  Biological flapping wing fliers operate efficiently and robustly in a wide
range of flight conditions and are a great source of inspiration to engineers.
The unsteady aerodynamics of flapping-wings are dominated by large-scale
vortical structures that augment the aerodynamic performance but are sensitive
to minor changes in the wing actuation. We experimentally optimise the pitch
angle kinematics of a flapping wing system in hover to maximise the stroke
average lift and hovering efficiency using a evolutionary algorithm and in-situ
force and torque measurements at the wing root. Additional flow field
measurements are conducted to link the vortical flow structures to the
aerodynamic performance for the Pareto-optimal kinematics. The optimised pitch
angle profiles yielding maximum stroke-average lift coefficients have
trapezoidal shapes and high average angles of attack. These kinematics create
strong leading-edge vortices early in the cycle which enhance the force
production on the wing. The most efficient pitch angle kinematics resemble
sinusoidal evolutions and have lower average angles of attack. The leading-edge
vortex grows slower and stays close-bound to the wing throughout the majority
of the stroke-cycle. This requires less aerodynamic power and increases the
hovering efficiency by 93% but sacrifices 43% of the maximum lift. In all
cases, a leading-edge vortex is fed by vorticity through the leading edge
shear-layer which makes the shear-layer velocity a good indicator for the
growth of the vortex and its impact on the aerodynamic forces. We estimate the
shear-layer velocity at the leading edge solely from the input kinematics and
use it to scale the average and the time-resolved evolution of the circulation
and the aerodynamic forces.
