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Fig. 3. Mean lift production in dragonfly model wings depends on both the
phase-shift between fore- and hindwing stroke cycle and the vertical
separation between the two wing hinges. (A) Vortical structures produced by a
dragonfly hindwing at 0.35 hindwing stroke cycle. The wing moves from left to
right (open arrow). The wing blade element that runs through the center of
force at 0.65 wing length is indicated by a white line and the leading edge is
indicated by a triangle, as shown in G. Inclination and length of the black
vectors indicate direction and relative magnitude of fluid velocity. (B,C)
Schematic explanation of how vertical spacing ( s) between
fore- and hindwing stroke plane changes kinematic phase relationship between
both wings (t) due to vortex travel time at 0.35 stroke cycle.
When the forewing leads wing motion, destruction of hindwing LEV by the
forewing's start vortex depends on the phase-shift between both stroke cycles
and the vertical distance between both ipsilateral wing hinges. (D) DPIV image
showing the interference between vortical structures produced by fore- and
hindwing at 0.15 hindwing stroke cycle. The hindwing leads wing motion by 0.25
stroke cycle. While the forewing (upper blade element) starts wing rotation at
the end of the downstroke, its trailing edge vortex interferes with the LEV
produced by the hindwing (lower blade element). The hindwing's start vortex
still appears to be attached to the wing's trailing edge. (E,F,H,I) Vertical
position (E,F) and vertical travel velocity of start vortices (H,I) shed from
the fore- (black) and hindwing (blue). The vortex positions were only
reconstructed from flow images in which the vortical structures were clearly
visible. The data are recorded while the forewing (E,H) and the hindwing (F,I)
was leading wing motion by a quarter stroke cycle, respectively. Shaded areas
in H and I indicate the period during which the forewing start vortex
interferes with the hindwing wake, and the dotted lines indicate maximum
downwash velocity measured in the hindwing wake. R=wing length,
LEV=leading edge vortex, HW=hindwing, FW=forewing.
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).
Chordwise wing segments at the end of the upstroke (F), during the clap phase
(G), and during the fling phase (H) before the two wings separate for the
downstroke. Leading and trailing edge vortices are shed into the wake at the
end of each half stroke. The low-pressure region evolving between the wings
during the fling pulls fluid around the leading and the trailing wing edge
into the opening cleft. (I–K) Reconstruction of vortices and local flow
conditions at maximum transient lift production in tandem model wings of a
dragonfly. (I) Wing kinematics follows a generic pattern, as found in various
species (Maybury and Lehmann,
2004
in the leading edge vortex
(LEV), measured in a region of interest (ROI, white box). LEV circulation when
flapping one and two wings are plotted in red and black, respectively. Gray
bars in the graphs indicate wing clap and time at which the DPIV analysis was
performed, respectively. White lines in panels indicate wing sections. The
leading edge of the dorsal wing surface is indicated by a white triangle. The
magnitude of vorticity is plotted in color code and arrows correspond to the
magnitude of the velocity vector at each point in the fluid, longer arrows
signify larger velocities. t=stroke cycle (0–1),
R=wing length. See Lehmann et al.
(Lehmann et al., 2005
).
(C) Phase-shift between the stroke cycles of both wings during mean peak lift
changes with changing vertical distance between the two wing hinges. Black,
forewing; red, hindwing; aspect ratio of the wings=2.7; flapping frequency=666
mHz; wing rotation symmetrical, starting 10% prior to and ending 10% after
stroke reversal; Reynolds number=137;
