Download The Aerodynamics of Flapping Animal Flight1

AMER. ZOOL., 24:95-105 (1984)
The Aerodynamics of Flapping Animal Flight1
CHARLES P. ELLINGTON
Department of Zoology, University of Cambridge,
Cambridge, CB2 3EJ, England
SYNOPSIS. Our understanding of the aerodynamics of flapping animal flight is largely
based on the quasi-steady assumption: the instantaneous aerodynamic forces on a flapping
wing are assumed to be identical with those which the wing would experience in steady
motion at the same instantaneous speed and angle of attack. Research up to a decade ago
showed that the assumption was sufficient to explain the flight of the vast majority of
animals, but did not rule out the possibility that alternative aerodynamic mechanisms were
employed instead. Results are presented here for four hovering animals for which the
quasi-steady explanation fails. These animals apparently use lift mechanisms that rely on
vortices shed during the rotational motion of the wing at either end of the wingbeat. The
postulated rotational lift mechanisms should also apply to other hovering animals, even
though the quasi-steady assumption could explain their flight. Measurements of the wing
forces produced by locusts cast doubt on the validity of the quasi-steady assumption for
fast forward flight as well.
problem. A decisive test of the validity can
Studies on the aerodynamics of animal only be accomplished by comparing meaflight have periodically sparked off contro- sured instantaneous wing forces with those
versy and amusement, with rumours still predicted by the theory. A direct meaabounding that bumblebees cannot fly. surement of the cyclic forces from flapping
Arguments have centred around a animal wings has only been achieved
straightforward question which has proved recently, however (Cloupeau et al., 1979;
extremely difficult to answer: can the aero- Buckholtz, 1981), and a comprehensive test
dynamics of flapping animal flight be of the assumption using these difficult
explained by the conventional aerodynam- experimental techniques is still lacking.
ics of airplane wings? By the 1920s aero- Research into the aerodynamics of animal
dynamicists had a fairly complete under- flight has therefore relied on a debatable
standing of how airplane wings work in assumption which could not be verified
steady motion, and biologists were very experimentally.
The validity of the assumption can be
quick in applying this knowledge to flapping flight. To extend the aerodynamics tested theoretically only in a proof-by-conof steady wing motion to a flapping motion, tradiction. The mean forces generated by
they invoked the quasi-steady assumption: the the flapping wings are calculated according
instantaneous aerodynamic forces on a to the quasi-steady assumption. If these
flapping wing were assumed to be those mean forces do not satisfy the net force
which the wing would experience in steady balance of the flying animal, then the
motion au.hesame instantaneous speed and assumption is contradicted and the aeroangle of attack. Thus the dynamics of flap- dynamics must be different from convenping flight were reduced to a succession of tional wings in steady motion. If the mean
forces are sufficient for flight, this only
independent, static conditions.
proves
that the wings may be operating
Whether or not the quasi-steady assumpthe animal might actually
conventionally:
tion is valid for large amplitude, high freuse
some
alternative
aerodynamic mechaquency flapping motions is the crux of the
nism, even though the quasi-steady
assumption could provide a satisfactory
explanation.
However, this rigorous inter1
From the Symposium on Biomechanus presented pretation slides all too easily into a belief
at the Annual Meeting of the American Society of that the flapping wings indeed work like
Zoologists, 27-30 December 1982, at Louisville, Kenconventional wings.
tucky.
INTRODUCTION
95
96
CHARLES P. ELLINGTON
TESTS OF THE QUASI-STEADY
ASSUMPTION
The early quantitative studies on the
aerodynamics of flapping flight were
plagued with bad assumptions, incomplete
and often unreliable data, and have been
reviewed by Weis-Fogh and Jensen (1956).
Although a few of the better studies concluded that the wing forces were not consistent with a quasi-steady mechanism, the
sources of error were too large for an
unqualified acceptance of that conclusion.
In a classic series of papers, Weis-Fogh and
Jensen then presented for the desert locust
Schistocerca gregaria what is still the most
complete study of flapping flight. The
kinematics, or wing motion, in fast forward
flight were measured by Weis-Fogh (1956),
and Jensen (1956) determined the aerodynamic characteristics of the wings in
steady motion. Jensen combined this data
in a quasi-steady analysis, and found that
the calculated mean wing forces agreed to
within a few percent with those required
for flapping flight. This result certainly
provides very persuasive support for the
quasi-steady explanation of fast forward
flight, but it must be remembered that
alternative aerodynamic mechanisms were
neither investigated nor disproved.
We expect the quasi-steady mechanism
to apply to fast flapping flight because the
changes in wing velocity and angle of attack
are spread out over a long flight path. During the downstroke of the locust, which
generates most of the lift, the wings travel
about 20 times their chord (chord =
dimension of the wing perpendicular to its
long axis); thus the velocity and angle of
attack (the angle between a chord and the
direction the wing moves relative to the
oncoming air) vary slowly compared with
the mean flight velocity, which dominates
the flow over the wings. These are conditions which aerodynamicists associate with
low values of the reduced frequency
parameter, and which they expect to be
closely approximated by the quasi-steady
assumption. The reduced frequency represents the ratio of the flapping velocity to
the mean flight velocity of the wings. This
ratio may be expressed in several ways, and
was first introduced to animal flight studies
by Walker (1925).
The reduced frequency increases with
slower flight velocities, where any unsteady
aerodynamic effects due to the flapping
motion should become more important.
Hovering flight provides the extreme case
with a zero flight velocity, large angles of
wing rotation, high accelerations, and wing
travel of only a few chord lengths on each
half-stroke. Deviations from the quasisteady mechanism will therefore be most
pronounced for hovering animals, as
emphasized by Bennett (1966) and WeisFogh (1972, 1973). However, Weis-Fogh
(1973) concluded that the mean forces predicted by the quasi-steady assumption were
sufficient for most hovering animals, and
that they "perform hovering on the basis
of the well-established principles of quasisteady flow." In a few exceptional cases the
maximum lift which the wings could produce in steady motion was not enough to
support the body weight in hovering,
though, and Weis-Fogh proposed two new
aerodynamic mechanisms to account for
the flight of these animals.
In the early 1970s it thus appeared that
the simple quasi-steady mechanism was a
satisfactory explanation for the flapping
flight of the vast majority of animals, from
fast forward flight to hovering. This is a
pleasant conclusion for most biologists since
the quasi-steady interpretation of flight is
relatively easy—as much as any aerodynamics can be easy. The concern that alternative aerodynamic mechanisms were not
actually disproved was relegated to a nagging uncertainty, and there seemed little
incentive to discard a plausible explanation
that appeared to work.
HOVERING FLIGHT
Weis-Fogh's conclusion that the quasisteady assumption is generally valid for
hovering flight is of prime importance: if
true, then the assumption is automatically
verified for lower values of the reduced
frequency parameter, and hence for all
types of forward flight. Weis-Fogh's comparative study of hovering flight was a
pioneering investigation, using a simple
aerodynamic analysis, many approxima-
AERODYNAMICS OF FLAPPING FLIGHT
97
tions and assumptions, and incomplete data
scattered throughout the literature. It
obviously needed to be repeated more
accurately—a task which Weis-Fogh started
me on before his untimely death in 1975.
The project required accurate morphological and kinematic data for a variety of hovering animals, and the insects were chosen
for their diversity. High-speed films at FIG. 1. (A) A side view of the drone-fly Eristahs tenax
5,000 frames per sec were taken of the hovering with a horizontal stroke plane. The curve
insects in free flight, and from several shows the path of the wing tip, and the wing attitude
hundred films of over 40 different species is indicated for a position 70% along the wing length.
there were 11 sequences that showed hov- The location of the wing base is marked by a cross
the body. (B) The hover-fly Episyrphus balteatus
ering flight. The three-dimensional wing on
hovering with an inclined stroke plane.
motion was determined from these
sequences using a computer-linked film
analysis system. Combining the kinematic
data with the detailed morphological mea- in Figure 1A for the drone-fly Eristalis tenax.
surements, the aerodynamic analysis could This group was extensively discussed by
be performed more accurately than Weis- Weis-Fogh (1973), who called the pattern
Fogh was able to do. A new, generalized "normal hovering," and includes the humvortex theory of hovering flight was also mingbirds (Stolpe and Zimmer, 1939;
developed, from which the analyses of Greenewalt, 1960) and the majority of
quasi-steady and alternative mechanisms insects (Weis-Fogh, 1973). The wings gencan be derived as special cases. Some of the erate lift on both the morphological downresults of this study will be presented here, stroke and upstroke: angles of attack are
and details will appear in a series of papers typically about 35° at a position 70% along
(Ellington, 1984).
the wing length for the insects I studied.
We begin with a re-evaluation of the The wings are twisted along their length,
quasi-steady assumption for hovering flight, like propeller blades, with angles of attack
to see whether the maximum lift which the at the wing base some 10-20° greater than
wings could produce in steady motion is at the tip. Although the wings flap through
sufficient to support the body weight. The a large stroke angle (110-180°), the dislift coefficient CL is a useful non-dimensional tance travelled by the wing on each halfmeasure of the lift force, and the maximum stroke is only 3-6 chord lengths. At either
value CLm(lx reached before the wing stalls end of the wingbeat the wings rotate
is about 0.8-1.3 for animal wings (Jensen, through some 110° to set the angle of attack
1956; Vogel, 1967; Pennycuick, 1968, for the next half-stroke. Rotational motion
1971; Tucker and Parrott, 1970; Nachti- at the dorsal end of the wingbeat is called
gall and Kempf, 1971; Nachtigall, 1977, pronation, and at the ventral end it is supi1979a; Withers, 1981). If the mean lift coef- nation; both last 10-20% of the wingbeat
ficient CL required for hovering exceeds period.
the maximum value CLmax measured in
Values of the mean lift coefficient CL
steady flow, then the quasi-steady assump- required for the wing lift on the downtion will be disproved. The results for hov- stroke and upstroke to balance the body
ering animals fall into three groups, weight range from 0.9-1.2 for a crane-fly
depending on the orientation of the plane Tipula paludosa, hover-fly Episyrphus balin which the wings beat—the stroke plane. teatus, the drone-fly Eristalis, a honeybee
Apis mellifera, and two bumblebees Bombus
Horizontal stroke plane
hortorum and B. lucorum. These values are
The most commonly observed type of less than the maximum lift coefficient in
hovering is characterized by an approxi- steady motion, so the quasi-steady mechmately horizontal stroke plane, as shown anism could generate the lift demanded for
98
CHARLES P. ELLINGTON
hovering. Weis-Fogh reached the same dynamics because the mean lift coefficient
conclusion for all of his insects that hov- was greater than the maximum possible
ered with a horizontal stroke plane except under quasi-steady conditions. However,
for the tiny wasp Encarsia formosa, which U. M. Norberg (1976) pointed out that his
needs a mean lift coefficient of 1.6 (Elling- analytical method was invalid for animals
ton, 1975). Two of my insects also require using an inclined stroke plane. Combining
mean lift coefficients which exceed the her estimates for the bat Plecotus auritus
maximum found for steady motion: a lady- with mine, it seems likely thatjCj. on the
bird beetle Coccinella 7-punctata needs 1.7,downstroke is about 3-4. CL for the
and another crane-fly T. obsoleta requires dragonfly Aeschna lies in the same range
1.2, which is 50% more than CLmax mea- (R. A. Norberg, 1975; my estimates), and
sured for T. oleracea by Nachtigall (1977). the pied flycatcher Ficedula hypoleuca
Re-analysis of Weis-Fogh's (1972, 1973) requires about 5-6 (U. M. Norberg, 1975;
data for the hummingbird Amazilia fim- my estimates). It should be noted that the
briatajluviatilis provides another exception morphological and kinematic data were not
to the general rule, giving a mean lift coef- taken from the same specimens of Ficedula
and Aeschna, so those results could be
ficient of 2.3.
considerably in error. My analysis of the
Inclined stroke plane
hover-fly Episyrphus confirms Weis-Fogh's
Small passerine birds (Zimmer, 1943; conclusion, and reveals that CL on the
Brown, 1963; U. M. Norberg, 1975), bats downstroke is between 4 and 5. Thus all
(Eisentraut, 1936; U. M. Norberg, 1970, of the animals hovering with an inclined
1976) and the hover-flies of the subfamily stroke plane must rely on unsteady aeroSyrphinae (Weis-Fogh, 1973) hover with dynamic mechanisms, and the quasi-steady
the stroke plane inclined at an angle of 30- mechanism is insufficient even as a crude
40° to the horizontal (Fig. IB). Dragonflies approximation to the aerodynamics.
(Odonata) also hover in this manner,
although the inclination is about 60° (R. A. Vertical stroke plane
Norberg, 1975). The stroke angle is reducA unique kinematic pattern—an aped for this group, often only 60-70°, and proximately vertical stroke plane—is often
the wings travel less than 3 chord lengths seen during take-off" and hovering on my
on each half-stroke. These animals appear films of the Large Cabbage White butterfly
to generate relatively small forces on the Pieris brassicae. Figure 2 shows several stages
upstroke. The dragonfly Aeschna juncea of the downstroke which initiates a vertical
strongly supinates its wings on the upstroke, take-off from a small platform. The wings
resulting in an angle of attack near zero are clapped together dorsally at the start
(R. A. Norberg, 1975). Excluding the hum- of the downstroke, and then "fling" open
mingbirds, vertebrate fliers are anatomi- (Weis-Fogh, 1973) as in Figure 2A. The
cally unable to rotate their wings to this wings move with the chord perpendicular
extent, and the wings are typically flexed to their motion (Fig. 2B, C) and nearly clap
on the upstroke with individual primaries together at the end of the downstroke (Fig.
rotated to negligible angles of attack. Any 2D). The body pitches nose-up and the
lift on the upstroke of an inclined stroke wings strongly supinate during the
plane would produce a large horizontal upstroke, which is not shown here, prothrust component, and this probably ducing an angle of attack near zero. Thus
explains the absence of upstroke lift. The little force is generated on the upstroke,
mean lift on the downstroke is thus pri- as for the inclined stroke plane.
marily responsible for weight support, and
The sustaining vertical force obviously
large downstroke lift coefficients will be results from the pressure drag on the
necessary to compensate for the dimin- wings during the downstroke. A drag
ished upstroke lift.
mechanism of flight has been suggested
Weis-Fogh (1973) concluded that bats several times for the flight of tiny insects
and hover-flies must rely on unsteady aero- at Reynolds numbers Re below about 100
AERODYNAMICS OF FLAPPING FLIGHT
99
clearly different from the quasi-steady
explanation of wing lift, and it can be
understood from the vortex pattern created by the wing motion. Air is sucked into
the gap between the wings as they fling
open at the beginning of the downstroke,
and this downward air motion is maintained and strengthened during the downstroke (Fig. 2A, B, C). The downward
momentum imparted to that mass of air
carries it below the animal after the end of
the downstroke. Whenever a mass of fluid
(water or air) is given momentum, its
resulting motion must take the form of a
vortex ring of some sort, swirling that mass
through the surrounding fluid. The downstroke of the Cabbage White creates such
a vortex ring, which I have demonstrated
by flow visualization (Ellington, 1980) and
is shown in Figure 2D.
FIG. 2. The downstroke of a vertical take-offby Puns
brassicae. The stroke plane is vertical, and the wing
motion is perpendicular to the chord. The vortex
pattern created by the downstroke is indicated, and
the resulting vortex ring is shown in vertical section
in (D).
AERODYNAMIC MECHANISMS
Weis-Fogh (1973) found only one insect,
Encarsia, for which the quasi-steady mechanism of lift production failed to explained
hovering with a horizontal stroke plane.
From the new results and the re-analysis
(Horridge, 1956; R. A. Norberg, 1972a, b; of his data, three more animals can now be
Bennett, 1973), where thick boundary lay- added to that list: Amazilia, Coccinella and
ers reduced the steady-state lift coefficients T. obsoleta. The studies of R. A. and U. M.
of wings. The drag is mainly due to viscous Norberg plus my results for Episyrphus also
skin friction at low Re, however, and is not confirm that the quasi-steady mechanism
very sensitive to the angle of attack of the is inadequate for all animals hovering with
wings. A drag mechanism which relies on an inclined stroke plane. How do these
a differential velocity of the half-strokes anomalous animals generate the necessary
was therefore proposed (Bennett, 1973), lift? What are the aerodynamic mechasuch that the downstroke velocity and nisms responsible for producing as much
hence drag were greater than the upstroke. as 4 times the maximum lift observed in
The small wasp Encarsia formosa was found steady motion?
to use a lift mechanism for flight, though
(Weis-Fogh, 1973; Lighthill, 1973; Elling- Delayed stall
ton, 1975), and this is also true of the fruitThe only conventional aerodynamic
fly Drosophila melanogaster and the tiny mechanism that can enhance lift is delayed
fringe-winged thysanopteran Thrips phy- stall, which enables a wing to operate for
sapus (Ellington, in preparation). Ironi- a short time at high angles of attack withcally, the drag mechanism does not operate out stalling. If the angle of attack is sudfor small insects as predicted, but rather denly increased above the stall angle for
for a large insect at higher Re (about 2,800). steady motion, a wing can travel several
The pressure drag during the downstroke chord lengths before the separation assois much greater than the skin friction drag ciated with stall begins. During that brief
on the upstroke at high Re, so the need for period lift can exceed the maximum stalled
value by some 40-55% (Francis and Cohen,
a velocity differential is eliminated.
This drag-based mechanism of flight is 1933). The enhanced lift must eventually
100
CHARLES P. ELLINGTON
be lost as the flow separates from the upper
wing surface and the steady-state stall is
reached, but this does not occur for at least
5 chords of travel.
Delayed stall is an ideal candidate for
explaining high lift coefficients when the
wings move but a short distance, as in hovering flight (Ellington, 1980). However,
visual estimation of the effective angles of
attack (measured with respect to the relative air velocity) for my insects indicates
that delayed stall is not employed. The
effective angle of attack ar for the ladybird
Coccinella is about 25° on the downstroke
and upstroke, the same as for the dronefly Eristalis, the honey bee Apis, and the
bumblebees B. hortorum and B. lucorum. It
is therefore unlikely that the excessive lift
coefficient of the ladybird is due to delayed
stall at an increased angle of attack. For
the anomalous crane-fly T. obsoleta ar is 16°
on the downstroke and 27° on the upstroke,
compared with 27° and 37° respectively for
the crane-fly T. paludosa which did not fail
the quasi-steady test. Any lift mechanism
based on the angle of attack would thus
predict a higher CL for the second cranefly, instead of the lower value actually
found. Finally, three sequences for the
hover-fly Episyrphus conclusively rule out
delayed stall. When Episyrphus hovers with
an inclined stroke plane CL on the downstroke is 3-4 times greater than when it
uses a horizontal stroke plane, yet the
effective angles of attack differ by only 6°.
These results show that hovering insects
do not rely on delayed stall to increase lift,
even though it is an ideally suited mechanism. Indeed, the results rule out any
mechanism of lift enhancement which is
based on the angle of attack during the
translational phases of wing motion;
whether this is also true for hovering birds
and bats is unknown at present. If the
translational phases do not provide a satisfactory account of the high lift generated
by some insect wings, we must turn instead
to the rotational phases of the wingbeat.
To understand the new rotational lift
mechanisms possibly employed by hovering animals, a brief digression on the conventional quasi-steady lift mechanism
proves useful.
-c
~o
Fie. 3. The three-dimensional vortex wake created
by a wing suddenly set in motion is shown at the top.
Dashed lines indicate future vortices generated by the
wing. A two-dimensional view is given below.
Circulatory lift
Regardless of the aerodynamic mechanism, any wing lift will impart downward
momentum to the air. The resulting air
motion must correspond to a vortex ring
structure, similar to that produced by the
drag-based mechanism of flight for the
butterfly. Consider a conventional wing
initially at rest with respect to the air, and
the wing is then given a constant forward
velocity (Fig. 3). Air is pushed downwards
in reaction to the wing lift, and this air
motion can be described by a rectangular
vortex "ring" enclosing the air which has
passed over the wing surface. The area of
this ring increases as the wing moves forward, imparting downward momentum to
more air.
The upward lift force which the wing
experiences must correspond to an average air pressure which is greater below the
wing than above. From Bernoulli's principle the pressure of a moving fluid
decreases as the velocity increases, so the
pressure difference across the wing indicates that the average air velocity is higher
above the wing than below. This velocity
difference can be represented by a vortex
"bound" to the wing, as shown in the middle of Figure 3; by adding the circulating
flow of the bound vortex to the linear airflow due to the wing motion, the resultant
flow is faster over the upper wing surface
than the bottom surface. This velocity difference across the wing is measured by the
strength or circulation of the bound vortex,
and the wing lift is directly proportional to
that circulation.
AERODYNAMICS OF FLAPPING FLIGHT
Although there is an average pressure
difference over the wing, at the trailing
edge the pressure must be the same on the
upper and lower surfaces. Otherwise, air
would swirl around the trailing edge, shedding vortices into the wake. This requirement—the Kutta condition—is met when
the air flows smoothly and tangentially from
the trailing edge. For a given speed and
angle of attack, there is but one value of
the circulation which satisfies this condition; the strength of the bound vortex will
adjust automatically by the shedding of
vorticity from the trailing edge until this
unique circulation and hence unique lift is
attained. As the circulation builds up to the
Kutta value at the beginning of motion,
the shed vorticity rolls up into a concentrated "starting" vortex. This forms one
side of the vortex ring in Figure 3, and the
resulting bound vortex comprises another.
"Trailing" or "tip" vortices seal the threedimensional ring structure, and are created by the swirling motion as air moves
around the wing tips from the high pressure region below the wing to the lower
pressure above.
When the wing motion stops there should
be no lift or circulation around the wing.
The circulating flow around the wing then
swirls off the trailing edge, shedding the
bound vortex as a "stopping" vortex. The
net result from the lift of a wing which
travels a given distance and then stops is
therefore the shedding of a vortex ring
into the wake. The aerodynamics of flapping flight can be analyzed, in fact, from
the shed vortex rings instead of a direct
analysis of the wing lift (Ellington, 1978,
1980; Rayner, 1979a, b, c): they are simply
alternate views of the same phenomenon
of lift.
From this description of wing lift, we can
now define more precisely what the aerodynamic problem is for some hovering animals. The circulation and lift is uniquely
determined by the speed and angle of attack
for a wing in steady motion. The maximum
lift of a wing, imposed by stall, places an
upper limit on the circulation that can be
achieved by the quasi-steady mechanism.
For animals that require a mean lift in
excess of the steady stalled value, aerody-
101
FIG. 4. (A) The airflow and circulation created by
the fling mechanism. (B) The peeling motion characteristic of Lepidoptera and Drosophila The drawing
also illustrates a partial peel, or partial fling. (C) The
near peel, or near fling.
namic mechanisms must be found that
create larger circulations than possible
under normal conditions.
The fling mechanism: a theme
and variations
Weis-Fogh (1973) proposed a novel lift
mechanism, the fling, to explain the high
lift produced by the wings of Encarsia. The
fling creates circulation around the wings
during the rotational phase of the wingbeat, and this circulation then determines
the lift on the subsequent half-stroke. Prior
to beginning a downstroke, the wings of
Encarsia are "clapped" together dorsally
with the longitudinal wing axes horizontal,
as shown in vertical section in Figure 4A.
The wings then fling open about their trailing edges, and the flow of air into the opening gap creates a circulation around each
wing. This circulation is proportional to
the angular velocity of rotation, and thus
can exceed the maximum quasi-steady value
for translational motion. When the fling
motion ends, the wings separate and begin
the downstroke, immediately generating
an enhanced lift from the fling circulation.
The lift and circulation must eventually fall
to the maximum quasi-steady values, but
delayed stall will prevent a substantial
decrease over the short distance travelled
by the wings during the downstroke.
102
CHARLES P. ELLINGTON
far: the greenhouse white-fly Trialeurodes
vaporariorum (Weis-Fogh, 1975), Encarsia,
Thrips, and Drosophila. It is also characteristic of many moths and butterflies (R. A.
Norberg, 1972a; Chance, 1975; Dalton,
1975, 1977; Weis-Fogh, 1975; my films of
Pieris, Emmelina monodactylus, and Ephestia
kuehniella), and it has been reported for the
hindwings of the locust Locusta migratoria
in climbing flight (Cooter and Baker, 1977).
The fling is more aptly described as a peel
for the Lepidoptera and Drosophila, however, and is rather like pulling two pieces
of paper apart by their leading edges. The
wings are curved along their chords, and
the point of separation moves smoothly
from leading to trailing edges as the peel
proceeds (Fig. 4B). Such a curvature is normally observed during the latter half of
rotation for all insects, but it may be
enhanced to some extent by elastic deformation under the aerodynamic and inertial
loads of the peel. Charles Williamson and
I have analyzed the peel motion (in preparation), and found that it can create circulations comparable with those measured
by Maxworthy for the fling. The vorticity
should be distributed more uniformly over
the wing instead of being concentrated in
a large leading edge vortex, though, and
this may improve the stability of the cirFie. 5. The large leading edge vortices created by
culation
during the subsequent half-stroke.
the fling mechanism. From Maxworthy (1979).
The list of animals which benefit from
the fling (or peel) mechanism is quite long,
and will undoubtedly grow as research proBennett (1977) and Maxworthy (1979) ceeds. Except for Encarsia, however, that
have experimentally verified the creation list does not include the animals where CL
of large circulations during the fling is known to be greater than CLmax: Amazilia,
motion. Maxworthy's flow visualization Coccinella and T. obsoleta using a horizontal
photographs (Fig. 5) show that this circu- stroke plane, and all of the animals hovlation is primarily due to an enormous vor- ering with an inclined stroke plane. Coccitex formed as the air swirls around the nella performs a partial fling at the dorsal
leading edge of each wing. Unlike the end of the wingbeat, though; the wings
"starting" vortex shed into the air as a wing touch rather late in pronation and only
starts moving, the leading edge vortex from along the more proximal, posterior regions
the fling remains attached to the wing dur- of the chord (Fig. 4B). The separation
ing its subsequent translation, and hence between the wings gradually increases
contributes to the circulation around the towards the wing tip, where the partial fling
merges into a nearfling(Fig. 4C). The parwing.
tial and near flings have not been investiThe fling is a very effective lift mecha- gated experimentally yet, but it seems quite
nism, and it has been found instead of the likely that they also generate circulations
proposed drag-based flight mechanism for prior to translation. The partial fling should
all small insects that have been studied so
AERODYNAMICS OF FLAPPING FLIGHT
103
be somewhat less effective than a complete
fling, and the near fling even more so,
because air swirling around the trailing
edges will reduce the flow past the leading
edges. Nevertheless, if they create even half
the circulation of a complete fling, that will
be sufficient to explain the flight of Coccinella.
Isolated rotation and
the flex mechanism
Except for a near fling restricted to
extreme basal wing areas during pronation, the wings of the crane-fly T. obsoleta
are well clear of each other during the rotational phases. The wings of the hover-fly
Episyrphus also rotate in isolation, and can
gain no benefits from the fling mechanism
or variations on it. Such mechanisms rely
on strong vortex shedding from the leading edge during rotation, forming a leading edge vortex that remains attached to
the wing on the following half-stroke. For
a wing rotating in isolation, a similar shedding would be obtained if the leading edge
moved faster with respect to the air than
the trailing edge. This could be accomplished simply by rotating the wing as a flat
plate about its trailing edge, but the axis
of rotation for insect wings seems to be
located instead about lA of the way from
leading to trailing edge. That axis would
concentrate the shed vorticity at the trailing edge, were it not for the fact that the
wingsy?»c during the latter half of rotation.
As shown in Figure 6, this flexion causes
the trailing edge to become stationary while
the leading edge continues rotation, ensuring the correct leading edge shedding. Air
is also forced around the trailing edge by
the wing rotation, causing vorticity of the
opposite sense to be shed there. Strong
vortex shedding must occur during the
rapid wing rotations of hovering, and it can
be exploited by shedding the right vorticity
at the proper wing edge: only about lA of
the vorticity likely to be shed during rotation need be recovered as a leading edge
vortex to account for the enhnaced lift of
the crane-fly. Nachtigall (19796) has also
suggested that circulation might be created by wing rotation, but details of the
pattern of vortex shedding were not given.
FIG. 6. Wing flexion during the second half of rotation, and the suggested vortex patterns created by the
flex mechanism.
This flex mechanism is quite different
from the "flip" which Weis-Fogh (1973)
proposed for the hover-flies. He suggested
that flexion alone would shed vortices similar to those of Figure 6, in the manner of
a reversed fling motion. However, these
vortices would be cancelled as the wing
unflexes towards the end of rotation, and
there would be no net benefit. It is the gross
rotation of the wing which imparts a chordwise asymmetry to the shedding, with flexion controlling the pattern.
My films of Episyrphus reveal that pronation is delayed and overlaps the beginning
of the downstroke when it hovers with an
inclined stroke plane. This increases the
velocity differential of the leading and
trailing edges at an earlier stage in rotation
than flexion alone would accomplish, and
should enhance the vortex shedding proposed in Figure 6. Indeed, delayed pronation is the most striking difference between
the inclined and horizontal stroke planes
for Episyrphus, so it must be the prime candidate for explaining the large downstroke
lift coefficients. If the leading edge vortex
contains only 2/s of the vorticity shed during rotation, then the downstroke lift will
be sufficient for hovering.
104
CHARLES P. ELLINGTON
CONCLUSION
as hovering and, one decade after WeisThese considerations of rotational Fogh's (1973) landmark paper, we now
mechanisms stray far from the usual quasi- seem to be making a U-turn in our understeady interpretation of hovering flight. standing of flapping animal flight.
Strong vortex shedding must occur during
ACKNOWLEDGMENTS
wing rotation, and the postulated rotaIt is a pleasure to thank Dr. K. E. Machin
tional mechanisms simply rely on concentrated shedding from the leading edge, for many useful and stimulating discusexploiting that vorticity as an attached sions, and Mr. G. G. Runnalls for his assisleading edge vortex during the following tance with the high-speed cinematograhalf-stroke. Leading edge shedding should phy. Financial support was provided by the
be enhanced by delayed pronation for the Winston Churchill Foundation and the Scihover-fly Episyrphus, a near fling and par- ence and Engineering Research Council.
tial fling for the ladybird Coccinella, and
profile flexion (the flex mechanism) for the
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