Photogrammetric reconstruction of high-resolution surface topographies and deformable wing kinematics of tethered locusts and free-flying hoverflies

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Abstract
Here, we present a suite of photogrammetric methods for reconstructing insect wing kinematics, to provide instantaneous topographic maps of the wing surface. We filmed tethered locusts (Schistocerca gregaria) and free-flying hoverflies (Eristalis tenax) using four high-speed digital video cameras. We digitized multiple natural features and marked points on the wings using manual and automated tracking. Epipolar geometry was used to identify additional points on the hoverfly wing outline which were anatomically indistinguishable. The cameras were calibrated using a bundle adjustment technique that provides an estimate of the error associated with each individual data point. The mean absolute three-dimensional measurement error was 0.11 mm for the locust and 0.03 mm for the hoverfly. The error in the angle of incidence was at worst 0.51 degrees (s.d.) for the locust and 0.88 degrees (s.d.) for the hoverfly. The results we present are of unprecedented spatio-temporal resolution, and represent the most detailed measurements of insect wing kinematics to date. Variable spanwise twist and camber are prominent in the wingbeats of both the species, and are of such complexity that they would not be adequately captured by lower resolution techniques. The role of spanwise twist and camber in insect flight has yet to be fully understood, and accurate insect wing kinematics such as we present here are required to be sure of making valid predictions about their aerodynamic effects.