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, ei, 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 ei 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.
Highlights
The efficiency of lift production, span efficiency, significantly influences the limits of performance of all flying animals and has wide ranging implications for ecologically important variables such as maximum range of flights between feeding, maximum load lifting capacity and peak acceleration during manoeuvres.An ideal wing generating lift in the optimal way, i.e. with the least amount of induced drag, does so by deflecting the oncoming airflow downwards uniformly across the span [1,2]
Mean wingbeat-averaged span efficiency across individuals and sequences, as calculated according to equation (2.1), for the six moth species was ei 1⁄4 0.31 + 0.038 (N 1⁄4 4), 0.46 + 0.067 (N 1⁄4 6), 0.51 + 0.036 (N 1⁄4 4), 0.60 + 0.019 (N 1⁄4 3), 0.41 + 0.049 (N 1⁄4 2) and 0.46 + 0.11 (N 1⁄4 6), respectively (N-values, means and standard deviations correspond to total number of sequences per species)
The results show that two factors have a significant effect on span efficiency: normalized lift ( p 1⁄4 0.007, R2 1⁄4 0.28 of complete model, slope 1⁄4 0.078) and advance ratio ( p 1⁄4 0.004, R2 1⁄4 0.31 of complete model, slope 1⁄4 20.202)
Summary
An ideal wing generating lift in the optimal way, i.e. with the least amount of induced drag, does so by deflecting the oncoming airflow downwards uniformly across the span [1,2]. The reason this configuration is the most efficient is simplest to understand when examining the equation for kinetic energy, Ek 1⁄4 mv2/2, where m is mass and v is velocity. By quantifying the deviation from uniformity of the downwash distribution for a given wing, the inviscid span efficiency, ei, can be calculated [2,3]. We expect wing loading and aspect ratio (AR) to affect span efficiency as well as wingbeat frequency or perhaps more relevantly, advance ratio, which includes wingbeat frequency [4,5,6]
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