Fig. 1. Wing design and the experimental method. (A) The wing planform used for all
experiments. The wing was scaled directly from a Drosophila
melanogaster wing and equipped with multiple slots at the base to allow
the axis of rotation to be changed. The leading edge corresponds to a
non-dimensional rotational axis
(
0) value of 0, whereas
the trailing edge corresponds to a value of 1. (B,C) Two-dimensional cartoons
showing the kinematics of rotation and translation. The wing translates from
left to right at a velocity Ut and rotates about a fixed
axis of rotation with varying angular velocity, 
. The leading edge of
the wing is indicated by a filled circle. (D,E) Kinematic variables as a
function of time. Translational velocity is shown in blue, rotational velocity
in red. Data are shown for two representative rotational velocities of 1.5 rad
s-1 (D) and 0.667 rad s-1 (E). In both cases, the
translational velocity is 0.272 m s-1. (F,G) Net aerodynamic forces
as a function of time. The continuous red line indicates the measured forces
and the dotted red line indicates the quasi-steady translational estimates.
The difference between these traces (double-headed arrow) is used to calculate
rotational force coefficients over the shaded region. The early peaks in both
force traces are due to inertial transients caused by rapid acceleration of
the wing at the start of each trial. Similar inertial effects also occur as a
result of rapid rotational acceleration, as is evident in the force traces.
Although detectable, these effects are small in comparison with the
circulatory forces.
