First published online August 4, 2005
Journal of Experimental Biology 208, 3075-3092 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01744
The aerodynamic effects of wing–wing interaction in flapping insect wings
Fritz-Olaf Lehmann1,*,
Sanjay P. Sane2 and
Michael Dickinson3
1 Biofuture Research Group, Department of Neurobiology, University of Ulm,
89069 Ulm, Germany
2 Department of Biology, University of Washington, Seattle, WA 98195-1800,
USA
3 California Institute of Technology, MC 138-78, Pasadena, CA 91125,
USA
View larger version (34K):
[in a new window]
|
Fig. 1. Wing motion and force production of a robotic wing performing a
clap-and-fling kinematic maneuver. (A–D) Diagrams of wing motion
indicating magnitude and orientation of total force vector measured by a force
transducer during the downstroke (red) and upstroke (green) of a dynamically
scaled robotic model wing (stroke amplitude=160°; cycling frequency=0.16
Hz; geometrical angle of attack at midstroke=45°; wing shape similar to a
Drosophila wing; mean Reynolds number is 134 and typical to
Drosophila wing motion). Small circles at the beginning of each wing
section (blue line) indicate the leading edge of the moving wing. The
kinematic pattern was derived from kinematic data published for a tethered
flying fruit fly Drosophila
(Zanker, 1990a ). The
performance of flapping a single wing is shown in A and B. The vectors in C
and D demonstrate forces produced by the wing when simultaneously flapping an
imaged wing in close distance to promote the clap-and-fling maneuver at dorsal
reversal. (E) Relative augmentation of the mean force vector coefficient due
to the clap-and-fling wing beat, scaled to the performance of a single wing
flapping. Data are plotted as a function of the angular distance between the
two wing hinges. The pictogram illustrates the position of the wing's leading
edge (blue line) during the clap and the location of the two robotic wing
hinges (view normal to the stroke plane). To avoid direct mechanical stress on
the force transducer, the wing tips do not physically touch during the clap
phase. (F) Alterations of the mean force vector inclination with respect to
the horizontal stroke plane when varying the angular distance between the two
wings during the clap-and-fling maneuver. An angle of inclination greater than
90° indicates that the force vector points slightly into a ventral
direction, which results in a pitching (nose) down moment. (G) The ratio
between mean lift and drag coefficients (averaged over the entire stroke
cycle) demonstrates how aerodynamic efficacy changes with decreasing angular
distance of wing separation during dorsal stroke reversal.
|
|
View larger version (17K):
[in a new window]
|
Fig. 2. Enhancement of mean lift coefficient for different near-clap conditions
scaled to the performance of a single flapping robotic wing. The magnitude of
lift coefficient CL augmentation is 1.0 at large
separation angles where the lift coefficients for one-wing and two-wing
flapping are equal. Due both to the separation between the two wing hinges
(gear box of the robot) and the rigidity of the model wing, the wings are
closest at their tips (blue). Adding spacers at the wing hinge (red) reduces
the dead space within the gap formed by the two wings during the clap. This
experimental modification results in a higher aerodynamic performance at
minimum angular distance between the two wings.
|
|
View larger version (33K):
[in a new window]
|
Fig. 3. Time traces of aerodynamic force production of the robotic wing throughout
the stroke cycle when flapping a single wing (red) and when simultaneously
flapping an imaged wing (blue) in close distance to elicit the clap-and-fling
maneuver. (A) Total force production, (B) lift force that is equal to the
force component in the vertical and (C) drag that is equal to force parallel
to the horizontal. The broken lines in A–C indicate aerodynamic force
production derived from a conventional analytical model for aerodynamics that
solely depends on wing translational velocity and time averaged force
coefficients (quasi-steady approach; for more details, see methods in
Dickinson et al., 1999). (D)
Translational wing motion (purple), the wing's angle of attack (yellow) and
heaving motion (green) for a single stroke cycle.
|
|
View larger version (18K):
[in a new window]
|
Fig. 4. Differences in aerodynamic force production between the performance of a
single flapping wing (b) and when simultaneously flapping an imaged wing (a)
at close distance to elicit a clap-and-fling wing beat. (A) Difference in
total force production (a–b) normal to the wing surface due to
wing–wake interaction are plotted in black; differences in lift
production are shown in red and differences in drag are plotted in blue. The
time traces demonstrate that dorsal wing interaction due to clap-and-fling may
augment but also diminish force and lift production throughout the entire
stroke cycle. Roman numbers (I–VI) label the main force peaks found in
the data traces. (B) The small black dots during clap-and-fling indicate the
times in fractions of the stroke cycle at which digital particle image
velocimetry (DPIV) was performed. The stroke cycle starts and ends at
 =1.00 (dorsal wing excursion);
however, due to the employed kinematic pattern the two wings clap (wings are
held in parallel) about 1% or 50 ms after the beginning of the downstroke.
|
|
View larger version (110K):
[in a new window]
|
Fig. 5. Sequence of wake structure during dorsal clap-and-fling maneuver when
flapping one wing (upper rows, A–L) and flapping two wings (lower rows,
M–X) generated by 2-D digital particle image velocimetry. The time
values for each panel correspond to the time section before (negative values)
or after (positive values) the clap occurs. Values in the images are fractions
of the stroke cycle (0–1).
(A,M) –350 ms (=0.94); (B,N)
–200 ms (=0.97); (C,O)
–50 ms(=0.99); (D,P) 0 ms
(=1.00); (E,Q) +50 ms
(=1.01); (F,R) +100 ms
(=1.02); (G,S) +150 ms
(=1.03); (H,T) +300 ms
(=1.05); (I,U) +450 ms
(=1.08); (J,V) +600 ms
(=1.10); (K,W) +750 ms
(=1.13); (L,X) +900 ms
(=1.15). The wing section at the
center of wing area is indicated by a white line. The leading edge of the
dorsal wing surface is marked by a white half circle. Fluid flow velocities
are plotted in color code and arrows correspond to velocity vector at each
point in the fluid; longer arrows signify larger velocities.
|
|
View larger version (14K):
[in a new window]
|
Fig. 6. Estimation of fluid velocity and acceleration in a local area near the
trailing wing edge during one-wing and two-wing flapping conditions. (A) Grey
areas indicate the regions of interest at eight different times during dorsal
stroke reversal. (B) Mean flow velocity and (C) acceleration in the fluid when
flapping one (red, lower pictogram) and two wings (image wing, blue, upper
pictogram). Green data in B (right scale) show the difference in flow velocity
between both flapping conditions. Acceleration fields were calculated from the
difference of two subsequent DPIV images taken at 65% wing length (center of
wing area). Stroke kinematics is the same as in
Fig. 1.
|
|
View larger version (117K):
[in a new window]
|
Fig. 7. Sequence of vorticity distribution in the wake at 65% wing length during
single wing flapping (upper rows, A–L) and flapping two wings
(M–X) using clap-and-fling wing beat pattern in the robotic wing. White
boxes in the images show the region in which leading edge vorticity has been
measured within the fluid. Vorticity is plotted according to the pseudo color
code and arrows indicate the magnitude of fluid velocity; longer arrows
signifying larger velocities. See Fig.
5 for temporal spacing between the images and more details. Values
in the images are fractions of the stroke cycle
(0–1).
|
|
View larger version (26K):
[in a new window]
|
Fig. 8. Estimates of circulation of leading edge vortex (LEV) during dorsal stroke
reversal in the robot while flapping its wings as shown in
Fig. 1A–D. (A–E)
LEV circulation measured at five different distances from the wing base.
Pictograms illustrate wing shape and the yellow layer in each pictogram
indicates the DPIV layer that was used for the analysis. LEV circulation for a
single wing flapping is shown in red; when flapping two wings, in blue. (F)
LEV circulation throughout the clap-and-fling maneuver and averaged over all
five DPIV layers (cf. Materials and methods). Green data show the difference
between both flapping conditions and demonstrate how LEV vorticity increases
due to wing–wake interference during clap-and-fling.
|
|
View larger version (22K):
[in a new window]
|
Fig. 9. Peak vorticity of LEV core and difference in peak vorticity between
single-wing and two-wing flapping conditions. Peak vorticity was measured
within the investigation areas shown in
Fig. 7. (A) Difference
(a–b) in peak vorticity between the one- (b) and two-wing (a) flapping
conditions at five different DPIV layers, as indicated by the pictograms. (B)
Averaged values of all five DPIV layers. Absolute LEV peak vorticity while
flapping one wing is plotted in red; peak vorticity while flapping two wings
is shown in blue. Vorticity difference (a–b) in B is shown in green.
|
|
View larger version (26K):
[in a new window]
|
Fig. 11. Augmentation of mean force coefficient during clap-and-fling wing beat
plotted as a function of duration of wing rotation within the stroke cycle (A)
and Reynolds number based on wing tip speed velocity (B). Augmentation of mean
lift and drag coefficient due to clap-and-fling, scaled to the performance a
single flapping wing is shown in (C) and (D), respectively. Angular distance
between the wings during clap was –4.95°. For these experiments we
modified a conventional stroke pattern (stroke amplitude=160°, cycling
frequency=0.16 Hz, geometrical angle of attack at mid stroke=50°, up/down
ratio=0.5 and approximately symmetrical timing of wing rotation at which 50%
of the rotational phase occurs before and 50% after the clap) by systemically
varying the onset of wing rotation at the end of each half stroke (in A) and
stroke frequency (in B–D).
|
|
View larger version (17K):
[in a new window]
|
Fig. 12. Fluid jet velocities associated with fluid motion out of the gap during
wing motion preceding the clap, and fluid motion into the gap during fling
phase. (A) Pictogram illustrating wing shape and the layers (as a % of
R) used for digital particle image velocimetry (DPIV). (B) Temporal
change of local vertical fluid velocities averaged along a line between the
two trailing wing edges during clap-and-fling wing motion. Data were derived
from DPIV images and show fluid velocities at five different distances to the
wing base. A negative value means that the fluid is moving downwards in a
vertical direction (downward jet). A positive value means that fluid is sucked
around the trailing wing edges into the `v'-shaped cleft from below. Color
coding as in A.
|
|
View larger version (24K):
[in a new window]
|
Fig. 13. Schematic reconstruction of vortex generation and shedding during the
clap-and-fling maneuver using a generic Drosophila stroke kinematics.
(A) Chordwise wing segments at the end of the upstroke, (B) during the clap
phase of the two wings, (C) during the early fling phase and (D) the late
fling right before the two wings separate for the downstroke. Leading and
trailing edge vortices that are generated during the upstroke are shed into
the wake at the end of each half stroke. The vortex system generates an
inter-vortex stream towards the wing that is thought to enhance flight forces
via momentum transfer. Due to near-clap conditions the low pressure
region evolving between the wings during the fling pulls fluid around the
leading and the trailing wing edges into the opening cleft.
|
|
© The Company of Biologists Ltd 2005
) is equal to
LEV circulation normalized to angular speed of wing rotation and wing chord.
Color coding of the data points corresponds to the five different layers used
for the DPIV measurements (see pictogram). (C) Mean values for the rotational
coefficient g(