The hoverfly is interesting because of its maneuverability, high peak speed, and relatively low wing stroke amplitude compared to some other insects. The wing kinematics are still non-trivial.
(figures from J. Brackenbury, Insects in Flight London: Blandford.)

beginning of downstroke (Brackenbury, fig. 11a, p.28)

end of downstroke (Brackenbury, fig. 11b, p.28)

end of downstroke during take off (Brackenbury, fig. 12a, p.29)

Front and back view at same phase in stroke cycle. Note deformed wing shape. (Brackenbury, fig. 51, p.98)

Wing Engineering

Wings are not rigid and not smooth. Wing bending will increase tip velocity during certain phases of the wing stroke, which may affect performance. (What affect does wing compliance have on lift/drag?)

Note deformed wing shape in leptoterna bug during downstroke (Brackenbury fig.58, p.106).

Wing features less than 100 micron in height may help to improve laminar flow properties (Brackenbury fig.75, p.142).

Dragon Flies

Dragon Flies have great agility and power, but the wing kinematics seem as compex as the hover flies. The extra set of wings probably increases fabrication difficulty. (Figures from I. Pecile, Libellule Udine: Carlo Lorenzini Editore, 1984.

C. erythraea. (Pecile, fig.133, p.121)

Detail of thorax of A. cyanea. Insect is about 50% muscle by weight. (Pecile, fig.88, p.89)

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