Passive wing pitch reversal in insect flight

Abstract

Wing pitch reversal, the rapid change of angle of attack near stroke transition, represents a difference between hovering with flapping wings and with a continuously rotating blade (e.g. helicopter flight). Although insects have the musculature to control the wing pitch during flight, we show here that aerodynamic and wing inertia forces are sufficient to pitch the wing without the aid of the muscles. We study the passive nature of wing pitching in several observed wing kinematics, including the wing motion of a tethered dragonfly, Libellula pulchella, hovering fruitfly, hovering hawkmoth and simplified dragonfly hovering kinematics. To determine whether the pitching is passive, we calculate rotational power about the torsion axis owing to aerodynamic and wing inertial forces. This is done using both direct numerical simulations and quasi-steady fluid force models. We find that, in all the cases studied here, the net rotational power is negative, signifying that the fluid force assists rather than resists the wing pitching. To further understand the generality of these results, we use the quasi-steady force model to analyse the effect of the components of the fluid forces at pitch reversal, and predict the conditions under which the wing pitch reversal is passive. These results suggest the pitching motion of the wings can be passive in insect flight.

A predictive quasi-steady model of aerodynamic loads on flapping wings

“…However, the pitching motion of flapping wings of insects, especially during wing reversals, is not always actively controlled. Torsional wave along the trailing edge (TE) of a wing travelling from the wing tip to root is considered as a signature of passive or partly passive wing pitching and has been observed on wings of Deptera [Ennos, 1989] and dragonfly [Bergou et al, 2007]. To simplify the drive mechanism, wings of FWMAVs are also designed to pitch passively [de Croon et al, 2009;Bolsman et al, 2009;Ma et al, 2013].…”

Wing Geometry and Kinematic Parameters Optimization of Flapping Wing Hovering Flight

“…It is worth noting that the aerodynamic damping moment, which plays an important role in realizing smooth pitch rotation of wing planform [25], is introduced into the pitch-axis aerodynamic moment. Moreover, the aerodynamic damping moment that stems from the velocity gradient of each strip along chordwise differential elements due to pitch motion of wing planform [8,25,[38][39][40] is also included to complete the development of aerodynamic moments. Thus, the current aerodynamic model can be termed an extended version of quasi-steady aerodynamic model.…”

“…Here,M coeff,trans,z and M coeff,rot,z in (22) and (24), can be termed non-dimensional translational and rotational aerodynamic moments, respectively.M coeff,rd,x andM coeff,rd,z in (26) and (27) can be termed non-dimensional rotational damping coefficient.Î xz,am ,Î xx,am andM coeff,add,z,1 in (28) and (29) can be termed non-dimensional added mass moments coefficients, respectively. Regarding the pitching moment component of wing planform arisen from the rotational circulation term, it is necessary to tackle the problem of chordwise acting point distribution of rotational normal aerodynamic force since it might play an improving or resisting role during the passivity of pitch reverse dynamic of wing planform [40]. Here, taking the difficulty of direct measurements of rotational moments into consideration, we assume that chordwise location distribution of COP for rotational normal aerodynamic force is the same as the one for translational normal aerodynamic force (d cop (α)) in the light of translational circulation and rotational circulation stemming from the same mechanism of circulatory-and-attached-vortex force [45,46].…”

“…In short, here, the extended quasi-steady aerodynamic forces and moments model is derived from previous revised quasi-steady aerodynamic model [25,32,34,35], but it has two different points from the latter one. The first one is that it includes the contribution of aerodynamic damping moment along z-axis of wing shoulder frame, which is scarcely considered in previous research [8,25,40]. The second one is that the assumption of uniform distribution about non-dimensional chordwise location of COP for translational and rotational circulation aerodynamic mechanism is introduced to simplify the calculation of rotational aerodynamic moment.…”

“…The second one is that the assumption of uniform distribution about non-dimensional chordwise location of COP for translational and rotational circulation aerodynamic mechanism is introduced to simplify the calculation of rotational aerodynamic moment. Because of the difficulty of direct measurements of rotational moments and the lack of exploring possible chordwise location of COP of rotational circulation aerodynamic mechanism [8,40,47,48], the calculation of rotational aerodynamic moment is either neglected [25] or consciously executed by assumption that the chordwise position distribution of COP for aerodynamic force arising from translational and rotational circulation is identical, and located at the geometric center of the wing strip elements [8,40].…”