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First published online December 14, 2005
Journal of Experimental Biology 209, 43-56 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01958
Induced airflow in flying insects II. Measurement of induced flow
Department of Biology, University of Washington, Seattle, WA 98195, USA
* Author for correspondence (e-mail: sane{at}u.washington.edu)
Accepted 21 October 2005
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Summary |
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 TOP Summary IntroductionMaterials and methodsResultsDiscussionReferences |
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Key words: hot wire anemometry, Manduca sexta, wing flutter, odor tracking, convective heat loss, airflow sensing
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Introduction |
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;
Horsmann et al., 1983),
olfactory sensors (Loudon and Koehl,
2000), heat exchange
(Heinrich, 1993;
Roberts and Harrison, 1998)
and various mass exchange processes such as oxygen, carbon dioxide and water
(Wasserthal, 2001), are all
profoundly affected by the structure of such flows. Thus, there exists a
biophysical feedback relationship between the wing kinematics and
flight-related sensory-motor physiology that is entirely mediated by the
external air medium.
One important biological consequence of induced airflow is its influence on
mechanosensory and chemosensory organs, which receive their stimulus
via the surrounding fluid medium. For example, the flightless
silkworm moth Bombyx mori actively fans its wings to increase the air
flux over its body, thereby enhancing the rate at which its antennae encounter
odor molecules (Loudon and Koehl,
2000). In flying locusts, wind sensory hairs located on the head
are activated by motion of the head and induced air flow and provide phasic
input entraining the flight motor output
(Horsmann et al., 1983). These
few examples illustrate how flying animals rely on the mechanical feedback
from their surrounding fluid medium to perceive mechanosensory and
chemosensory cues. However, in many important areas of research, the role of
the feedback mediated via induced airflow remains under-appreciated.
For example, we know very little about how entrainment of the upwind fluid due
to flapping activity affects odor sampling and odor tracking during flight
(Willis and Arbas, 1991;
Vickers, 2000). In addition to
the sensory biology, induced airflow also influences the thermal biology of
flying insects through enhanced convection. Yet, although there are several
detailed studies and related models on thermoregulation in flying insects that
emphasize convection as a dominant mode of heat loss, none account for the
enhancement in convective heat loss from induced airflow
(Church, 1959; for reviews, see
Heinrich, 1993;
Roberts and Harrison,
1998).
To some extent, induced airflow in actively flapping insects may have been
overlooked due to the lack of data on flow fields around a flying insect.
There are several available methods for measurement of flows around flapping
insect wings (for a review, see Sane,
2003). In larger insects and birds, it is increasingly possible to
image these flows with fine spatial resolution using modern techniques such as
smoke visualization combined with high-speed videography (hawk moths,
Ellington et al., 1996;
Willmott et al., 1997;
butterflies, Brodsky, 1991;
Grodnitsky and Morozov, 1992;
Srygley and Thomas, 2002) and
digital particle image velocimetry (DPIV; flies,
Dickinson and Gotz, 1996; hawk
moths, Bomphrey et al., 2005;
hummingbirds, Warrick et al.,
2005). While DPIV offers a fine spatial quantification of flow
fields with resolutions previously not possible, it remains limited in its
ability to acquire and store the data at the frequencies typical of insect
wing beats. Hence, DPIV studies on actual animals have typically not been able
to explore the finer temporal aspects of flow. Similarly, smoke visualization
techniques are able to capture flows with a good spatial and temporal
resolution but do not offer an easy means to quantify these flows. In
contrast, traditional flow measurement techniques such as hot wire anemometry,
although poor at determining the spatial variation in the flow field, offer an
excellent temporal resolution of the flows around the bodies of flying insects
(bats, Norberg et al., 1993,
insects, Bennett, 1970;
Loudon and Koehl, 2000) and in
their wakes (Lehmann, 1994).
Using hot wire anemometry, it is possible to address how flapping wings affect
the temporal dynamics of flows due to flapping and, furthermore, how such
time-variation affects delivery of the airborne stimuli to the sensory organs
of insects.
To understand how flight activity and related flow disturbances influence
the fluid-mediated mechanical feedback in flying insects, it is first
necessary to estimate and measure induced airflow. In a companion paper, we
outlined a theoretical framework to calculate the mean induced flow in a
flying insect (Sane, 2006).
Here, we measure induced airflow on tethered hawk moths Manduca
sexta, with high temporal sensitivity. These insects are convenient to
work with because they flap readily and uninterruptedly under tethered
conditions. They also present an interesting experimental system in which all
of the physiological effects of induced airflow outlined above are likely to
be important. Not surprisingly, they are also one of the best-studied
organisms for thermoregulation (Heinrich,
1971; for a review, see
Heinrich, 1993). Using hot
wire anemometry, the airflow was measured at two point locations: an axial
inflow location between the antenna and a radial outflow location above the
thorax. This paper also showcases the power of conventional hot wire
anemometery as a remarkable tool to study aerodynamics of flying insects due
to its high temporal sensitivity. These studies reveal that in addition to the
gross flow predicted by the theory, the flows contain higher frequency
fluctuations that may be of considerable biological importance.
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Materials and methods |
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Wind tunnel construction
The calibration of the airflow was carried out within a custom Plexiglas
wind tunnel. The area of the square working section of the wind tunnel was 15
cmx15 cm. The laminarity of the flow within the working section of the
wind tunnel was established using a pre-calibrated anemometer (Kestrel 3000,
Richard Paul Russell Ltd, Lymington, UK) in combination with smoke
visualization. For a given position within the wind tunnel, a constant reading
of the anemometer indicated that there were no temporal changes in the flow
pattern at that point. Similarly, a constant reading of the anemometer between
any two or more arbitrary points within the working area indicated that there
were no significant spatial gradients of velocity within the working area of
the wind tunnel. Thus, for a given setting of the motor speed of the wind
tunnel exhaust fan, it was always possible to assign a single value for the
air speed.
Anemometer calibration
To establish the precision and accuracy of anemometric readings, we
calibrated the anemometer readout in a custom wind tunnel using two separate
methods. In one method, to ensure initially that the anemometer galvanometer
was reliable, we adjusted the wind tunnel motor speed to a fixed value and
confirmed that these readings held steady for a given motor speed. We then
changed the wind tunnel motor speed to random high or low values using a
controller. After the initial transients, we read the steady needle reading in
each of the two anemometers. Because readings from both anemometers always
matched over a wide range of speeds of the wind tunnel and they always showed
the same values for any given wind tunnel controller settings, we concluded
that the anemometers read-outs are reasonably precise, i.e. they are
repeatable. In a second method, we determined the accuracy of the two
anemometers by comparing their values with those of a standard propeller
anemometer (Kestrel 3000) placed within the working section. The values of air
speed measured by both types of anemometers matched to about 0.05 m
s-1, indicating that their values are reasonably accurate in the
range tested (0-4 m s-1). Using these measurements, the anemometers
were calibrated to obtain air speeds from voltage measurements. All anemometry
described in these papers was carried out using the analog voltage
readout.
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Anemometer time constant
To determine how rapidly the anemometer reading reaches its steady value,
we characterized the time constant 
for an anemometer using a step input
of air speed from zero to a constant value. The airflow in the wind tunnel was
initially held at a constant speed of 3.92 m s-1. We then placed
the anemometer inside a small but deep hole in the wall with no airflow. After
the needle was steady at the zero value for a few seconds, we plunged the
anemometer rapidly into the wind tunnel. Following an initial peak due to the
disturbances associated with the motion of the anemometer in moving air, the
anemometer readings rapidly stabilized to a steady value of 3.92 m
s-1. We fitted the measured airspeed with an exponential function
A0(1-et/), where A0 is
the asymptotic average speed of the airflow and is the time constant of
the anemometer. Due to limitations on how fast the anemometer can be manually
plunged and the time it takes for the resultant fluid disturbance to
dissipate, the value of this time constant only provides a conservative
estimate of the actual time constant of the anemometer. For the Kurz 490
anemometer used in these experiments, we measured a time constant of 0.0103 s
(Fig. 1C), corresponding to a
frequency of 97 Hz. This is nearly four times the wing beat frequency of a
typical Manduca sexta wing. Although the anemometer can register
frequencies higher than 97 Hz, these time constant values suggest that they do
not provide a reliable value for the airspeed of events occurring at
frequencies above 97 Hz.
Measurement of induced airflow
The adult moths Manduca sexta (Linnaeus) used in these experiments
were collected from the colony maintained in the Department of Biology at the
University of Washington. The moths were kept at a temperature of 26°C
with a 17 h:7 h L:D photoperiod, and were used within a week of eclosion. The
data presented here was collected from 12 moths. Each moth was
cold-anesthesized in a freezer for approximately 12 min. After freezing, we
weighed the moth and placed it upside down in a `V' shaped metal trough. The
scales surrounding the meta-thoracic episternum were removed by a low pressure
air source, and the cuticle of the meta-thoracic episternum was scratched a
few times with a scalpel blade to create a better gluing surface.
A tether post was made from a 6 mmx6 mmx0.25 mm rounded brass
plate soldered to the end of a brass rod that was 50 mm in length and had a
diameter of 2 mm. The overlap between the plate and the rod was 2 mm. The end
of the tether plate was attached to the metathoracic episternum on the
underside of the moth using cyanoacrylate glue and baking soda. The tether
post was positioned at a 40° angle with respect to the moth's body. The
glue was allowed to set for 10 min with the moth immobilized. During the
setting time, we measured the length of the wings, body and antennae. The
tether post was secured to a 99 mmx19 mmx2.5 mm horizontal
aluminum beam forming a force sensor. The vertical deflections of the beam and
tether post are linearly proportional to the vertical forces exerted by the
moth for small deflection angles (such that sin
when
0). Vertical deflection of the beam was measured by mounting a
first-surface mirror on the end of the beam and reflecting a laser from the
mirror onto a vertical optical sensor strip. The output of the sensor strip
was converted by an analog divider circuit to produce a voltage signal, which
varies linearly with the vertical force exerted on the beam
(Fig. 2A).
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We placed a pair of hot wire anemometers (Kurz 490M mini-anemometers
modified to get the analog voltage readout as described in the section on
anemometry) at fixed near-field positions along the midline of tethered,
actively flapping hawk moths. One anemometer (or the `axial inflow
anemometer') was placed at roughly the mid-point between the antennae. A
second anemometer (or the `radial outflow anemometer') was placed at a radial
position at roughly 3/4 of the wing length from the base
(Fig. 2A). The anemometric data
acquired at these positions allowed us to determine the changes of induced
airflow and test predictions of a theoretical model proposed in the companion
paper (Sane, 2006).
To induce flapping, the tethered moths were presented with a continually varying visual stimulus on the LCD monitor placed in front of it (Fig. 2A). Tethering the insect allowed us to accurately maintain a steady distance between the insect and the anemometers. Although the LCD monitor was used to motivate the insects to fly, in all the experiments reported here we turned off the visual stimulus after the moth initiated flapping to limit visual influence on wing kinematics. We allowed the insect to flap for at least 10 s after the LCD monitor had been turned off and then closed the lid of the flight chamber to reduce ambient light. Although this does not ensure that insects will flap with steady kinematics, it does assure us that the visual stimulus did not contribute significantly to changes in wing flapping frequency or amplitude.
Because the time constant of the anemometers is about 1/4 of the stroke period, it was possible to measure induced flow at the time scales of flapping wings. We verified that the periodicity of the flow measured by both anemometers matched the periodicity of the corresponding record from the vertical force beam recording the wing vibrations (Fig. 2B), thus ascertaining that the anemometers accurately measured the aerodynamic result of wing movement. The force beam record itself cannot accurately measure aerodynamic force because it integrates the aerodynamic and inertial input from the two pairs of wings and the body in addition to the resonant properties of the force beam itself (resonance in horizontal direction was 71 Hz and in vertical direction was 96 Hz).However, the vertical force record was highly sensitive to wing motion and thus could be used to independently determine stroke frequency. Whereas the anemometric record showed clear peaks at the driving or wing beat frequency (for example, ca. 20 Hz in Fig. 2C) and much diminished peaks at higher frequencies, the force beam record shows several large peaks at multiple harmonics of the fundamental frequency (Fig. 2B,C). Because the anemometers and force beam are mechanically uncoupled, a perfect matching of the dominant period from these two records indicated that the anemometer readings precisely captured the periodic airflow fluctuations due to the beating wings at both the upstream and downstream locations.
All voltage data from the actual moths were acquired using a National Instruments Data Acquisition card (Austin, TX, USA; PCI-MIO 16E-4) attached to a Multiple Input-Output (MIO) BNC-2090 adapter (National Instruments) at 4000 Hz. Data from the artificial wing experiments was acquired on the same system at 10 000 Hz. A custom graphic user interface was programmed in MATLAB (The Mathworks, Inc., Natick, MA, USA) to simultaneously acquire the data and send output commands.
Spectral analysis of anemometric measurements
The high sensitivity of the anemometric measurements allowed us to perform
a detailed analysis on these data to determine their spectral properties. The
data for all bouts of all moths were Fourier transformed using custom MATLAB
programs and plotted as a function of frequency vs amplitude of the
underlying periodic phenomena. When discussing them individually, these moths
will be referred to as Moth 1 through 12, for convenience.
A first analysis involved a standard Fourier transformation of the entire raw time series. Because the lengths of these records vary from trial to trial, the frequency resolution (inverse of the total time length of the record) varies from one trial to another.
These analyses allowed us to determine the frequency composition of the records and identify the principal frequency components of each time series. To selectively focus on the higher frequency contributions due to flapping wings, when presenting these data in Fig. 4, we eliminated these low frequency contributions by operating a high-pass, 4-pole Butterworth filter on the data with a cutoff at 3 Hz.
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). This method allowed us to reduce the variance of the
spectral estimate, with the trade-off that spectral resolution also decreased.
In this method, the time series was first divided into multiple overlapping
time blocks. For each block, we subtracted the signal mean and multiplied by a Hann taper to reduce transient effects, followed by a Fourier transform on each tapered block. The squared magnitude of each transformed block was then averaged together to form the WOSA estimate. In the experiments described here, we used a block size of 128 000 samples (32 s) with 50% overlap between blocks, which gives a frequency resolution of 0.0606 Hz. This resolution is more than 400 times finer than the typical wing beat frequency of 25 Hz.
The results of these analyses are plotted in Fig. 4 for the sample cases of Moth 7 and Moth 12. The standard Fourier transforms for axial inflow records are shown in Fig. 4A (Moth 7) and Fig. 4C (Moth 12) and for the radial outflow records are shown in Fig. 4E (Moth 7) and Fig. 4G (Moth 12). The corresponding WOSA plots are in Fig. 4B,D,F,H respectively. A summary of the Fourier data for all moths is provided in Table 1.
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In a third analysis, we determined the effect of wing beat frequency on mean air flow. For this analysis, we focused on 5 of the 12 moths, which (i) flew uninterruptedly for at least 150 s at a wing beat frequency representative of normal flight (20-30 Hz), and (ii) showed greater variation in wing beat frequency. For these records, the air speed time-series was subdivided arbitrarily into 1 s time bins for further analysis because a 1 s time bin was able to include most wing beats within that time bin while still capturing the functional relationship between the mean air flow and stroke frequency. Thus, in the subsequent analysis, we assumed that every second of flight was independent of the following or preceding seconds. Although not strictly valid for wing beats in an immediate sequence, this assumption is reasonable for majority of the wing beats within two sequential time bins. Each second of flight thus obtained was Fourier transformed to measure the instantaneous wing beat frequency and the mean airspeed. Because the Fourier analysis is carried over 1 s at a time, the minimum frequency resolution of these data was 1 Hz. A summary of these data are provided in Fig. 5 and Table 2 for all 5 moths chosen for the study.
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Experimental investigation of higher frequency peaks
To determine the consequences of wing flexion on the aerodynamic signature
of flapping wings, we used the apparatus illustrated in
Fig. 1A and described in the
section on anemometer calibration. This apparatus allowed us to rapidly
oscillate an artificial wing back and forth and measure the resulting
anemometric signal at preset frequencies. We generated periodic air
disturbances using to two types of artificial wings by oscillating them back
and forth at 50 Hz. The first wing, made of balsa wood, was rigid and did not
flex at these frequencies. The second wing, made of paper, was flexible and
fluttered considerably when oscillated back and forth at 50 Hz. An anemometer
placed very close to the oscillating airfoil and aligned near the center of
the rectangular wing measured the periodic air disturbances due to the
oscillating plate. This ensured that the periodic edge-related disturbances to
the airflow were minimal and most of the airflow measured by the anemometer
was along a single axis due to the relatively simple back and forth motion of
the volume of air close to the rectangular plate.
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At the scale of 102 s, the airflow shows a wide range of values depending on the changes in kinematics of the flapping wings. The magnitude of axial inflow is much lower than the radial outflow. For instance, in the sample flight bout shown in Fig. 3A-C the axial inflow measured between the antennae ranges between 0 and 0.52 m s-1 as compared to the radial outflow range of 0 to 3.55 m s-1 for the identical flight bout in Fig. 3D-F. At the scale of 101 s, the measurements at these two locations show a greater fluctuation in the radial outflow than axial inflow (Fig. 3B,E). At the scale of 100 s at both locations, the measurements reveal a clear periodicity in the airflow records due to oscillatory wing motion (Fig. 3C,F). The 24 peaks seen in the 1 s upstream record in Fig. 3C each represent a wing beat of the flapping moth. Because the period of each wing beat (ca. 0.04 s) is approximately four times the time constant of the anemometers (ca. 0.01 s), the peak amplitudes capture the full range of the actual signal. The periodicity of axial inflow is considerably more regular than the radial outflow, indicating that the radial outflow anemometer captures much of the unsteadiness due to the complex aerodynamic perturbations caused by wing rotations and wing-wing interactions at dorsal stroke reversal. Fig. 3C shows a range of axial inflow from 0.19-0.36 m s-1 whereas the range of radial outflow in Fig. 3F is slightly higher and between the values of 0.8-2.8 m s-1.
Spectral properties of the anemometric records
In all the experiments reported here, we turned off the LCD monitor and
closed the flight chamber lid to remove the visual stimuli to the tethered
moths. Thus, any changes in wing kinematics may be interpreted as `voluntary'.
The Fourier transforms of the time series data
(Fig. 4A,C,E,G) of the airflow
generated by these kinematics typically showed a fixed pattern of peaks
occurring at (i) wing beat frequency, (ii) twice the wing beat frequency, and
in a few cases (iii) three times the wing beat frequency, in addition to the
initial offset at 0 Hz, representing the mean induced air flow about which the
higher frequency fluctuations occur. However, in many cases, several higher
frequency peaks not obvious in the standard Fourier plots are revealed by the
WOSA plots (Fig. 4B,D,F,H),
suggesting that this type of time-series analysis may be particularly useful
in analysis of hot wire anemometric data of high frequency flapping. This
section focuses primarily on the first three peaks observable in every bout of
every moth tested.
To highlight the effect of second and third peaks due to wing beat frequency and its double, the data presented in Fig. 4 were filtered under 3 Hz to eliminate the offset value and other lower frequency components that typically overwhelm other higher frequency contributions in long time series records. Also in Fig. 4, the Fourier plots are normalized with respect to the maximum peak to allow easy comparison of the relative contributions of the higher frequency contribution with respect to the dominant wing beat frequency component.
Fig. 4A,C,E,G shows two samples (Moth 7 and Moth 12) of the Fourier records from the 12 moths in this study. Fig. 4A,C shows the Fourier transforms of axial inflow anemometric data for the longest flight bouts in these two sample cases and Fig. 4E,G shows similar data for the radial outflow anemometer. Moth 7 (Fig. 4A,B,E,F) flew for about 178 s and Moth 12 (Fig. 4C,D,G,H) flew for 323 s. Because the frequency resolution of the Fourier transformed data is the inverse of the length of the time record, the Fourier transformed data have different resolutions. Specifically, shorter time records have a coarser frequency resolution whereas the longer time records have a comparatively finer resolution of frequency. However, even the lowest resolution in the Fourier data was 0.08 Hz (for Moth 10), which is more than two orders of magnitude lower than the wing beat frequency. The absolute amplitude of the transform at each frequency presented in Table 1 thus represents the average amplitude of airspeed fluctuation at that frequency.
The data from Moths 7 and 12 showcase some of the key general features of the induced airflow discussed in this section. First, there is always a peak at wing beat frequency; however, this peak may be sharp or diffuse, depending on the degree to which the moth varied its stroke frequency within each flight bout. For example, Moth 7 in Fig. 4A,B,E,F shows a rather steep peak at wing stroke frequency with very little spread around this peak, suggesting that it maintained its wing beat frequency in a very narrow range. In contrast, Moth 12 in Fig. 4C,D,G,H shows a substantial spread of wing stroke frequency with more than one peak, suggesting that it varied its stroke frequency within the flight bout. Second, the airflow signal contains information about the subtler phasic phenomena occurring at frequencies higher than stroke frequency. This is particularly evident in the WOSA plots (Fig. 4B,D,F,H). All the plots shown in Fig. 4 (and summarized in Table 1) show a prominent peak at precisely double the wing beat frequency in addition to the peak at wing beat frequency. If the wing beat frequency peak is sharp, then the higher frequency peaks are also sharp (Fig. 4A,B,E,F for example). On the other hand, if the moth varies its stroke frequency to cause a spread in the stroke frequency peak, then a similar spread is evident in the higher frequency peaks (Fig. 4C,D,G,H for example). This suggests that the higher frequency events are closely tied to the aerodynamic events within each wing stroke. Further, the ratio between the magnitude of the first and second peaks tends to be greater in the inflow recordings as compared to the outflow recordings (Fig. 4A,E,C,G). This suggests that the higher frequency disturbances are relatively more attenuated upstream of the wings (against the mean air flow) than downstream (along the mean airflow). Further, as revealed by the WOSA plots, more high frequency peaks are visible in the axial inflow record as compared to the radial outflow record, suggesting that, in general, the signal-to-noise ratio is better at the axial inflow location than at the radial outflow location.
Because anemometers are mechanically decoupled from the rest of the apparatus and from each other, the co-occurrence of the various peaks in the two anemometers and the force beam data suggests that these higher frequency peaks are not artefacts. Rather, these peaks reveal the air disturbances caused by aerodynamic events occurring at least twice at every wing beat. Finally, the frequency contributions below 10 Hz arise from the slower and more persistent changes in the flow velocity lasting over several wing strokes. Table 1 also reveals the variability in the range of frequencies of each moth as well as the differences between moths. Typical sustained flapping frequencies of moths tested in these experiments ranged from 14 Hz to 28 Hz, excluding rare (<1 s) bouts of 30 Hz or more. Presently, it is not clear to what extent these differences are due to tethering, nor can we fully rule out the possibility that some of the lower frequency bouts may be associated with thermogenesis rather than flight. For example, the dominant frequency peak for Moth 1 is around 16 Hz (Table 1) with minor fluctuations about this value. Although this moth had been flapping for more than 5 min, we cannot completely rule out the possibility that it was still undergoing thermogenesis.
Dependence of induced airflow on wing beat frequency
How does an increase in wing beat frequency influence the induced airflow?
To address this question, we investigated five moths which flapped
continuously for over 150 s and showed some variability in their wing beat
frequency. Fig. 5 shows plots
of mean airspeed as a function of wing beat frequency for these five moths
labeled Moths 5, 6, 7, 11 and 12. A summary of the regression data is given in
Table 2. Because these records
were chopped into 1 s bins for analysis, the Fourier analysis of each second
of flight offers a maximum frequency resolution of 1 Hz resulting in integer
frequency values. Although we chose moths of roughly the same age
(approximately 2 days old), size (mean body length=53.21±2.34 mm) and
mass (2.11±0.33 g), there may be many inter-individual differences
between their flight ability, motivation or other physiological differences.
Hence the data from all moths were not pooled but each moth was treated
separately. For each moth however, the data from different flight bouts were
pooled because the above differences were minimal from bout to bout.
A model for calculating the induced flow resulting from flapping wings
appears in the companion paper (Sane,
2006). Here we test some specific predictions of that model. From
the model, the equation for axial induced flow is given by:
 | (1) |
where 
L is the average
lift coefficient, 
is the stroke amplitude, n is the wing beat
frequency 
is the mean chord length
and si(0) is a wing-shape dependent parameter
(Sane, 2006). Because it is
derived from propeller theory, this equation assumes a constant angle of
attack during the stroke and predicts that, for a given wing shape and stroke
amplitude, the induced axial velocity is directly proportional to the wing
beat frequency.
As seen in Fig. 5, there is
a large variability in the measured airspeed at any value of wing beat
frequency. Similarly, at any given mean induced airspeed, there may be some
variability in the wing beat frequency because other kinematic variables such
as angle of attack, stroke amplitude or stroke position also influence induced
airflow (Sane and Dickinson,
2001). Even with these caveats, the two regressions show
significant r2 values
(Table 2) suggesting that the
model prediction (Sane, 2006)
of a linear relationship between induced airflow and wing beat frequency is
valid in the limited range of variability in wing beat frequency. Furthermore,
the range of measured values of mean induced flow velocity lies within the
range prescribed by the model (Fig.
5, grey region) in the corresponding frequency range.
It is important to note that Eqn 1 assumes that the fluid is inviscid and irrotational. This assumption holds for higher Reynolds number flows occurring at higher wing beat frequency, but may not accurately represent flows at Reynolds numbers below about 100 corresponding to very low wing beat frequency. Hence, Eqn 1 may not be extrapolated to zero wing beat frequency and the linear relationship between axial velocity and wing beat frequency predicted by this equation holds only in a high frequency range. Thus although we provide the values of y-intercept for completeness, these values do not provide any information about the relationship between wing beat frequency and mean airflow at very low values of wing beat frequency.
Aerodynamic signature of wing flutter
One hypothesis of the higher frequency peaks is that they result from
flutter phenomena in the wings. Alternatively, these peaks could primarily
arise from measurement artefacts due to limitations of the instrument e.g.
rectification of signal due to its inability to sense the direction of airflow
etc. To test these hypotheses, we compared the anemometric records of the
flexible paper wing with that of the rigid balsa wood wing when both were
oscillated at 50 Hz. Like natural wings, the paper wings are flexible and
flutter during rapid oscillations thus generating air disturbances that occur
not only at the driving frequency but also at higher frequencies. In contrast,
balsa wood offers a rigid non-aeroelastic alternative to reduce the flutter.
If the double frequency peak is a measurement artefact, then it should be
present in the frequency signature of both the flapping of rigid and flexible
wings. At this frequency, however, the double frequency peak is absent from
the frequency signatures of rigid wings
(Fig. 6B), whereas it is
present in the frequency signatures of flexible wings
(Fig. 6C). The paper wing also
shows contributions at twice and thrice the flapping frequency in addition to
some lower frequency peaks, whereas the rigid wing shows a single peak at the
flapping frequency. Because the motion of the servomotor lever was exactly the
same in both cases and because the dimensions of the plates are also the same,
these results suggest that the higher frequency peaks in the anemometric
record arise from fluttering in a flexible wing rather than measurement
artefacts. Thus, the higher frequency effects we measure are likely to be the
aerodynamic consequence of the higher frequency components of the airfoil
motion in flexible wings. These results agree well with the Fourier transform
of the actual movement of the flexible wings
(Combes and Daniel, 2003; see
Fig. 7B). Together these
results show that hot wire anemometry can be a useful tool for quantifying and
analyzing the aerodynamic signature of fluttering wings. This phenomenon will
be investigated in greater detail in a future research.
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;
moths, Bomphrey et al., 2005)
and hummingbirds (Warrick et al.,
2005). These studies allow us to test the predictions of the model
for gross near-field and far-field flow velocities. The model does not however
predict higher order effects such as those occurring at wing beat frequency or
higher. In contrast, the fine temporal resolution of hot wire anemometry,
while spatially limited, affords new insights into the aerodynamics of flying
insects. Hot wire anemometry has been used in only a few previous studies on
animal flight (Bennett, 1970;
Norberg et al., 1993;
Lehmann, 1994) however these
measurements were not concerned with the spectral characteristics over a broad
frequency range. Here we show the first order effects such as mean induced
flow from anemometric data, in addition to disturbances occurring at wing beat
frequency and events occurring multiple times during each wing beat.
Effect of wing flutter on induced airflow
The high sensitivity of the anemometric records and the high sampling rate
used in these experiments allow us to be reasonably certain that the higher
frequency peaks (Fig.
4,Table 1) observed
in the anemometric records arise from aerodynamic disturbances occurring at
these frequencies. Because anemometers are mechanically decoupled from the
rest of the apparatus, these peaks are unlikely to be measurement
artefacts.
To test the hypothesis that the higher peaks arise from wing flutter, we measured the aerodynamic signature of artificial rigid vs flexible wings using hot wire anemometers. In oscillating flexible wings, we would expect flutter to cause aerodynamic disturbances primarily at the driving frequency but also at smaller or larger frequencies depending stiffness values of the material bending properties. Hence, in carefully controlled situations, any multiple frequency peaks observed in these anemometric measurements must arise from wing flutter. Conversely, because flutter is absent in a rigid wing, the multiple frequency peaks must be absent from anemometric measurements on rigid wings. The results shown in Fig. 6 suggest that the higher frequency peaks arise principally from wing flutter phenomena. Flexible paper wings oscillated by a mechanical lever at 50 Hz show peaks not only at 100 Hz. but also at 12.5, 25 and 75 Hz. In contrast, a rigid balsa wood wing, with the same mass and similar dimensions as the paper wing, shows a prominent peak only at the driving frequency of 50 Hz. Because all other experimental conditions were carefully controlled and the only variable was wing flexibility, the higher and lower frequency peaks in the aerodynamic signature can only be interpreted as resulting from wing flutter.
If true, these results predict that the actual motion of the flexible wings
must also show similar higher frequency peaks.
Fig. 7B shows the Fourier
transforms of actual wing motion from Combes and Daniel
(2003) compared to the Fourier
transform aerodynamic signature of one of the moths in this study
(Fig. 7C). Both records clearly
show frequency peaks at two and three times the wing beat frequency. Together,
these results strongly argue that the multiple frequency terms in the induced
airflow records are influenced by wing flutter. We cannot, however, rule out
contributions due to other phenomena such as the rapid efflux-influx of air
due to the near clap-and-fling events at the end of every upstroke
(Ellington et al., 1996;
Lehmann et al., 2005) or to
the aerodynamic effects of wing rotation at either each stroke reversal
(Dickinson et al., 1999;
Sane and Dickinson, 2002). If
the contributions of these phenomena are minimal, then hot wire anemometry in
the near field offers us a simple method to quantify the aerodynamics of
flutter in the wings of larger insects and birds.
The biological relevance of induced airflow
The effect of phasic airflow on airflow sensing in insects
Induced flow is a necessary byproduct of high Reynolds numbers fin-based or
wing-based locomotion such as swimming or flying. As illustrated by this case
study of Manduca sexta, there is both a phasic and a tonic component
in the induced airflow around the mechanosensory structures. The phasic signal
has a primary contribution from wing beat frequency and smaller tonic
components at higher multiples of wing beat frequency arise from wing
flexibility, and perhaps other phenomena such as clap-and-fling or wing
rotation. The experiments reported here were performed on tethered moths
flapping in absence of visual stimuli. However, visual stimuli play an
important role in the control of wing kinematics in Manduca sexta
(Frye, 2001) and are thus
likely to add further complexity to the overall magnitude of induced air flow.
Thus, the actual air speed experienced by the sensory structures of flying
insects may be highly complex and dependent on their sensory environment.
The periodic fluctuations in air flow due to stroke frequency provide the
timing cues that insects may use to tune their wing motion. The evidence for
this hypothesis comes primarily from extensive work on locust flight. In a
series of experiments, Horsmann et al.
(1983) showed that tethered
locusts flying in a wind tunnel coordinate the phase of their flight muscle
activity in response to the phase of an external air flow varied within 3 Hz
of the wing beat frequency of the locusts. This coordination was achieved
primarily via mechanosensory head hairs stimulated by the external
airflow. There is also strong evidence that locusts coordinate their wing
movements with the periodic disturbances to the external airflow, such as the
presence of another locust beating its wings upstream
(Kutsch et al., 1994).
Together, these studies suggest that induced airflow provides an important
timing signal, allowing the mechanosensory organs of flying animals to finely
tune their wing kinematics and synchronize their wing movements with the
neighboring insects during aggregation or swarming.
Effect of mean and phasic airflow on odor tracking in moths
Previous work on the flightless moth Bombyx mori has elucidated
how flapping wings can significantly enhance the flux of air over the antenna,
thereby increasing the effective volume of air sampled for odors
(Loudon and Koehl, 2000).
Because active flight typically demands higher wing amplitudes and wing beat
frequencies than the flightless case, enhancement of odor sampling is likely
to be even more pronounced during active flight.
Yet, in spite of its potential importance, the possibility that flying enables a better sampling of odor has received very little attention in most studies on odor tracking. The influence of wings on olfactory processes may be quite significant. The experiments reported here show that in hovering or stationary moths, there is significant upwind disturbance to the odor plumes and very likely an alteration of the filamentous structure of the incoming plumes. In hovering moths, practically all of the airflow experienced at the antennae results from entrained induced flow. With increasing ambient flow, the upwind disturbance due to flapping wings decreases. Thus, under windless conditions the pheromone or odor plumes may not retain much directional information after they are entrained by the wings, thus interfering with the insect's ability to precisely determine the source direction by purely olfactory means.
Accounting for self-generated airflow is also likely to provide new
insights into the timescales involved in odor discrimination. Because the fine
structure of odor plumes influences the orientation of flying moths
(Mafra-Neto and Carde, 1994),
it is important to determine the alterations to plume structure in the
vicinity of the antennae of a flying moth and its effect on odor tracking. For
example, a series of recent experiments on the moth Helicoverpa zea
suggest that these moths are able to distinguish between pheromone and
antagonist odor sources separated by at most 1 ms or 1 mm distance when
tracking odor plumes in a wind tunnel
(Baker et al., 1998;
Fadamiro et al., 1999). In
these moths, individual sensilla may contain at least two receptors, one
sensitive to pheromone and another to antagonistic odor. The
co-compartmentalization of these two neurons allows them to sample odors at a
single point in space and time and thus report on the synchronous arrival of
the two odors in a well-blended plume, thereby suppressing upwind flight to an
interspecific odor source. However, even the slightest separation (estimated
at 1 ms in time or 1 mm in distance) between the pheromone and antagonist
filaments detected by these moths indicates the presence of a conspecific
female in presence of other interspecific females and thus elicits plume
tracking behavior. Our studies suggest that if we take induced velocity into
account, the relative velocity of the plume strands with respect to the moth
antenna may be even greater than estimated previously, and thus the estimate
of temporal separation between the two odor plumes is likely to be well under
the 1 ms value reported in literature. Likewise, the spatial separation is
also likely to be lower than previously estimated. Further, an upwind mixing
of these plumes during flight is likely to blend the odor plumes to a greater
degree before they reach the moth's antenna.
It is also well known that moths show a better response to pulsatile odor
delivery as compared to uniformly distributed odors
(Baker et al., 1985). Our
results also suggest that an inherent pulsatility to odor delivery, arising
with each wing flap, exists in all flapping moths regardless of the ambient
plume structure and will further amplify this effect. Thus, the mere
initiation of flapping is likely to enhance the response to odor while
compromising the resolution between individual filaments of odor plumes.
Effect of mean induced airflow on thermoregulation in insects
In many insects, flight is possible only after the thoracic temperature
rises above a certain threshold value, well above the ambient temperature. In
Manduca sexta and other moths, this value is attained by muscle
thermogenesis through rapid wing vibration (shivering), whereas in some other
insects it is attained by behavioral themoregulatory mechanisms such as
basking in the sun. Forced convection is the main agent of heat loss as
compared to evaporative or radiative heat loss in insects
(Church, 1959). In hovering
insects, the heat loss due to induced airflow is particularly important. For
instance in Manduca sexta, samples of the speed of this airflow
(shown in Fig. 3) measured by
the axial inflow anemometer ranged from 0 to 0.52 m s-1 whereas the
radial outflow anemometer, which measures flow enveloping the insect's body,
measured a typical range between 0.25 to 3.55 m s-1 during flight.
Although these flows are of comparable magnitude to the airflow relative to
body arising from the moth's motion in air (observed mean horizontal speed of
3.6 m s-1; Stevenson et al.,
1995), there are very few published estimates on forced convection
in flying insects account for induced airflow (but see
May and Casey, 1983;
Borrell and Medeiros, 2004).
The induced flow at the outflow location for the bumblebee Bombus
terrestrus is estimated at approximately 1.8 m s-1 (Dudley and
Ellington,
1990a,b),
also significant compared to their maximum forward flight speeds of 5-6 m
s-1 (Ellington,
1999). Similarly, in Drosophila melanogaster (not a
thermoregulating insect), induced flow at the antennae is estimated at 0.15 m
s-1 and higher by a factor of 2-5 at the outflow location, and are
a significant percentage of their typical top flight speeds of 0.45-0.8 m
s-1 (Marden et al.,
1997; Frye et al.,
2003). Indeed, the flow immediately behind the wings is likely
always to be significant compared to forward flight speeds in most
insects.
In the case of Manduca sexta, cooling rates vary rapidly as the
air flow speed increases rapidly from 0 to 3 m s-1 before slowly
attaining a plateau at values higher than 5 m s-1
(Heinrich, 1971). When
calculating convective heat losses, the value of air flow used in the
calculation is usually the relative velocity of the moth in air, i.e. with
respect to far-field flow. For the case of hovering moths, these calculations
would therefore predict very little heat loss due to convection. Our studies
show that when we account for self-generated airflow, the calculated heat loss
would be substantially higher. A mean self-generated airflow of approximately
1.5 m s-1, typical of hovering hawk moths, doubles the estimated
cooling rates.
As shown in Fig. 5 and Table 2, the induced airflow increases with wing beat frequency, thereby further enhancing the cooling of the body. However, because an increase in wing beat frequency is also associated with greater heat generation within the thorax due to greater muscle activity, it is unlikely that insects increase their wing beat frequency to actively cool down during flight. However it is likely to be less effective at increasing thoracic temperatures than has been previously thought and induced airflow must be taken into account when considering the hypothesis that insects actively increase wing beat frequency for thermoregulation.
Similarly, just as the pulsatile mean fields due to induced flow augments transport of odors and heat, they would also augment a host of other flow-mediated transport processes including gas exchange and water loss, and hence it is important for researchers studying these phenomena in flying insects to account for the influence of induced flow due to flapping wings.
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