Wing Rotation and the

Wing Rotation and the

(Parte 1 de 3)

Wing Rotation and the Aerodynamic Basis of

Insect Flight Michael H. Dickinson,1* Fritz-Olaf Lehmann,2 Sanjay P. Sane1

The enhanced aerodynamic performance of insects results from an interaction of three distinct yet interactive mechanisms: delayed stall, rotational circulation, and wake capture. Delayed stall functions during the translational portions of the stroke, when the wings sweep through the air with a large angle of attack. In contrast, rotational circulation and wake capture generate aerodynamic forces during stroke reversals, when the wings rapidly rotate and change direction. In addition to contributing to the lift required to keep an insect aloft, these two rotational mechanisms provide a potent means by which the animal can modulate the direction and magnitude of ßight forces during steering maneuvers. A comprehensive theory incorporating both translational and rotationalmechanismsmayexplainthediversepatternsofwingmotiondisplayed by different species of insects.

Insects were the first animals to evolve active flight and remain unsurpassed in many aspects of aerodynamic performance and maneuverability. Among insects, we find animals capable of taking off backwards, flying sideways, and landing upside down (1). While such complex aerial feats involve many physiological and anatomical specializations that are poorly understood, perhaps the greatest puzzle is how flapping wings can generate enough force to keep an insect in the air. Conventional aerodynamic theory is based on rigid wings moving at constant velocity. When insect wings are placed in a wind tunnel and tested over the range of air velocities that they encounter when flapped by the animal, the measured forces are substantially smaller than those required for active flight (2). Thus, something about the complexity of the flapping motion increases the lift produced by a wing above and beyond that which it could generate at constant velocity or that can be predicted by standard aerodynamic theory.

The failure of conventional steady-state theory has prompted the search for unsteady mechanisms that might explain the high forces produced by flapping wings (3, 4). The wingstroke of an insect is typically divided into four kinematic portions: two translational phases (upstroke and downstroke), when the wings sweep through the air with a high angle of attack, and two rotational phases (pronation and supination), when the wings rapidly rotate and reverse direction. The unsteady mechanisms that have been proposed to explain the elevated performance of insect wings typically emphasize either the translational or rotational phases of wing motion (3, 5–8). The first unsteady effect to be identified was a rotational mechanism termed the “clap and fling,” a close apposition of the two wings preceding pronation that hastens the development of circulation during the downstroke (9). Although the clap and fling may be important, especially in small species, it is not used by all insects (10) and thus cannot represent a general solution to the enigma of force production. Recent studies using real and dynamically scaled models of hawk moths suggest that a translational mechanism, termed “delayed stall,” might explain how insect wings generate such large forces (1). At high angles of attack, a flow structure forms on the leading edge of a wing that can transientlygeneratecirculatoryforcesin excess of those supported under steady-state conditions (7). On flappingwings, this leadingedge vortex is stabilized by the presence of axial flow, thereby augmenting lift throughout the downstroke(5, 1). Severaladditionalunsteady mechanisms have been proposed (6), mostly based on wing rotation,but recentstudieshave found little or no evidence for their use by insects (1). Despite this lack of evidence,it is unlikelythat insectsrely solely on translational mechanismsto fly.Whereasdelayedstallmight accountfor enoughliftto keepan insectaloft,it cannot easily explain how many insects can generateaerodynamicforces that exceed twice their body weight while carryingloads (10).

One persistent obstacle in the search for additional unsteady mechanisms is the difficulty in directly measuring the forces produced by a flapping insect (12). In order to further explore the aerodynamic basis of in- sect flight, we built a dynamically scaled model of the fruit fly, Drosophila melanogaster, equipped with sensors at the base of one wing capable of directly measuring the time course of aerodynamic forces (Fig. 1A). The forces generated by a pattern of wing motion based on Drosophila kinematics (13) are shown in Fig. 1, C through G. Both the magnitude and the orientation of the mean force coefficient (C#L5 1.39, inclined at 10.3° with respect to vertical) closely match values measured on tethered flies (14, 15). The instantaneous forces are roughly normal to the surface of the wing at all times, indicating that at this Reynolds number, pressure forces dominate the shear viscous forces acting parallel to the wing (Fig. 1C). The records show a transient peak in aerodynamic force at the start and end of each upstroke and downstroke (Fig. 1, D and E). The timing of these force transients relative to stroke reversal suggests that they result from some undetermined rotational effect and not from a translational mechanism such as delayed stall.

Translational forces. In order to test more rigorously whether rotational mechanisms were responsible for the two force peaks straddling stroke reversal, we estimated the forces that are generated solely by translation (Fig. 2). We calculated mean translational force coefficients (CL and CD) from data obtained by moving the wing through a 180° arc at constant velocity and fixed angle of attack (14). To obtain a representative mean value, we averaged the measured force coefficients over the interval indicated by the dotted lines in Fig. 2A. The values of the resulting translational lift and drag coefficients are consistent with similar measurements made on a two-dimensional (2D) model wing at an identical Reynolds number (7). The force coefficients of the 3D wing are slightly smaller than the maximum transient values generated by a 2D wing, but larger than the 2D steady-state values (Fig. 2D). These results confirm the important contribution of delayed stall in lift production during the translational portion of the wing stroke. The observation that the 3D force coefficients are lower than the 2D peak transient values, but higher than the 2D steadystate values, is entirely consistent with the flow patterns generated during force production. Whereas wing motion in 2D gives rise to an alternating pattern of unstable vortices termed a “von Karman street” (7), the leading edge vortex generated by the 3D model fly wing was stable throughout motion (16). The stability of the flow structure is manifest as constant force generation during translation (Fig. 2, A and B), in marked contrast to the 2D case (7). Thus, as has been previously suggested, axial flow along the length of the wing appears to stabilize the leading edge vortex throughout translation (5, 1). Where-

1Department of Integrative Biology, University of California, Berkeley, CA 94720, USA. 2Theodor-Boveri- Institute, Department of Behavioral Physiology and Sociobiological Zoology, University of Wu‹rzburg am Hubland, 97074 Wu‹rzburg, Germany.

*To whom correspondence should be addressed. E- mail: ßymanmd@socrates.berkeley.edu

18 JUNE 1999 VOL 284 SCIENCE w.sciencemag.org1954 on February 20, 2007 w.sciencemag.org Downloaded from as axial flow stabilizes force production at a level greater than that possible under steadystate conditions in 2D, the loss of energy from the vortex core probably limits force generation below the maximum 2D level.

The stability of the force coefficients following an impulsive start justifies the attempt to reconstruct a “quasi-steady” estimate of translational forces based on stroke kinematics. The results of such predictions for Drosophila kinematics are shown in Fig. 1, D and E. The calculations do not account for delays in the development of force via the Wagner effect (17) and probably represent a slight overestimate of the translational component. Although the translational values closely match the magnitude of the measured force near the middle of each half-stroke, they do not accurately predict the forces during stroke reversal. One potential artifact in the measurements of aerodynamic forces during stroke reversal is the contamination by inertial forces due to the linear and angular acceleration of the wing. However, a series of

lift (N) drag (N)

rotational lift (N)

down up down up trans. velocity (m s ang. velocity (degrees s) chord force vector motor assembly force sensor coaxial drive shaftmineral oil model wing

500 mN downstroke upstroke model wing force sensor gearbox total force translational component

Fig. 1. (A) Robotic ßy apparatus. The motion of the two wings is driven by an assembly of six computer-controlled stepper motors attached to the wing gearbox via timing belts and coaxial drive shafts. Each wing was capable of rotational motion about three axes. The wing was immersed ina1mb y 1 m by 2 m tank of mineral oil (density 5 0.8 3 103 kg m—3; kinematic viscosity 5 115 cSt). The geometry of the tank was designed to minimize potential wall effects (25). The viscosity of the oil, the length of the wing, and the ßappingfrequencyof the model werechosentomatchtheReynoldsnumber(Re) typicalofDrosophila(Re5 136).The25-cm-longmodelwingswereconstructedfromPlexiglas(3.2mm thick)cut accordingto the planiformof a Drosophilawing (26). The base of one wingwas equippedwitha 2D forcetransducerconsistingof two setsof strain gauges wired in full-bridge conÞguration (27). (B) Close-up view of robotic ßy. In Figs. 1, 3, and 5, measured forces are plotted as vectors superimposed over wing chords inclined at the instantaneous angle of attack. The vectors and wing chords are drawn as if viewed from a line of sight that runs axially along the length of the wing. (C) Diagram of wing motion indicating magnitude and orientation of force vectors generated throughout the stroke by a kinematic pattern based on Drosophila (stroke amplitude 5 160¡; frequency 5 145 mHz; angle of attackat midstroke 5 20¡ upstroke, 40¡ downstroke). Black lines indicate the instantaneous position of the wing at 25 temporally equidistant points during each half-stroke. Small circles mark the leading edge. Time moves right to left during downstroke, left to right during upstroke. Red vectors indicate instantaneous ßight forces. The large black vector at the right indicates the orientation of the mean force coefÞcient. (D and E) The time history of lift and drag forces. The measured forces are plotted in red, and forces predicted from translation force coefÞcients are plotted in blue (see text and Fig. 2). Data are plotted over two stroke cycles, with downstroke indicated by gray background. (F) Time course of rotational lift, deÞned as the difference between measured and estimated translational values of lift. (G) Translational (green) and rotational (purple) velocities of the wing.

w.sciencemag.org SCIENCE VOL 284 18 JUNE 1999 1955 on February 20, 2007 w.sciencemag.org Downloaded from control experiments indicated that the forces generated during stroke reversal could not be explained by either translational or rotational inertia (18). To provide a rough time course of rotational effects we subtracted the translational prediction of lift from the measured value (“rotational lift,” Fig. 1F). The subtraction reveals two clear force peaks bracketing each stroke reversal. For the Drosophila kinematics shown in Fig. 1, rotational effects contribute roughly 35% of the total lift production throughout the stroke—a high value considering the brief duration over which they act.

Rotational circulation. The presence of two rotational force peaks separated in time suggests that they might represent distinct aerodynamic mechanisms. One possible explanation for the force peak at the end of each half-stroke is that the wing’s own rotation serves as a source of circulation to generate an upward force (6, 19). This mechanism, rotational circulation, is akin to the Magnus effect, which makes a spinning baseball curve from its path toward the plate (20). The surface of a rotating ball pulls air within the boundary layer as it spins, thus serving as a source of circulation. As the ball moves through the air, this circulation will increase the total flow velocity on one side and decrease it on the other. If the velocity is higher on the top, as in the case of backspin, the ball is pulled upward by the lower pressure. In the case of topspin, the net velocity is higher below and the ball is pulled downward. If a flapping wing generates lift via a mechanism similar to the Magnus effect, then the orientation of the resulting force should also depend critically on the direction of wing rotation. To adopt the proper angle of attack for each translational phase, the wing must pronate before the downstroke and supinate before the upstroke (see wing sections in Figs. 1C and 3E). If the wing flips early, before reversing direction, then the leading edge rotates backward relative to translation

(“backspin”) and should produce an upward component of lift. If the wing flips late, after reversing direction, then the leading edge rotates forward relative to translation (“topspin”) and should create a downward force. If the process of rotation spans the end of one half-stroke to the beginning of the next, then the wing will generate first an upward force and then, following stroke reversal, a downward force. These predictions were verified by systematically changing the phase between wing translation and wing rotation in a

Fig. 2. Measurement of translational force coefÞcients. In each trial, we rapidly accelerated the wing from rest to a constant tip velocity of 0.25 m s—1. The angle of attack was increased between trials in 4.5¡ increments. (A and B) The time history of lift (CL) and drag (CD) coefÞcients. Data are shown for seven different angles of attack, as indicated by the labels to the right of the traces in

(A). Each trace begins with a large inertial transient caused by the rapid acceleration of the wing at the start of translation. After the inertial forces decay, the force trajectories are stable throughout translation. The dotted lines indicate the interval over which the values were averaged to calculate the mean values that were used to construct the relationships shown in (C) and (D). (C) Average translational force coefÞcients as a function of angle of attack. The two sets of data are well Þt by simple harmonic relationships: CL 5 0.225 1 1.58sin(2.13a — 7.20), CD 5 1.92 — 1.55cos(2.04a — 9.82), where a5 angle of attack. These formulas are used throughout the paper to estimate the translation component of ßight force. (D) Polar representation of translational force coefÞcients and comparison with 2D measurements at a comparable Reynolds number (7). The inßuence of induced drag on the 3D wing is manifest by the small right shift of the curve relative to the 2D data.

(Parte 1 de 3)

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