The flight of insects has fascinated physicists and biologists for more than a century. Yet, until recently, researchers were unable to rigorously quantify the complex wing motions of flapping insects or measure the forces and flows around their wings. However, recent developments in high-speed videography and tools for computational and mechanical modeling have allowed researchers to make rapid progress in advancing our understanding of insect flight. These mechanical and computational fluid dynamic models, combined with modern flow visualization techniques, have revealed that the fluid dynamic phenomena underlying flapping flight are different from those of non-flapping, 2-D wings on which most previous models were based. In particular, even at high angles of attack, a prominent leading edge vortex remains stably attached on the insect wing and does not shed into an unsteady wake, as would be expected from non-flapping 2-D wings. Its presence greatly enhances the forces generated by the wing, thus enabling insects to hover or maneuver. In addition, flight forces are further enhanced by other mechanisms acting during changes in angle of attack, especially at stroke reversal, the mutual interaction of the two wings at dorsal stroke reversal or wing-wake interactions following stroke reversal. This progress has enabled the development of simple analytical and empirical models that allow us to calculate the instantaneous forces on flapping insect wings more accurately than was previously possible. It also promises to foster new and exciting multi-disciplinary collaborations between physicists who seek to explain the phenomenology, biologists who seek to understand its relevance to insect physiology and evolution, and engineers who are inspired to build micro-robotic insects using these principles. This review covers the basic physical principles underlying flapping flight in insects, results of recent experiments concerning the aerodynamics of insect flight, as well as the different approaches used to model these phenomena.

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The aerodynamics of insect flight

Recent progress in flapping wing aerodynamics and aeroelasticity

▪ Abstract “What force does an insect wing generate?” Finding answers to this enduring question is an essential step toward our understanding of interactions of moving objects with fluids that enable most living species such as insects, birds, and fish to travel efficiently and us to follow similar suit with sails, oars, and airfoils. We give a brief history of research in insect flight and discuss recent findings in unsteady aerodynamics of flapping flight at intermediate range Reynolds numbers (10–104). In particular, we examine the unsteady mechanisms in uniform and accelerated motions, forward and hovering flight, as well as passive flight of free-falling objects. The results obtained by “taking the insects apart” helped us to resolve previous puzzles about the force estimates in hovering insects, to ellucidate basic mechanisms essential to flapping flight, and to gain insights about the efficieny of flight.

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Dissecting insect flight

1. Introduction 2. Fixed, rigid wing aerodynamics 3. Flexible wing aerodynamics 4. Flapping wing aerodynamics.

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Aerodynamics of Low Reynolds Number Flyers

We compare computational, experimental and quasi-steady forces in a generic hovering wing undergoing sinusoidal motion along a horizontal stroke plane. In particular, we investigate unsteady effects and compare two-dimensional (2D) computations and three-dimensional (3D) experiments in several qualitatively different kinematic patterns. In all cases, the computed drag compares well with the experiments. The computed lift agrees in the cases in which the sinusoidal changes in angle of attack are symmetrical or advanced with respect to stroke positions, but lags behind the measured 3D lift in the delayed case. In the range of amplitudes studied here, 3-5 chords, the force coefficients have a weak dependence on stroke amplitude. As expected, the forces are sensitive to the phase between stroke angle and angle of attack, a result that can be explained by the orientation of the wing at reversal. This dependence on amplitude and phase suggests a simple maneuver strategy that could be used by a flapping wing device. In all cases the unsteady forces quickly reach an almost periodic state with continuous flapping. The fluid forces are dominated by the pressure contribution. The force component directly proportional to the linear acceleration is smaller by a factor proportional to the ratio of wing thickness and stroke amplitude; its net contribution is zero in hovering. The ratio of wing inertia and fluid force is proportional to the product of the ratio of wing and fluid density and the ratio of wing thickness and stroke amplitude; it is negligible in the robotic wing experiment, but need not be in insect flight. To identify unsteady effects associated with wing acceleration, and coupling between rotation and translation, as well as wake capture, we examine the difference between the unsteady forces and the estimates based on translational velocities, and compare them against the estimate of the coupling between rotation and translation, which have simple analytic forms for sinusoidal motions. The agreement and disagreement between the computed forces and experiments offer further insight into when the 3D effects are important. A main difference between a 3D revolving wing and a 2D translating wing is the absence of vortex shedding by a revolving wing over a distance much longer than the typical stroke length of insects. No doubt such a difference in shedding dynamics is responsible in part for the differences in steady state force coefficients measured in 2D and 3D. On the other hand, it is unclear whether such differences would have a significant effect on transient force coefficients before the onset of shedding. While the 2D steady state force coefficients underpredict 3D forces, the transient 2D forces measured prior to shedding are much closer to the 3D forces. In the cases studied here, the chord is moving between 3 to 5 chords, typical of hovering insect stroke length, and the flow does not appear to separate during each stroke in the cases of advanced and symmetrical rotation. In these cases, the wing reverses before the leading edge vortex would have time to separate even in 2D. This suggests that the time scale for flow separation in these strokes is dictated by the flapping frequency, which is dimensionally independent. In such cases, the 2D unsteady forces turn out to be good approximations of 3D experiments.

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Unsteady forces and flows in low Reynolds number hovering flight:two-dimensional computations vs robotic wing experiments

A computational fluid-dynamic analysis was conducted to study the unsteady aerodynamics of a model fruit fly wing. The wing performs an idealized flapping motion that emulates the wing motion of a fruit fly in normal hovering flight. The Navier-Stokes equations are solved numerically. The solution provides the flow and pressure fields, from which the aerodynamic forces and vorticity wake structure are obtained. Insights into the unsteady aerodynamic force generation process are gained from the force and flow-structure information. Considerable lift can be produced when the majority of the wing rotation is conducted near the end of a stroke or wing rotation precedes stroke reversal (rotation advanced), and the mean lift coefficient can be more than twice the quasi-steady value. Three mechanisms are responsible for the large lift: the rapid acceleration of the wing at the beginning of a stroke, the absence of stall during the stroke and the fast pitching-up rotation of the wing near the end of the stroke. When half the wing rotation is conducted near the end of a stroke and half at the beginning of the next stroke (symmetrical rotation), the lift at the beginning and near the end of a stroke becomes smaller because the effects of the first and third mechanisms above are reduced. The mean lift coefficient is smaller than that of the rotation-advanced case, but is still 80 % larger than the quasi-steady value. When the majority of the rotation is delayed until the beginning of the next stroke (rotation delayed), the lift at the beginning and near the end of a stroke becomes very small or even negative because the effect of the first mechanism above is cancelled and the third mechanism does not apply in this case. The mean lift coefficient is much smaller than in the other two cases.

Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion.

SUMMARY The lift and power requirements for hovering flight in Drosophila
virilis were studied using the method of computational fluid dynamics.
The Navier-Stokes equations were solved numerically. The solution provided the
flow velocity and pressure fields, from which the unsteady aerodynamic forces
and moments were obtained. The inertial torques due to the acceleration of the
wing mass were computed analytically. On the basis of the aerodynamic forces
and moments and the inertial torques, the lift and power requirements for
hovering flight were obtained. For the fruit fly Drosophila virilis in hovering flight (with
symmetrical rotation), a midstroke angle of attack of approximately 37°
was needed for the mean lift to balance the insect weight, which agreed with
observations. The mean drag on the wings over an up- or downstroke was
approximately 1.27 times the mean lift or insect weight (i.e. the wings of
this tiny insect must overcome a drag that is approximately 27 % larger than
its weight to produce a lift equal to its weight). The body-mass-specific
power was 28.7 W kg-1, the muscle-mass-specific power was 95.7 W
kg-1 and the muscle efficiency was 17 %. With advanced rotation, larger lift was produced than with symmetrical
rotation, but it was more energy-demanding, i.e. the power required per unit
lift was much larger. With delayed rotation, much less lift was produced than
with symmetrical rotation at almost the same power expenditure; again, the
power required per unit lift was much larger. On the basis of the calculated
results for power expenditure, symmetrical rotation should be used for
balanced, long-duration flight and advanced rotation and delayed rotation
should be used for flight control and manoeuvring. This agrees with
observations.

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Jian Tang

Papers

Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion.

Lift and power requirements of hovering flight in Drosophila virilis.