Four-Winged Flapping Flyer in Forward Flight - Selected Topics of Computational and Experimental Fluid Mechanics - page 146

and cruising speed measurements was then an estimate of the aerodynamic power
P a = FU . One of the disadvantages of that procedure was that the two measurements

did not correspond to the same flight configuration: while U corresponds to self-
propelled cruising flight, F measured at a fixed station corresponds to a “hovering”
flight configuration. Here we avoid that problem by using an estimate of aerodynamic
power obtained only from the velocitymeasurements, as explained in the next section.

3 Results

(i) Flying performance . The aerodynamic interactions are thus ruled by and their

effect can be directly measured in the performance parameters of the experiment:
the cruising speed U and the consumed power P i . In order to get a clear picture of
the effect of each parameter we first show in Fig. 2 two data series corresponding to
different flapping frequencies, where U and P i are plotted as functions of

˕

.Itcan
be seen that the phasing between the wings produces a net effect in performance, the
fastest cruising flight velocities corresponding to a range around in-phase flapping
(

˕

0), but the picture becomes richer when looking at the consumed power. Indeed,
the latter has two peaks around

˕ =

. The previous series lie in a regime
where increasing the flapping frequency shifts the curves to higher flying speeds
and higher consumed power. The observed trend is readily explained using the non-
dimensional expressions p

˕ ≈ 0 and ˀ

A 0 ˉ f defined by Ramananarivo
et al. ( 2011 ), where A 0 is the amplitude of oscillation of the leading edge at mid span
given by A 0 = (

= / ˉ f and u = /

P i c B U

L / 2 ) sin ʸ 0 and ˉ f = 2 ˀ f . The insets in Fig. 2 show the behaviour

of the dimensionless quantities.
The increase of speed with increasing flapping frequency is not indefinite how-
ever, an effect shown in Fig. 3 , where U is plotted in coloured contours in a (˕, f ) -

Fig. 2 Cruising speed and consumed power as a function of the forewing-hindwing phase lag for
two different flapping frequencies