Wing kinematics measurement and aerodynamics of hovering droneflies

Abstract

SUMMARYThe time courses of wing and body kinematics of three freely hovering droneflies (Eristalis tenax) were measured using 3D highspeed video, and the morphological parameters of the wings and body of the insects were also measured. The measured wing kinematics was used in a Navier-Stokes solver to compute the aerodynamic forces and moments acting on the insects. The time courses of the geometrical angle of attack and the deviation angle of the wing are considerably different from that of fruit flies recently measured using the same approach. The angle of attack is approximately constant in the mid portions of a half-stroke (a downstroke or upstroke) and varies rapidly during the stroke reversal. The deviation angle is relatively small and is higher at the beginning and the end of a half-stroke and lower at the middle of the half-stroke, giving a shallow U-shaped wing-tip trajectory. For all three insects considered, the computed vertical force is approximately equal to the insect weight (the difference is less than 6% of the weight) and the computed horizontal force and pitching moment about the center of mass of the insect are approximately zero. The computed results satisfying the equilibrium flight conditions, especially the moment balance condition, validate the computation model. The lift principle is mainly used to produce the weight-supporting vertical force, unlike the fruit flies who use both lift and drag principles to generate the vertical force; the vertical force is mainly due to the delayed stall mechanism. The magnitude of the inertia power is larger than that of the aerodynamic power, and the largest possible effect of elastic storage amounts to a reduction of flight power by around 40%, much larger than in the case of the fruit fly. Supplementary material available online at

Hovering of model insects: simulation by coupling equations of motion with Navier–Stokes equations

“…For the dronefly, Eqns 9 and 10 are good approximations to the measured data (Liu and Sun, 2008;Ellington, 1984b); whilst for the hawkmoth, φ(t) is a little different from the simple harmonic function (Willmott and Ellington, 1997a;Willmott and Ellington, 1997b). From Eqns 9 and 10, we see that to prescribe the flapping motion, the stroke amplitude Φ, the wingbeat frequency n, the time duration of wing rotation Δt r , the angles of attack in the downstroke and upstroke translations α d and α u , and the mean positional angle φ must be given.…”

“…On the basis of experimental observations (e.g. Ellington, 1984b;Liu and Sun, 2008), the body oscillations are very small. In our computations, the initial values of the body motion variables are set as zero, and hence are not far from the realistic solution.…”

“…From Eqns 9 and 10, we see that to prescribe the flapping motion, the stroke amplitude Φ, the wingbeat frequency n, the time duration of wing rotation Δt r , the angles of attack in the downstroke and upstroke translations α d and α u , and the mean positional angle φ must be given. Morphological and wing motion parameters for the dronefly are taken from the data of Liu and Sun (Liu and Sun, 2008) and that for the hawkmoth from the data of Willmott and Ellington (Willmott and Ellington, 1997a;Willmott and Ellington, 1997b). It should be noted that moments and products of inertia of the wing are not given in these references and they are estimated using the data of Liu and Sun, Willmott and Ellington, and Ennos (Liu and Sun, 2008;Willmott and Ellington, 1997a;Willmott and Ellington, 1997b), according to the density distribution of a dronefly wing measured by Ennos (Ennos, 1989b).…”

“…The lift and drag of a wing are perpendicular and parallel to the stroke plane, respectively (e.g. Liu and Sun, 2008). Thus the vertical force is mainly contributed by the lift of the wing and the horizontal force by the drag of the wing.…”

Aerodynamic effects of corrugation in flapping insect wings in hovering flight

“…It is assumed that the axis of the pitching rotation is located at 0.25c from the leading edge of the wing. For many insects, Eqns1 and 2 are good approximations to the measured data (Liu and Sun, 2008;Ellington, 1984). From Eqns1 and 2, we see that to prescribe the flapping motion, , the wingbeat frequency (n), t r and the angles of incidence in the downstroke and upstroke translations,  d and  u , respectively, need to be given.…”