Abstract

A computational fluid dynamic (CFD) modelling
approach is used to study the unsteady aerodynamics of the
flapping wing of a hovering hawkmoth. We use the
geometry of a Manduca sexta-based robotic wing to define
the shape of a three-dimensional ‘virtual’ wing model and
‘hover’ this wing, mimicking accurately the threedimensional
movements of the wing of a hovering
hawkmoth. Our CFD analysis has established an overall
understanding of the viscous and unsteady flow around the
flapping wing and of the time course of instantaneous force
production, which reveals that hovering flight is dominated
by the unsteady aerodynamics of both the instantaneous
dynamics and also the past history of the wing.
A coherent leading-edge vortex with axial flow was
detected during translational motions of both the up- and
downstrokes. The attached leading-edge vortex causes a
negative pressure region and, hence, is responsible for
enhancing lift production. The axial flow, which is derived
from the spanwise pressure gradient, stabilises the vortex
and gives it a characteristic spiral conical shape.

The leading-edge vortex created during previous
translational motion remains attached during the
rotational motions of pronation and supination. This
vortex, however, is substantially deformed due to coupling
between the translational and rotational motions, develops
into a complex structure, and is eventually shed before the
subsequent translational motion.
Estimation of the forces during one complete flapping
cycle shows that lift is produced mainly during the
downstroke and the latter half of the upstroke, with little
force generated during pronation and supination. The
stroke plane angle that satisfies the horizontal force
balance of hovering is 23.6 °, which shows excellent
agreement with observed angles of approximately 20–25 °.
The time-averaged vertical force is 40 % greater than that
needed to support the weight of the hawkmoth.