  Medium and large insects in normal hovering have horizontal, planar up- and
downstrokes1-4. The lift of the two half-strokes, generated by the leading-edge
vortex, provides the weight-supporting vertical force. But for small insects
(wing length R less than about 4 mm and Reynolds number Re very low, about 80
to 10), because of the large effect of air viscosity (as Re becomes very low,
moving in air is like in oil), sufficient vertical force could not be produced
if using the above wing kinematics. Small insects must use different flapping
mode. Here, through analyzing flight data from our recent studies on a
relatively-large small insect (fruitfly: R=3 mm, Re=80) and a very small insect
(wasp: R=0.5 mm, Re=10), we put forward a hypothesis on how the flapping
pattern will change: as insect-size or Re decreasing, a deeper and deeper
U-shape upstroke will be used to overcome the viscous effect. And we test this
hypothesis by measuring the wing kinematics for species of different sizes to
obtain data for Re ranging from 80 to 10 and by computing the aerodynamic
forces. The data and computation support our hypothesis: the planar upstroke
changes to U-shape upstroke which becomes deeper as size or Re becomes smaller;
for relatively-large small insects, the U-shape upstroke produces a larger
vertical force than a planar upstroke by having a larger wing velocity, and for
very small insects, the deep U-shape upstroke produces a large transient drag
that points almost upwards by fast downward acceleration of the wing, providing
the required vertical force.
