J. Exp. Biol. (1970), 53, 17-25
jy
With 4 text-figures
Printed in Great Britain
A STUDY OF THE
INSTANTANEOUS AIR VELOCITIES IN A PLANE BEHIND
THE WINGS OF CERTAIN DIPTERA FLYING IN A
WIND TUNNEL
BY JAMES WOOD, Ph.D.*
Department of Biological Sciences, University of Connecticut, Storrs,
Connecticut
(Received 10 April 1969)
INTRODUCTION
Most recent studies of insect flight assume that the forces produced by a flapping
wing can be determined from measurements on wings exposed to a series of steadyflow situations duplicating the instantaneous velocities and angles of attack to which
the wing would be exposed during flight if the air and wing velocities were constant.
This method has been used by Jensen (1956) on the locust Shistocerca gregaria, a large
insect with a relatively low wingbeat frequency (17 Hz.) and by Vogel (1967) on the
fruit fly Drosophila virilis, a small insect with a relatively high wingbeat frequency
(195 Hz.). The assumption that periodic unsteady flow can be described in terms of a
series of steady-flow situations is also implicit in many theoretical analyses of flapping
flight, including those of Hoist & Kuchemann (1941, 1942) and Walker (1925, 1927)
on bird flight. Osborne (1951) using similar methods concluded that in many instances
insect flight could not be explained in terms of conventional (steady-state) aerodynamics. Bennett (1966) has recently produced further evidence that unsteady effects are
important in the flight of the beetle Melolontha vulgaris, one of the insects whose flight
Osborne was unable to explain in terms of conventional aerodynamics. There is no
assurance that deductions based upon steady-state measurements are valid. There is,
in fact, evidence that transient increases in the angle of attack to values beyond those
at which stall would occur in steady flow can be accompanied by transient increases in
lift (Silverstein & Joyner, 1939).
Nachtigall (1966), on the basis of his detailed study of the kinematics of Calliphora
erythrocephala and Phormia regina, concluded that in both insects most lift and some
thrust were produced in the downstroke, while some lift and most thrust were produced
during the first one-third of the upstroke. The latter parts of both the down- and upstrokes appeared to be aerodynamically poor on the basis of the high angles of attack
experienced by the wing during these parts of the wing cycle.
In the experiments reported here the instantaneous horizontal and vertical velocities
were determined in a plane behind the wingbeat planes of Calliphora erythrocephala
and Phormia reginaflyingin a wind tunnel. In addition to providing qualitative information on which portions of the wing beat cycle produced lift, this information
• Present address: Department of Zoology, University of Rhode Island, Kingston, Rhode Island,
02881.
2
EXB52
18
JAMES W O O D
provided an indication of the average lift produced by the insects and the immediate
detection of stall as an increase in the level of turbulence. Additional experiments
allowed a determination of the lift produced by the body, of interest because of the
large lift attributed to the bodies of several insects by Hocking (1953) in contrast to
Jensen's (1956) finding that the body of Shistocerca could produce but little lift.
METHOD AND MATERIALS
Calliphora erythrocephala and Phormia regina anaesthetized with carbon dioxide
were mounted on short steel wires 0-2 mm. in diameter by means of a small drop of
dental wax on the mesonotum. One hr. to several days passed between mounting the
flies and their use in experiments. Flies released with the wire attached flew normally.
In preparation for an experiment, the wire with attachedflywas twisted onto a 0-5 mm.
diameter wire attached to a bearing above the working section of a low-turbulence
open-throat wind tunnel. This support wire was free to rotate between two stops in a
vertical plane parallel to the flow of the wind tunnel. After the initiation of flight the
wind velocity was adjusted until the fly flew in an equilibrium position midway beween the stops. The support wire was next locked into place in order to prevent the
fly from moving backward into the anemometer probe in case of a decrease in flying
speed or the cessation of flight.
The method of attaching the flies differed from that used by Nachtigall (1966) who
mounted flies by their abdomens. Although the latter method may have been preferable, the flies' greater freedom of movement would have necessitated making measurements at greater distances behind the wing plane in order to prevent the insects from
breaking the probe wires. To determine whether the motion of the wings was affected
by the mounting procedure, high speed films (1000 pictures/sec.) were taken of
Calliphoraflyingin the working section of the wind tunnel. Pictures were taken from
the side and a strobe triggered once per picture provided a 9 /jsec. flash for each picture. The path of the wings was determined in three dimensions using co-ordinate
systems analogous to those of Jensen (1956) and Nachtigall (1966). Three mutually
perpendicular axes, X, Y and Z, originated at the wing hinge: X horizontally from
posterior to anterior (positive anterior); Y horizontally along a line piercing both wing
hinges (positive laterally); and Z vertically perpendicular to the other two axes
(positive dorsally). Since the wing beats nearly in a plane, the tip of the wing describes
approximately a section of a great circle on a sphere having the wing length as its
radius. An imaginary circular cylinder was next wrapped around the sphere tangent to
the great circle and the path traced by the wingtip on the sphere was projected on to the
cylinder maintaining its distance along the cylinder axis constant. Note that this differed from Jensen's (1956) and Nachtigall's (1966) method which essentially produced
a Mercator projection. The imaginary cylinder was next unrolled after cutting it along
its upper and lower surfaces. Distance parallel to the cylinder axis was measured along
an axis T, and distance parallel to the wingbeat plane along an axis <j). The origin of the
co-ordinate system was at the intersection of the Y axis with the cylinder. This procedure was carried out on a digital computer given the wing length and the X and Z
co-ordinates of the wingtip. These were read from a calibrated grid on to which pictures taken over several cycles were projected frame-by-frame.
Instantaneous air velocities behind the wrings of diptera
19
Air velocities were measured in a plane approximately parallel to the wingbeat plane
located 0-5 cm. posterior and ventral to it. Position in the measurement plane was
specified by two additional axes which lay in the measurement plane. The W axis was
parallel to the Y axis (zero at its interception with the ZX plane and positive laterally)
while the L axis was perpendicular to the W axis and zero where a perpendicular line
passing through the wing hinge intersected the measurement plane. L was positive
posterior-dorsally and negative anterior-ventrally to this point. This is to say, if this
measurement plane were moved 0*5 cm. in the direction of the wingbeat plane, the two
would have coincided with W identical to Y. The probe was mounted on a micromanipulator equipped with three verniers (accurate to o-1 mm.) which were used to
set the distance of the measurement plane from the wingbeat plane and to move the
probe along the L and W axes respectively. Measurements of air velocity were made at
regular intervals of L and W(z or 3 mm. separating adjacent probe positions depending
upon the experiment) throughout the measurement plane. The velocity measurements
employed a Disa 55 A38 miniature X-wire probe and two Disa 55D05 constant
temperature anemometers followed by Disa 55 D15 linearizers. The gains of the two
anemometer-linearizer systems were set equal. The 1*2 mm. length of the probe wires
and their narrow separation (0-2 mm.) justified treating the records as velocity
fluctuations at a point. The system was calibrated by means of a pitot tube and butyl
alcohol micromanometer at 20° C and 50 % relative humidity, the conditions under
which the experiments were carried out. The time constant of the system in still air
was 8 /jsec. assuring a linear frequency response from zero to 20 KHz. Initial experiments demonstrated that no error was introduced when the system's upper frequency
limit was reduced to 2-5 KHz., the upper frequency limit of the Sony PFM-15 tape
recorder used to record all signals in subsequent experiments.
For determining vertical velocity components (Uz) the wires were oriented parallel
to the ZX plane with the wires making angles of ±45° with the X axis. In this configuration Uz was proportional to the difference between the two linearizer outputs
(Flow Corporation Series 900 application notes). Lateral velocity components ([/„)
which cooled both wires equally did not introduce errors in the values determined for
Uz, but velocity components in the direction of the wind-tunnel velocity (Ux) were
indistinguishable from Uv. This made the interpretation of horizontal velocities calculated from the sum of the two linearizer outputs as Ux unreliable. The horizontal
velocities recorded were actually the sum Ux+ 1-4] Uy\since Uy was perpendicular to
the probe wires while Ux made an angle of 450. Separate determinations of Uy and of
its absolute value (| Uv\) in which the wires lay parallel to the XY plane and made an
angle of ±45° with the X axis demonstrated that i^C/Jwas as large as or slightly
larger than AUX (the increase Ux above the wind-tunnel velocity) throughout the measurement plane.
In all experiments where instantaneous air velocities were determined a narrow
beam of light directed through the insect's wing plane on to a photodiode was interrupted by the wing near the top of each wingstroke. The resulting time mark was used
to fix corresponding points on velocity recordings made at different positions in the
measurement plane. In order to be sure that the records from different parts of the
measurement plane were comparable, the measurement plane was mapped twice and
results in which the average velocities at any point differed by more than 10% were
20
JAMES W O O D
discarded. A total of 12 complete mappings meeting this criterion were recorded, five
for Phormia regina and seven for Calliphora erythrocephala. The instantaneous velocities were resolved into the components Uz and Ux+i-^\Uy\. Uz and the change in
horizontal velocities (the difference between Ux+i-\\Uy\ measured and the windtunnel velocity) were plotted as functions of time after the end of the upstroke. An
index of the average vertical force acting upon the fluid passing through the measurement plane was obtained from the momentum equation. The sum Ux + 1-4! t/Jwas
treated as Ux and a two-dimensional approximation of the flow was used. This procedure, although crude, allowed comparison of the forces developed by different flies.
The momentum equation can be applied to conditions of periodic unsteadyflowin the
form
FK = p\ UnUzdS
Is
(von Mises, 1945), where Fz is the force acting on the fluid in the Z direction (here
defined positive downward); p is the density of the fluid (1*15 x io~3 g./cm.3 for the
conditions of this experiment); 5 is a surface enclosing the region of interest; Un is the
instantaneous component of velocity normal to an incremental area of the surface; and
Uz is the instantaneous Z component of velocity. Note that Un Uz is the average of the
product of Un and Uz and not the product of the average Un and average Uz. The
calculation assumed that the velocity anterior to the fly was that of the wind-tunnel
(with Uz = o). To approximate the average vertical forces acting on the fluid, Un Uz
was calculated for each probe position as the average of the instantaneous product
Un Uz at each of twenty equally-spaced instants over the wingbeat cycle. The product
p Un Uz was multiplied by the area of the rectangle formed by four adjacent probe
positions (4 mm.2 or 9 mm.2 depending upon whether the distance between adjacent
probe positions was 2 or 3 mm.). The sum of these forces calculated for each measurement position was taken as the total force acting upon the fluid in the vertical direction.
The force obtained was doubled to take account of the two wings, but no account was
taken of the forces which acted on the fluid which passed between the two wing hinges.
RESULTS
The wingtip path most frequently observed in these experiments was one in which
the wingtip on the downstroke moved along a path posterior to that followed during
the upstroke. A figure-of-eight path in which the downstroke path lay anterior to that
followed during the upstroke for most of the cycle was observed in one film, but for
most of this film also the wingtip path was open. Throughout most of the downstroke
the wing was moderately pronated. At the end of the downstroke the wing was curved
about its long axis. At the beginning of the upstroke the wing chord lay parallel to the
Z axis and the wing moved posteriorly and dorsally. During this phase of the stroke the
tip of the wing was flexed forward. Later in the upstroke the wing moved rapidly
dorsally and posteriorly. Supination was extremely pronounced during this phase of the
stroke. At the end of the upstroke the wing was pronated, the chord briefly passing
through a phase where it was perpendicular to the X axis.
A number of kinematic parameters were variable (Table 1). The downstroke was
Instantaneous air velocities behind the wings of diptera
21
always of longer duration than the upstroke although the relative durations varied. The
separation between the downstroke and upstroke paths was nearly maximal at the level
of the wing hinge, but the distance between them varied (F at hinge, Table 1) as did
Table 1. Characteristics of the wing cycle of Calliphora erythrocephala
> and F are in mm., the wingbeat period is in msec.)
Tat
hinge
Fly no.
1-5
1-5
2'2
3O
2-O
2-2
2-2
3-5
1-5
2-2 + 0-7
Wingbeat Downstroke duration
period
Upstroke duration
8-8
8-4
6-i
64
5-5
6-5
8-8
'•3
1-3
1-5
18
80
1-7
2-5
7-3
7-2 ±1-3
1-7 + 0-3
P
I 2 mm.
'L
Fig. 1. Wingbeat paths followed by the wings of Calliphora. The open path was observed much
more frequently than thefigure-of-eightpath.
the amplitude which was equally variable at both the top and bottom of the stroke
(0max. a n d 0mm.> Table 1), while the most constant parameter was the position of the
wing at mid-upstroke, where it passed through the Y axis.
Vertical forces calculated from the momentum equation varied from 4-9 to 30-2 mg.
in different flies. No evidence of stall as indicated by turbulence was visible at any point
in the measurement plane for any of thefliesflyingin moving air (Fig. 1). The wakes of
flies flying in still air exhibited considerable turbulence (Fig. 2). The distribution of
22
JAMES W O O D
Uz over time and over the measurement plane revealed a number of characteristics
common to all of the insects. The wakes of Phormia and Calliphora had very similar
velocity distributions. The velocities recorded in the wake of a typicalfly{Calliphora)
are shown in Fig. 3. For small values of W, a single maximum and a single minimum
occured once in each cycle. At large values of W, Uz was zero or negative for much of
L
r
12
L'
.J-.I
l r
! ' i
•I
10)
•«ipl""
Jr
I
'
M
!
'
! 1
'
!
i
r1
'
1 I
Li ; r '
hJJ'U-U-'.
:MU^^-4
0
2
4
6
W
Fig. 2. Velocity distribution in the wake of Calliphora flying in moving air. Note the) low
level of turbulence. Horizontal scale: one division is 2 msec. Two hundred superimposed
sweeps. Vertical scale = 0-70 m./sec./division. Zero levels: Channel 1, 2 cm. above lowest line;
channel 2, 3 cm. above lowest line
Instantaneous air velocities behind the wings of diptera
23
the wing cycle and only one peak was present. At intermediate values of W, Uz usually
exhibited two peaks per cycle. The larger peaks in Uz lasted for greater than one-half of
the cycle, and the second peak, where present, was of shorter duration and decreased
amplitude. The two peaks were more nearly equal in amplitude lower in the measurement plane, with the second peak being absent for larger values of L. One peak in Uz
(the only one present in some cases and the larger where two peaks are present) is, on
the basis of its longer duration, probably produced by the downstroke. In the regions
-1
Fig. 3. Velocity recordings made in the wake of Calliphoraflyingin still air. Note the larger
amount of turbulence reflected in the non-periodicity of the two hundred superimposed sweeps.
W = O; Horizontal scale = 2 msec/division; vertical scale = 0-73 m./sec./division. Zero levels:
Channel 1, 1 cm. above lowest horizontal line; channel 2, 2 cm. above lowest horizontal line.
—3
-50-I
3 4 5
12
3 4 5
1 2
3 4
5
W
Fig. 4. Horizontal and vertical velocities in the wake of Calliphora. Dashed line: Ux+ 1-4 [Uy];
dotted line: U,; solid horizontal line: o cm./sec. Vertical scale in cm./sec.
24
JAMES W O O D
where two peaks in Uz are observed, the smaller peak is probably produced by the
upstroke.
Lift produced by the bodies of wingless flies in flight posture exposed to steady flow
was found to be small (less than 2 mg. for a 50 mg. Phormia with an angle of attack of
io° and airspeed to 2 m./sec).
DISCUSSION
The wingtip path found for Calliphora in these experiments differed considerably
from that found by Nachtigall (1966) whose results showed the downstroke path to lie
anterior to the upstroke path. The changes in wing twisting and wing contour observed in these experiments were qualitatively similar to those observed by Nachtigall.
The most frequently occuring wingtip path resembled that reported by Hollick (1940)
for Muscina in still air, while the figure-of-eight path resembled closely that of Muscina
in moving air. It appears that the wingpath is influenced by the method of attaching
the fly, but it is uncertain which method gives more normal results. That the abdomen
might be used in flight control was indicated by the response of animals exposed to a
sudden decrease in wind-tunnel velocity. Such flies strongly flexed their abdomens
ventrally. This manoeuvre has been repeatedly and reproducibly elicited. It may be
that in a freely-flying insect the abdomen is used as a flap to produce slight increases in
lift at low airspeeds or to bring about changes in body angle appropriate to the insect's
airspeed.
The lack of any appreciable turbulence in the wakes of flies flying in moving air
contrasted sharply with the high level of turbulence observed at low values of W in still
air. The irregularity of the velocity fluctuations recorded in still air did not result from
aperiodic wing movements since wing position and twisting are periodic functions of
time in still air as well as in moving air (Nachtigall, 1966). The presence of turbulence
in still air indicated that the Reynolds number was high enough for stall to occur. The
absence of turbulence in moving air indicated that stall did not occur over any appreciable part of the cycle at normal flight speed. Stall in still air probably resulted from
increased angles of attack (the angle between the wing chord and the direction of the air
velocity to which the wing is exposed) during the downstroke. The velocity to which
the wing is exposed depends upon the forward velocity of the insect as well as the
velocity of the wing element under consideration. In still air the absence of the horizontal velocity produced by the wind tunnel causes an increase in the angle of attack
throughout most of the downstroke. These results indicate that studies of insect
flight carried out in still air are of questionable validity, as was pointed out by WeisFogh & Jensen (1956) on theoretical grounds.
The larger peak in Uz which was associated with the downstroke on the basis of its
longer duration indicated that during the downstroke the wing affected a relatively
large mass of air, accelerating it downward. This is consistent with the production of
the major lift during the downstroke. The larger amplitude of the second peak in U.
(associated with the upstroke) lower in the measurement plane indicated that lift was
also produced during the first part of the upstroke. This interpretation is consistent
with Nachtigall's (1966) conclusions based upon kinematic studies.
The relatively large lateral velocities were reflected in the small velocity fluctuations
measured at W = 9 mm. For all values of L the small fluctuations at this distance from
Instantaneous air velocities behind the zvings of diptera
25
the wing hinge indicated medially-directed velocities, since wing lengths were between
9 and 10 mm. in all Calliphora studied. Similar results were encountered in Phormia.
The low lift produced by the body contrasted with the high values of lift found by
Hocking (1953) for several insects. Several explanations are possible. It is unlikely that
there are major differences in the aerodynamic characteristics of the bodies between
the insects studied by Hocking and those studied here. Hocking's measurements were
carried out in a wind tunnel using an aerodynamic balance. It is possible that the flow
of air produced by the wind tunnel was not horizontal but that large upward velocity
components were present as well.
SUMMARY
1. The variations in several kinematic parameters of Calliphora erythrocephala were
studied on flies flying in a wind tunnel. Variation was equally pronounced at both the
and bottom of the wingstroke.
2. The wakes of Calliphora erythrocephala and Phormia reginaflyingin moving air
exhibited extremely low turbulence, while considerable turbulence indicative of stall
was present in the wakes of flies flying in still air.
3. The air velocities recorded as functions of time in the wakes of both Phormia and
Calliphora are consistent with most lift being produced in the downstroke, with the
first part of the upstroke also contributing to the production of lift.
Part of a thesis submitted for the degree of Ph.D. in Biological Engineering from
the University of Connecticut, Storrs, Connecticut, 1968. Supported by Inst. Gen.
Med. Sci. Training Grant in Bioengineering GM13088 and by the University of
Connecticut Research Foundation.
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