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First published online May 5, 2005
Journal of Experimental Biology 208, 1835-1847 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01580
Effects of size and behavior on aerial performance of two species of flying snakes (Chrysopelea)
Department of Organismal Biology and Anatomy, University of Chicago, Chicago, IL, 60637, USA
* Author for correspondence (e-mail: jjsocha{at}midway.uchicago.edu)
Accepted 9 March 2005
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Key words: snake, gliding, parachuting, performance, kinematics, behavior, scaling, Chrysopelea paradisi, Chrysopelea ornata
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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;
Socha et al., 2005).
Generally, most gliders use a fixed wing or wings to generate lift. Powered
flyers generate aerodynamic forces either through wing oscillation (flapping),
jetting or rotating. In stark contrast, when flying snakes
(Chrysopelea) move through the air, they pass lateral traveling waves
posteriorly along a long, dorsoventrally flattened body. When a flying snake
takes to the air, it becomes a `wing' that constantly reconfigures throughout
flight, moving in a complex motion in three dimensions. Thus, not only do
flying snakes possess a unique body shape among flying and gliding animals,
but their aerial behavior is the most dynamic of any vertebrate glider. Given
this combination of morphology and behavior, it is unclear to what extent
predictions of flight performance based on simple aerodynamic expectations
conform to actual snake gliding performance.
Basic aspects of aerial locomotion have been described for adult
individuals of the paradise tree snake, Chrysopelea paradisi
(Socha, 2002b;
Socha et al., 2005). C.
paradisi usually begin aerial locomotion with a jumping takeoff. A short
jump up and away from the branch is followed by a 1-5 m ballistic dive in
which the snake travels at an angle of 52-62° relative to the horizon.
During this dive, the snake's body rotates from a nose-up to a nose-down
position, and it begins to undulate, with the waves originating at or near the
head. The snake takes on a wide `S' shape (in plan view) in fully developed
aerial undulation, with low frequency (1-2 Hz), high-amplitude (wave heights,
20-34% SVL) traveling waves that differ in shape from undulations used during
terrestrial and aquatic locomotion in this species. As the snake falls, its
speed increases linearly with time until it either transitions to a steady
speed, or the rate of increase falls dramatically. Concurrently, the snake's
trajectory shallows; the glide angle (defined relative to the horizon)
decreases and the glide path becomes more horizontal. During this shallowing
phase of the glide, the snake undulates in a plane tilted upward towards the
head at approximately 20-40° to the direction of forward movement; the
posterior body translates substantially in the vertical axis. These data
indicate that several aspects of flight behavior show moderate to substantial
variability. However, because of the unusual morphology and flight dynamics of
C. paradisi, it is unclear if and how variation in these parameters
affects gliding performance.
The aerial snake's constantly changing body orientation should have profound consequences for its aerodynamic force production and stability. The snake's aerodynamic force production is a function of the geometry of its individual segments. Each segment's cross sectional shape, angle of attack, and position relative to the other segments will influence the net aerodynamic force vector. It is therefore likely that the magnitude, direction and location of this force changes as the snake's body constantly reconfigures while gliding. Similarly, stability is determined by the relative locations of the net aerodynamic force vector and the weight vector. The center of gravity is a function of the spatial distribution of mass; because the snake's body continuously reconfigures in three dimensions, its center of gravity also must shift continuously.
Consequently, the shifting of the center of gravity and center of pressure (the location of the net aerodynamic force vector) should influence the snake's kinematics. For example, when the tail swings downward in the undulatory cycle, the angle of attack of the posterior segment may differ from that of the anterior. With the anterior segment in a more horizontal posture, the difference in magnitude and direction of the forces acting on the anterior and posterior segments of the snake may create a moment that rotates the snake about the pitching axis. If this posture results in less lift on the snake as a whole, the glide angle may momentarily increase or the shallowing rate may decrease, with velocity changing in kind.
In addition to variability in flight behavior, flying snakes also exhibit
variation in body size and shape among different species and through ontogeny.
In addition to becoming less flattened during flight than C. paradisi
(Socha, 2002a), C.
ornata reaches larger body size in both length and mass
(Mertens, 1968). Body size has
pervasive effects on organismal function
(Schmidt-Nielson, 1984), and
scaling effects on flight performance have been shown in gliding lizards, one
of the few gliders in which flight trajectories have received detailed study
(McGuire, 1998). Therefore, in
addition to effects of flight behavior, the potential effects of size and
shape on flight performance also deserve attention in
Chrysopelea.
For gliders that operate at moderate Reynolds numbers (which encompasses
most animal gliders), a priori predictions can be made regarding the
scaling of some glide performance parameters. At glide equilibrium, by
definition the net aerodynamic force (the vector sum of the lift and drag) is
equal to the glider's weight. Lift and drag, in turn, are both proportional to
some characteristic area multiplied by the square of speed. Therefore,
 | (1) |
where M is mass, g is acceleration due to gravity,
S is area and U is speed. Rearranging and recognizing that
weight divided by area defines wing loading (WL), gives the
following:
 | (2) |
Dimensional analysis of this expression predicts that gliding speed should
vary as a function of body length or mass:
 | (3) |
 | (4) |
where l is body length and M is mass. Therefore a glider
with greater length, mass, or wing loading is predicted to require a higher
speed at glide equilibrium. Because lift and drag both increase proportionally
with speed squared, the lift-to-drag ratio should remain constant. The
lift-to-drag ratio determines glide angle and, therefore, gliders of the same
geometry but different size are theoretically capable of traveling at equal
glide angles (Vogel, 1994).
Thus, glide speed might be expected to increase, and glide angle remain
constant, if body size increases isometrically in flying snakes.
A complicating factor in such analyses is that much (and sometimes all) of a glider's trajectory may not be at equilibrium. The ballistic dive and shallowing glide phases (Fig. 1) of a trajectory are by definition non-equilibrium; it is unclear how size should affect performance during these portions of a snake's glide trajectory, given the snake's complex postural changes. It is also possible that the snake may actively choose to employ non-equilibrium gliding, even given sufficient takeoff height to reach equilibrium. For example, a snake might maximize takeoff speed for escape, with overall horizontal distance traveled unimportant, or it might maximize maneuverability to avoid collisions with obstructions. Such variation is possible only if the snake is able to modulate behavior to control performance.
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Thus, active behavioral modulation is a second major consideration in the
analysis of gliding flight performance. Animal gliders have been traditionally
viewed as `static' or `passive' flyers, implying rigidly held postures similar
to those of man-made gliding craft (from paper airplanes to sailplanes).
However, animal gliders can manipulate the size, shape and orientation of
their body and wings, and these behavioral adjustments can alter simple size
dependencies of flight parameters. For example, flying squirrels pitch nose-up
prior to landing by increasing the camber of the patagium to effect stall
(Scholey, 1986); flying
lizards may use similar fine adjustments of their rib-reinforced `wings'
(McGuire, 1998). Active and
continuous movement stands out as a hallmark of aerial locomotion in
Chrysopelea, suggesting that behavior features prominently in
determining performance. However, unlike other gliders that can effectively
change the size and shape of their `wings', flying snakes have no obvious
morphological control surfaces. Instead, whole body movements - frequency,
amplitude and orientation of body waves - may be used by the snake to control
flight speed, direction or orientation. In most other animals that locomote
using undulation, posteriorly directed waves propel the animal forwards
(Gray, 1968). Alternatively,
these behaviors may simply be a performance-neutral vestige of lateral
undulation (the most prominent locomotor mode in snakes;
Pough et al., 2001), in the
context of movement through a different medium (air).
In this study, we empirically test the effects of size and behavior on gliding performance in flying snakes. We examine size effects by measuring flight performance in different ontogenetic stages of C. paradisi, and by comparing the performance of C. paradisi to that of C. ornata, which reaches larger adult sizes than C. paradisi. Using data from these snakes, we also test two hypotheses of behavioral effects of undulation on the gliding performance in snakes. (1) The rate of undulation affects aerodynamic forces. Specifically, we test the prediction that snakes that use higher undulation frequencies generate more lift and glide farther than those with lower undulation frequencies. (2) The amplitude of undulation affects aerodynamic forces. Specifically, we test whether snakes that use greater amplitudes of undulation (a wider `S', in effect) generate more lift and hence travel farther than do snakes with smaller amplitudes. Together, these comparisons will contribute substantially to the understanding of how a highly non-standard body form can be used for aerial locomotion.
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Materials and methods |
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). Animal care and experimental procedures were approved by
the University of Chicago Animal Care and Use Committee (IACUC #70963),
Singapore Zoological Gardens and the Thailand National Research Council.
Performance trials
Snakes were manually placed on a horizontal branch at the top of a
scaffolding tower and were allowed to aerially descend to a grassy field below
(see Movies 1-4 in supplementary material). Digital videocameras and 35 mm SLR
cameras were used to record various aspects of the aerial locomotion. Snakes
were marked on the dorsal surface with 1 cm bands of non-toxic white paint
(Wite-Out, Bic Corporation, Milford, CT, USA) at the head-body junction,
midpoint and vent. All trials were conducted under similar ambient conditions
(temperatures from 25-32°C, humidity 50-70%). Wind speed was measured with
a Kestrel 2000 digital anemometer (Nielsen-Kellerman, PA, USA) at the top of
the tower. For most trials there was no noticeable wind; the maximum recorded
wind speed was less than 0.5 m s-1.
Two different methods were used to record performance in the two species.
C. ornata trials were conducted first, in two different locales - on
the Prince of Songklha University campus in Hat Yai, Thailand from a height of
8.87 m, and in an open field in Lockport, Illinois from heights of 7.3-8.3 m.
One videocamera (Sony DCR-TRV900, Tokyo, Japan) was placed to the side to
record a lateral view of the snake's trajectory, and a second videocamera was
placed at the top of the tower to record an overhead view. Video records from
the overhead camera were used to determine frequency of undulation and to
observe the orientation of the trajectory; only trials in which the snake
moved perpendicularly to the lateral view camera were used for analysis. The
lateral view video records were used to reconstruct the path of the snake in
two dimensions. Video records were transferred at highest quality to a
Macintosh G4 computer via Firewire (IEEE 1394) using Adobe Premiere
(version 6.0) software, with a raw image size of 720x480 pixels. Video
sequences were deinterlaced using NIH Image software (version 1.62, National
Institutes of Health, Bethesda, Maryland), yielding a sampling frequency of 60
Hz. In each sequence, the position of the snake was digitized using QuickImage
(Walker, 2001), a modified
version of NIH Image. Because the snake was small relative to the size of the
frame, the three landmarks could not be seen consistently from frame to frame.
Instead, the midpoint was digitized by either directly digitizing the midpoint
landmark (where visible) or by visually estimating the location of the middle
of the snake. The two-dimensional midpoint coordinates were smoothed with a
Lanczos five-point moving regression using QuickSAND software
(Walker, 1997).
Instantaneous glide angle was calculated as the angle between the horizon and a least-squares fit line of three temporally consecutive midpoint coordinates. Speeds were calculated by taking the first derivative of the position data in QuickSAND. Error due to visual estimation of the midpoint of the snake led to apparent fluctuations of about 5° in glide angle and about 1 m s-1 in gliding speed. Trends in glide angle and speed were identified by visually fitting a curve to coincide with the midpoint of these fluctuations. Over 200 trials were recorded from C. ornata; data from eight trials (representing eight snakes) were selected for analysis based on the quality and completeness of the video records.
A more precise data collection method, stereo photogrammetry using
videocameras, was used to obtain 3-D trajectory coordinates from C.
paradisi trials (Socha et al.,
2005). Snakes were launched from a height of 9.62 m in an open
field at the Singapore Zoological Gardens in Singapore. Two digital
videocameras (Sony DCR-TRV900) recorded the trajectories in stereo from the
top of the tower. Videocameras were synchronized by matching short-duration,
high-amplitude peaks in the audio signals. Better resolution (relative to the
C. ornata footage) permitted direct digitization of the marked bands
on the snake. The 3-D coordinates of the head, midpoint and vent landmarks
were reconstructed at 30 Hz using ERDAS Imagine with Orthobase software
(version 8.4; Leica Geosystems GIS and Mapping, LLC, Atlanta, USA). The mean
RMS coordinate error ranged from 1-14 cm, with error increasing as the
trajectory progressed. A total of 237 trials was recorded; data from 20 trials
(representing 20 snakes) were used for inter-individual comparisons, and nine
trials (representing two snakes) were used for preliminary intra-individual
analyses. See Socha et al.
(2005) for details of this
protocol and analysis.
Variables
The size and behavior variables quantified for analysis are given in
Table 1. Snout-vent length,
mass, projected area, wing loading and the square-root of wing loading were
used as metrics of size. The projected area of the entire snake, measured from
photographs of the snake's ventral silhouette in mid-trajectory, was used to
calculate wing loading. Mid-flight photographs were needed for these
calculations because airborne Chrysopelea have a different
cross-sectional shape relative to their non-flight configuration.
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Two aspects of aerial behavior were quantified - the frequency and the
lateral amplitude of the snake's aerial undulation. Undulation frequency was
calculated as the inverse of the period of one undulatory cycle, either
calculated from the reconstructed 3-D data of the head's side-to-side movement
(C. paradisi) or estimated directly from the video records by
visually identifying the lateral-most extent of the midpoint throughout its
cycle (C. ornata). The two methods were tested for consistency using
the C. paradisi records and found to produce indistinguishable
results. Because no single amplitude metric was obviously superior, three
measures of amplitude were used - the undulation wave heights of the head, the
vent and their average. Undulation wave height was measured as the maximum
lateral separation (based on the direction of forward travel) between the
landmark and the midpoint, and represents a proxy for the width of the snake's
traveling waves (see Socha et al.,
2005). (For the reader's benefit, hereafter the term `amplitude'
will be used in place of `wave height'. Strictly, amplitude values are
one-half of wave height values.) Amplitude data were also normalized by
snout-vent length to create dimensionless measures of amplitude. Amplitude
data for C. ornata are not available because only 2-D trajectory data
were recorded for this species, and it was not possible to measure
side-to-side excursion of the snake from the single overhead view with
sufficient accuracy. For C. paradisi, the possibility of an
interactive effect of frequency and amplitude was explored by defining six
interaction effect variables - the amplitudes (absolute and relative) of the
head and vent separately, and the average amplitude (absolute and relative) of
the head and vent, each multiplied by the undulation frequency. Furthermore,
to test for effects of interactions between size and behavior, each relative
amplitude variable and frequency were separately multiplied by snout-vent
length to create four behavior by size interaction variables.
Because it is not known how Chrysopelea uses aerial locomotion in
the wild (e.g. to traverse short gaps or to travel long distances), multiple
measures of performance were analyzed. Seven variables associated with the
beginning of the trajectory were considered - the airspeed at takeoff, the
ballistic dive angle (the maximum glide angle during the dive; the larger the
angle, the more vertical the dive), the ballistic dive depth (the vertical
travel of the dive), the ballistic dive time, and the acceleration in the
initial (pre-transition; see Fig.
1) phase of the trajectory. Assuming equal performance in the
shallowing phase, snakes that use a smaller ballistic dive angle or a smaller
ballistic dive depth should travel farther horizontally. Twelve variables
associated with the shallowing glide phase of the trajectory were considered.
These include the speed and time at transition; the shallowing rate (the rate
of change of glide angle during the shallowing phase of the trajectory); the
maximum speed and minimum glide angle achieved; and total horizontal distance
traveled. Because the snakes' trajectories were still shallowing when they
exited the view of the cameras or landed
(Socha et al., 2005), the
minimum observed glide angle was not an equilibrium glide angle (which defines
the absolute minimum glide angle obtainable in still air at a given speed). To
compare minimum glide angle in trajectories of different length and video
recording coverage, the minimum glide angle was defined at the lowest common
vertical height for all snakes, 7 m below the starting height. Detailed
definitions of these performance variables can be found in Socha et al.
(2005).
Data selection criteria
Because this study is concerned with the upper limits of performance, only
data from the `best' trajectories were used, where `best' is defined as the
trial with adequate video records in which the snake traveled the greatest
horizontal distance. We attempted to minimize the effect of motivation on
performance by recording as many trials as possible and by using the same
stimulus protocol for each snake. Because the path of the snake in its `best'
trial did not always coincide with the region of overlap in the views of the
two videocameras, some variables in certain trials were undetermined. For the
two intra-individual analyses, all digitizable trials (regardless of
horizontal distance traveled) were examined.
Statistical analyses
To separate the effects of size and behavior on C. paradisi flight
performance, a multiple regression was performed on each performance variable
using all size, behavior and interaction variables as possible predictors. The
goal of this exploratory analysis was to eliminate spurious correlations and
only include variables that significantly contribute to the overall
performance variation. Because there were no a priori reasons to
exclude any size, behavior, or interaction variable prior to analysis, a
stepwise regression technique was employed
(Sokal and Rohlf, 1995).
Variables entered the model at a probability of 0.25 ('P-to-enter')
and were removed at a probability of 0.10 ('P-to-remove'). For
regressions on airspeed at takeoff and ballistic dive performance variables,
behavioral variables were not included because, within this early stage of the
trajectory, aerial undulation was not fully developed. After the winnowing of
variables via multiple regression, each significant predictor was
regressed on its associated performance variable to determine the direction
and strength of trends. All statistical analyses were conducted using JMP
statistical software (version 5.0, SAS Institute, Cary, NC, USA).
To test the effects of behavior on performance independent of size, we conducted the same multiple regression tests on multiple trials within an individual. Because sufficient data were only available from two snakes (four and five trials each), results from these tests should be regarded as preliminary.
To evaluate the hypotheses of performance variable scaling among
individuals, airspeed and minimum glide angle were regressed on wing loading,
snout-vent length, and body mass using reduced major-axis (RMA) regressions
(LaBarbera, 1989;
Rayner, 1985). Ninety-five
percent confidence intervals of the slopes were estimated using bootstrap
standard errors (10,000 bootstrap replicates; analyses performed using a
custom Hi-Q program written by M.L.). To evaluate the scaling of basic
morphological features, a permutation test with was used to compare the RMA
slopes and intercepts of the snout-vent length/mass regressions for each
species (2000 replicates; analyses performed using a custom Hi-Q program
written by M.L.). All data were log-transformed prior to analysis.
Student's t-tests were used to compare behavior and performance between C. paradisi and C. ornata. To accommodate different launch heights for the two species, horizontal distance traveled was measured after the snake reached at a common vertical drop 7.5 m below the takeoff branch. Note that this is a different standard than that used to determine a common point for glide angle within C. paradisi. Some performance variables were not compared between species due to lack of sufficient data for C. ornata.
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Each significant size and behavior predictor was regressed on its associated performance variable. Maximum sinking speed and minimum glide angle were directly proportional to snout-vent length and mass, respectively; shallowing rate and horizontal distance traveled were indirectly proportional to snout-vent length (Fig. 2). Thus smaller snakes traveled farther than larger snakes (Fig. 2A), with trajectories that shallowed more quickly (Fig. 2B), and reached lower minimum glide angles (Fig. 2C) and lower maximum sinking speeds (Fig. 2D). Airspeed at transition, maximum airspeed and maximum horizontal speed were directly proportional to the interaction of vent relative amplitude by snout-vent length; sinking speed at transition was directly proportional to the interaction of average relative amplitude by snout-vent length, and horizontal speed at transition was directly proportional to average relative amplitude (Fig. 3). Thus snakes with higher interactions between relative amplitude and body size transitioned out of the initial acceleration at higher airspeeds (Fig. 3A) and sinking speeds (Fig. 3B), and attained higher maximum airspeeds (Fig. 3C) and horizontal speeds (Fig. 3D). Snakes that used higher average relative amplitudes transitioned out of the initial acceleration at higher horizontal speeds (Fig. 3E).
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Within individuals, there were few consistent trends (Table 3). For the most part, performance variables that yielded significant predictors were not congruent either between the two individuals or in comparison with the inter-individual data. However, both maximum airspeed and horizontal speed included vent relative amplitude (either alone or interacting with another variable) as a consistent predictor between the individual and inter-individual data. In contrast to the inter-individual analysis, undulation frequency figured prominently as a predictor for five of nine performance variables. For one individual, using lower undulation frequencies yielded longer trajectories.
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In scaling of performance comparisons, RMA slopes for snout-vent length vs airspeed (equation 3) and mass vs airspeed (equation 4) were not significantly different from those expected under isometry, whereas the slope of wing loading vs airspeed (equation 2) was significantly different (Table 4). The RMA regressions for each size variable on minimum glide angle were significantly different from zero, meaning that size significantly affected glide angle at a given point in the trajectory (namely after 7 m of vertical drop).
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Because size was found to influence most aspects of performance, the relationships among size variables within C. paradisi were examined further. Projected area, mass and wing loading were regressed on snout-vent length using RMA regressions as described above. The RMA slopes for mass and area relative to snout-vent length were not significantly different from those expected under isometry (Table 4). Wing loading exhibited positive allometry with snout-vent length - larger snakes had relatively higher wing loadings than smaller snakes. To explore the effect of the smallest snake (a young juvenile) on these relationships, the RMA regressions and bootstrap algorithms were rerun with this individual removed; no effect was found on mass or area, and the positive allometry with wing loading was further strengthened.
Interspecific comparisons
C. paradisi and C. ornata differed significantly in most
performance comparisons (Fig.
4). C. paradisi traveled a greater horizontal distance
(7.9±1.3 m vs 3.6±0.9 m, mean ±
S.D., d.f.=21, P<0.0001), with trajectories
that started with a lower ballistic dive angle (57±4° vs
74±3°, d.f.=24, P<0.0001), shallowed at a higher rate
(21±7° s-1 vs 11±8° s-1,
d.f.=24, P=0.002), and achieved a lower minimum glide angle
(34±8° vs 65±6°, d.f.=24, P<0.0001)
and higher maximum horizontal speed (8.0±0.9 m s-1
vs 3.3±0.6 m s-1, d.f.=18, P<0.0001).
Mean undulation frequency (1.3±0.3 Hz vs 1.1±0.2 Hz),
sinking speed at transition (6.0±0.7 vs 6.6±1.3 m
s-1), and maximum sinking speed (6.3±0.9 vs
6.9±1.0 m s-1) were not significantly different between the
two species.
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To evaluate factors that might contribute to the performance differences
between C. paradisi and C. ornata, we compared basic
morphological features between these species. C. ornata were
generally more massive than C. paradisi at any given snout-vent
length (Fig. 5). Permutation
tests revealed that the intercepts of the RMA regression lines of mass on
snout-vent length are significantly different (-4.26 vs -5.23 for
C. paradisi and C. ornata, respectively; P=0.01,
one-sided test), with marginally different slopes (3.16 vs 3.79,
P=0.07, one-sided test). Furthermore, unlike C. paradisi, C.
ornata shows strong positive allometry, with longer snakes having
relatively higher masses than expected under isometric scaling. Projected area
could not be measured for C. ornata, but it is likely that wing
loading is also higher than in C. paradisi (at equal snout-vent
lengths) because C. ornata are more massive and do not flatten to the
same extent (a smaller change in relative body width;
Socha, 2002a).
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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). However, this method, which produces the smallest set of
predictor variables `adequate' to explain the variation, should only be viewed
as exploratory. As described by Sokal and Rohlf
(1995), the addition or
subtraction of a single variable can cause radical changes in the composition
of the final predictor set (although this effect was not apparent here). In
addition, in a stepwise regression the `P-to-enter' and
`P-to-leave' values (corresponding to the significance values to
include or remove a regressor term from the model, respectively) are
arbitrarily chosen and can similarly produce differences in predictor sets.
(However, the results here were generally robust to small changes in
P-value.) Lastly, the predictor variables chosen by the stepwise
regression should not be viewed as the most important or sole set of
variables. Some variables may be functionally important but can be excluded
due to correlation with variables in the predictor set. Therefore, the results
presented here should not be viewed as a `solution', but rather as a starting
point for further investigation, particularly by informing attempts to
experimentally examine questions about the aerodynamics of snake flight. Given these caveats, it can be broadly stated that size had a strong influence on gliding flight performance in C. paradisi. Of the nine significant relationships determined by multiple regression analysis, eight were influenced by size alone or by size interacting with behavior. Furthermore, the trends for performance variables with size predictors all pointed in the same direction. Within a 7 m vertical drop, smaller snakes were more capable of long-distance travel - they used higher shallowing rates, lower minimum glide angles and achieved greater horizontal distances. Although these variables appear to be correlated, their relationship is not physically constrained - it is possible for snakes to use different shallowing rates for different amounts of time to reach the same minimum glide angle. Furthermore, smaller snakes reached lower maximum sinking rates. Therefore, smaller snakes must generate relatively more lift and/or create less drag than do larger snakes. How they do so is unclear, but it is evident that within C. paradisi, smaller snakes are better gliders. Although there were insufficient data for rigorous testing, this trend appears to be true for C. ornata as well.
Only one performance variable, horizontal speed at transition, was related to a behaviorial variable alone. All but one other speed variable were related to the interaction between amplitude and size. Within individuals (and thus independent of size), vent amplitude was related to multiple performance variables, strengthening the conclusion that the larger the lateral sweep of the vent during undulation (relative to body size), the faster the snake traveled, from the start of the shallowing phase onward. Functionally, it is unclear if it is the movement, posture, or size of the posterior end of the snake that drives this relationship. One possibility is that the greater the relative vent amplitude, the greater the length of snake body that lies perpendicular to the oncoming airflow, with relatively more lift produced in this region. If this were the case, the lift vector would have to be angled in a direction that favors increasing the flight speed. However, the limited number and position of landmarks preclude the precise determination of how vent amplitude relates to snake posture and shape in the air. Another possibility is that the lengths of the snake's body that are perpendicular to the flow may be physically closer together, making them act increasingly like one larger airfoil with a bigger chord length, rather than as two separate airfoils with smaller chord lengths. As the two body sections move closer together at higher undulation amplitudes, the aerodynamic effects on the two body sections may become coupled, with the emergent property of higher aerodynamic force. Future studies that provide a greater number of landmarks on the snake during flight would more precisely resolve these issues.
The fact that undulation frequency was not related to any performance variable strongly suggests that frequency has a relatively minor role, if any, in aerodynamic force production during snake flight. Additionally, no significant differences in frequency were found between the species, even though there were large differences in performance. This means that the traveling wave motion of aerial undulation is probably not involved in generating aerodynamic forces. If true, then standard fixed-airfoil theory should be sufficient to explain snake flight aerodynamics. By contrast, frequency had an effect on five of eight performance variables within individuals. However, these results should be viewed with caution because there was no replication of frequency effects between the two individuals. This lack of consistency may be a consequence of small sample size, both in number of trials analyzed per individual (four and five), and in total number of individuals (two). To resolve this issue, it is necessary for future studies to analyze trials from multiple individuals, with trials encompassing the full range of performance for each individual.
Although it would appear surprising that the most prominent feature of
snake flight (undulation) plays little role in force generation, this does not
preclude the possibility of second-order effects of undulation on glide angle
(see Socha et al., 2005).
Aerial undulation may serve other roles, such as maintenance of stability, in
which undulation would prevent rolling or pitching by moving the centers of
gravity and pressure so that their average locations coincide
(Thomas and Taylor, 2001).
Alternatively, aerial undulation may be a functionless behavioral vestige.
However, given the considerable sophistication of gliding in C.
paradisi (e.g. control of flight direction, morphological specialization;
Socha et al., 2005), it seems
plausible that undulation plays a functional role in snake flight, related to
stability or control.
It is possible that the behavioral correlations with flight performance
reflect an underlying relationship to size. In fact, both absolute undulation
amplitude and frequency are size-dependent - larger snakes produce larger
amplitudes and lower undulation frequencies
(Fig. 6). Flapping frequencies
decrease with increasing size in insects and birds
(Greenwalt, 1975), a similar
effect of body size. However, only relative amplitude variables, not absolute,
affected performance in C. paradisi, and relative undulation
amplitude is not correlated with body size. Vent relative amplitude in
particular was a prominent predictor of performance, both in combination with
size among C. paradisi, and in combination with frequency within
individuals. Although the preliminary intra-individual results suggest that
vent amplitude may be a size-independent predictor of performance for certain
features of the glide trajectory, performance variables may respond
differently in comparisons of intra- and inter-individual relationships.
|
No combination of size, behavior, or interaction variables significantly explained the variation in over half of the performance variables for C. paradisi. All of these performance variables were related to the initial phases of the trajectory, which suggests that performance in the initial phase is determined by unexamined variables, or that it is uncoupled from late-glide performance. Whatever the proximate cause, it is clear that performance differences among individuals developed in the shallowing phase of the trajectory, and not during the ballistic dive. This conclusion is somewhat surprising, as it would be expected that the steeper the ballistic dive, the shorter the horizontal distance traveled. However, this is indeed the case when the data are compared at sufficiently shallow points in the trajectory.
Predicted scaling of performance
Following basic aerodynamic theory, flight speed was predicted to be
positively correlated with length, mass and wing loading. Indeed, airspeed
scaled isometrically with snout-vent length and mass; however, it increased at
a marginally slower rate than expected with respect to wing loading. These
results suggest that as size increases, some other control features partially
compensate for increased wing loading, presumably by generating extra lift
and/or drag and thus slowing descent.
Minimum glide angle was predicted to be size-independent, but here was
found to be positively correlated with all size variables. The prediction was
based on the assumption that minimum glide angle was measured at equilibrium,
a condition not met by the snakes in this study. Reasons that equilibrium
gliding flight was not observed include experimental design (see
Socha et al., 2005), but it is
also possible that snake gliding flight is inherently unsteady. This
possibility is seldom discussed in the gliding literature - equilibrium
gliding is generally assumed as the norm. Given complex 3-D environments and
multiple reasons for gliding, it is possible that equilibrium gliding in many
gliders is the exception rather than the rule. To address this hypothesis, it
is most relevant to measure the kinematics of gliding flight in animals that
are locomoting in the wild, rather than in controlled settings such as in this
study.
Clearly, size plays a major role in driving performance differences within C. paradisi. Larger snakes should be equally good gliders (traveling equal distances, but at higher speeds) as smaller snakes if equilibrium theory is a reliable guide; instead, smaller snakes are much better gliders. That this result was not predicted may simply reflect that this study did not model the non-equilibrium aspects of a glider's trajectory. Future studies comparing full trajectories that reach equilibrium with theoretical models that consider how drag and lift change from takeoff will help further clarify if and how gliders modify their performance through behavior. In addition, unexamined variables, such as cross-sectional shape and angle of attack, may have strong effects on performance. Angle of attack was not addressed due to lack of precise data; similarly, there are no data available on if and how cross-sectional shape differs within a trajectory or among snakes.
In the few other gliders that have been examined in detail, performance
also generally decreases as size increases. McGuire
(1998) found similar patterns
of size and performance among flying lizard species (Draco) -
interspecifically, smaller lizards achieved lower glide angles and were
generally more flexible in performance. In parachuting geckos (Ptychozoon
lionatum), horizontal distance traveled decreases with wing loading
(Marcellini and Keefer, 1976).
By contrast, larger birds achieve lower glide angles (e.g. pigeon, 9.5°;
falcon, 5.5°; albatross, 3°;
Vogel, 1994), but body size is
only one of many differences among these flyers; wing shape (particularly wing
aspect ratio) may strongly drive these differences.
Interspecific differences in performance
Differences in performance between the two snake species were striking. In
all aspects, C. paradisi outperformed C. ornata, traveling
more than twice as far using a shallower ballistic dive and higher shallowing
rate, and achieving a lower minimum glide angle and lower maximum sinking
speed. Although this study identifies these differences, their causes remain
unclear. There are no significant differences in undulation frequency between
the two species, although individual C. paradisi reach higher maximum
frequency and C. ornata lower minimum frequency. At least three other
possibilities remain untested. First, the species may differ in undulation
amplitude. Amplitude could not be measured from the footage we were able to
collect from C. ornata but, as shown, undulation amplitude can affect
multiple aspects of glide performance in C. paradisi. Second, there
may be differences in body orientation throughout flight, which was unexamined
for both species. Differences in orientation should cause differences in
wakeflow patterns, and therefore the resulting aerodynamic forces, which in
turn may affect performance. Comparisons of both amplitude and orientation
could be accomplished through further work to document the 3-D kinematics of
C. ornata. Third, differences in flight morphology between the
species have only been partially examined here. C. ornata are more
robust (greater mass per length) than C. paradisi and likely have
higher wing loadings. Furthermore, C. ornata's cross-sectional shape
is more rounded on the ventral surface than that of C. paradisi
(Socha, 2002a). Modeling
studies of the effects of cross-sectional shape on aerodynamic force
generation are required to relate these morphological differences to
performance differences.
The performance differences between the two species are likely to be even
more pronounced when snakes take off from greater heights. Heyer and
Pongsapipatana (1970) launched
C. ornata from a 41 m tower, a height that should have provided
sufficient vertical distance for the snakes to reach equilibrium. Even from
this great height, the maximum distance traveled by C. ornata was
only 30 m. In marked contrast, the `best' C. paradisi specimen in
this study would travel an estimated 142 m if launched from the same height
(assuming a linear scaling of performance with launch height). Given such
differences, C. paradisi should be classified as `gliders' and C.
ornata as `parachuters' (sensu
Oliver, 1951) although the
value of this terminology has been questioned
(Moffett, 2000;
Vogel, 2003). Furthermore,
this study confirms the prediction of Mertens
(1970), who suggested that
such differences in flight ability would exist based on his observation that
C. paradisi dorsoventrally flattened when sunning in captivity,
whereas C. ornata did not.
Ecological implications
Differences in morphology and locomotor performance can drive differences
in ecology (e.g. Losos, 1990;
Garland and Losos, 1994;
Norberg 1994; and references
therein). Intra- and inter-specific differences in performance ability in
flying snakes can be used to generate hypotheses of ecological differences in
their usage of flight, which in turn should be tested with field data. Within
C. paradisi, smaller snakes are better gliders and therefore might
glide more often and/or travel greater distances between trees. Larger snakes
cannot glide as far from a given height and therefore might use aerial
locomotion primarily to traverse small gaps between trees or branches.
Furthermore, these differences in performance may influence microhabit
utilization in the trees. For example, smaller snakes need less vertical
height to travel a given distance in the air, so they may spend more time at
lower levels of the tree or take off from lower average heights. Between
C. paradisi and C. ornata, C. paradisi are better gliders,
which suggests that C. paradisi use flight more often and travel
greater distances than C. ornata. Unlike C. paradisi, C.
ornata appear to be unable to maneuver in the air
(Socha, 2002a); therefore,
flight may pose a greater risk from potential aerial predators.
Because size is related to age in reptiles (at least until growth
asymptotes; see Andrews, 1982),
size-related performance differences found in this study should also reflect
ontogenetic differences in performance. The C. paradisi used in this
study approximately span the full size range of the species and, thus, the
full ontogenetic range was nearly represented. Although on the whole smaller
snakes were better gliders, the smallest snake (a young juvenile, mass = 3 g)
did not have the highest scores for any performance variable. This suggests
that performance ability peaks at an intermediate point in ontogeny. This peak
seems to occur at a fairly small body size - the `best' snake was about four
times greater in mass than the young juvenile, but about eight times less
massive than the largest snake. This ontogenetic pattern contrasts with
locomotor performance in terrestrial snakes. For example, larger (and thus
older) garter snakes have higher absolute burst speeds and endurances than
smaller snakes (Jayne and Bennett,
1990), a difference that reflects effects of size rather than
experience. That the young juvenile could glide well suggests that little to
no learning period exists in ontogeny - C. paradisi are likely
functional gliders upon emerging from the egg.
In conclusion, it is clear that size and behavior strongly affect gliding flight performance in the flying snake, C. paradisi. Smaller snakes travel farther, using higher shallowing rates and lower speeds. These results can be used to inform future studies in which these features are isolated to determine their physical affect on aerodynamic force generation. C. paradisi are significantly better gliders than C. ornata, which are more robust but use the same undulation frequency. The differences in cross-sectional shape between the two species may be largely responsible for their performance differences; modeling studies should therefore highlight the effects of variation of body shape on aerodynamics. This study is a first step to understanding which factors most significantly affect flight performance in snakes, a novel form of gliding locomotion in animals.
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Acknowledgments |
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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