Span efficiency in hawkmoths

Abstract

Flight in animals is the result of aerodynamic forces generated as flight muscles drive the wings through air. Aerial performance is therefore limited by the efficiency with which momentum is imparted to the air, a property that can be measured using modern techniques. We measured the induced flow fields around six hawkmoth species flying tethered in a wind tunnel to assess span efficiency, e i , and from these measurements, determined the morphological and kinematic characters that predict efficient flight. The species were selected to represent a range in wingspan from 40 to 110 mm (2.75 times) and in mass from 0.2 to 1.5 g (7.5 times) but they were similar in their overall shape and their ecology. From high spatio-temporal resolution quantitative wake images, we extracted time-resolved downwash distributions behind the hawkmoths, calculating instantaneous values of e i throughout the wingbeat cycle as well as multi-wingbeat averages. Span efficiency correlated positively with normalized lift and negatively with advance ratio. Average span efficiencies for the moths ranged from 0.31 to 0.60 showing that the standard generic value of 0.83 used in previous studies of animal flight is not a suitable approximation of aerodynamic performance in insects.

Flapping wing aerodynamics: from insects to vertebrates

“…Most of the force data available for insects and hummingbirds only pertain to hovering flight; thus, to make this comparison, we pooled data for hovering insects and hummingbirds with that derived from slow-flying (∼2-3 m s −1 ) bats and birds. Although insects in forward flight generate more lift during the downstroke than the upstroke (Willmott et al, 1997;Ennos, 1989;Young et al, 2009;Henningsson and Bomphrey, 2013), many hovering insects support their body weight relatively symmetrically during the upstroke and downstroke (Dickinson et al, 1999). In contrast, most bats and birds support their body weight primarily during the downstroke across all flight speeds.…”

Optimum hovering wing planform

“…(9) This shows that the elliptic chord distribution leads to a constant induced angle of attack distribution for both parallel and revolving translations, which is, to the authors at least, a delightful result. The constant sectional velocity distribution associated with parallel translation motion (fixed wing) leads in turn to a constant downwash velocity distribution and thus a unity induced power factor, where the induced power factor (denoted as k ind ) is the ratio of the actual induced power to minimum ideal induced power for a given lift [21][22][23][24]. On the other hand, the linear downwash distribution of the elliptic chord for a revolving wing leads to a k ind value of 1.13 (i.e.…”

On the quasi-steady aerodynamics of normal hovering flight part I: the induced power factor

“…Henningsson & Bomphrey [4] obtained a maximum span efficiency within the flapping cycle of forward flying locusts of 0.79 and an average span efficiency value of 0.53, implying k-values of 1.27 and 1.89, respectively. Recently, Henningsson & Bomphrey [5] assessed the span efficiency of six hawkmoth species flying tethered in a wind tunnel. The obtained average span efficiencies for the moths ranged from 0.31 to 0.6; equivalent to k-values ranging from 1.67 to 3.23.…”

“…A significant amount of work on flapping animals has been undertaken with the aim of identifying wing inviscid span efficiency (inverse of induced power factor [2,3]) in forward flight through experiments [1,[4][5][6][7][8], with the downwash velocity distribution measured using digital particle image velocimetry (DPIV) techniques. These data are then used within the actuator disc theory framework to define the real lift and induced power values.…”