TY - JOUR
T1 - Wing motion measurement and aerodynamics of hovering true hoverflies
JF - The Journal of Experimental Biology
JO - J. Exp. Biol.
SP - 2832
LP - 2844
DO - 10.1242/jeb.054874
VL - 214
IS - 17
AU - Mou, Xiao Lei
AU - Liu, Yan Peng
AU - Sun, Mao
Y1 - 2011/09/01
UR - http://jeb.biologists.org/content/214/17/2832.abstract
N2 - Most hovering insects flap their wings in a horizontal plane (body having a large angle from the horizontal), called `normal hovering'. But some of the best hoverers, e.g. true hoverflies, hover with an inclined stroke plane (body being approximately horizontal). In the present paper, wing and body kinematics of four freely hovering true hoverflies were measured using three-dimensional high-speed video. The measured wing kinematics was used in a Navier–Stokes solver to compute the aerodynamic forces of the insects. The stroke amplitude of the hoverflies was relatively small, ranging from 65 to 85 deg, compared with that of normal hovering. The angle of attack in the downstroke (∼50 deg) was much larger that in the upstroke (∼20 deg), unlike normal-hovering insects, whose downstroke and upstroke angles of attack are not very different. The major part of the weight-supporting force (approximately 86%) was produced in the downstroke and it was contributed by both the lift and the drag of the wing, unlike the normal-hovering case in which the weight-supporting force is approximately equally contributed by the two half-strokes and the lift principle is mainly used to produce the force. The mass-specific power was 38.59–46.3 and 27.5–35.4 W kg–1 in the cases of 0 and 100% elastic energy storage, respectively. Comparisons with previously published results of a normal-hovering true hoverfly and with results obtained by artificially making the insects' stroke planes horizontal show that for the true hoverflies, the power requirement for inclined stroke-plane hover is only a little (<10%) larger than that of normal hovering. Asystem matrixcmean chord lengthCDwing drag coefficientCGweight coefficientCHhorizontal force coefficientCLwing lift coefficientCpnon-dimensional powerCVvertical force coefficientVmean vertical force coefficientDdrag of a wingfstroke frequencyggravitational accelerationHhorizontal forceh1distance from wing-root axis to long axis of the bodyIx,b, Iy,b, Iz,bmoments of inertia of the body about the center of mass of the bodyIx,w, Iy,w, Iz,wmoments of inertia of a wing about the wing rootIxz,bproduct of inertia of the bodyIxz,wproduct of inertia of a wingJadvance ratioLlift of a wingl1distance from wing-root axis to body center of massl2distance from anterior end of body to center of masslbbody lengthlrdistance between two wing rootsmmass of an insectMtotal aerodynamic pitching moment about center of massMaaerodynamic moment of wing around wing rootMiinertial moment of wing around wing rootMqderivative of M with respect to qMuderivative of M with respect to uMwderivative of M with respect to wmwgmass of one wingP*body-mass-specific powerPaaerodynamic powerPiinertial powerqpitching angular velocity about the center of massRwing lengthr2radius of the second moment of wing areaSarea of one wingttimetcwingbeat periodnon-dimensional time ( =0 and 1 at the start and end of a cycle, respectively)ucomponent of velocity along the x-axisUreference velocity (mean flapping velocity at r2)Vvertical force of a wingwcomponent of velocity along the z-axisXx-component of the total aerodynamic forcex, y, zcoordinates in the body-fixed frame of reference (with origin at center of mass)Xqderivative of X with respect to qXuderivative of X with respect to uXwderivative of X with respect to wZz-component of the total aerodynamic forceZqderivative of Z with respect to qZuderivative of Z with respect to uZwderivative of Z with respect to w+non-dimensional quantityαangle of attack of wingβstroke plane angleθdeviation angle of wingλgeneric notation for an eigenvalueρdensity of fluidϕpositional angle of wingmean positional angleΦstroke amplitudeχbody angleΨpitch angle of wingωwing rotation velocity vector
ER -