Four-Winged Flapping Flyer in Forward Flight - Selected Topics of Computational and Experimental Fluid Mechanics - page 147

Fig. 3 Cruising speed, consumed power and efficiency (see text) as a function of the forewing-
hindwing phase lag and the flapping frequency. Only the first half of the phase-lag ˕ range, where
the forewing is leading, was examined here

space for and scanning the full range of flapping frequencies available

experimentally. For all phase lags, a clear maximum of the attained cruising speed
occurs always around 24Hz. We will discuss in the following that this optimal fre-
quency is related to the elastic properties of the wings. The second plot in Fig. 3
shows the consumed power P i in the same parameter space. Here the main obser-
vation is that, while not surprisingly consumed power increases monotonically with
increasing flapping frequency, the effect of the phase lag on energy expenditure,
shown previously in Fig. 2 , is clearly present regardless the flapping frequency. Be-
cause of this effect, the ranges of frequency explored changed for different phase
lags, giving, for instance, a maximum frequency for

˕ ∈[ 0 ,ˀ ]

˕ = 0 of around 30Hz, while at

˕ ∈[ ˀ/ the frequency could reach 35Hz. We use those two measurements

to define the following expression of efficiency, considering that the aerodynamic
thrust power is proportional to U 3 (velocity times thrust force, the latter being

2 , 3 ˀ/ 4 ]

U 2 ):

∼

1

SU 3
P i

2 ˁ

ʷ = (2)

where S is the effective wing surface. Other definitions of efficiency using purely
dynamical parameters (Kang et al. 2011 ) should give equivalent results to expression
( 2 ) chosen here in terms of the measured consumed power P i . It can be seen that the
optimum in terms of efficiency is shifted toward larger phase lags (around ˕ ≈ ˀ/ 2)

than the optimum in terms of maximum cruising speed.

(ii) Wing kinematics . In addition to the performancemeasurements, thewingmotion
was recorded using high-speed video in a fixed frame. That is, with the mechanical
insect not mounted on the merry-go-round but on a fixed base. Figures 4 and 5 show
typical time series for

˕ = 0 and 1 . 3 ˀ , respectively. A dark screen was used to mask