The authors also wish to thank Masateru Maeda and Hao Liu for fruitful discussions on insect modeling, and Malcolm Roberts for contributing to the code development.International audienceWe introduce FluSI, a fully parallel open source software package for pseudospectral simulations of three-dimensional flapping flight in viscous flows. It is freely available for noncommercial use from GitHub (https://github.com/pseudospectators/FLUSI). The computational framework runs on high performance computers with distributed memory architectures. The discretization of the three-dimensional incompressible Navier-Stokes equations is based on a Fourier pseudospectral method with adaptive time stepping. The complex time varying geometry of insects with rigid flapping wings is handled using the volume penalization method. The modules characterizing the insect geometry, flight mechanics, and wing kinematics are described. Validation tests for different benchmarks illustrate the efficiency and precision of the approach. Finally, computations for a model insect in the turbulent regime demonstrate the versatility of the software

High-resolution numerical simulations of a tethered model bumblebee in forward flight are performed superimposing homogeneous isotropic turbulent fluctuations to the uniform inflow. Despite tremendous variation in turbulence intensity, between 17% and 99% with respect to the mean flow, we do not find significant changes in cycle-averaged aerodynamic forces, moments or flight power when averaged over realizations, compared to laminar inflow conditions. The variance of aerodynamic measures, however, significantly increases with increasing turbulence intensity, which may explain flight instabilities observed in freely flying bees.Insect flight currently receives considerable attention from both biologists and engineers. This growing interest is fostered by the recent trend in miniaturization of unmanned air vehicles that naturally incites reconsidering flapping flight as a bio-inspired alternative to fixed-wing and rotary flight. For all small flyers it is challenging to fly outdoors in an unsteady environment, and it is essential to know how insects face that challenge.Field studies show variations of insect behavior with changing weather conditions, including the atmospheric turbulence [1]. Earlier laboratory research on aerodynamics of insect flight assumed quiescent air, and only some more recent experiments focused on the effect of different kinds of unsteady flows. The behavior of orchid bees flying freely in a turbulent air jet has been studied in [2]. The authors found that turbulent flow conditions have a destabilizing effect on the body, most severe about the animal's roll axis. In response to this flow, bees try to compensate the induced moments by an extension of their hindlegs, increasing the roll moment of inertia. Interaction of bumblebees with wake turbulence has also been considered in [3]. These experiments were performed in a von Kármán-type wake behind cylinders. The bees displayed large rolling motions, pronounced lateral accelerations, and a reduction in their upstream flight speed. In [4] a comparative study on the sensitivity of honeybees and stalk-eye flies to localized wind gusts was performed. The study found that bees and stalkeye flies respond differently to aerial perturbations, either causing roll instabilities in bees or significant yaw rotations in stalk-eye flies. In [5] feeding flights of hawkmoths in vortex streets past vertical cylinders were analyzed. Depending on distance of the animal from the cylinder and cylinder size, destabilizing effects on yaw and roll and a reduction in the animal's maximum flight speed have been observed. Kinematic responses to large helical coherent structures were also found in hawkmoths flying in a vortex chamber [6]. A study on the energetic significance of kinematic changes in hummingbird feeding flights further demonstrated a substantial increase in metabolic rate during flight in turbulent flows, compared to flight in undisturbed laminar inflow [7,8]. All studies reported significant changes in the behavior of insects when they fly in turbulent...

No abstract

The natural wind environment that volant insects encounter is unsteady and highly complex, posing significant flight-control and stability challenges. It is critical to understand the strategies insects employ to safely navigate in natural environments. We combined experiments on free flying bumblebees with high-fidelity numerical simulations and lower-order modeling to identify the mechanics that mediate insect flight in unsteady winds. We trained bumblebees to fly upwind towards an artificial flower in a wind tunnel under steady wind and in a von Kármán street formed in the wake of a cylinder. Analysis revealed that at lower frequencies in both steady and unsteady winds the bees mediated lateral movement with body roll - typical casting motion. Numerical simulations of a bumblebee in similar conditions permitted the separation of the passive and active components of the flight trajectories. Consequently, we derived simple mathematical models that describe these two motion components. Comparison between the free-flying live and modeled bees revealed a novel mechanism that enables bees to passively ride out high-frequency perturbations while performing active maneuvers at lower frequencies. The capacity of maintaining stability by combining passive and active modes at different timescales provides a viable means for animals and machines to tackle the challenges posed by complex airflows.

No abstract

Mechanical properties of insect wings are essential for insect flight aerodynamics. During wing flapping, wings may undergo tremendous deformations, depending on the wings’ spatial stiffness distribution. We here show an experimental evaluation of wing stiffness in three species of flies using a micro-force probe and an imaging method for wing surface reconstruction. Vertical deflection in response to point loads at 11 characteristic points on the wing surface reveals that average spring stiffness of bending lines between wing hinge and point loads varies ∼77-fold in small fruit flies and up to ∼28-fold in large blowflies. The latter result suggests that local wing deformation depends to a considerable degree on how inertial and aerodynamic forces are distributed on the wing surface during wing flapping. Stiffness increases with an increasing body mass, amounting to ∼0.6 Nm−1 in fruit flies, ∼0.7 Nm−1 in house flies and ∼2.6 Nm−1 in blowflies for bending lines, running from the wing base to areas near the center of aerodynamic pressure. Wings of house flies have a ∼1.4-fold anisotropy in mean stiffness for ventral versus dorsal loading, while anisotropy is absent in fruit flies and blowflies. We present two numerical methods for calculation of local surface deformation based on surface symmetry and wing curvature. These data demonstrate spatial deformation patterns under load and highlight how veins subdivide wings into functional areas. Our results on wings of living animals differ from previous experiments on detached, desiccated wings and help to construct more realistic mechanical models for testing the aerodynamic consequences of specific wing deformations.

Flight speed is positively correlated with body size in animals1. However, miniature featherwing beetles can fly at speeds and accelerations of insects three times their size2. Here we show that this performance results from a reduced wing mass and a previously unknown type of wing-motion cycle. Our experiment combines three-dimensional reconstructions of morphology and kinematics in one of the smallest insects, the beetle Paratuposa placentis (body length 395 μm). The flapping bristled wings follow a pronounced figure-of-eight loop that consists of subperpendicular up and down strokes followed by claps at stroke reversals above and below the body. The elytra act as inertial brakes that prevent excessive body oscillation. Computational analyses suggest functional decomposition of the wingbeat cycle into two power half strokes, which produce a large upward force, and two down-dragging recovery half strokes. In contrast to heavier membranous wings, the motion of bristled wings of the same size requires little inertial power. Muscle mechanical power requirements thus remain positive throughout the wingbeat cycle, making elastic energy storage obsolete. These adaptations help to explain how extremely small insects have preserved good aerial performance during miniaturization, one of the factors of their evolutionary success.

The aerial performance of flying insects ultimately depends on how flapping wings interact with the surrounding air. It has previously been suggested that the wing's three-dimensional camber and corrugation help to stiffen the wing against aerodynamic and inertial loading during flapping motion. Their contribution to aerodynamic force production, however, is under debate. Here, we investigated the potential benefit of three-dimensional wing shape in three different-sized species of flies using models of micro-computed tomography-scanned natural wings and models in which we removed either the wing's camber, corrugation, or both properties. Forces and aerodynamic power requirements during root flapping were derived from three-dimensional computational fluid dynamics modelling. Our data show that three-dimensional camber has no benefit for lift production and attenuates Rankine–Froude flight efficiency by up to approximately 12% compared to a flat wing. Moreover, we did not find evidence for lift-enhancing trapped vortices in corrugation valleys at Reynolds numbers between 137 and 1623. We found, however, that in all tested insect species, aerodynamic pressure distribution during flapping is closely aligned to the wing's venation pattern. Altogether, our study strongly supports the assumption that the wing's three-dimensional structure provides mechanical support against external forces rather than improving lift or saving energetic costs associated with active wing flapping.