Download - Insect Flight

Biol. Rev. (2001), 76, pp. 449–471 " Cambridge Philosophical SocietyDOI: 10.1017}S1464793101005759 Printed in the United Kingdom

449

Mechanics and aerodynamics of insect flight

control

GRAHAM K. TAYLOR

Department of Zoology, Oxford University, South Parks Road, Oxford, OX1 3PS, UK

(E-mail : graham.taylor!zoo.ox.ac.uk)

(Received 7 November 2000; revised 14 June 2001

ABSTRACT

Insects have evolved sophisticated flight control mechanisms permitting a remarkable range of manoeuvres.Here, I present a qualitative analysis of insect flight control from the perspective of flight mechanics, drawingupon both the neurophysiology and biomechanics literatures. The current literature does not permit aformal, quantitative analysis of flight control, because the aerodynamic force systems that biologists havemeasured have rarely been complete and the position of the centre of gravity has only been recorded in afew studies. Treating the two best-known insect orders (Diptera and Orthoptera) separately from otherinsects, I discuss the control mechanisms of different insects in detail. Recent experimental studies suggestthat the helicopter model of flight control proposed for Drosophila spp. may be better thought of as afacultative strategy for flight control, rather than the fixed (albeit selected) constraint that it is usuallyinterpreted to be. On the other hand, the so-called ‘constant-lift reaction’ of locusts appears not to be a reflexfor maintaining constant lift at varying angles of attack, as is usually assumed, but rather a mechanism torestore the insect to pitch equilibrium following a disturbance. Differences in the kinematic controlmechanisms used by the various insect orders are related to differences in the arrangement of the wings, theconstruction of the flight motor and the unsteady mechanisms of lift production that are used. Since theevolution of insect flight control is likely to have paralleled the evolutionary refinement of these unsteadyaerodynamic mechanisms, taxonomic differences in the kinematics of control could provide an assay of therelative importance of different unsteady mechanisms. Although the control kinematics vary widely betweenorders, the number of degrees of freedom that different insects can control will always be limited by thenumber of independent control inputs that they use. Control of the moments about all three axes (as usedby most conventional aircraft) has only been proven for larger flies and dragonflies, but is likely to bewidespread in insects given the number of independent control inputs available to them. Unlike inconventional aircraft, however, insects’ control inputs are likely to be highly non-orthogonal, and this willtend to complicate the neural processing required to separate the various motions.

Key words : Insect flight control, steering, unsteady aerodynamics, kinematics, constant-lift reaction, turning,manoeuvre.

CONTENTS

I. Introduction ............................................................................................................................ 450II. Manoeuvre control versus reflex stabilisation ........................................................................... 451

III. General principles of control ................................................................................................... 452IV. Flight control in Diptera (true flies)........................................................................................ 454

(1) Longitudinal control ......................................................................................................... 454(2) Lateral control .................................................................................................................. 456

450 Graham K. Taylor

V. Flight control in Orthoptera (locusts and crickets) ................................................................. 459(1) Longitudinal control ......................................................................................................... 459(2) Lateral control .................................................................................................................. 460

VI. Flight control in other insects .................................................................................................. 461(1) Longitudinal control ......................................................................................................... 461(2) Lateral control .................................................................................................................. 463

VII. Discussion ................................................................................................................................ 463(1) How many degrees of freedom do insects control?............................................................ 463(2) Evolution of insect flight control systems .......................................................................... 466

VIII. Conclusions .............................................................................................................................. 467IX. Acknowledgements .................................................................................................................. 467X. References................................................................................................................................ 467

I. INTRODUCTION

Insect flight control has been studied extensivelyfrom a physiological perspective, but its mechanicsare less well known. Even where the kinematicchanges elicited by a given stimulus have beendefined, their consequences for aerodynamic forceproduction often remain obscure. Earlier work onflight control was firmly rooted in the assumptions ofquasi-steady aerodynamics. However, since detailedquasi-steady analyses and direct force measurements(e.g. Weis-Fogh, 1973; Norberg, 1975; Cloupeau,Devillers & Devezeaux, 1979; Ellington, 1984 c ;Ennos, 1989; Dudley & Ellington, 1990b ; Wilkin,1990; Zanker & Go$ tz, 1990; Wilkin & Williams,1993) indicate that aerodynamic force production ininsects generally relies upon unsteady mechanisms(Willmott, Ellington & Thomas, 1997; Dickinson,Lehmann & Sane, 1999), our understanding ofinsect flight control must necessarily incorporateunsteady effects. Although our understanding ofunsteady mechanisms is still very limited, morerecent experimental studies (Go$ tz, 1987; Dickinson,Lehmann & Go$ tz, 1993; Dickinson, 1999; Dickinsonet al., 1999) have begun to investigate their role ininsect flight control.

An experimental approach integrating physio-logical and mechanical observations is clearly de-sirable. For example, although electromyographicstudies have demonstrated that migratory locustsLocusta migratoria generate different motor patterns inresponse to roll and yaw stimuli (Zarnack & Mo$ hl,1977), they cannot tell us whether this is sufficient toallow roll and yaw rotations to be producedseparately. This can only be resolved by directlymeasuring the torques and forces that the insectsproduce, or by analysing high-speed film of theinsects in flight. Although the current literature doespermit some synthesis of aerodynamics and kin-

ematics with neurobiology and muscle mechanics(see Kammer, 1985 for a review of this type), I havechosen to concentrate in detail upon the aero-dynamics and kinematics of flight control. Thisapproach is similar to that of most texts on aircraftflight mechanics (e.g. Nelson, 1989; Etkin & Reid,1996; Cook, 1997; Vinh, 1993) in that it does notcomplicate the discussion of flight dynamics withdetails of the engineering mechanism that adjusts anaircraft’s elevators or varies an insect’s wingbeatfrequency. Instead, I will concentrate upon howdifferent kinematic inputs affect the dependentvariables of position and velocity, as illustratedschematically in Fig. 1. The more general question ofhow many degrees of freedom insects can control isone of the central issues of insect flight control andwill form the theme of this review.

The ‘black box’ between the inputs and outputsof Fig. 1 is properly replaced by the equations ofmotion for a flying body together with a system of

control inputse.g. stroke amplitude,wingbeat frequency

position

attitude

velocity

angularvelocity

angular acceleration

position

attitude

velocity

angularvelocity

acceleration

Fig. 1. Block diagram illustrating the overall approach ofthis review. The black box represents the equations ofmotion for a flying body, together with a system oftransfer functions providing the mathematical relation-ship between control inputs and their effects upon thedependent variables.

451Mechanics of insect flight control

transfer functions providing the mathematical re-lationship between the control inputs and theireffects upon the dependent variables. I shall only bediscussing the mechanics of insect flight control inqualitative terms, however, as the current literaturedoes not allow for even a formal static, let alonedynamic, quantitative framework to be applied. Thereasons for this are best seen by considering the twopossible approaches to the quantitative analysis ofinsect flight control. The first is to correlate free-flight manoeuvres with observed changes in wingkinematics. For example, Wakeling & Ellington(1997) correlated velocity and flight force withseveral basic kinematic parameters measured fromhigh-speed film of free-flying dragonflies. However,the purpose of fitting regression lines in that studywas ‘only to identify trends and not to estimate afunctional relationship’ (Wakeling & Ellington,1997, p. 566) and since the equations for theregressions were not recorded, it is difficult to drawany further quantitative conclusions. In any case,accurately determining the three-dimensional wingkinematics of even a stationary insect presentsformidable technical difficulties, and to do so duringfree-flight manoeuvres is very difficult indeed.

An alternative approach is to measure directly theforces and moments on tethered insects and tocorrelate these with the observed changes in wingkinematics. Unfortunately, although many studieshave measured selected forces and torques generatedby tethered insects, the resulting force systems arerarely complete, in the sense of defining the point ofaction, as well as the magnitude and direction, of theresultant flight force. Only two published studies(Hollick, 1940; Blondeau, 1981) appear to havemade the necessary measurements to determine thepoint of action of the resultant flight force, yet this isessential in determining the effect of a force, as anychild who has ever played on a see-saw will know.The position of the centre of gravity has likewiserarely been recorded, but is critical in determiningboth the animal’s responsiveness to control inputsand its characteristics of stability and equilibrium.Its role in flight dynamics is analogous to that of thefulcrum in a game of see-saw. For a full dynamicanalysis of insect flight control, it will be necessaryalso to determine the insect’s moments of inertia.The importance of the distribution of mass indetermining the envelope of insect flight control hasbeen emphasised by recent experimental work onthe flight performance of neotropical butterflies(Srygley & Dudley, 1993; Srygley, 1994, 1999;Srygley & Kingsolver, 2000). A more rigorous

experimental approach is clearly required before wewill make any further inroads towards a quantitativeanalysis of insect flight control.

As a final caveat, it is worth emphasising that thepicture of insect flight mechanics portrayed in thisreview is far from complete. For example, althoughthe open-loop conditions that are normally imposedby tethering often lead to exaggerated turningresponses (Robert & Rowell, 1992a), laboratoryexperiments may not reveal the full gamut of controlresponses used by insects flying under naturalconditions. Only where we can identify clearphysiological limits upon performance can we besure that we have correctly identified the boundaryof the flight envelope. As the quantity and detail ofexperimental work on insect flight control improves,our knowledge of insects’ flight envelopes lookscertain to expand.

II. MANOEUVRE CONTROL VERSUS REFLEX

STABILISATION

Insect control systems serve two discrete functions :to allow controlled manoeuvres and to augment orprovide stability in the face of external (or possiblyinternal) perturbations. Since stability will tend tooppose both accidental and deliberate deviationsfrom steady flight, these two functions are expectedto be in direct conflict unless some mechanism ispresent to bypass or desensitise the reflex stabilisationsystem during manoeuvres. In the absence of such amechanism, the command to elicit a manoeuvrewould need to override any signals from the reflexstabilisation system, presumably with a consequentdrop in nervous, if not also mechanical, efficiency.From the viewpoint of enhancing manoeuvrability,the potential temporarily to disable a reflex stabil-isation system makes active control of stabilitypreferable to passive stability, which cannot gen-erally be ‘ switched off’. The impressive flightenvelopes of flies and other highly manoeuvrableinsects must reflect in large part a strong relianceupon active, rather than passive, maintenance ofstability.

On the other hand, since active control mayaugment, rather than completely replace, passivestability, a brief discussion of the latter may be usefulin setting corrective flight control in context. Thefirst point to note is that hovering insects, likehovering helicopters (Gessow & Amer, 1949;Johnson, 1980; Padfield, 1996), possess no first-orderpassive stability about any axis. This is because the


resultant flight force vector passes through the centreof gravity at equilibrium and remains fixed inmagnitude, position and direction with respect tothe body axes as the insect’s orientation changes.The net turning moment on the insect is thereforealways zero and a stabilising moment can only arisethrough second-order changes in the aerodynamicforces caused by translation of the insect as the flightforce is redirected with respect to gravity. This is themeans by which the dihedral of a fixed wing aircraftprovides roll stability, and it is possible that themean upward-canted coning angle of the wings of aflapping insect could provide both pitch and rollstability in a similar way (Dudley, 2000).

The situation may be very different in forwardflight, where a nose-up pitching disturbance willincrease the angle of incidence of the wings, therebyincreasing quasi-steady lift production. Provided thisadditional lift acts behind the centre of gravity, thiswill tend to generate a stabilising nose-down momentabout the centre of gravity. Alternatively, if themean flight force acts well above the centre ofgravity, the insect will gain stability much like thatof a ship through a ‘pendulum effect ’ (Lighthill,1974). It is harder to predict how unsteady mech-anisms of force production will affect stability. Some,like Weis-Fogh’s (1973) ‘clap-and-fling’ and itsderivatives (Ellington, 1984b) or generation of acirculation via wing rotation (Ellington, 1984b ;Dickinson et al., 1999), are unlikely to be greatlyaffected by changes in the insect’s orientation, andare therefore unlikely to provide any passive stab-ility. On the other hand, translational mechanisms,such as the maintenance of a leading edge vortex(Ellington, 1984b ; Dickinson, and Go$ tz, 1993;Ellington et al., 1996; Willmott et al., 1997),effectively magnify the wing lift coefficients and willtherefore tend to enhance any passive stability orinstability that would be present if the flow werequasi-steady (G. K. Taylor & A. L. R. Thomas, inpreparation).

In the absence of detailed empirical data on thepassive stability of insects, it is difficult to make anyreliable predictions about how reflex stabilisationand passive control will interact. Suffice it to say thatactive control may be required to provide not juststatic stability, in the sense of returning the insecttowards equilibrium immediately following a dis-turbance, but also dynamic stability, in the sense ofdamping out any oscillatory modes that may beexcited by a disturbance. For example, most aircraftpossess some degree of passive static stability, butpilot or computer control input is generally required

to maintain an acceptable level of dynamic stability.The same may be expected to be broadly true offlying insects. With these considerations in mind, Iwill go on to consider some more general principlesof control.

III. GENERAL PRINCIPLES OF CONTROL

We will begin by analogy with a more familiarcontrol system. A car on a skidpan has three degreesof freedom. This is equivalent to saying that we needthree pieces of information to completely describe itsposition and orientation in space (for example, an x

coordinate and a y coordinate for its position, and acompass bearing for its heading). To describecompletely the motion of the system we would, ofcourse, need also the first-order and second-orderderivatives of the three positional degrees of freedom,but for simplicity we will only consider termsreferring to position and orientation. By Newton’ssecond law, the application of a force or moment toa mechanical system produces an acceleration orangular acceleration of equivalent sense or directionthat can be used to control position or orientation.Hence, the number of controlled degrees of freedomcannot exceed the number of independent control

roll pitch

yaw

Fig. 2. A flying insect, like this hummingbird hawkmothMacroglossum stellatarum, has six degrees of freedom. Theinsect is free to move in translation along or rotate aboutthree orthogonal axes, centred upon the centre of gravity(part-filled circle). Rotations about these axes are termedpitch, roll and yaw.


inputs. This is the first and most fundamentalprinciple of control.

Our second principle is that it is often unnecessary(or even undesirable) to control all of the possibledegrees of freedom. For example, a car gives itsdriver control of just two of its three degrees offreedom, making it easier to keep on the road, butsomewhat harder to parallel park. Our thirdprinciple is that one or more redundant controlinputs can often be used to provide enhanced controlof a given degree of freedom. For example, easing offa car’s accelerator has the same qualitative effect asbraking, but most of us would find it difficult to stopat traffic lights without the aid of brakes.

Such considerations allow us to frame two over-arching questions that we may ask of insect flightcontrol. How many independent control inputs doesthe insect use? How many degrees of freedom doesthis allow the insect to control? Independent controlof all six of an insect’s degrees of freedom (Fig. 2)would require a minimum of six independent controlinputs. Full six-degree-of-freedom control is super-fluous in most aerial applications and appears not tobe used by insects, which lack the ability to flysideways without banking. In fact, for control ofposition in space, independent modulation of pitch,heading and longitudinal acceleration will suffice,requiring just three independent control inputs.Two-axis control systems like these are a feature ofsome high-performance model sailplanes and couldbe used by insects with no great need for manoeuvra-bility.

Three-axis control systems permit independentmodulation of pitch, roll and yaw and thus enable afar wider range of manoeuvres. Depending uponwhether the direction as well as the magnitude oflongitudinal acceleration can be varied independentof pitch, three-axis control systems require a mini-mum of either four or five independent controlinputs. In fixed-wing aircraft and helicopters, thedirection of longitudinal acceleration is normallydependent upon pitch, although flaps may be usedto steepen a descent without upsetting pitch equi-librium. Amongst operational aircraft, perhaps onlythe Harrier jump jet can be considered to possesscomplete five-degree-of-freedom control in the senseof being able to accelerate at any angle to the groundwithout varying pitch. However, whereas five-degree-of-freedom control is the exception in aircraftand four-degree-of-freedom control the rule, theopposite may be the case in insects with three-axiscontrol because of important differences in themechanisms by which control inputs are produced.

Fig. 3. Conventional aircraft use mechanically separatecontrol surfaces (shaded) to separate control of the threemoments. In the simple system shown here, the tailelevators are used to control pitch, the ailerons to controlroll, and the rudder to control yaw. Insects lack separatecontrol surfaces and must instead use different rotations ofthe wings to separate the moments.

Early experiments in wing warping aside, theconventional aircraft design paradigm has long beento use separate control surfaces to isolate pitch, rolland yaw (Fig. 3). This differs markedly from thecontrol systems of insects in which the samekinematic parameters are varied symmetrically forcontrol of the longitudinal forces and moments, andasymmetrically for control of the lateral forces andmoments. For example, in locusts, pronation (nose-down rotation of the wing at the top of the stroke) isincreased symmetrically between the forewings inresponse to a nose-up pitching disturbance, but isonly increased on the inside forewing during turns(Gettrup & Wilson, 1964). The result is an effectivedoubling of the number of control inputs and aremarkable economy of control. It follows thatinsects that modulate the direction of longitudinalacceleration by symmetrically varying the balance oflift and thrust on their wings should also be able toseparate roll and yaw by varying the same kinematicparameters asymmetrically. Conversely, insects thatmodulate roll via asymmetric lift production, andyaw via asymmetric thrust production, should alsobe able to modulate the direction of longitudinalacceleration to some degree. Hence, we would expectmany insects using three-axis control to modulatemotions in five, rather than four, of their six degreesof freedom, although this is not to say that allcombinations of these motions will be possible.


Having considered some general principles ofcontrol, I will now go on to apply these specificallyto insects. Although insect flight control has onlybeen studied in detail in two orders (Diptera andOrthoptera), there are major systematic differencesin the mechanics of control. These relate primarily todifferences in the construction of the flight motorand the arrangement of the wings and to probabledifferences in the unsteady mechanisms of aero-dynamic force production used. I will thereforeconsider each of the different orders in turn, treatinglateral and longitudinal control separately.

IV. FLIGHT CONTROL IN DIPTERA (TRUE

FLIES)

Flies are the most aerobatic of insects, able to turn ona pinpoint, fly sideways and even land upside-downon a ceiling (Kammer, 1985), but since they possessjust one pair of wings the mechanics of their flightcontrol should be amongst the simplest to under-stand. Specifically, there can be no question ofinterference between the fore- and hindwings, or of achanging balance of forces between the two. Fliesexhibit two main classes of manoeuvre: fast, vol-untary, turns, known as saccades because of theirkinematic resemblance to the tracking movements ofvertebrate eyes, and slower, often corrective, turnsunder the influence of the optomotor control system.Other classes of turn have been also recorded, oftenas pursuit responses by courting males. For example,dolichopodid flies Poecilobothrus nobilitatus have beenfilmed executing 180° yaw turns in less than 40 msduring courtship (Land, 1993). Hovering maletabanid flies Hybomitra hinei have even been recordedusing a modified form of the Immelmann turn – aclassic aerobatic manoeuvre consisting of a half-loopfollowed by a half-roll, used to effect rapid reversalsof flight direction (Wilkerson & Butler, 1984).Throughout this review I will be presenting resultsrelating to both voluntary and corrective control,and it should be borne in mind that control inputsthat are suitable for one type of control may not besuitable for the other, especially where the speed ofthe motion is very different.

(1) Longitudinal control

Stroke amplitude – the angle of the planar arc orgreat circle described by the wing leading edgebetween the top and bottom of the stroke (Fig.

A B

stroke plane

stroke plane

Fig. 4. (A, B). Stroke amplitude is the planar angle of thearc described by the wing leading edge between the topand bottom of the stroke (dotted line in column A).Column B shows the corresponding points of action of themean flight force. Decreasing the stroke amplitude(bottom row) causes the flight force to shift back,generating a nose-down pitching moment about thecentre of gravity (part-filled circle).

4A) – is normally considered the main controlparameter determining aerodynamic power outputin fruit flies Drosophila spp. Stroke amplitude shows astrong positive correlation with aerodynamic forceproduction (Vogel, 1967; Go$ tz, 1968; Lehman &Dickinson, 1997; Dickinson, Lehmann & Chan,1998) and is referred to as stroke angle in somestudies. Wingbeat frequency is the other principaldeterminant of aerodynamic power output, andappears to be an important control parameter in flies(Dickinson et al., 1998). For example, Drosophila

melanogaster increase their wingbeat frequency inresponse to an increase in the speed of optic flowsimulating forward flight (Friedrich, Spatz &Bausenwein, 1994).

In Drosophila melanogaster, wingbeat frequency ispositively correlated with aerodynamic force belowapproximately the force required to support bodyweight, but is negatively correlated with aerody-namic force at peak outputs (Lehmann & Dickinson,1997). Decreases in wingbeat frequency appear to becompensated by steeper increases in stroke am-plitude, however, and the product of frequency and


amplitude (which determines the translational vel-ocity of the wing) rises linearly with increasing forceproduction (Lehmann & Dickinson, 1997). Thedrop in wingbeat frequency at peak force productionmay result from physiological constraints, so strokeamplitude and wingbeat frequency are probably notstrictly independent control inputs, even thoughthey are not coupled in a straightforward fashion. Atpeak levels of force production, D. melanogaster

appear to be limited to a unique combination ofstroke amplitude, wingbeat frequency and flightforce coefficient, and this in turn constrains theirability to generate the asymmetries in force pro-duction necessary for lateral control (Lehmann &Dickinson, 2001). An analogous degradation ofturning ability with increasing flight speed wasfound by Buelthoff, Poggio & Werhahn (1980), whofound the maximum angular velocity attained byfree-flying D. melanogaster to decrease with increasingforward velocity, although in this case the effect islikely to result from aerodynamic, rather thanphysiological, constraints.

In larger calypterate flies (blowflies, houseflies,etc.), frequency and amplitude are both positivelycorrelated with aerodynamic force, but since the twoparameters are likely to be mechanically linked, it isnot necessarily easy to separate cause from effect(Nachtigall & Wilson, 1967). Symmetrical changesin stroke amplitude are also correlated with cor-rective pitch control in larger flies such as Muscina

stabulans and Calliphora erythrocephala, which decreasethe amplitude of both wings in response to anincrease in body angle (Hollick, 1940; Nalbach &Hengstenberg, 1994). Changes in amplitude areeffected by adjusting the lower turning point of thewings, which shifts back with a decrease in amplitudeas the wings sweep less far forward on the down-stroke. This causes the point of action of the meanflight force to shift back (Fig. 4B), generating apitching moment with the fly’s weight of appropriatedirection to restore it to equilibrium (Hollick, 1940).Similar, albeit smaller, changes in stroke amplitudeare observed during pitching responses in Drosophila

spp. (Zanker, 1988b, 1990), which may use a similarmechanism for pitch control (Vogel, 1967). How-ever, the smaller magnitude of the response issuggestive of a slightly different mechanism. Aprominent feature of unsteady lift-production inDrosophila spp., at least in tethered flight, is the clap-and-peel process in which the opening wings drawadditional air into the circulation at the start of thedownstroke (see Ellington, 1984a, b). The extent ofcontact between the wings increases with increasing

stroke amplitude, which should increase lift andthrust production dorsally, inducing a restoringnose-up torque in response to nose-down stimuli(Zanker, 1990).

Drosophila melanogaster are also able to vary thelongitudinal position of the stroke plane independentof amplitude (Zanker, 1988b), which should allowpitch to be modulated independent of aerodynamicforce output. Similar shifts in stroke plane positionhave also been observed in the hoverflies Eristalis

tenax and Episyrphus balteatus (Ellington, 1984a).Stroke plane inclination varies too during pitchingresponses in Drosophila spp., but this is tightlycorrelated with changes in amplitude, which causethe lower turning point to move almost horizontally,rather than parallel to the stroke plane, therebyaltering stroke inclination (Vogel, 1967; Zanker,1988b). Drosophila spp. do not seem to vary the angleof attack of the wings for longitudinal control (Vogel,1967), although the constancy of the angle of attacksuggests that they might actively stabilise it atdifferent speeds (Zanker, 1990). The speed andtiming of wing rotation do appear to be importantlateral control parameters in D. melanogaster (Zanker,1990; Dickinson et al., 1993), but have not beeninvestigated in the context of longitudinal control.

In addition to varying their wing kinematics, fliesmay control pitch by varying their posture, muchlike a hang-glider pilot. Drosophila melanogaster elevatetheir abdomen in response to nose-down disturb-ances (Zanker, 1988a, b), displacing the centre ofgravity dorsal to the line of thrust, which thereforegenerates a restoring nose-up moment with the fly’sinertia. The concurrent increase in drag on thedorsal side will further add to this torque (Zanker,1988b). Similar postural changes have been observedin Calliphora erythrocephala (Nalbach & Hengstenberg,1994), so abdominal deflection may be a widespreadmechanism of pitch control in flies. Drosophila virilis

have also been observed to elevate their hindlegsfollowing a nose-down disturbance, which shouldincrease drag dorsally and generate a nose-uppitching moment (Vogel, 1967). The raised hindlegscan hardly fail to meet with interference from thewake of the wings, and this could enhance theirturning effect in much the same way that a ship’srudder is more effective if placed in the wake of thepropeller (Vogel, 1967).

The various kinematic and postural changesdescribed above are only sufficient to provide twodegrees of freedom for longitudinal control, sincenone of them permits control of the direction of theresultant flight force relative to the body axes. This


would result in essentially the same situation as inhelicopters, in which the direction of the rotor forceis fixed with respect to the body. Hence, although ahovering helicopter’s vertical displacement can becontrolled directly by varying the aerodynamic forceon the blades, it can only be given horizontalvelocity by changing the body angle to redirect theflight force forward (e.g. Johnson, 1980). This doesin fact appear to be the mechanism by whichDrosophila spp. normally control their trajectory(Vogel, 1966; David, 1985; Zanker, 1988b), sincethe elevation of the aerodynamic force is apparentlykept fixed relative to the body axes (Vogel, 1966;Go$ tz, 1968; David, 1978; Go$ tz & Wandel, 1984;but see Ennos, 1989). The relative proportions of liftand thrust are thus varied primarily by adjusting thebody angle (David, 1985; Zanker, 1988b), which isnegatively correlated with flight speed (Vogel, 1966;David, 1978) to allow level flight to be maintained asaerodynamic power output is increased. However,the fact that Drosophila spp. normally modulate liftand thrust together need not imply that they arestrictly coupled as in helicopters, and the helicoptermodel may perhaps be better thought of as afacultative strategy for flight control rather than as afixed constraint.

Similar results have been reported for tetheredhouseflies Musca domestica flying in still air (Go$ tz &Wandel, 1984), but the generality of this result isquestionable because M. domestica does not hover(Wagner, 1986) and a flow of air over the antennaeis necessary for a normal stroke path in Muscina

stabulans (Hollick, 1940). Free-flying M. domestica doappear to be able to vary the direction of the flightforce vector, but only within a limited range(Wagner, 1986). Force measurements in tetheredCalliphora spp. have confirmed that they also are ableto modulate thrust independent of lift within acertain range (Blondeau, 1981, Nachtigall & Roth,1983), although the relation may be asymmetricbecause lift appears never to be modulated in-dependent of thrust (Blondeau, 1981).

Any ability to alter the direction of the flight forceindependent of its magnitude implies that someother kinematic parameter must be varied inde-pendent of stroke amplitude and wingbeat fre-quency, which together provide control of only themagnitude of the flight force, albeit with an elementof redundancy. Changes in stroke plane inclinationwill certainly alter the direction of the resultantflight force, and would almost certainly affect theforces generated by wake capture mechanisms inwhich the wings gain an additional ‘kick’ from

vortices shed at the end of the previous half-stroke(see Dickinson et al., 1999). This is one potentialmechanism by which larger flies could vary thedirection of the flight force. Changes in stroke planeinclination observed in Drosophila melanogaster areprobably too small to be used for control purposes(! 0±5° ; Zanker, 1988b), and being linked tochanges in stroke amplitude should probably not becounted as a separate control input anyway. Otherkinematic parameters have not been investigated inthe context of longitudinal control, but since longi-tudinal forces and moments can be produced bysymmetrically adjusting parameters used for lateralcontrol, we will consider other potential candidatesin the context of lateral control.

(2) Lateral control

Although changes in wing kinematics are likely to bemore important for fast flight manoeuvres, posturaladjustments are commonly associated with slowoptomotor steering responses in flies (Zanker,1988a). Typically, the abdomen is deflected into aturn (Go$ tz, Hengstenberg & Biesinger, 1979;Zanker, 1988a ; Zanker, Egelhaaf & Warzecha,1991), often together with the inside hindleg(Hollick, 1940; Faust, 1952; Nachtigall & Roth,1983; Nalbach, 1989). Occasionally both hindlegsare extended together into the turn (Go$ tz et al.,1979). Similar adjustments in locusts have beeninterpreted as producing drag-based yaw torqueslike a ship’s rudder (Camhi, 1970) and most workershave followed the same interpretation for flies (e.g.Go$ tz et al., 1979). Postural adjustments in otherinsects have been suggested to produce lateralmoments by a different mechanism, shifting thecentre of gravity sideways from the centre of pressure(Govind & Burton, 1970; May & Hoy, 1990a). Thiswould normally be expected to generate a roll ratherthan a yaw torque, but abdominal deflections inDrosophila melanogaster do appear to generate yawtorques gravimetrically (Zanker, 1988a). This isbecause the axis about which yawing occurs is tiltedback approximately 30° from the vertical such thata significant component of the animal’s weight actsnormal to the yaw axis and can therefore produce ayaw couple with the flight force.

Until recently, stroke amplitude was thought to bethe only kinematic parameter consistently correlatedwith roll and yaw responses in flies (Drosophila spp. :Vogel, 1967; Go$ tz, 1968; Go$ tz et al., 1979, Musca

domestica : Srinivasan, 1977, Calliphora spp. : Heide,1971; Nachtigall & Roth, 1983; Hengstenberg,


Sandeman & Hengstenberg, 1986; Nalbach, 1989;Nalbach & Hengstenberg, 1994). According to theclassical interpretation, the amplitude of the insidewing is lowered to reduce the aerodynamic force byshortening the stroke, with opposite changes oc-curring on the outside wing. This will generaterolling moments directly through asymmetric liftproduction and should also generate yaw momentsdirectly through asymmetric thrust production.Since flying insects usually produce much less thrustthan lift (typically an order of magnitude less inDrosophila virilis ; Vogel, 1966), the resulting torquesabout the yaw axis would normally be expected tobe correspondingly small compared to those in roll.

Although this classical view was originally rootedin the assumptions of quasi-steady aerodynamics, theoutcome could be the same for an unsteadytranslational mechanism such as delayed stall, inwhich flow remains attached to the wing at higherangles of attack than would be possible under steadyconditions. Hence, although control torques meas-ured in Drosophila melanogaster are generally greaterthan those calculated from blade-element theory,which assumes quasi-steady aerodynamics (Zanker,1990; Zanker & Go$ tz, 1990), stroke amplitude couldstill play a direct role in dipteran flight control ifunsteady translational mechanisms were important.Dickinson et al.’s (1993) comment that changes inamplitude may not be directly responsible forturning in D. melanogaster (on the grounds thatcorrelated changes in the timing of stroke reversalwill be more important than stroke length per se ifunsteady rotational mechanisms overwhelm quasi-steady lift production) implicitly assumes thatunsteady translational mechanisms (which also havethe potential to overwhelm quasi-steady lift pro-duction) are insignificant.

Changes in amplitude do not permit the directionof the flight force to be varied directly, unless thepart of the stroke that is curtailed generates a forcein a different direction to the remainder of thestroke. In general, since rolling moments are nor-mally generated by asymmetric lift and yawingmoments by asymmetric thrust, separate control oflift and thrust will usually be required for roll andyaw to be varied independently. Roll and yaw havetherefore been suggested to be unavoidably coupledin Drosophila spp. (Srinivasan, 1977), which normallymodulate lift and thrust together. To conclude thatDrosophila spp. are unable to uncouple lift and thrustwould seem premature, however, and althoughdirect evidence that Drosophila spp. modulate rolland yaw independently is still lacking (Dickinson,

1999), the view that they are strictly coupled hasbegun to be challenged (Go$ tz, 1987; Ennos, 1989;Zanker, 1990; Dickinson et al., 1993). In any case,varying the relative proportions of lift and thrustindependently on each wing is not the only way togenerate a yaw torque. For example, the clap-and-peel process does not occur parallel to the sagittalplane during fictive turns in Drosophila melanogaster,and the jet of air produced is in the appropriatedirection to contribute to steering (Go$ tz, 1987;Zanker, 1990). This could allow yaw moments to begenerated independent of roll, although the torquesgenerated in this way may still be rather small(Dickinson et al., 1993; Dickinson, 1999).

Larger flies such as Calliphora spp. (Blondeau,1981; Schilstra & Van Hateren, 1999) and Musca

domestica (Wagner, 1986) can certainly generate rolland yaw torques separately, though the two areusually modulated together to produce a bankedturn (Blondeau, 1981). This presumably increasesmanoeuvrability in the same way as in a turningaircraft, by minimising sideslip and directing thenose into the turn. Sometimes, it may be useful toswing sideways without changing heading. Heli-copters achieve this by banking to one side toredirect a component of the flight force sideways.This is probably also the mechanism behind Collett& Land’s (1975) observation that the hoverfly Syritta

pipiens can fly sideways without changing its heading.This implies that hoverflies must also possess in-dependent control of roll and yaw. At least one otherkinematic parameter must be varied in addition tostroke amplitude for roll and yaw to be controlledseparately, because abdominal deflection occurs tooslowly to account for the rapid turns observed inflies. For example, in Drosophila melanogaster theabdomen only responds strongly to oscillating visualstimuli at frequencies below 5 Hz, and the responseis much stronger at lower frequencies (Zanker,1988a). Peak deflection is only attained at 0±05 Hz,suggesting that the response may be used to correctfor inherent asymmetries in the wings or flightmotor, rather than discrete disturbances (Zanker,1988a).

Wingbeat frequency can immediately be ruled outas a lateral control parameter because the con-struction of the dipteran flight motor makes it im-possible for the wings to operate at differentfrequencies (Hollick, 1940). Stroke plane inclinationalso appears not to offer an independent controlinput because it is closely linked to amplitude inmost studies in which both have been measured(Vogel, 1967; Nachtigall & Roth, 1983; Zanker,


1988b, see also Chadwick, 1951). For example, inCalliphora vicina the action of the basalar muscles hasbeen shown explicitly to determine both stroke planeinclination and amplitude (Tu & Dickinson, 1996).However, the precise three-dimensional trajectory ofthe wingtip can be varied independently of am-plitude in Muscina stabulans (Hollick, 1940) and C.vicina (Tu & Dickinson, 1996), and this might beused to produce control moments, perhaps byaltering the properties of wake capture. One wingmay even be completely folded over the body duringextremely fast turns (Nachtigall & Wilson, 1967),although this is unlikely to play any role incorrectional steering.

Increased pronation of the inside wing has beenobserved during roll and yaw responses in Calliphora

erythrocephala (Faust, 1952; Hengstenberg et al.,1986). Similar changes in pronation have been notedin the cranefly Tipula oleracea (Faust, 1952) and theblowfly Lucilia serricata (Sandeman, 1980). Unfortun-ately, the stage of wingbeat recorded was almostcertainly wrongly described in the latter study (D. C.Sandeman, pers. comm., cited in Kammer, 1985)and it is not clear whether the magnitude or only thetiming of rotation was varied. Angle of attackasymmetries are taken to an extreme in the doli-chopodid fly Poecilobothrus nobilitatus, which is able toexecute extraordinarily rapid 180° turns by holdingthe inside wing normal to the flow to act as anairbrake (Land, 1993).

In light of current views of insect flight controlimplicating unsteady aerodynamic mechanisms asthe main source of control moments (Zanker, 1990),the speed and timing of wing rotation are likely to beat least as important as the degree of pronation(Ennos, 1989; Dickinson et al., 1993, 1999;Dickinson, 1994, 1999). Supination (nose-up ro-tation of the wings towards the bottom of the stroke)occurs extremely rapidly in flies (Ennos, 1989). Flowvisualisation of tethered Drosophila melanogaster

(Dickinson & Go$ tz, 1996) appears to show thevorticity produced by the so-called ‘ventral flip’(Dickinson et al., 1993) fusing with the stoppingvortices shed at the end of the downstroke, so rapidwing rotation might be used for aerodynamic forceproduction. Experiments with model wings (Dickin-son, 1994; Dickinson et al., 1999) have demonstratedthat the timing of supination relative to strokereversal (the point at which wing translation reversesdirection) is critical in determining the magnitude ofthe forces produced. Large positive forces (attribu-table to both rotational mechanisms and wakecapture) are generated when supination precedes

stroke reversal, whereas negative forces are registeredif supination is delayed (Dickinson et al., 1999).

By asymmetrically varying force production inthis way, flies could readily produce turningmoments for control. For example, the results ofDickinson et al. (1999) indicate that the instan-taneous drag force may be extremely high on a wingusing rotational circulation and wake capture, andwell in excess of the instantaneous lift. Hence,though the instantaneous drag forces largely cancelover the course of a normal stroke, asymmetric dragproduction offers a potent means of generating rollor yaw torques in insects using rotational circulationand wake capture. The direction of the axis aboutwhich the resulting torque is generated will dependupon both the direction of the stroke and theorientation of the wing chord. For example, ininsects with a horizontal stroke plane, such ashoverflies, the potential to vary the horizontal forcecomponent may be far greater than the potential tovary the vertical lift. Asymmetric variation of theforces produced by rotational circulation and wakecapture would then tend to generate a yaw torque,and this may account for the remarkable ability ofhoverflies to turn full circle whilst otherwise re-maining stationary.

In Calliphora erythrocephala (Nalbach, 1989) andDrosophila melanogaster (Dickinson et al., 1993), su-pination is delayed on the inside wing and advancedon the outside wing during fictive turns. Parallelchanges in the timing of pronation have also beenobserved (Nalbach, 1989). Unfortunately, it has notbeen possible to resolve changes in the timing ofstroke reversal, so the phase of supination and strokereversal remains unknown. However, assuming thatan absolute delay in supination on the inside of aturn indicates that supination is also delayed relativeto stroke reversal, then the results of Dickinson et al.(1999) imply that the flight force will be reduced orreversed on the inside of a turn. Earlier supination isalso correlated with increased rotational velocity inD. melanogaster (Dickinson et al., 1993, see alsoZanker, 1990), which should increase aerodynamicforce production on the outside of a turn. Both effectsshould combine synergistically to produce a torquein the correct direction to steer into the turn.

The timing of supination seems to be independentof stroke amplitude in Drosophila melanogaster, eventhough the two are usually modulated together(Dickinson et al., 1993). Changes in stroke amplitudeand the timing of supination could therefore providethe two inputs necessary to separate control of rolland yaw. Alternatively, changes in stroke amplitude


might not effect steering directly, but could insteadeffect steering indirectly through correlated changesin the timing of stroke reversal (Dickinson et al.,1993). However, since it is the relative timing ofsupination and stroke reversal that primarily deter-mines aerodynamic force output, changes in strokeamplitude and the timing of supination would thencombine together to provide a single compositevariable, which would make changes in strokeamplitude redundant. In this case, some otherindependent control input (e.g. the speed of wingrotation) would still be required to separate controlof roll and yaw. It therefore seems likely that strokelength per se could be an important control par-ameter, at least in larger flies in which roll and yaware known to be controlled separately.

Returning briefly to longitudinal control, sym-metric changes in the speed or timing of supinationcould be used to vary the magnitude of the resultantflight force (Dickinson et al., 1999). Changes in thetiming of wing rotation might also provide theadditional control input required to separate controlof lift and thrust. Symmetric adjustment of theventral flip could certainly enhance the pitchingresponses discussed in the previous section, becausethe lever arm at the end of the downstroke willusually be such that even small changes in therotational forces will generate a large pitchingmoment. Finally, some control over the direction ofvortex shedding would permit an even greater degreeof control of the direction of the resultant flight force(Ellington, 1984b ; Dickinson et al., 1993).

V. FLIGHT CONTROL IN ORTHOPTERA

(LOCUSTS AND CRICKETS)


Flight control in locusts is likely to be complicated bythe interaction of flow over the fore- and hindwings,though some common principles remain. As in flies,stroke amplitude and wingbeat frequency are posi-tively correlated with aerodynamic force and flyingspeed in tethered Locusta migratoria able to controltheir own speed relative to the surrounding air(Gewecke, 1975; Kutsch & Gewecke, 1979). Teth-ered L. migratoria also increase their wingbeatfrequency in response to an increase in the speed ofoptic flow simulating forward flight (Baader, Scha$ fer& Rowell, 1992) and the same qualitative re-lationship between wingbeat frequency and flightspeed has been shown in free-flying L. migratoria

(Baker, Gewecke & Cooter, 1981). Moreover, strokeamplitude and wingbeat frequency are negativelycorrelated in tethered L. migratoria stimulated by aircurrents of fixed speeds (Gewecke, 1970, 1972), sothe two must also be able to be varied independently.

Locusts appear to regulate lift independent ofthrust and have also been claimed to exhibit a‘constant-lift reaction’ (Wilson & Weis-Fogh, 1962)in which the vertical component of force is kept moreor less constant following imposed changes of bodyangle of up to 20° (Weis-Fogh, 1956a, b ; Gewecke,1975). Electrophysiological (Wilson & Weis-Fogh,1962; Gettrup, 1966; Zarnack & Mo$ hl, 1977) andkinematic studies (Gettrup & Wilson, 1964; Gettrup,1966; Wortmann & Zarnack, 1993) have clearlydemonstrated that tethered locusts increase forewingpronation to compensate for the increase in theirangle of attack that would otherwise occur followinga nose-up disturbance. The same reaction alsoappears to occur in free flight, since climbing flight isassociated with both increased forewing pronationand increased body angle (Fischer & Kutsch, 2000).Hindwing pronation is largely independent of bodyangle (Gettrup & Wilson, 1964; Wortmann &Zarnack, 1993), however, so whereas the forewinglift coefficients should remain approximately con-stant, the hindwing lift should increase with in-creasing body angle, because the lift on a winggenerally increases with increasing angle of attack.According to Gettrup & Wilson’s (1964) model ofthe constant-lift reaction, the drop in flight speedthat accompanies an increase in body angle intethered locusts (Weis-Fogh, 1956a ; Gewecke, 1975)combines with these changes to keep the total liftapproximately constant.

The constant-lift reaction has been an influentialparadigm in the insect flight literature, and is stillreferred to frequently in discussions of insect flightcontrol (e.g. Zanker, 1990). However, quite apartfrom the objection that the quasi-steady aerody-namics implicit in Gettrup & Wilson’s (1964) modelhave been shown not to apply in locusts (Cloupeauet al., 1979; Wilkin, 1990), it is not clear why free-flying locusts should possess a reflex maintainingconstant lift at widely different body angles. Astabilising pitch reflex would seem to be of fargreater utility. Studies of free-flying locusts (Baker et

al., 1981) are consistent with the existence of astabilising pitch reaction, showing no evidence of thenegative correlation between body angle and flightspeed that forms an essential part of Gettrup &Wilson’s (1964) original scheme. Moreover, laterstudies (Zarnack & Wortmann, 1989; Wortmann &


Zarnack, 1993) have cast doubt on the existence of aconstant-lift reaction per se, finding no reliableevidence that individual locusts consistently main-tain constant lift at different body angles. Althoughconstant lift may occasionally be maintained, thereis usually considerable temporal variation in liftproduction (Zarnack & Wortmann, 1989). Weis-Fogh’s (1956a, b) original studies neglected temporalvariation in lift and were based upon data averagedacross individuals, so the apparent constancy of liftin his figures would certainly have been exaggeratedby the averaging process.

On the other hand, given that the angle of attackof the hindwings increases following an increase inbody angle, whilst the angle of attack of the forewingsremains approximately constant, the changing bal-ance of lift between fore- and hindwings shouldproduce a restoring nose-down pitching moment.Such a torque was in fact detected by Gettrup &Wilson (1964), but was considered to be an‘unpredicted outcome’ (Gettrup & Wilson, 1964, p.189) of the constant-lift reaction. This interpretationalmost certainly reverses cause and effect, since astabilising pitch response would negate any re-quirement to maintain constant lift across a range ofbody angles by restoring the animal to equilibrium.Indeed, loss of the sensory input supposed to mediatepronation in the constant-lift reaction leads to acomplete loss of stability (Gettrup, 1966), confirmingthat the reflex changes in pronation described aboveare used to maintain pitch stability. Constant liftmay occasionally be maintained in tethered locustsaccording to Gettrup & Wilson’s (1964) originalscheme, but probably as an epiphenomenon ofchanges adapted to restore pitch equilibrium in freeflight.

(2) Lateral control

Locusts swing their abdomen laterally and extendone or both hindlegs like a rudder during yaw turns(Gettrup & Wilson, 1964; Dugard, 1967; Camhi,1970; Cooter, 1979; Arbas, 1986; Baader, 1990;Preiss & Gewecke, 1991; Robert & Rowell, 1992a, b ;Robertson & Reye, 1992; Preiss & Spork, 1993;Robertson & Johnson, 1993; Lorez, 1995; Robert-son, Kuhnert & Dawson, 1996; Dawson et al., 1997).Such postural changes are not always observedduring correctional responses, however, and may bemore important during voluntary turns (Zarnack &Mo$ hl, 1977; Gewecke & Philippen, 1978). Similarpostural changes have been observed in the bush-cricket Tettigonia viridissima (Schulze & Schul, 2001)

and the cricket Teleogryllus oceanicus during acousticavoidance responses (Moiseff, Pollack & Hoy, 1978;Pollack & Hoy, 1981; Pollack, Huber & Weber,1984; Miles et al., 1992), although abdominaldeflection alone is apparently insufficient to produceyawing in T. oceanicus (May & Hoy, 1990b). As wellas increasing drag on the inside of a turn, hindlegextension may effect a turn by impeding the motionof the inside hindwing (Camhi, 1970; May & Hoy,1990a). This mechanism would be expected to causesignificant wear to the wing and may therefore bereserved for extreme avoidance manoeuvres.

Lateral movements of the hindlegs and abdomenhave also been observed in response to visual rollstimuli in locusts (Taylor, 1981a, b), but are incon-sistently correlated with rolling (Thu$ ring, 1986) andsaid to be neither necessary nor sufficient to effect acorrectional roll response (Schmidt & Zarnack,1987; Waldmann & Zarnack, 1988). However,Zanker’s (1988a) careful study of abdominal de-flection in Drosophila melanogaster highlights the needto ensure that the rotational axis of a roll stimulus isexactly normal to the axis about which yawingoccurs. If this is not the case, then a supposed rollstimulus will induce a combined roll and yawresponse because the subject will perceive thestimulus to contain some component of yaw. Thisprobably explains why postural changes normallyassociated with yaw turns are observed in response toroll stimuli, although we cannot discount thepossibility that abdominal deflection might be usedto generate roll moments by shifting the centre ofgravity. Alternatively, if roll and yaw are modulatedtogether in free flight, then responses to roll and yawstimuli might be reflexly coupled to effect a tighterbanked turn.

Asymmetries in stroke amplitude do not appear tobe strongly correlated with turning in locusts (Baker,1979; Thu$ ring, 1986; Waldmann & Zarnack, 1988;Zarnack, 1988) or crickets (Wang & Robertson,1988; but see May, Brodfuehrer & Hoy, 1988),except during very sharp turns (Robertson & Reye,1992; Dawson et al., 1997). Likewise, there is noevidence that differences in stroke path are cor-related with turning in locusts (Zarnack, 1988),although changes in hindwing elevation may beimportant for steering in crickets (Wang & Robert-son, 1988; May et al., 1988) which also bank theirforewings relative to the body axes during turning(May et al., 1988).

Locusts (Gettrup & Wilson, 1964) and crickets(Pollack & Hoy, 1981) reliably increase pronation ofthe inside forewing during turning responses. In


locusts, this is usually correlated with early pronationof the inside wing (Dugard, 1967; Baker, 1979;Zarnack, 1988; Robertson & Reye, 1992; Dawson et

al., 1997). Muscle recordings from crickets aresuggestive of an analogous change in the timing ofthe hindwing elevators and depressors (Wang &Robertson, 1988). These changes should reduce liftand thrust on the inside wing by decreasing itseffective incidence and might allow it to act as a sortof brake (Zarnack & Mo$ hl, 1977). Antisymmetricchanges in pronation on the outside wing, possiblycombined with increased supination on the upstroke(Zarnack, 1988), should increase lift and thrust onthe outside of the turn. The net result will be acombined roll and yaw torque, leading directly intoa banked turn.

Intriguingly, opposite changes in the timing of theforewing downstroke muscles have been recorded intethered locusts during presumed correctional re-sponses to imposed yaw angles (Mo$ hl & Zarnack,1975, 1977; Zarnack & Mo$ hl, 1977). These dif-ferences seem to be real and may result fromdifferences in the turning stimuli used (Kammer,1985), although the oscillating yaw stimulus used byZarnack (1988) was qualitatively the same as thatused in the three studies for which atypical timeshifts were observed. Individual locusts may also usedifferent patterns of muscle burst length in responseto the same roll stimulus (Waldron, 1967), sodifferent motor patterns may be common when onlyone degree of freedom is considered. The magnitudeof a roll torque does not necessarily depend upon themotor pattern used (Thu$ ring, 1986), so differentmotor patterns must either produce the samekinematics, which seems unlikely, or they must causethe forces and moments about the other axes to vary(Kammer, 1985; Thu$ ring, 1986).

This second explanation seems quite likely. Forexample, whereas all of the inside forewing de-pressors contract early relative to some constantreference during a typical roll response (Mo$ hl &Zarnack, 1977; Zarnack & Mo$ hl, 1977; Thu$ ring,1986; Schmidt & Zarnack, 1987; Waldmann &Zarnack, 1988), individual depressors may be time-shifted in opposite directions during yaw responses(Mo$ hl & Zarnack, 1975; Zarnack & Mo$ hl, 1977).In any case, Baker’s comment that roll and yawturns in locusts are ‘ just two ways of looking at thesame phenomenon’ (Baker, 1979, p. 57) is certainlyan over-simplification. Although independent modu-lation of roll and yaw has never been observed inlocusts (Hensler & Robert, 1990), simultaneousmeasurements of roll and yaw torques have not been

made and it remains an open question whetherdifferences in motor pattern will prove sufficient toseparate roll and yaw control in locusts.

Bulk phase shifts between contralateral wings arebound to induce lateral asymmetries in the phase ofthe fore- and hindwings during roll responses,because the timing of the hindwings changes lessthan that of the forewings (Schmidt & Zarnack,1987) and may even change in the opposite direction(Thu$ ring, 1986). Lateral asymmetries in the relativepositions of the fore- and hindwings are certainlycorrelated with yaw responses in locusts (Dugard,1967; Baker, 1979; Cooter, 1979; Robertson &Reye, 1992; Robertson & Johnson, 1993) and willinevitably alter the aerodynamic coupling of thewings (Zarnack, 1982, 1983; Schwenne & Zarnack,1987; Schmidt & Zarnack, 1987; Waldmann &Zarnack, 1988; Robertson & Reye, 1992). Whilstthere is now little doubt that ipsilateral phase shiftsare important in locust flight control (Rowell, 1988),the aerodynamic changes involved are unknown.Contralateral interference remains unquantified inlocusts, and it is not known whether interferencebetween contralateral wings has any direct effectupon steering.

VI. FLIGHT CONTROL IN OTHER INSECTS


Studies of flight control in other insects have beenrather limited. Negative correlations between bodyangle and flight velocity similar to those observed inDrosophila spp. have been observed in dragonflies(Wakeling & Ellington, 1997), heteropteran bugs(Betts, 1986), bumblebees (Dudley & Ellington,1990a), honeybees (Nachtigall, Widmann &Renner, 1971; Esch, Nachtigall & Kogge, 1975) andmoths (Dudley & DeVries, 1990; Willmott &Ellington, 1997). Butterflies exhibit considerablevariation in the way in which body angle varies withflight speed, although this is perhaps not surprisinggiven the extent to which butterflies ’ bodies pitch upand down through the course of the wingbeat cycle(Betts & Wootton, 1988; Brackenbury, 1995). Forexample, whereas free-flying Papilio rumanzovia adopthigher body angles and shallower stroke planesduring fast flight, free-flying Troides rhadamantus

appear to show the opposite trend (Betts & Wootton,1988). Such variation is presumably indicative ofdifferences in the aerodynamic mechanisms beingused.


It is important to realise that a negative cor-relation between flight speed and body angle neednot imply a helicopter-like mode of flight control, inwhich the direction of the flight force is fixed withrespect to the body axes. Such a model may apply inhoneybees Apis mellifica, in which the partitioning oflift and thrust seems to depend directly upon bodyangle (Esch et al., 1975), but in heteropteran bugs,for example, the inclination of the stroke plane to thebody may be varied by as much as 20° (Betts, 1986).Likewise in hawkmoths Manduca sexta the strokebecomes steeper relative to the body at higher speeds(Willmott & Ellington, 1997) and the same trendhas been observed in the dragonfly Anax parthenope

(Azuma & Watanabe, 1988). No such trend wasdetected in the dragonfly Sympetrum sanguinem inwhich the stroke plane was apparently kept fixedwith respect to the body (Wakeling & Ellington,1997). Nevertheless, the direction of the flight forcedoes not correlate closely with the orientation ofeither the body or the stroke plane in this or otherdragonflies (Wakeling & Ellington, 1997), and theorientation of the stroke plane with respect to flightdirection is generally rather variable (Ru$ ppell,1989). The correlation of body angle with flightspeed and direction in dragonflies has therefore beensuggested to be an adaptation more to minimisebody drag than to redirect the flight force (Wakeling& Ellington, 1997).

In bumblebees Bombus terrestris, the angle of attackthe wings is increased relative to the stroke plane asthe body angle is decreased (Dudley & Ellington,1990a), with the result that the effective angle ofincidence of the wings remains more or less un-changed (Dudley & Ellington, 1990b). In contrastto Drosophila spp., however, the position and am-plitude of the wingbeat do not appear to vary withairspeed, and it is not known how changes in bodyangle are brought about (Dudley & Ellington,1990a). Stroke amplitude does appear to be animportant longitudinal control parameter in heter-opteran bugs, which display decreased stroke ampli-tudes during climbing flight, together with anincrease in the speed of stroke reversal and a decreasein the wingbeat frequency (Betts, 1986). No cleartrend has been found with respect to flight speed ordirection and stroke amplitude in butterflies. Forexample, whereas free-flying Papilio rumanzovia andGraphium sarpedon have been observed to increasestroke amplitude during slow flight, free-flying Precis

iphita adopt sharply increased stroke amplitudesduring bursts of fast flight (Betts & Wootton, 1988).In hawkmoths Manduca sexta, stroke amplitude

appears to decrease slightly with increasing speed(Willmott & Ellington, 1997). This is due to a lessventral excursion of the wings on the downstroke,which would tend to shift the resultant flight forcerearward as in flies and presumably provides thenose-down pitching moment required to decreasethe body angle for fast flight.

Opposite trends have been noted in the dragonflySympetrum sanguinem and the damselfly Calopteryx

splendens. In these species, hindwing stroke amplitudeincreases with increasing speed (Wakeling & Elling-ton, 1997), although the regressions were notsignificant at the 95% confidence level and therewas no apparent change in the mean positionalangle of the wings. This does not appear to reflect ageneral trend in dragonflies. For example, whereasno correlation was found between stroke amplitudeand flight speed in free-flying Anax parthenope (Azuma& Watanabe, 1988), a strong negative correlationwas observed in tethered Orthetrum cancellatum

(Gewecke, Heinzel & Philippen, 1974). Decreasedstroke amplitudes in the latter were associated withreductions in only the dorsal excursions of the wings,which would tend to shift the resultant flight forceforward, rather than rearward as in flies andhawkmoths. If nothing else, these results cautionagainst extrapolating control mechanisms from onegroup of insects, or even one species, to another.

Wingbeat frequency appears not to be an im-portant longitudinal control parameter in eitherhawkmoths (Willmott & Ellington, 1997) or dragon-flies (Azuma & Watanabe, 1988; Wakeling &Ellington, 1997), and has also been found to beuncorrelated with flight speed in damselflies (Sato &Azuma, 1997; Wakeling & Ellington, 1997), andbumblebees (Dudley & Ellington, 1990a). Wakeling& Ellington (1997) did, however, note a trend forwingbeat frequency to increase with increasing forceproduction in the damselfly Calopteryx splendens

(P! 0±1). Although trends at the 90% significancelevel were deemed ‘good’ in that study (Wakeling &Ellington, 1997, p. 566), the significance of trendsreaching even the 95% level should be viewed withcaution given that some 52 independent regressionswere performed, grossly inflating the risk of makinga Type I error. Wingbeat frequency is decreasedduring rising flight in heteropteran bugs (Betts,1986), and there is reasonably strong evidence thatwingbeat frequency is positively correlated withflight speed in butterflies (Betts & Wootton, 1988).However, given the high degree of interspecificvariation revealed by the latter study in thecorrelations between other kinematic parameters


and flight velocity, it would seem premature tointerpret data from a few species as indicative of amore general trend.

(2) Lateral control

Postural adjustments like those observed in flies andlocusts appear to be ubiquitous steering responses ininsects, having also been observed in mantids(Brackenbury, 1995), heteropteran bugs (Govind &Burton, 1970; Govind, 1972), strepsipterans (Pix,Nalbach & Zeil, 1993) and moths (Roeder, 1967;Kammer, 1971; Kammer & Nachtigall, 1973).Asymmetries in stroke amplitude like those observedin turning flies have also been observed in dragonflies(Alexander, 1986), beetles (Burton, 1964, 1971;Schneider & Kramer, 1974), moths (Kammer, 1971)and heteropteran bugs (Govind & Burton, 1970;Govind, 1972). In bugs, the stroke path of theoutside wing may also be shifted dorsal to the insidewing (Govind & Burton, 1970), which is similar to asteering mechanism identified by Stellwaag (1916)in bees and similar to an atypical steering patternobserved during yaw turns in locusts (Cooter, 1979).In moths and butterflies, the wings on the inside ofa turn are typically held more posteriorly than theoutside wings, and may be slightly flexed (Roeder,1967). These changes probably correlate withchanges in the timing of muscle firing (Kammer,1971, 1985; Kammer & Nachtigall, 1973; Obara,1975) and presumably reduce lift and thrust on theinside wing.

In dragonflies, amplitude asymmetries lead tobanking with a strong component of sideslip withinone or two strokes, usually followed by a componentof yaw (Alexander, 1986). This time lag suggeststhat yawing may arise indirectly through aero-dynamic coupling of the moments, rather thandirectly through asymmetric thrust production.Specifically, the component of sideslip resulting frombanking means that the oncoming flow is no longerparallel to the longitudinal axis, which could lead tothe production of a coupled yaw moment. The insidewing may also be more strongly pronated than theoutside wing during banked turns, although this isusually secondary to changes in amplitude and mayonly be used to fine-tune the response (Alexander,1986). Very sharp yaw turns involving much moreextreme rotation of the wings have also beenobserved in dragonflies (Alexander, 1986), sug-gesting three-axis control of the moments. Phaseshifts between the fore- and hindwings analogous tothose observed in locusts have also been implicated

in free-flight manoeuvres in dragonflies (Alexander,1984, 1986; Ru$ ppell, 1989) and hawkmoths (A. L. R.Thomas, personal communication). In hawkmoths,the wings (which are normally physically coupled)may be completely uncoupled so as to operate inantiphase. Such phase shifts are likely to be a com-mon feature of flight control in four-winged insectsand need not necessarily be restricted to insectsin which the wings are normally uncoupled.

VII. DISCUSSION

(1) How many degrees of freedom do insectscontrol?

To date, three-axis control of the moments has onlybeen proven in larger flies and dragonflies. Exper-iments to determine whether other insects canmodulate roll and yaw separately have simply notbeen performed. However, since the most commonmode of turning is the banked turn, in which roll andyaw are advantageously coupled to reduce theturning circle, two-axis control of the lateral andlongitudinal moments could also suffice (Dickinson,1999). Roll and yaw would then be modulatedtogether about an axis lying somewhere between themorphological roll and yaw axes. Tables 1 and 2provide a summary of the various kinematic par-ameters available for lateral and longitudinal controlin flying insects. In the case of locusts, it is notobvious whether independent control of forewingpronation and ipsilateral coupling would permitseparate control of roll and yaw, or whether thedifferent motor patterns observed during roll andyaw responses result in further kinematic changesthat have so far gone undetected. In Drosophila spp.,on the other hand, there are more than enoughindependent kinematic inputs to permit separatecontrol of roll and yaw, although it is equallypossible that one or more of these inputs is redundantand is simply used to provide finer control of themoments. For example, Zanker (1988a) has foundthat abdominal deflection and changes in strokeamplitude are modulated together in Drosophila

melanogaster to produce a common torque about theyaw axis. Three-axis control must therefore beconsidered an unproven possibility in Drosophila spp.

Even where three-axis control of the moments canbe proven, this does not imply that the control axesmust be identical with the main body axes or indeedthat the control axes must be strictly orthogonal(that is, perpendicular to one another). For example,the nominal yaw axis is tilted some 30° back from the

464

Gra

ham

K.T

aylo

r

Table 1. Independent kinematic parameters (bold) available for longitudinal control in different insects

Stroketrajectory

Strokeamplitude

Wingbeatfrequency

Clap-and-peelor clap-and fling

Supination:speed andtiming ofrotation

Degree ofpronation

Phase ofipsilateralfore- andhindwings

Diptera:calypterateflies

Independentparameter;could be usedforlongitudinalcontrol

Amplitudedecreased inresponse tonose-updisturbances

Could be usedfor longitudinalcontrol, butlikely to betightly linked toamplitude

? Independentparameter;could beused forlongitudinalcontrol

Independentparameter;could beused forlongitudinalcontrol

Notapplicable

Diptera:drosophilidflies

Longitudinalposition ofstroke planeshiftedindependentof amplitude;strokeinclinationapparentlylinked toamplitude

Amplitudedecreased inresponse tonose-updisturbances;amplitudeincreases withincreasingforceproduction

Frequencyincreases withincreasing forceproduction, butdecreases againat peak outputs,probablybecause ofphysiologicalconstraints

Wingsapproachmore closelyin response tonose-updisturbances;may bedirectlylinked toamplitude?

Independentparameter;could beused forlongitudinalcontrol

Degree ofpronationappears not tobe varied

Notapplicable

Orthoptera:locusts

Probably not animportantcontrolparameter

Amplitudeincreases withincreasingforceproduction

Frequencynormallyincreases withincreasingforceproduction,but may bevaried in theoppositedirectionunderopen-loopconditions

Generally notapplicable

Probably not animportantcontrolparameter

Pronationincreased inresponse tonose-updisturbances

Likely to beimportant;effectsunknown

465

Mechanics

ofinsect

flightcontrol

Table 2. Independent kinematic parameters (bold) available for lateral control in different insects

Stroke trajectory Stroke amplitudeClap-and-peel orclap-and fling

Supination: speedand timing ofrotation

Degree ofpronation

Phase of ipsilateralfore- and hindwings

Diptera:calypterateflies

Independentparameter; couldbe used for lateralcontrol.

Amplitudedecreased oninside wing

? Supination delayedon inside wing

Pronationsometimesincreased oninside wing

Not applicable

Diptera:drosophilidflies

Independentparameter; couldbe used for lateralcontrol; strokeinclinationapparently linkedto amplitude

Amplitudedecreased oninside wing

Wings meet at anangle to thesagittal planeduring turns

Supination delayedon inside wing;speed ofsupinationincreased onoutside wing

Degree of pronationprobably not animportant controlparameter

Not applicable

Orthoptera:locusts

Probably not animportant controlparameter


Not usuallyapplicable


Pronationincreased oninside wing

Likely to beimportant. Effectsunknown

Odonata:dragonflies

? Amplitudedecreased oninside wingduring bankedturns

Not applicable todragonflies

? Pronationincreased oninside wing,especially duringyaw turns

Likely to beimportant; effectsunknown


dorso-ventral body axis in Drosophila melanogaster

(Zanker, 1988a), though whether an independentroll axis exists or whether this represents a combinedroll-yaw axis in a two-axis system is unknown.Orthogonality of the lateral control axes is notessential for three-axis control, but any non-ortho-gonality that may exist will complicate the neuralprocessing required to separate the various motions.As a useful but rather imperfect analogy, considerhow difficult it is to predict the path of a bouncingrugby ball compared to a bouncing football (it isdifficult to find a better analogy, precisely becausemanmade control systems are usually designed to actorthogonally). The lack of separate control surfacesto isolate the three moments actually makes it ratherlikely that insect control systems will be non-orthogonal. For example, there is no particularreason to suppose that changes in stroke amplitudewill result in a torque about an axis orthogonal tothat due to asymmetric changes in the degree ofpronation or supination. Hence, although the con-trol inputs of aircraft are not always strictlyorthogonal, non-orthogonality is likely to be muchmore pronounced in insects and this will tend tocomplicate their flight control. This is likely to beone of the most significant differences between theflight control systems of insects and conventionalaircraft. The evolved interface between mechanicsand processing in a non-orthogonal control systemshould prove an especially fruitful field for inter-disciplinary research.

(2) Evolution of insect flight control systems

The ubiquity of postural flight control suggests thatit may be a primitive character amongst pterygoteinsects. The necessary neuromuscular mechanismsfor postural control would have been in place longbefore the evolution of the stroke cycle, so it wouldnot be surprising if this were the main means ofcontrol during the early evolution of flight. Indeed,if flapping flight evolved via an intermediate glidingstage, then postural control could even have beenused to stabilise the descent of smaller insects prior tothe evolution of wings (Flower, 1964). Currentdevelopmental, neurological and morphological evi-dence suggests that the wings themselves evolvedfrom gills or associated epipodal structures on thelimbs of an aquatic ancestor (Wigglesworth, 1973,1976; Kukalova! -Peck, 1978, 1983; Wootton, 1981;Robertson, Pearson & Reichert, 1982; Kingsolver &Koehl, 1994; Thomas & Norberg, 1996; Averof &Cohen, 1997). Under this scenario, the incipient

wings would already have been articulated andmuscularised at their base. However, they wouldprobably not have possessed the degree of controlrequired for successful modulation of the flappingcycle, unless their gill-like precursors were used forswimming. Hence, the evolution of improved wingcontrol – whether for gliding or for some otherputative intermediate stage such as surface-skim-ming (Marden & Kramer, 1994; Marden et al.,2000) – would almost certainly have been prerequi-site for the evolution of flapping flight. Indeed, awing that has evolved rotations about three axes forcontrol already has at least a rudimentary version ofeach of the fundamental motions of the stroke cycle,offering one possible route to the evolution of thestroke cycle (Hinton, 1963; Wigglesworth, 1963,1976; Wootton, 1976).

It is difficult to draw any firm conclusions as to thestage of evolution at which different kinematiccontrol mechanisms would have been acquired. Itseems likely that the earliest flapping insects wouldhave had some control of stroke amplitude, allowingdirect modulation of the aerodynamic power outputand at least a rudimentary degree of lateral control.Changes in the degree of wing pronation are alsolikely to have been important from the outset, beinga fundamental motion of any flapping wing. Changesin stroke amplitude or the degree of wing pronationwould be expected to affect both steady andunsteady mechanisms of force production, thoughtheir effects could be qualitatively different de-pending upon the mechanism used. For example,increasing the stroke amplitude on one wing shouldincrease quasi-steady lift production, but might alsolower unsteady lift production by destabilising theleading edge vortex associated with delayed stall(C. P. Ellington, personal communication, cited inBetts, 1986).

Many of the other control inputs that insects usecan only be understood in the context of unsteadyaerodynamics. This is especially true of those relatingto the speed and timing of wing rotation or to thephase of the fore- and hindwings. To a large degree,then, the evolution of flight control in insects mustparallel their evolutionary refinement of unsteadyaerodynamic mechanisms, and differences in thekinematics of flight control between insect orders willtherefore reflect differences in the unsteady mech-anisms used. For example, the reason that changes inthe speed and timing of supination are an importantcontrol input in Drosophila spp., whereas changes inthe degree of pronation are not, is presumably thatrotational and wake-capture mechanisms are the


major source of unsteady force production inDrosophila spp. On the other hand, changes in thedegree of pronation do appear to be important inlocusts, which presumably reflects the importance tolocusts of translational mechanisms of aerodynamicforce production.

A corollary of this is that as our knowledge ofunsteady mechanisms and their relationship to wingkinematics improves, it may become possible torecognise the aerodynamic mechanisms being usedby a given insect on the basis of how the insect variesits wing kinematics during real or fictive man-oeuvres. This is potentially more powerful thanlooking merely at the kinematics of steady flight,since it will always be difficult to assess theimportance of translational mechanisms such asdelayed stall, which, in contrast to rotationalmechanisms, may have no clear kinematic mani-festation. For example, the counter-intuitive re-duction in stroke amplitude that accompanieselevated force production in heteropteran bugs(Betts, 1986) and hawkmoths (Willmott & Ellington,1997) may indicate that delayed stall accounts for asignificant portion of peak force production, es-pecially if the wingbeat frequency is reducedsimultaneously as in bugs. Future studies of themechanics of insect flight control will have to takeunsteady aerodynamics explicitly into account.Experiments correlating changes in the wing kin-ematics with instantaneous force measurements andflow visualisation offer one way in which this mightbe achieved.

VIII. CONCLUSIONS

(1) The current literature does not permit aformal, quantitative analysis of insect flight control,because the aerodynamic force systems that biol-ogists have measured have rarely been complete,and because the position of the centre of gravity hasrarely been recorded in studies of insect flightcontrol. Future experimental studies will need to payclose attention to both these points. For a fulldynamic analysis, it will be necessary also todetermine the insect’s moments of inertia.

(2) Two influential paradigms in the insect flightcontrol literature appear either to have been widelymisinterpreted or to be a misinterpretation of theempirical data. Specifically, although Drosophila spp.normally modulate lift and thrust together, thehelicopter model of their flight control is probablybetter thought of as a facultative strategy, rather

than as a fixed constraint. On the other hand, the so-called ‘constant-lift reaction’ of locusts (Wilson &Weis-Fogh, 1962) appears not to be a reflex formaintaining constant lift at varying angles of attack,but rather a mechanism to restore the insect to pitchequilibrium following a disturbance.

(3) The number of degrees of freedom that insectsare able to control cannot exceed the number ofindependent control inputs. Since the latter is usuallyquite high, it seems likely that some of the controlinputs will be redundant, providing finer control ofthe various degrees of freedom.

(4) Although most insects are likely to generatecontrol moments about all three axes, full three-axiscontrol has only been proven for larger flies anddragonflies.

(5) Control inputs are unlikely to operate evenapproximately orthogonally in insects. This will tendto complicate the neural processing required toseparate out the various motions.

(6) Taxonomic differences in insect flight controlkinematics probably reflect differences in the un-steady aerodynamic mechanisms being used. Theevolution of insect flight control is therefore likely tohave paralleled the evolutionary refinement ofunsteady aerodynamic mechanisms.

(7) Classification of an insect’s control kinematicsduring real or fictive turns could provide a relativelysimple assay for determining the dominant unsteadyaerodynamic mechanisms being used.

IX. ACKNOWLEDGEMENTS

I am grateful to Adrian Thomas and Robert Nuddsfor their comments upon the manuscript and thankBob Srygley for the image of the hawkmoth. Thecomments of an anonymous referee were extremelyhelpful in improving the manuscript. This work wasfunded by a Christopher Welch Scholarship fromthe University of Oxford.

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