Fluid-dynamic characteristics of a bristled wing
1 National Institute of Industrial Science and Technology, Ministry of
Economy, Trade and Industry, 1-2-1 Namiki, Ibaraki 305-8964, Japan
2 Nihon University, 7-24-1 Narashinodai, Funabashi, Chiba 274-0081,
Japan
3 Research Center for Advanced Science and Technology, University of Tokyo,
4-6-1 Komaba, Meguro, Tokyo 153-8904, Japan
* Author for correspondence at present address: Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan (e-mail: sunada{at}aero.osakafu-u.ac.jp)
Accepted 6 June 2002
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Summary |
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Key words: thrips, Thripidae frankliniella, bristled wing, membranous wing, fluid-dynamics, constant-velocity translation/rotation, accelerating translation/rotation
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Introduction |
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To estimate the fluid-dynamic forces acting on the hairy appendages and understand the fluid-dynamic mechanisms of thrips flight, we measured the fluid-dynamic characteristics of a dynamically scaled model of the forewing. Four different wing motions were studied: forward motion at a constant velocity (constant-velocity translation), forward motion at a translational acceleration (accelerating translation), rotational motion at a constant angular velocity (constant-velocity rotation) and rotational motion at an angular acceleration (accelerating rotation). For comparison, the fluid-dynamic characteristics of a solid model wing were also measured. The solid wing had the same outline as the bristled model, but was made from a solid flat plate of the same thickness as the bristle diameter. Comparing the fluid-dynamic performance of the bristled and the solid wing might help to clarify why a small insect, such as a thrips, uses bristled wings for flight.
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Materials and methods |
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Forward motion
Fig. 2 shows the apparatus
used to measure the fluid-dynamic forces acting on the model wings in forward
motion. A tank (dimensions in X, Y and Z directions,
LX=800 mm, LY=400 mm and
LZ=500 mm, respectively) was filled with an aqueous
solution of glycerine. The wing was suspended from a load cell (LMC3729-1N,
Nissho Electric Works, Japan) via an 8 mm diameter joint cylinder.
The load cell can measure forces in the x and z directions,
Fx and Fz, and the moment around the
y axis, My. The maximum load for
Fx and Fz was 1 N and that for
My was 0.01 N m.
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The cross talk between Fx, Fz and My was small, and the measured forces Fx and Fz were considered to be equal to the normal and tangential forces, Fn and Ft, respectively, on the wing (Fx=Fn, Fz=-Ft).
The wing was moved in the X direction at a constant angle of
attack between -10° and 45° as described for constant-velocity
translation and accelerating translation in
Table 2. During
constant-velocity translation, the wing moved at a constant forward velocity
V0. During accelerating translation, the wing underwent
sinusoidal acceleration for t
T0t
(t
T0t =4 or 10 s), where t is time
and T0t is the period of accelerated motion. The forward
velocity reached a terminal value V0 at
t=T0t. Because the tank was much larger than the
model wings, wall and surface effects can be ignored.
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Table 2 also shows the
Reynolds number Re calculated as follows:
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The fluid-dynamic forces acting on the wing were measured as follows. First, the normal and tangential forces Fn,c and Ft,c were measured for the wing mount only without the wing connected to the joint cylinder. Next, we measured the normal and tangential forces Fn and Ft generated by both the wing and its mount. The fluid-dynamic forces acting on the wing only were calculated from the measured forces, Fn, Ft, Fn,c and Ft,c for the two translational motions.
Constant-velocity translation
The forces Fn, Ft,
Fn,c and Ft,c were measured when they
reached constant values. The fluid-dynamic forces acting on the wing only were
calculated using the expressions,
FnFn,c and
FtFt,c. The lift coefficient
CL and drag coefficient CD were
obtained by non-dimensionalizing the measured fluid-dynamic forces as follows:
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Accelerating translation
The forces Fn, Ft,
Fn,c and Ft,c were measured at
0t
T0t. Fn and
Ft are the sum of the fluid-dynamic and inertial forces
acting on the joint cylinder, the fluid-dynamic and inertial forces acting on
the wing and the inertial forces on the load cell. Fn,c
and Ft,c are the sum of the fluid-dynamic and inertial
forces acting on the joint cylinder and the inertial forces acting on the load
cell. The load cell measured an inertial force proportional to the accelerated
mass attached to the strain gauge in the load cell. Therefore,
FnFn,c and
FtFt,c are the sum of the
fluid-dynamic and inertial forces acting on the wing. The normal and
tangential fluid-dynamic forces acting only on the wing are given by
FnFn,cmw
sin
and
FtFt,cmw
cos
,
respectively, where mw is the mass of the wing, and
mw
sin
and
mw
cos
are
the normal and tangential components, respectively, of the inertial force
acting on the wing. CL and CD were
obtained by non-dimensionalizing the measured fluid-dynamic forces as follows:
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Rotational motion
Fig. 3 shows the apparatus
used to measure the fluid-dynamic forces acting on the model wings in
rotational motion. The model wing was suspended in a tank
(LX, LY=500 mm and
LZ=1000 mm) filled with an aqueous solution of glycerine.
The wing was mounted onto a load cell (LMC2909, Nissho Electric Works, Japan)
and a motor via a 6 mm diameter joint cylinder. The wing rotated
around the joint cylinder in the XY plane. The load cell
measured force in the Z direction, Fz, and the
moment around the Z axis, Mz. The maximum load
was 5 N for Fz and 0.25 N m for Mz.
When forces in the X, Y and Z directions and moments around
the X, Y and Z axes act on the load cell, the output signal
from the load cell, Fz and Mz are
affected by all the forces and moments acting on the load cell. However,
because the cross talk between Fz and
Mz was small, measured values of Fz
and Mz were considered to be equal to the force in the
Z direction and the moment around the Z axis actually acting
on the load cell, respectively.
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The tank was filled to the depth LZ1 of 980 mm with an aqueous solution of glycerine. The rotational axis of the wing was at the centre of the tank in the XY plane. The distance between the rotational plane and the bottom of the tank was 0.7LZ1. All tank dimensions are large enough for surface and wall effects to be negligible.
The geometrical angle of attack was defined as the angle between
the Z axis and a vector normal to the wing. The angle of attack
was set between -10° and 45°.
Table 2 lists the rotational
angle during constant-velocity rotation and accelerating rotation and
lists Re defined for constant-velocity rotation as
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Constant-velocity rotation
We measured the force in the -Z direction, i.e. thrust T,
and the moment around the Z axis, i.e. torque Q, after the
wing had completed 30 rotations. The measured T and Q were
considered to be equal to the fluid-dynamic thrust and torque of the wing
because the forces acting on the joint cylinder were much smaller than those
acting on the wing. CL and CD were
determined by non-dimensionalizing the measured fluid-dynamic thrust and
torque as follows (Ellington,
1984):
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Accelerating rotation
Thrust T and torque Q were measured for
0t
T0r in an aqueous solution of glycerine. As in
the case of constant-velocity rotation, we neglected the forces acting on the
joint cylinder and assumed that the measured thrust T is equal to the
fluid-dynamic thrust. The measured torque is the sum of the fluid-dynamic
torque acting on both the wing and the joint cylinder, as well as the inertial
torque acting on the wing, on the joint cylinder and on the load cell. Because
the fluid-dynamic torque acting on the joint cylinder is much smaller than
that acting on the wing, the former torque can be neglected. We measured the
torque in air to estimate the inertial torque acting on the wing, on the joint
cylinder and on the load cell. The measured torque in air,
Qc, was approximately equal to the inertial torque acting
on the wing, on the joint cylinder and on the load cell because their density
is much larger than the density of air and, hence, the fluid-dynamic torque in
air was much smaller than the inertial torque acting on these three components
(wing, joint cylinder and load cell). Therefore, the fluid-dynamic torque
acting on the wing was obtained from QQc.
CL and CD were determined by
non-dimensionalizing the measured fluid-dynamic thrust and torque as follows
(Ellington, 1984):
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Results |
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Fig. 5 shows
CL and CD plotted versus
for constant-velocity translation and constant-velocity rotation. For
both motions, CL and CD of the
bristled wing were larger than those of the solid wing. The differences in
CL and CD between constant-velocity
rotation and constant-velocity translation for the bristled wing are larger
than those for the solid wing. Hence, the flow around the bristled wing should
exhibit large differences between constant-velocity rotation and
constant-velocity translation than the solid wing.
Fig. 6 shows how lift and drag
change with distance travelled for the solid wing during accelerating
translation (
=45 ° and T0t=4 s). The
lift-to-drag ratio was between 0.8 and 1. During this unsteady translation,
the fluid-dynamic forces acting on the bristled wing were smaller than those
acting on the solid wing. Fig.
7A shows how CL and CD
vary with distance travelled for accelerating translation when
=45
° and T0t=4 s. When
t=T0t, the non-dimensional displacement
X/c was approximately 0.8. The figure shows that neither
CL nor CD reached a constant value
when t=T0t and that the forward velocity
reached its terminal value
V0. Furthermore, CL and
CD were larger for t
T0t
than at t=T0t. Fluid-dynamic forces due to added
mass (Ellington, 1984
), which
act on the wings when t<T0t, are negligible.
The larger values of CL and CD for
t
T0t might be explained in two ways. First,
Re defined by instantaneous forward velocity
was smaller for
t<T0t than at
t=T0t. For Re<103,
CL and CD, which are
non-dimensionalized by
2,
increase as Re decreases. For Re<1,
CL and CD are proportional to
1/Re and ReCL and ReCD are
independent of Re (e.g. Hoerner,
1965
). Second, wing motion accelerated while
t
T0t, and this acceleration caused an
increase in CL and CD. This increase
is expected to be caused by `delayed stall'
(Dickinson et al., 1999
).
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To test the first hypothesis, we looked at how ReCL and
ReCD changed over time for accelerating translation when
=45 ° and T0t=4 s
(Fig. 7B). These changes over
time were smaller than those of CL and
CD shown in Fig.
7A. However, ReCL and ReCD
were larger for t<T0t than at
t=T0t. Therefore, the second hypothesis is also
needed to explain the differences in CL and
CD for t<T0t than at
t=T0t. This might apply not just for
T0t=4 s but also for T0t=10 s.
Fig. 8 shows the changes
over time of the ratios of thrust T and torque Q acting on
the bristled wing to those acting on the solid wing for accelerating rotation
for =20 ° and 45 °. These ratios were less than 1, except for
the ratio at
=20 °, when the fluid-dynamic forces acting on the
bristled wing were larger than those acting on the solid wing.
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Fig. 9A shows changes over
time of CL and CD for accelerating
rotation when =45 °. The coefficients CL and
CD of the solid wing were smaller than those of the
bristled wing. The CL and CD for
t<T0r were larger than those at
t=T0r. The fluid-dynamic forces due to added mass
(Ellington, 1984
) are
negligible while t<T0r. The changes over time
of ReCL and ReCD in
Fig. 9B show the differences
in CL and CD for
t<T0r and t=T0r.
Just as during accelerating translation, ReCL and
ReCD are larger for t<T0r,
and again this difference is due to delayed stall.
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Discussion |
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Fig. 10A shows the
relationship between mass m and wing-beat frequency f for a
thrips (Tanaka, 1995) and a
variety of other insects (Azuma,
1992
). The wing-beat frequency f of the thrips is 200 Hz,
which is relatively low for its body mass
(m
6x10-8 kg) compared with larger insects, but
similar to that of other small insects, such as Bemisia tabaci,
Aleurothrixus floccosus, Aphis gossypii and Acyrthosiphon kondoi
(numbered 1-4 in Fig. 10A, respectively). Fig. 10B shows
the values of
mg/Stot(xwf)2
for the insects listed in Fig.
10A, where g is the acceleration due to gravity,
Stot is the total wing surface area of four wings of an
insect, and xw is the length of the forewing. The
fluid-dynamic force generated by a wing is proportional to
Stot(xwf)2, where
xwf is proportional to the mean velocity of the
flow around the wing. Therefore, the parameter
mg/Stot(xwf)2
reflects the coefficient of vertical fluid-dynamic force generated by an
insect. For the thrips
mg/Stot(xwf)2
25;
this is larger than that for Bemisia tabaci, Aleurothrixus floccosus,
Aphis gossypii and Acyrthosiphon kondoi, which have membranous
wings. The larger value of
mg/Stot(xwf)2
25
for thrips can be explained by the larger values of CL and
CD for a bristled model wing compared with the
coefficients for the solid model wing.
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The resultant force of the lift and drag generated by the thrips was approximately 5x107 N at any flapping angle with the following assumptions: (i) the thrips has four wings whose size is shown in Table 1; (ii) the flapping motion is the same as defined for the accelerating rotation at f=200 Hz; and (iii) the geometrical angle of attack is 45°, and changes over time in the lift and drag coefficients are given by those of the bristled wing in Fig. 9A. The estimated value of the vector sum of lift and drag is close to the gravitational force acting on the thrips (6x107 N). However, to understand more fully the flight of the thrips, we need a more precise estimate of the fluid-dynamic forces generated by their wings, based on more accurate data on wing morphology and kinematics, on the variation in angle of attack (feathering angle), and lift and drag coefficients measured over several consecutive wing beats.
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Acknowledgments |
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References |
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