerodynamic forces and power requirements of the flies. As flight speed increases, the body angle decreases and the stroke plane angle increases; the wingbeat frequency only changes slightly; the geometrical angle of attack in the middle upstroke increases; the stroke amplitude first decreases and then increases. The mechanical power of the fruitflies at all flight speeds is dominated by aerodynamic power (inertial power is very small), and the magnitude of aerodynamic power in upstroke increases significantly at high flight speeds due to the increase of the drag and the flapping velocity of the wing. The specific power (power required for flight divided by insect weigh) changes little when the advance ratio is below about 0.45 and afterwards increases sharply. That is, the specific power varies with flight speed according to a J-shaped curve, unlike those of aircrafts, birds and large-sized insects which vary with flight speed according to a U-shaped curve.

Retinal slip compensation of pitch-constrained blue bottle flies flying in a flight mill

In the presence of wind or background image motion, flies are able to maintain a constant retinal slip velocity by regulating flight speed to the extent permitted by their locomotor capacity. Here we investigated the retinal slip compensation of tethered blue bottle flies (Calliphora vomitoria) flying semi-freely along an annular corridor in a magnetically levitated flight mill enclosed by two motorized cylindrical walls. We perturbed the flies' retinal slip by spinning the cylindrical walls, generating bilaterally averaged retinal slip perturbations from -0.3 to 0.3 m s-1 (or -116.4 to 116.4 deg s-1). When the perturbation was less than ∼0.1 m s-1 (38.4 deg s-1), the flies successfully compensated the perturbations and maintained a retinal slip velocity by adjusting their airspeed up to 20%. However, with greater retinal slip perturbation, the flies' compensation became saturated as their airspeed plateaued, indicating that they were unable to further maintain a constant retinal slip velocity. The compensation gain, i.e. the ratio of airspeed compensation and retinal slip perturbation, depended on the spatial frequency of the grating patterns, being the largest at 12 m-1 (0.04 deg-1).

Forward flight stability in a drone-fly

Previous studies on forward flight stability in insects are for low to medium flight-speeds. In the present work, we investigated the stability problem for the full range of flight speeds (0-8.6 m/s) of a drone-fly. Our results show the following: The longitudinal derivatives due to the lateral motion are approximately 3 orders of magnitude smaller than the other longitudinal derivatives. Thus, we can decouple these two motions of the insect, as commonly done for a conventional airplane. At hovering flight, the motion of the dronefly is weakly unstable owing to two unstable natural modes of motion, a longitudinal one and a lateral one. At low (1.6 m/s) and medium (3.1 m/s) flight-speeds, the unstable modes become even weaker and the flight is approximately neutral. At high flight-speeds (4.6 m/s, 6.9 m/s and 8.6 m/s), the flight becomes more and more unstable due to an unstable longitudinal mode. At the highest flight speed, 8.6 m/s, the instability is so strong that the time constant representing the growth rate of the instability (disturbance-doubling time) is only 10.1 ms, which is close to the sensory reaction time of a fly (approximately 11 ms). This indicates that strong instability may play a role in limiting the flight speed of the insect.

Speed control and force-vectoring of blue bottle flies in a magnetically-levitated flight mill

Flies fly at a broad range of speeds and produce sophisticated aerial maneuvers with precisely controlled wing movements. Remarkably, only subtle changes in wing motion are used by flies to produce aerial maneuvers, resulting in little directional tilt of aerodynamic force vector relative to the body. Therefore, it is often considered that flies fly according to a helicopter model and control speed mainly via force-vectoring by body-pitch change. Here we examined the speed control of blue bottle flies using a magnetically-levitated (MAGLEV) flight mill, as they fly at different body pitch angles and with different augmented aerodynamic damping. We identified wing kinematic contributors to the changes of estimated aerodynamic force through testing and comparing two force-vectoring models: i.e., a constant force-vectoring model and a variable force-vectoring model, while using the Akaike's information criterion for the selection of best-approximating model. Results show that the best-approximating variable force-vectoring model, which includes the effects of wing kinematic changes, yields a considerably more accurate prediction of flight speed, particularly in higher velocity range, as compared with those of the constant force-vectoring model. Examining the variable force-vectoring model reveals that, in the flight-mill tethered flight, flies use a collection of wing kinematic variables to control primarily the force magnitude, while the force direction is also modulated, albeit to a smaller extent compared to those due to the changes in body pitch. The roles of these wing kinematic variables are analogous to those of throttle, and collective and cyclic pitch of helicopters.