Four-Winged Flapping Flyer in Forward Flight - Selected Topics of Computational and Experimental Fluid Mechanics - page 144

have been studied extensively (Alexander 1984 , 1986 ; Azuma and Watanabe 1988 ;
Rüppell 1989 ; Wakeling and Ellington 1997a , b ) and flow visualizations in tethered-
and free-flight configurations have demonstrated the crucial role of unsteady
mechanisms such as the formation of leading-edge vortices in the production of lift
(Thomas et al. 2004 ). Forewing-hindwing phase-lag has been shown in hovering con-
figurations to be determinant for flight performance (Maybury and Lehmann 2004 ):
optimal efficiencies have been found for out-of-phase beating whereas in-phase mo-
tion of forewings and hindwings has been shown to produce stronger force (Wang
and Russell 2007 ; Usherwood and Lehmann 2008 ). The physical mechanisms be-
hind these differences in performance have nonetheless not yet been completely eluci-
dated, and open questions remain in particular when considering the role of wing elas-
ticity. Wing deformation is important because it can passively modify the effective
angle of attack of a flapping wing, thus determining its force production dynamics.
In the present paper we address this problem experimentally using a four-winged
self-propelled model mounted on a “merry-go-round”. The setup is a modified ver-
sion of the one used by Thiria and Godoy-Diana ( 2010 ) and Ramananarivo et al.
( 2011 ), where the thrust force produced by the wings makes the flyer turn around a
central axis. A constant cruising speed is achieved for a given wingbeat frequency
when the thrust generated is balanced by the net aerodynamic drag on the flyer.
These previous works have shown that passive mechanisms associated to wing flexi-
bility govern the flying performance of a flapping wing flyer with chord-wise flexible
wings. These determine, for instance, that the elastic nature of the wings can lead
not only to a substantial reduction of the consumed power, but also to an increment
of the propulsive force. Here we introduce a new parameter using a model with two
pairs of wings. In addition to the flapping frequency and wing flexibility, the thrust
production is now also determined by the phase lag

˕ between the forewings and the

hindwings.

2 Experimental Setup

Figure 1 shows a sketch of the experimental setup. As in Thiria and Godoy-Diana
( 2010 ), the stroke plane is parallel to the shaft linking the flyer to the central bearing
of the wheel. In addition to the four-winged instead of two-winged flyer, the setup
also differs from Thiria and Godoy-Diana ( 2010 ) in that a counterweight has been
added using an opposite radial shaft to balance the system. The fluctuating lift force
is thus directed radially and absorbed by the shaft. The two wings are driven by a
single direct-current motor with a set of gears that allows to fix the phase difference
between the forewings and the hindwings. All wings beat thus at the same frequency
which was varied between 15 and 30Hz. We have reduced the parameter space
in the experiments reported here by fixing the physical characteristics of the flyer.
Namely, the distance between the wings d , the stroke amplitude ʸ 0 and the chord-

wise flexural rigidity of the wings. Of course, it should be noted that these parameters
in the present tandem wing configuration, in particular the wing spacing d , should in