  The aerial environment in the operating domain of small-scale natural and
artificial flapping wing fliers is highly complex, unsteady and generally
turbulent. Considering flapping flight in an unsteady wind environment with a
periodically varying lateral velocity component, we show that body rotations
experienced by flapping wing fliers result in the reorientation of the
aerodynamic force vector that can render a substantial cumulative deficit in
the vertical force. We derive quantitative estimates of the body roll amplitude
and the related energetic requirements to maintain the weight support in free
flight under such conditions. We conduct force measurements of a miniature
hummingbird-inspired robotic flapper and numerical simulations of a bumblebee.
In both cases, we demonstrate the loss of weight support due to body roll
rotations. Using semi-restrained flight measurements, we demonstrate the
increased power requirements to maintain altitude in unsteady winds, achieved
by increasing the flapping frequency. Flapping fliers may increase their
flapping frequency as well as the stroke amplitude to produce the required
increase in aerodynamic force, both of these two types of compensatory control
requiring additional energetic cost. We analyze the existing data from
experiments on animals flying in von K\'arm\'an streets and find reasonable
agreement with the proposed theoretical model.
