The fluid dynamics of flight control by kinematic phase lag variation between two robotic insect wings

Abstract

Functionally four-winged insects such as dragon-and damselflies use a large variety of wingbeat kinematics to produce and control aerodynamic forces for flight (Alexander, 1984;Azuma et al., 1985;Azuma and Watanabe, 1988;Chadwick, 1940;Grodnitsky and Morozov, 1992;Reavis and Luttges, 1988;Rüppell, 1989;Rüppell and Hilfert, 1993;Sato and Azuma, 1997;Somps and Luttges, 1985;Wakeling, 1993;Wakeling and Ellington, 1997;Wang et al., 2003;Weis-Fogh, 1967). The neuromuscular system allows these animals to actively manipulate many aspects of wing motion such as stroke amplitude, stroke frequency, the angle of attack and stroke plane (Norberg, 1975;Rüppell, 1989), but also to actively control the timing between the fore-and hindwing stroke cycles (kinematic phase relationship, Alexander, 1984;Azuma and Watanabe, 1988;Clark, 1940;Grodnitsky and Morozov, 1992;May, 1995;Sato and Azuma, 1997; Simmons, 1977a,b;Wakeling and Ellington, 1997;Wang et al., 2003). Thus dragonflies and damselflies differ significantly from other four-winged insect species such as butterflies, bees, wasps and ants, whose fore-and hindwings always beat in phase, due to a sophisticated joint that mechanically couples the motion of both wings throughout the entire stroke cycle (Gorb, 2001). Other insects of more primitive orders, such as locusts, lie somewhere between both extremes; in locust, the stroke-phase relationship seems to be highly consistent, with little variation during flight control (Chadwick, 1953;Weis-Fogh, 1956;Wilson, 1968;Wortmann and Zarnack, 1993). Cooter and Baker (1977) reconstructed wing motion of freely flying locust Locusta migratoria and found a fixed phase relationship between their fore-and hindwings in which the forewing slightly leads by approximately 61°.In contrast, dragonflies vary the phase relationship between ipsilateral fore-and hindwings with different behaviors (Norberg, 1975;Reavis and Luttges, 1988;Wakeling and Ellington, 1997;Wang et al., 2003). Three categories of phase relationship between fore-and hindwing have been established: phase-shifted stroking, counterstroking and parallel stroking. A highly consistent characteristic for the Insects flying with two pairs of wings must contend with the forewing wake passing over the beating hindwing. Some four-winged insects, such as dragonflies, move each wing independently and therefore may alter the relative timing between the fore-and hindwing stroke cycles. The significance of modifying the phase relationship between fore-and hindwing stroke kinematics on total lift production is difficult to assess in the flying animal because the effect of wing-wake interference critically depends on the complex wake pattern produced by the two beating wings. Here we investigate the effect of changing the fore-and hindwing stroke-phase relationship during hovering flight conditions on the aerodynamic performance of each flapping wing by using a dynamically scaled electromechanical insect model. By varying the relative phase difference between fore-and hindwing stroke cycles we...

The aerodynamic benefit of wing–wing interaction depends on stroke trajectory in flapping insect wings

“…This method has already been published elsewhere in greater detail, so we provide only a brief description here (Dickinson et al, 1999;Maybury and Lehmann, 2004). We used two computer-controlled dynamically scaled Plexiglas TM wings (left and right wing) programmed to flap back and forth in prescribed kinematic patterns.…”

Elastic deformation and energy loss of flapping fly wings

“…Besides aerodynamic force, inertia is a major source for wing flexing and bending in insects (Combes and Daniel, 2003a;Ennos, 1988). These forces may simply be calculated from each wing blade mass element, translational and rotational wing motion (Maybury and Lehmann, 2004). Vertical inertia during in-plane flapping results from vertical displacement of wing mass during the rotational phases.…”

“…The majority of experimental studies using either robotic wings (e.g. Birch and Dickinson, 2003;Maybury and Lehmann,properties: the spanwise stiffness and the chordwise flexibility. The leading edge of most insect wings is composed of a stiff structure with a three-dimensional relief, providing high rigidity in the spanwise direction (Combes and Daniel, 2003b).…”

Flexible Wing Kinematics of a Free-Flying Beetle (Rhinoceros Beetle Trypoxylus Dichotomus)

“…On the other hand, other insects usually have small Reynolds number. The Reynolds number is from 100 to 200 for Drosophila melanogaster [27] , around 333 for Crane fly [28] , from 1200 to 3000 for Bumblebee [29] , around 1140 for dragonfly [13] , and from 250 to 500 for smallest dragonfly [30] . There were 53 frames for a single stroke, which means that the duration of one cycle (T) lasted 0.027 s and that the frequency (f) was (37.7 ± 0.3) Hz.…”