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Wing Rotation and the Aerodynamic Basis of Insect Flight

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Abstract

The enhanced aerodynamic performance of insects results from an interaction of three distinct yet interactive mechanisms: delayed stall, rotational circulation, and wake capture. Delayed stall functions during the translational portions of the stroke, when the wings sweep through the air with a large angle of attack. In contrast, rotational circulation and wake capture generate aerodynamic forces during stroke reversals, when the wings rapidly rotate and change direction. In addition to contributing to the lift required to keep an insect aloft, these two rotational mechanisms provide a potent means by which the animal can modulate the direction and magnitude of flight forces during steering maneuvers. A comprehensive theory incorporating both translational and rotational mechanisms may explain the diverse patterns of wing motion displayed by different species of insects.
DOI: 10.1126/science.284.5422.1954
, 1954 (1999);284 Science
, et al.Michael H. Dickinson
Wing Rotation and the Aerodynamic Basis of Insect Flight
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Wing Rotation and the
Aerodynamic Basis of
Insect Flight
Michael H. Dickinson,
1
* Fritz-Olaf Lehmann,
2
Sanjay P. Sane
1
The enhanced aerodynamic performance of insects results from an interaction
of three distinct yet interactive mechanisms: delayed stall, rotational circula-
tion, and wake capture. Delayed stall functions during the translational portions
of the stroke, when the wings sweep through the air with a large angle of attack.
In contrast, rotational circulation and wake capture generate aerodynamic
forces during stroke reversals, when the wings rapidly rotate and change
direction. In addition to contributing to the lift required to keep an insect aloft,
these two rotational mechanisms provide a potent means by which the animal
can modulate the direction and magnitude of flight forces during steering
maneuvers. A comprehensive theory incorporating both translational and ro-
tational mechanisms may explain the diverse patterns of wing motion displayed
by different species of insects.
Insects were the first animals to evolve active
flight and remain unsurpassed in many as-
pects of aerodynamic performance and ma-
neuverability. Among insects, we find ani-
mals capable of taking off backwards, flying
sideways, and landing upside down (1).
While such complex aerial feats involve
many physiological and anatomical special-
izations that are poorly understood, perhaps
the greatest puzzle is how flapping wings can
generate enough force to keep an insect in the
air. Conventional aerodynamic theory is
based on rigid wings moving at constant ve-
locity. When insect wings are placed in a
wind tunnel and tested over the range of air
velocities that they encounter when flapped
by the animal, the measured forces are sub-
stantially smaller than those required for ac-
tive flight (2). Thus, something about the
complexity of the flapping motion increases
the lift produced by a wing above and beyond
that which it could generate at constant ve-
locity or that can be predicted by standard
aerodynamic theory.
The failure of conventional steady-state
theory has prompted the search for unsteady
mechanisms that might explain the high forc-
es produced by flapping wings (3, 4). The
wingstroke of an insect is typically divided
into four kinematic portions: two translation-
al phases (upstroke and downstroke), when
the wings sweep through the air with a high
angle of attack, and two rotational phases
(pronation and supination), when the wings
rapidly rotate and reverse direction. The un-
steady mechanisms that have been proposed
to explain the elevated performance of insect
wings typically emphasize either the transla-
tional or rotational phases of wing motion (3,
5– 8). The first unsteady effect to be identi-
fied was a rotational mechanism termed the
“clap and fling,” a close apposition of the two
wings preceding pronation that hastens the
development of circulation during the down-
stroke (9). Although the clap and fling may
be important, especially in small species, it is
not used by all insects (10) and thus cannot
represent a general solution to the enigma of
force production. Recent studies using real
and dynamically scaled models of hawk
moths suggest that a translational mecha-
nism, termed “delayed stall,” might explain
how insect wings generate such large forces
(11). At high angles of attack, a flow structure
forms on the leading edge of a wing that can
transiently generate circulatory forces in excess
of those supported under steady-state condi-
tions (7). On flapping wings, this leading edge
vortex is stabilized by the presence of axial
flow, thereby augmenting lift throughout the
downstroke (5, 11). Several additional unsteady
mechanisms have been proposed (6), mostly
based on wing rotation, but recent studies have
found little or no evidence for their use by
insects (11). Despite this lack of evidence, it is
unlikely that insects rely solely on translational
mechanisms to fly. Whereas delayed stall might
account for enough lift to keep an insect aloft, it
cannot easily explain how many insects can
generate aerodynamic forces that exceed twice
their body weight while carrying loads (10).
One persistent obstacle in the search for
additional unsteady mechanisms is the diffi-
culty in directly measuring the forces pro-
duced by a flapping insect (12). In order to
further explore the aerodynamic basis of in-
sect flight, we built a dynamically scaled
model of the fruit fly, Drosophila melano-
gaster, equipped with sensors at the base of
one wing capable of directly measuring the
time course of aerodynamic forces (Fig. 1A).
The forces generated by a pattern of wing
motion based on Drosophila kinematics (13)
are shown in Fig. 1, C through G. Both the
magnitude and the orientation of the mean
force coefficient (C
L
1.39, inclined at 10.3°
with respect to vertical) closely match values
measured on tethered flies (14, 15). The in-
stantaneous forces are roughly normal to the
surface of the wing at all times, indicating
that at this Reynolds number, pressure forces
dominate the shear viscous forces acting par-
allel to the wing (Fig. 1C). The records show
a transient peak in aerodynamic force at the
start and end of each upstroke and down-
stroke (Fig. 1, D and E). The timing of these
force transients relative to stroke reversal
suggests that they result from some undeter-
mined rotational effect and not from a trans-
lational mechanism such as delayed stall.
Translational forces. In order to test
more rigorously whether rotational mecha-
nisms were responsible for the two force
peaks straddling stroke reversal, we estimat-
ed the forces that are generated solely by
translation (Fig. 2). We calculated mean
translational force coefficients (C
L
and C
D
)
from data obtained by moving the wing
through a 180° arc at constant velocity and
fixed angle of attack (14). To obtain a repre-
sentative mean value, we averaged the mea-
sured force coefficients over the interval in-
dicated by the dotted lines in Fig. 2A. The
values of the resulting translational lift and
drag coefficients are consistent with similar
measurements made on a two-dimensional
(2D) model wing at an identical Reynolds
number (7). The force coefficients of the 3D
wing are slightly smaller than the maximum
transient values generated by a 2D wing, but
larger than the 2D steady-state values (Fig.
2D). These results confirm the important con-
tribution of delayed stall in lift production
during the translational portion of the wing
stroke. The observation that the 3D force
coefficients are lower than the 2D peak tran-
sient values, but higher than the 2D steady-
state values, is entirely consistent with the
flow patterns generated during force produc-
tion. Whereas wing motion in 2D gives rise to
an alternating pattern of unstable vortices
termed a “von Ka´rma´n street” (7), the leading
edge vortex generated by the 3D model fly
wing was stable throughout motion (16). The
stability of the flow structure is manifest as
constant force generation during translation
(Fig. 2, A and B), in marked contrast to the
2D case (7 ). Thus, as has been previously
suggested, axial flow along the length of the
wing appears to stabilize the leading edge
vortex throughout translation (5, 11). Where-
1
Department of Integrative Biology, University of Cal-
ifornia, Berkeley, CA 94720, USA.
2
Theodor-Boveri-
Institute, Department of Behavioral Physiology and
Sociobiological Zoology, University of Wu¨rzburg am
Hubland, 97074 Wu¨rzburg, Germany.
*To whom correspondence should be addressed. E-
mail: flymanmd@socrates.berkeley.edu
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as axial flow stabilizes force production at a
level greater than that possible under steady-
state conditions in 2D, the loss of energy
from the vortex core probably limits force
generation below the maximum 2D level.
The stability of the force coefficients fol-
lowing an impulsive start justifies the attempt
to reconstruct a “quasi-steady” estimate of
translational forces based on stroke kinemat-
ics. The results of such predictions for Dro-
sophila kinematics are shown in Fig. 1, D and
E. The calculations do not account for delays
in the development of force via the Wagner
effect (17) and probably represent a slight
overestimate of the translational component.
Although the translational values closely
match the magnitude of the measured force
near the middle of each half-stroke, they do
not accurately predict the forces during stroke
reversal. One potential artifact in the mea-
surements of aerodynamic forces during
stroke reversal is the contamination by iner-
tial forces due to the linear and angular ac-
celeration of the wing. However, a series of
lift (N) drag (N)
-0.25
0.00
0.25
0.50
0.75
1.00
rotational lift (N)
-0.25
0.00
0.25
0.50
0.75
0.0
0.2
0.3
-0.1
cycles
0
12
-100
-50
0
50
100
-0.25
0
0.25
down up down up
C
D
E
F
A
trans. velocity
(m s
-1
)
ang. velocity (degrees s
–1
)
G
0.1
B
wing
chord
force
vector
motor
assembly
force
sensor
coaxial
drive shaft
mineral
oil
model
wing
500
mN
downstroke
upstroke
model
wing
force
sensor
gearbox
total
force
translational
component
C
L
=1.39
Fig. 1. (A) Robotic fly apparatus. The motion of the two wings
is driven by an assembly of six computer-controlled stepper
motors attached to the wing gearbox via timing belts and
coaxial drive shafts. Each wing was capable of rotational
motion about three axes. The wing was immersed ina1mby
1 m by 2 m tank of mineral oil (density 0.88 10
3
kg m
–3
;
kinematic viscosity 115 cSt). The geometry of the tank was
designed to minimize potential wall effects (25). The viscosity
of the oil, the length of the wing, and the flapping frequency of the model
were chosen to match the Reynolds number (Re) typical of Drosophila (Re
136). The 25-cm-long model wings were constructed from Plexiglas (3.2 mm
thick) cut according to the planiform of a Drosophila wing (26). The base of
one wing was equipped with a 2D force transducer consisting of two sets of
strain gauges wired in full-bridge configuration (27). (B) Close-up view
of robotic fly. In Figs. 1, 3, and 5, measured forces are plotted as vectors
superimposed over wing chords inclined at the instantaneous angle of
attack. The vectors and wing chords are drawn as if viewed from a line of
sight that runs axially along the length of the wing. (C) Diagram of wing
motion indicating magnitude and orientation of force vectors gener-
ated throughout the stroke by a kinematic pattern based on Drosoph-
ila (stroke amplitude 160°; frequency 145 mHz; angle of attack at
midstroke 20° upstroke, 40° downstroke). Black lines indicate the
instantaneous position of the wing at 25 temporally equidistant
points during each half-stroke. Small circles mark the leading edge.
Time moves right to left during downstroke, left to right during
upstroke. Red vectors indicate instantaneous flight forces. The large
black vector at the right indicates the orientation of the mean force
coefficient. (D and E) The time history of lift and drag forces. The
measured forces are plotted in red, and forces predicted from trans-
lation force coefficients are plotted in blue (see text and Fig. 2). Data
are plotted over two stroke cycles, with downstroke indicated by gray
background. (F) Time course of rotational lift, defined as the differ-
ence between measured and estimated translational values of lift. (G)
Translational (green) and rotational (purple) velocities of the wing.
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control experiments indicated that the forces
generated during stroke reversal could not be
explained by either translational or rotational
inertia (18). To provide a rough time course
of rotational effects we subtracted the trans-
lational prediction of lift from the measured
value (“rotational lift,” Fig. 1F). The subtrac-
tion reveals two clear force peaks bracketing
each stroke reversal. For the Drosophila ki-
nematics shown in Fig. 1, rotational effects
contribute roughly 35% of the total lift pro-
duction throughout the stroke—a high value
considering the brief duration over which
they act.
Rotational circulation. The presence of
two rotational force peaks separated in time
suggests that they might represent distinct
aerodynamic mechanisms. One possible ex-
planation for the force peak at the end of each
half-stroke is that the wing’s own rotation
serves as a source of circulation to generate
an upward force (6, 19). This mechanism,
rotational circulation, is akin to the Magnus
effect, which makes a spinning baseball
curve from its path toward the plate (20). The
surface of a rotating ball pulls air within the
boundary layer as it spins, thus serving as a
source of circulation. As the ball moves
through the air, this circulation will increase
the total flow velocity on one side and de-
crease it on the other. If the velocity is higher
on the top, as in the case of backspin, the ball
is pulled upward by the lower pressure. In the
case of topspin, the net velocity is higher
below and the ball is pulled downward. If a
flapping wing generates lift via a mechanism
similar to the Magnus effect, then the orien-
tation of the resulting force should also de-
pend critically on the direction of wing rota-
tion. To adopt the proper angle of attack for
each translational phase, the wing must pro-
nate before the downstroke and supinate be-
fore the upstroke (see wing sections in Figs.
1C and 3E). If the wing flips early, before
reversing direction, then the leading edge
rotates backward relative to translation
(“backspin”) and should produce an upward
component of lift. If the wing flips late, after
reversing direction, then the leading edge
rotates forward relative to translation (“top-
spin”) and should create a downward force. If
the process of rotation spans the end of one
half-stroke to the beginning of the next, then
the wing will generate first an upward force
and then, following stroke reversal, a down-
ward force. These predictions were verified
by systematically changing the phase be-
tween wing translation and wing rotation in a
Fig. 2. Measurement of translational force coefficients. In each trial, we rapidly accelerated the
wing from rest to a constant tip velocity of 0.25 m s
–1
. The angle of attack was increased between
trials in 4.5° increments. (A and B) The time history of lift (C
L
) and drag (C
D
) coefficients. Data are
shown for seven different angles of attack, as indicated by the labels to the right of the traces in
(A). Each trace begins with a large inertial transient caused by the rapid acceleration of the wing
at the start of translation. After the inertial forces decay, the force trajectories are stable
throughout translation. The dotted lines indicate the interval over which the values were averaged
to calculate the mean values that were used to construct the relationships shown in (C) and (D).
(C) Average translational force coefficients as a function of angle of attack. The two sets of data
are well fit by simple harmonic relationships: C
L
0.225 1.58sin(2.13 7.20), C
D
1.92
1.55cos(2.04 9.82), where ␣⫽angle of attack. These formulas are used throughout the paper
to estimate the translation component of flight force. (D) Polar representation of translational
force coefficients and comparison with 2D measurements at a comparable Reynolds number (7).
The influence of induced drag on the 3D wing is manifest by the small right shift of the curve
relative to the 2D data.
Fig. 3 (opposite). Effects of rotational timing on lift generated using
simplified stroke kinematics. In (A) through (C), the red trace indicates
measured lift, and the blue trace represents the estimated translational
component. Rotational circulation is the difference between the mea-
sured and predicted values. White dots indicate lift transients attributed
to wake capture; black dots indicate transients attributed to rotational
circulation. (A) Wing rotation precedes stroke reversal by 8% of the
wingbeat cycle. (B) Wing rotation occurs symmetrically with respect to
stroke reversal. (C) Wing rotation is delayed with respect to stroke
reversal by 8% of the stroke cycle. (D) Translational (green) and rota-
tional (purple) velocities for the experiments plotted in (A) through (C).
Only the timing of wing rotation varied among all three cases. (E)
Instantaneous force vectors superimposed on a diagram of wing motion
for the three kinematic patterns (stroke amplitude 160°, frequency
145 mHz, angle of attack at midstroke 40° for both upstroke and
downstroke). Small differences (4.5°) in upstroke and downstroke
angles due to inaccuracies in wing alignment at the start of each trial
result in slightly different force trajectories during upstroke and down-
stroke. The black vector to the right of each set of traces indicates the
magnitude and orientation of the mean force coefficient. (F) Measured
values of rotational circulation are plotted as a function of the position
of the rotational axis. The data were calculated using the total rotational
force generated by the “advanced” kinematic pattern, close to the point
of peak force generation (translational velocity at wing’s center of area
0.15 m s
–1
, angular velocity 74 degrees s
–1
). Each point represents a
separate experiment in which the rotational axis of the wing was set at
the value indicated by the abscissa. The straight line plots prediction
based on thin airfoil theory (6, 20):
r
⫽␲c
2
(3/4 xˆ
0
), where
r
is
total rotational circulation, is the instantaneous angular velocity of the
wing, c is chord length, and xˆ
0
is the normalized position of the rotational
axis. (G) Schematic representation of the proposed contribution of
rotational circulation and wake capture. In the top three panels, mea-
sured values of rotational circulation (black lines) for the three
kinematics conditions (advanced, symmetrical, and delayed rotation)
are superimposed with functions drawn by eye to represent the
hypothesized contribution of rotational circulation (red) and wake
capture (blue). As described in the text, both the timing and polarity
of rotational circulation depend on the phase of wing rotation. In
contrast, rotation phase affects the polarity and magnitude, but not
the timing of wake capture.
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lift (N)
-100
0
100
ang. velocity
(degrees s
–1
)
0
0.25
0.50
0
0.2
0.4
rotational lift (N)
cycles
012
lift (N)rotational lift (N)
0
0.25
0.50
0
0.2
-0.2
trans. velocity
(m s
-1
)
lift (N)rotational lift (N)
-0.25
0
0.25
-0.25
0
0.25
0
-0.3
A
B
C
D
down up down up
-0.1
0
0.2
-0.2
symmetrical
-0.3
0.1
0
delayed
wake
capture
rotational
circulation
0
0.4
rotational lift
(N)
advanced
E
G
0
cycles
1
down up
position of rotational axis (x
o
)
0.5 0.75
-0.005
0
0.005
0.010
0.015
F
delayed symmetrical advanced
total lift
translational
component
leading
edge
trailing
edge
0.25
rotational circulation (
r
)
(m
2
s
-1
)
advanced
500 mN
downstroke
upstroke
C
L
=1.74
symmetrical
downstroke
upstroke
C
L
=1.67
delayed
downstroke
upstroke
C
L
=1.01
rotational lift
(N)
rotational lift
(N)
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set of simplified wing kinematics (21) (see
peaks labeled with black dots in Fig. 3, A
through C). An advance in rotation relative to
translation (Fig. 3, A and G) results in a
positive lift peak at the end of each half-
stroke, whereas a delay in rotation results in
negative lift at the beginning of each half-
stroke (Fig. 3, C and G). As predicted, sym-
metrical rotation causes a positive peak be-
fore and a negative peak after stroke reversal
(Fig. 3, B and G). Thus, by properly adjusting
the timing of wing rotation, an insect can
generate lift via a rotational mechanism in
excess of that produced by delayed stall.
The physics of rotating wings and base-
balls differ in one important way, however:
baseballs are round and insect wings are flat.
This has two important consequences for the
forces generated by rotational circulation.
First, because pressure forces act at all times
perpendicular to an object’s surface, the ro-
tational force on a wing will act normal to its
chord, not perpendicular to the direction of
motion as is the case with a spinning baseball
(4). This influence is easily seen in the plots
of the instantaneous force vector superim-
posed over the wing chord (Figs. 1C and 3E).
As the angle of attack exceeds 90°, the force
vector dips below the stroke plane and the
sign of lift changes from positive to negative.
Second, viscous forces within the air will
make the flow above and below a flat wing
fuse smoothly at the sharp trailing edge. This
constraint, termed the Kutta condition, fixes a
fluid stagnation point at the trailing edge of
the wing. The functional consequence of the
Kutta condition is that the amount of circu-
lation and thus force produced by a rotating
wing will depend critically upon the position
of the rotational axis (6, 19). We confirmed
this prediction by measuring total rotational
circulation in a series of experiments in
which we systematically varied the axis of
rotation by changing the attachment point of
the wing on the flapping apparatus (Fig. 3F).
As predicted, rotational circulation decays as
the axis of rotation is moved toward the
trailing edge, changing sign at approximately
three-fourths of a chord length from the lead-
ing edge of the wing. This result provides
further evidence that force peaks generated
during stroke reversal are due to rotational
circulation.
Wake capture. Although rotational circu-
lation can explain one of the stroke reversal
forces, it cannot explain the large positive
transient that develops immediately after the
wing changes direction at the start of each
half stroke (white dots, Fig. 3, A through C).
These peaks are distinct from the rotational
circulation peaks in that their timing is inde-
pendent of the phase of wing rotation. One
possible explanation for these forces is the
mechanism of wake capture, in which the
wing benefits from the shed vorticity of the
previous stroke. As has been demonstrated on
2D models of flapping insect wings, the flow
generated by one stroke can increase the ef-
fective fluid velocity at the start of the next
stroke and thereby increase force production
above that which could be explained by trans-
lation alone (8). Because a significant portion
of the fluid velocity that a wing encounters at
the start of each stroke is due to the lingering
wake, one clear prediction of the wake cap-
ture hypothesis is that a wing should continue
to generate force at the end of a half-stroke
even if it came to a complete stop. We tested
this prediction by examining the time course
of forces after halting wing motion at the end
of the upstroke. As shown in Fig. 4, the wing
generates force for several hundred millisec-
onds following the end of translation. The
time course of this posttranslational force is
similar to that of the force transients at the
start of each half-stroke during continuous
flapping. The flow visualizations made im-
mediately before stroke reversal reveal peak-
induced velocities that are comparable to the
maximum translational velocity of the wing,
and of sufficient magnitude to generate the
observed forces after the wing changes direc-
tion (Fig. 4B).
Whereas the timing of the wake capture
force is constant, its magnitude and direction
depend on the phase relationship between
rotation and translation (Fig. 4, A and B). If
rotation precedes stroke reversal, the wing
intercepts its own wake so as to generate
positive lift. If rotation is delayed until the
start of the downstroke, then the flow intercepts
-0.4
0
0.4
0.8
drag
lift
advanced
A
0
1
-100
0
100
-0.25
0
0.25
down up stop
cycles
symmetrical
delayed
0
0.05
0.10
0.15
0.20
B
advanced symmetrical delayed
velocity (m s
-1
)
8 cm
ang. velocity
(degrees s
–1
)
trans. velocity
(m s
-1
)
force (N)
-0.4
0
0.4
0.8
-0.4
0
0.4
0.8
force (N) force (N)
Fig. 4. Evidence for wake capture at the end of each half-stroke. (A) Lift (red) and drag (blue) are
plotted for one continuous cycle preceding a complete stop at the end of the upstroke. When wing
rotation is advanced, the wing develops lift and drag after translation has ceased. When wing
rotation is symmetrical and stops in a vertical position, the posttranslation force is pure drag with
no lift component. When rotation is delayed, the wing generates negative lift at the end of
translation. The rising phase of the posttranslational transients is similar to that of the force
transients at the start of each half-stroke during continuous flapping (white dots). (B) Flows
through the midchord of the wing (white bar) immediately before a complete stop. Arrow lengths
and direction indicate magnitude and orientation of local fluid velocity. Fluid velocity is also
indicated by pseudocolor background. Although the gross orientation of the flow is similar in all
three cases, the flow velocities are greater when rotation is advanced, consistent with the
occurrence of stronger rotational circulation generated and subsequently shed during the upstroke.
The flow images were generated by particle image velocimetry (16).
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the wing at an angle that produces negative lift.
With symmetrical rotation, the wing has a 90°
angle of attack at the midpoint of stroke rever-
sal and produces no lift (but high drag) if
stopped at the end of the upstroke. Figure 4B
also shows that the peak velocities in the near
wake are much greater when rotation is ad-
vanced relative to stroke reversal. This result is
expected because the rotational circulation gen-
erated at the end of the previous half-stroke is
greater under these conditions, resulting in
stronger vorticity shed within the wake. Collec-
tively, the combined effect of wake strength
and the starting angle of attack explains why,
during continuous flapping, the lift peaks
caused by wake capture are large and positive if
rotation is advanced, small and positive if rota-
tional is symmetrical, and small and negative if
rotation is delayed (Fig. 3, A through C, and G).
The increased magnitude of the wake cap-
ture force following a prominent rotational
circulation effect underscores a remarkable
feature of the wake capture mechanism: the
animal’s ability to extract energy from its
own wake. In general, wakes are a manifes-
tation of the energy lost to the external me-
dium by a moving object. By rapidly chang-
ing direction at the end of each translational
phase, an insect wing can recover energy
from the air that was lost during the previous
stroke, greatly improving the overall efficien-
cy of force production.
Rotational forces and flight control.
Any general theory of insect flight aerody-
namics needs to explain not only how ani-
mals produce enough lift to stay in the air, but
also how they can modulate flight forces
during steering maneuvers. The results we
describe indicate that rotational circulation
and wake capture, though distinct phenome-
na, nevertheless interact synergistically in a
way that makes them useful mechanisms for
controlling aerodynamic forces. An advance
in wing rotation not only generates circulato-
ry forces at the end of each stroke, it also
increases the strength of the wake and en-
sures that the wing has the proper orientation
to use the shed vorticity for generating posi-
tive lift at the start of the next stroke. As a
consequence of this synergy, flight force is
exquisitely sensitive to the phase of wing
rotation. A phase advance of 8% (from the
“delayed” to “symmetrical” conditions of
Fig. 3) increases the mean lift coefficient by
67% (Fig. 3F). In contrast, the mean lift coef-
ficient predicted from translational mechanisms
does not change with the timing of wing rota-
tion. This sensitivity of the forces to rotational
timing is consistent with the kinematic changes
exhibited by Drosophila during steering be-
haviors. During visually induced maneuvers,
flies advance the timing of supination on the
wing outside of a turn and delay supination
on the wing inside of a turn (22). According
to the above results, this alteration would
help to generate the required change in yaw
torque. By advancing the timing of rotation
on both wings, a fly could generate the sym-
metrical increase in force required for for-
ward or upward acceleration.
A general theory of insect flight. The
ability to explain general phenomena deter-
mines the ultimate utility of any theory in
biology. Are these results based on the kine-
matics of small flies applicable to other in-
sects? Although our impression of insect di-
versity is strongly influenced by animals
large enough to be noticeable, the length of
the average insect is 4 to 5 mm, only slightly
larger than Drosophila (23). Therefore, most
insects operate within a Reynolds number
regime that is similar to that of our robotic
fly. However, the most rigorous test of our
model is in its application to insects using
radically different patterns of wing motion.
The peculiar kinematics of hoverflies, often
considered the most aerodynamically sophis-
ticated of all insects (1), provide one such
test. The stroke amplitude of hoverflies is
quite small and the angular rotation of the
wing is rapid. Using published data (13), we
generated a series of kinematic patterns based
on hoverfly wing motion. The forces gener-
ated by a simple hoverfly pattern consisting
of symmetrical upstroke and downstroke mo-
tion are shown in Fig. 5. The discrepancy
between measured forces and those predicted
from translational force coefficients is espe-
cially large. The wing motion generates two
distinct force peaks at the beginning and end
of each half-stroke that are consistent with
especially potent examples of rotational cir-
culation and wake capture. Although our con-
clusions are limited by the fact that most
hoverflies operate at a higher Reynolds num-
ber (Re 500) than we are currently able to
re-create (Re 140), these animals would
cycles
1
2
-100
-50
0
50
100
-0.2
0
0.2
0.4
0.6
0.8
0
0.1
0.2
0.3
0.4
-0.30
0
0.30
lift (N)rotational lift (N)
trans. velocity
(m s
-1
)
ang. velocity
(degrees s
–1
)
down up up down
A
B
500 mN
-0.1
downstroke
upstroke
total lift
translational
component
C
L
=1.87
Fig. 5. Forces generated by a kinematic pattern based on the wing motion of hoverflies. (A)
Instantaneous force vectors superimposed on a diagram of wing motion (stroke amplitude 69°,
frequency 0.402 mHz, angle of attack at midstroke 50° for both upstroke and downstroke).
(B) Time history of measured rotational (red) and translational estimates (blue) of lift, rotational
lift, and kinematic velocities. Translation (green) and rotational (purple) velocities are shown at
bottom.
R ESEARCH A RTICLES
www.sciencemag.org SCIENCE VOL 284 18 JUNE 1999 1959
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appear to make a more extensive use of ro-
tational mechanisms than do fruit flies. In any
event, this exercise indicates that while a
theory of insect flight based purely on trans-
lation could not explain the complex time
history of forces generated by hoverfly kine-
matics, the hoverfly pattern fits well within a
more general model that incorporates both
translational and rotational mechanisms.
In summary, direct measurements of the
forces produced by flapping wings suggest
that the aerodynamics of insect flight may be
explained by the interaction of three distinct,
yet interactive mechanisms: delayed stall,
rotational circulation, and wake capture.
Whereas delayed stall is a translational mech-
anism, rotational circulation and wake cap-
ture depend explicitly on the pronation and
supination of the wing during stroke reversal.
These findings are significant for several rea-
sons. First, delayed stall is not sufficient
alone to explain the elevated aerodynamic
performance required for active flight in Dro-
sophila. The rotational mechanisms we de-
scribe are necessary components of the basic
unsteady aerodynamic toolkit in this species
(24). Second, a more general theory of insect
aerodynamics that incorporates both transla-
tional and rotational mechanisms shows prom-
ise in explaining the force-generating mecha-
nisms of many species. As suggested by the
forces generated by hoverfly kinematics, differ-
ent insects may emphasize the translational and
rotational mechanisms to different degrees. It
will be of interest in the future to compare the
relative energetic and aerodynamic efficiency
of translationally and rotationally dominated
kinematic patterns. Finally, the regulation of
rotational phase provides insects with one of the
most potent means of controlling flight forces
during steering maneuvers. Thus, an under-
standing of rotational mechanisms provides a
link between the unsteady aerodynamics and
the behavior and neurobiology of flight control.
References and Notes
1. S. Dalton, Borne on the Wind (Reader’s Digest Press,
New York, 1975); T. S. Collett and M. F. Land,
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Insects in Flight (McGraw-Hill, New York, 1974).
2. C. P. Ellington, Philos. Trans. R. Soc. London Ser. B
305, 1 (1984).
3.
㛬㛬㛬㛬 ,inBiological Fluid Dynamics, C. P. Ellington
and T. J. Pedley, Eds. (Company of Biologists, London,
1995), pp. 109–129.
4. M. Dickinson, Am. Zool. 36, 537 (1996).
5. T. Maxworthy, J. Fluid Mech. 93, 47 (1981); Annu.
Rev. Fluid Mech. 13, 329 (1981).
6. C. P. Ellington, Philos. Trans. R. Soc. London Ser. B
305, 79 (1984).
7. M. H. Dickinson and K. G. Go¨tz, J. Exp. Biol. 174,45
(1993).
8. M. H. Dickinson, ibid. 192, 179 (1994).
9. T. Weis-Fogh, ibid. 59, 169 (1973); G. R. Spedding and
T. Maxworthy, J. Fluid Mech. 165, 247 (1986).
10. J. Marden, J. Exp. Biol. 130, 235 (1987).
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London Ser. B 352, 317 (1997); C. P. Ellington, C. Van
den Berg, A. P. Willmott, A. L. R. Thomas, Nature 384,
626 (1996); A. P. Willmott, C. P. Ellington, A. L. R.
Thomas, Philos. Trans. R. Soc. London Ser. B 352, 303
(1997).
12. M. Cloupeau, J. F. Devillers, D. Devezeaux, J. Exp. Biol.
80, 1 (1979); M. H. Dickinson and K. G. Go¨tz, ibid.
199, 2085 (1996); P. J. Wilkin and M. H. Williams,
Physiol. Zool. 66, 1015 (1993).
13. J. M. Zanker, Philos. Trans. R. Soc. London Ser. B 327,
1 (1990); C. P. Ellington, ibid. 305, 41 (1984); A. R.
Ennos, J. Exp. Biol. 142, 49 (1989); F.-O. Lehmann,
thesis, Eberhad-Karls-Universita¨t Tu¨bingen, Germany
(1994).
14. Translational lift coefficients were calculated accord-
ing to the following equation: C
L
2F
L
/(
ˆ
r
2
2
(S)U
2
S),
where ␳⫽fluid density (880 kg m
–3
),
ˆ
r
2
2
(S)isthe
second moment of wing area (0.40), S is surface area
(0.0167 m
2
), F
L
is the measured lift force, and U is
the path velocity of the wing tip. The drag coefficient,
C
D
, was calculated by similar means. The same for-
mulae were used in reverse to predict the transla-
tional component of flight force for a given set of
kinematics.
15. K. G. Go¨tz and U. Wandel, Biol. Cybernetics 51, 135
(1984).
16. To visualize the pattern of flow in the mineral oil, we
forced air through a series of aquarium stones at the
bottom of the tank. After a few large bubbles quickly
rose, the remaining small, slowly rising bubbles gen-
erated a stable seed for both qualitative and quanti-
tative analysis of the flow. To visualize a select
section, we used fiber-optic pipes and pairs of black
shutters to create thin slices of white light. For
particle image velocimetry, images of bubble motion
through a light slice were captured at 30 frames per
second using a 0.5-inch diagonal chip CCD (charge-
coupled device) camera. Flow fields were generated
by finding maxima in 2D spatial cross-correlations of
40 pixel by 40 pixel windows from successive images.
To reduce noise, adjacent windows overlapped by
50%. All software was written using MATLAB, version
5.2 (Mathworks, Inc.).
17. H. Wagner, Z. Angew. Math. Mech. 5, 17 (1925).
18. Our calibration procedure using a dummy inertial
wing automatically eliminates any contribution of
wing mass acceleration and gravity from our mea-
surements. However, the mass of fluid attached to
the wing (“added mass”) is a dynamic quantity that
may change with speed and angle of attack and is
thus difficult to model either physically or mathe-
matically. In order to test whether rotational tran-
sients might be caused by the translational inertia of
added mass, we repeated our experiments using a
modified kinematic pattern in which the translation
of the wing was limited to a flat stroke plane (Fig. 3).
Under these conditions, added mass acceleration
might contribute to an error in the measurement of
drag, but it should not contaminate the measure-
ment of the lift. As indicated in Fig. 3A, the two large
lift transients are still present during stroke reversal
when the wing is flapped using the simplified kine-
matic pattern, indicating that added mass accelera-
tions cannot explain the rotational forces. In order to
test whether our results were contaminated by rota-
tional inertia, we rotated the model wing according
to the same kinematic pattern used in the other
experiments, but in the absence of translation. The
forces generated by this purely rotational motion
were negligible.
19. Y. C. Fung, An Introduction to the Theory of Aeroelas-
ticity (Dover, New York, 1993).
20. R. K. Adair, The Physics of Baseball (Harper and Row,
New York, 1990).
21. To better study rotational effects, we used a simpli-
fied kinematics pattern in which translational motion
was limited to a flat stroke plane and the upstroke
and downstroke angles were equal (18).
22. M. H. Dickinson, F.-O. Lehmann, K. G. Go¨tz, J. Exp.
Biol. 182, 173 (1993).
23. R. M. May, in Diversity of Insect Faunas, L. A. Mound
and N. Waloff, Eds., no. 9 of the Symposia of the
Royal Entomological Society of London Series (Black-
well, New York, 1978), chap. 12, pp. 188 –204.
24. Drosophila are known to use the clap and fling at the
start of the downstroke [K. G. Go¨tz, J. Exp. Biol. 128,
35 (1987)]. Using the model fly, we measured a small
(5 to 10%) increase in the mean lift produced during
each cycle caused by this effect, which though sig-
nificant, is small relative the effects of delayed stall,
rotational circulation, and wake capture.
25. At closest approach, the wing tip came within 22 cm
of the top surface, 18 cm from the side walls, and 160
cm from the bottom of the tank. In order to test that
the forces measured within the enclosed tank did not
deviate from those expected in an infinite volume,
we carefully mapped the change in force production
with distance from the tank boundaries. In three
separate sets of experiments, we moved the robotic
apparatus incrementally toward each boundary and
measured the forces generated by the Drosophila
kinematic pattern shown in Fig. 1. The changes in
mean lift coefficient with distance from the solid-
liquid (side and bottom) and air-liquid (top) interfac-
es were closely approximated by exponential func-
tions (x in meters): side, C
L
1.38 0.59e
–33.1x
; top,
C
L
1.37 1.20e
–25x
; bottom, C
L
1.55e
–21.7x
1.39(1 e
–12.8x
). Thus, the forces generated by the
wing at the center location fell within 1% of asymp-
totic values in all dimensions, indicating that the
experimental conditions well approximate an infinite
volume. It should be noted that in shortening the
distance to the bottom of the tank, force production
passed through a global minimum at a depth of 8 cm.
The augmentation of lift at extremely low altitude is
a manifestation of the ground effect, an interaction
of a downward-directed wake with a solid boundary
[J. M. V. Rayner, Philos. Trans. R. Soc. London Ser. B
334, 119 (1991)].
26. High-speed video films indicate that Drosophila
wings do not twist extensively during flight. Howev-
er, to test for effects of wing flexion, we repeated
experiments using a flexible composite wing consist-
ing of a Plexiglas leading edge and a thin metal foil
blade. The thickness of the foil was chosen to pro-
duce deformations comparable to those observed in
real flies. The use of flexible wings did not signifi-
cantly alter any of the findings, although forces mea-
sured with rigid wings were typically higher than
those measured with flexible wings.
27. The sensor was a miniaturized version of a design used
in a previous 2D study (7). One sensor measured total
force normal to the surface of the wing, while the other
measured the force parallel to the surface in the chord-
wise direction. Preliminary experiments indicated that
lengthwise parallel forces were negligible compared to
the other components and have been ignored. Lift and
drag forces, defined conventionally with respect to wing
motion, were constructed trigonometrically from the
normal and parallel channels. We deliberately designed
the sensor to measure shear deflection and not canti-
lever bending so that measurements would not be
sensitive to the loading distribution on the wing. Forces
measured with calibration weights placed at the base,
tip, trailing edge, and leading edge of the wing differed
by 5%. The final calibration was based on static
loading at the wing’s center of area. During data col-
lection, we used a low-pass four-pole Bessel filter with
a cut-off frequency of 10 Hz, roughly 50 times the
flapping frequency. Spectral analysis indicated that this
filter introduced no appreciable phase lag within the
range of relevant frequencies. During subsequent offline
analysis, we conditioned each signal using an 8-pole
recursive digital filter (Butterworth) with a cut-off of 5
Hz and zero phase delay (implemented in MATLAB,
Mathworks, Inc.). Each trial consisted of a burst of four
continuous wing strokes; four such bursts were aver-
aged for each experimental condition. Force measure-
ments during the first cycle of each burst were slightly
different due to transient effects and have been exclud-
ed from the present analysis. Each experiment was
repeated using an inertial model, consisting of a short
brass cylinder machined to have an equal mass and
center of mass to that of the wing. The data from the
inertial model were subtracted from the raw wing data
to remove the contributions of wing inertia and gravity.
28. Supported by grants from NSF (IBN-9723424), De-
fense Advanced Research Projects Agency, and the
U.S. Office of Naval Research (M.H.D.).
25 January 1999; accepted 7 April 1999
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... However, owing to the inherent limitations of the multi-camera imaging system and laser reflection on the solid surface, three-dimensional flow measurement is significantly difficult in the near-field, leaving the flow field still unclear close to the insect wings and bodies. In the absence of such knowledge about the full flow field, our current understanding about the aerodynamics of flying insects/hummingbirds is primarily depending on local and static aerodynamic mechanisms [8][9][10][11][12][13]. For instance, the local flow structure of the leading edge vortex (LEV) is widely considered as a major mechanism of aerodynamic force generation/augmentation and has been extensively investigated in both experimental and numerical studies [8][9][10][11][14][15][16][17]. ...
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The synthesis of a comprehensive theory of force production in insect flight is hindered in part by the lack of precise knowledge of unsteady forces produced by wings. Data are especially sparse in the intermediate Reynolds number regime (10<Re<1000) appropriate for the flight of small insects. This paper attempts to fill this deficit by quantifying the time-dependence of aerodynamic forces for a simple yet important motion, rapid acceleration from rest to a constant velocity at a fixed angle of attack. The study couples the measurement of lift and drag on a two-dimensional model with simultaneous flow visualization. The results of these experiments are summarized below. 1. At angles of attack below 13.5°, there was virtually no evidence of a delay in the generation of lift, in contrast to similar studies made at higher Reynolds numbers. 2. At angles of attack above 13.5°, impulsive movement resulted in the production of a leading edge vortex that stayed attached to the wing for the first 2 chord lengths of travel, resulting in an 80 % increase in lift compared to the performance measured 5 chord lengths later. It is argued that this increase is due to the process of detached vortex lift, analogous to the method of force production in delta-wing aircraft. 3. As the initial leading edge vortex is shed from the wing, a second vortex of opposite vorticity develops from the trailing edge of the wing, correlating with a decrease in lift production. This pattern of alternating leading and trailing edge vortices generates a von Karman street, which is stable for at least 7.5 chord lengths of travel. 4. Throughout the first 7.5 chords of travel the model wing exhibits a broad lift plateau at angles of attack up to 54°, which is not significantly altered by the addition of wing camber or surface projections. 5. Taken together, these results indicate how the unsteady process of vortex generation at large angles of attack might contribute to the production of aerodynamic forces in insect flight. Because the fly wing typically moves only 2–4 chord lengths each half-stroke, the complex dynamic behavior of impulsively started wing profiles is more appropriate for models of insect flight than are steady-state approximations.
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Tethered flight in a 3-day-old female Drosophila was sustained for 32·2 h with only short interruptions during uptake of sucrose solution. The course-control reactions derived from the difference of the wingbeat amplitudes on either side have been used to simulate the rotatory displacement of the surrounding landmarks during a comparable turn in free flight. Stabilization of a target in the preferred area of the visual field requires continuous visual attention. A rate of about 5 course-correcting manoeuvres per second was maintained throughout the experiment. Drosophila seems to be able to cover long distances in search of a favourable habitat. Flight-specific carbohydrate consumption is equivalent to a metabolic power input per body weight of about 18 W N−1. The tethered fly produces about 40 % of the lift required to sustain hovering flight. The resulting mechanochemical efficiency of about 0·04-0·07 is within the expected order of magnitude for flying insects. Expenditure of reserve substances may account for the difference between the comparatively low power input of about 7 W N−1, derived from carbohydrate uptake in the first hours of flight (Wigglesworth, 1949), and the actual metabolic turnover of about 21 WN−1, derived from oxygen consumption during this period (Laurie-Ahlberg et al. 1985). Weis-Fogh’s ‘clap and fling’, a widespread lift-generating process exploiting the aerodynamic wing interference at the dorsal end of the wingbeat, was in action throughout the flight. However, there were two significant modifications (as first conceived by Ellington, 1980) : (1) during ‘clap’, there is a progress of wing contact from the leading to the trailing edge, which is likely to ‘squeeze’ a thrust-generating jet of air to the rear; (2) during ‘fling’, there is a progress of wing separation in the same direction, which is described as a ‘peel’ resembling the progressive separation of two plastic foils pulled apart against forces of mutual attraction. The wings of the test fly survived about 23 million such peels without damage. Increasing airspeed decreases the intensity of ‘clap and fling’ in Drosophila : results obtained in the wind tunnel show the transition to a ‘near clap and fling’, lacking mutual wing contact.
Article
Drift of the retinal images of the surroundings elicits optomotor responses of flight control in the fruitfly, Drosophila melanogaster, and in the housefly, Musca domestica. The present investigation deals with the responses of tethered flies in still air. The responses were elicited by continuous movement of striped patterns in front of the eyes, and characterized by the magnitude and elevation of the resulting force of flight which is the average of the forces produced during a wingbeat cycle. The force of flight is resolved into the upward directed lift and the forward directed thrust. In either species, pattern movement acts upon the magnitude, but not upon the elevation of the force of flight. The elevation relative to the longitudinal body axis is almost invariably 24° in Drosophila, and 29° in Musca. The lift/thrust ratio in still air is fixed accordingly, and can be changed only by variation of the body angle. Keeping an angle of minimum body drag does not contribute significantly to the efficiency of insect flight at very low Reynolds numbers (Re). Control of the lift/thrust ratio by variation of the body angle is, therefore, less surprising in Drosophila where Re is in the order of 102, than in Musca, where Re is in the order of 103. Control of this ratio without variation of the body angle is actually established in insects flying at even higher Re. Covariance of lift and thrust in the investigated flies is achieved by control of wingbeat amplitude or wingbeat frequency, but not by control of wing pitch or stroke plane. A change in the latter parameters would have deflected the force of flight and is, therefore, inconsistent with the constant elevation found in the present experiments. The results obtained, so far, do not exclude active deflections of the force vector during occasional bouts of aerobatics, or passive deflections of this vector during flight at non-zero airspeed.
Article
1. On the assumption that steady-state aerodynamics applies, simple analytical expressions are derived for the average lift coefficient, Reynolds number, the aerodynamic power, the moment of inertia of the wing mass and the dynamic efficiency in animals which perform normal hovering with horizontally beating wings.2. The majority of hovering animals, including large lamellicorn beetles and sphingid moths, depend mainly on normal aerofoil action. However, in some groups with wing loading less than 10 N m-2 (1 kgf m-2), non-steady aerodynamics must play a major role, namely in very small insects at low Reynolds number, in true hover-flies (Syrphinae), in large dragonflies (Odonata) and in many butterflies (Lepidoptera Rhopalocera).3. The specific aerodynamic power ranges between 1.3 and 4.7 WN-1 (11-40 cal h-1 gf-1) but power output does not vary systematically with size, inter alia because the lift/drag ratio deteriorates at low Reynolds number.4. Comparisons between metabolic rate, aerodynamic power and dynamic efficiency show that the majority of insects require and depend upon an effective elastic system in the thorax which counteracts the bending moments caused by wing inertia.5. The free flight of a very small chalcid wasp Encarsia formosa has been analysed by means of slow-motion films. At this low Reynolds number (10-20), the high lift co-efficient of 2 or 3 is not possible with steady-state aerodynamics and the wasp must depend almost entirely on non-steady flow patterns.6. The wings of Encarsia are moved almost horizontally during hovering, the body being vertical, and there are three unusual phases in the wing stroke: the clap, the fling and the flip. In the clap the wings are brought together at the top of the morphological upstroke. In the fling, which is a pronation at the beginning of the morphological downstroke, the opposed wings are flung open like a book, hinging about their posterior margins. In the flip, which is a supination at the beginning of the morphological upstroke, the wings are rapidly twisted through about 180°.7. The fling is a hitherto undescribed mechanism for creating lift and for setting up the appropriate circulation over the wing in anticipation of the downstroke. In the case of Encarsia the calculated and observed wing velocities at which lift equals body weight are in agreement, and lift is produced almost instantaneously from the beginning of the downstroke and without any Wagner effect. The fling mechanism seems to be involved in the normal flight of butterflies and possibly of Drosophila and other small insects. Dimensional and other considerations show that it could be a useful mechanism in birds and bats during take-off and in emergencies.8. The flip is also believed to be a means of setting up an appropriate circulation around the wing, which has hitherto escaped attention; but its operation is less well understood. It is not confined to Encarsia but operates in other insects, not only at the beginning of the upstroke (supination) but also at the beginning of the downstroke where a flip (pronation) replaces the clap and fling of Encarsia. A study of freely flying hover-flies strongly indicates that the Syrphinae (and Odonata) depend almost entirely upon the flip mechanism when hovering. In the case of these insects a transient circulation is presumed to be set up before the translation of the wing through the air, by the rapid pronation (or supination) which affects the stiff anterior margin before the soft posterior portions of the wing. In the flip mechanism vortices of opposite sense must be shed, and a Wagner effect must be present.9. In some hovering insects the wing twistings occur so rapidly that the speed of propagation of the elastic torsional wave from base to tip plays a significant role and appears to introduce beneficial effects.10. Non-steady periods, particularly flip effects, are present in all flapping animals and they will modify and become superimposed upon the steady-state pattern as described by the mathematical model presented here. However, the accumulated evidence indicates that the majority of hovering animals conform reasonably well with that model.11. Many new types of analysis are indicated in the text and are now open for future theoretical and experimental research.
Article
A camera and strain-gauge probe were used to record the wing beat and instantaneous vertical and horizontal forces on a sphingid moth flying in a wind of 3.36 m s⁻¹. The data were averaged over several wing beats to remove beat-to-beat variation. The moth was producing suffcient upward force to balance its weight of 14.7 mN and approximately sufficient thrust to balance its drag. The film of the wing beat was used to predict the wing inertial and virtual mass forces. The experimental aerodynamic force was obtained by subtracting the inertial force from the recorded force. The film was also used to predict the quasisteady aerodynamic forces due to wing translation and rotation. The vertical experimental aerodynamic and total predicted (quasi-steady plus virtual mass) forces have a similar shape, but the experimental downstroke peak (70 mN) was larger than predicted (47 mN). The horizontal recorded forces are smaller than the vertical forces, and wing inertia is a large component. However, a small aerodynamic thrust in the downstroke and a larger thrust of about 25 mN in the upstroke are both predicted and recorded. The experimental aerodynamic power output was between 21.6 and 30.0 W kg⁻¹ body mass or between 72 and 100 W kg⁻¹ of flight muscle.
Article
Instantaneous values of lift in the locust Schistocerca gregaria, flying in a wind tunnel, were measured by means of a piezo-electric probe. The airflow velocity was adjusted to be equal to that which would have been experienced by the freely flying insect. In order to obtain the true aerodynamic forces, the inertial forces must be subtracted from the gross forces measured. These inertial forces were calculated from the movement of the centre of gravity and from the mass of the different wing sections. The lift curves obtained have a shape similar to the curves deduced by Jensen from measurements on isolated wings in steady flows, but an approximately doubled amplitude. These amplitude differences appear to be caused by the existence of significant unsteady effects.