Supplementary material from "Quantifying the dynamic wing morphing of hovering hummingbird"

Animal wings are lightweight and flexible; hence, during flapping flight their shapes change. It has been known that such dynamic wing morphing reduces aerodynamic cost in insects, but the consequences in vertebrate flyers, particularly birds, are not well understood. We have developed a method to reconstruct a three-dimensional wing model of a bird from the wing outline and the feather shafts (rachides). The morphological and kinematic parameters can be obtained using the wing model, and the numerical or mechanical simulations may also be carried out. To test the effectiveness of the method, we recorded the hovering flight of a hummingbird (Amazilia amazilia) using high-speed cameras and reconstructed the right wing. The wing shape varied substantially within a stroke cycle. Specifically, the maximum and minimum wing areas differed by 18%, presumably due to feather sliding; the wing was bent near the wrist joint, towards the upward direction and opposite to the stroke direction; positive upward camber and the ‘washout’ twist (monotonic decrease in the angle of incidence from the proximal to distal wing) were observed during both half-strokes; the spanwise distribution of the twist was uniform during downstroke, but an abrupt increase near the wrist joint was found during upstroke.