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First published online October 18, 2006
Journal of Experimental Biology 209, 4203-4213 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02488
Aquatic turning performance of painted turtles (Chrysemys picta) and functional consequences of a rigid body design
Department of Biological Sciences, Clemson University, 132 Long Hall, Clemson, SC 29634, USA
* Author for correspondence (e-mail: grivera{at}clemson.edu)
Accepted 10 August 2006
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Summary |
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 TOP Summary IntroductionMaterials and methodsResultsDiscussionReferences |
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avg) as measures of maneuverability and agility,
respectively. We filmed turtles conducting forward and backward turns in an
aquatic arena. Each type of turn was executed using a different pattern of
limb movements. During forward turns, turtles consistently protracted the
inboard forelimb and held it stationary into the flow, while continuing to
move the outboard forelimb and both hindlimbs as in rectilinear swimming. The
limb movements of backward turns were more complex than those of forward
turns, but involved near simultaneous retraction and protraction of
contralateral fore- and hindlimbs, respectively. Forward turns had a minimum
R/L of 0.0018 (the second single lowest value reported from any
animal) and a maximum avg of 247.1°. Values of
R/L for backward turns (0.0091-0.0950 L) were much less
variable than that of forward turns (0.0018-1.0442 L). The
maneuverability of turtles is similar to that recorded previously for
rigidbodied boxfish. However, several morphological features of turtles (e.g.
shell morphology and limb position) appear to increase agility relative to the
body design of boxfish.
Key words: biomechanics, locomotion, swimming, performance, maneuverability, turtle
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; Blob et al.,
2006). For example, animals rarely move in a straight line for
prolonged durations. Animals that live in complex habitats or engage in
predator-prey interactions may need to change direction frequently as they
negotiate obstacles or attempt to evade predators or capture food. Thus,
turning performance may be a critical aspect of locomotion for many animals
(Howland, 1974;
Gerstner, 1999;
Domenici, 2001;
Hedenström and Rosén,
2001).
Turns generally incorporate two types of motion: (1) rotation about a
vertical axis through the center of an organism (reorientation), and (2)
translation of this axis (i.e. the center-of-rotation) across a horizontal
plane (Howland, 1974;
Norberg and Rayner, 1987;
Webb, 1994). Turning
performance can be measured with respect to both of these types of motion. The
speed of reorientation is generally measured as agility, which can be defined
as the angular velocity about a center-of-rotation on the animal (i.e.,
the turning rate), with higher values indicating superior performance
(Webb, 1994). Performance with
respect to translational movement is generally termed maneuverability, which
is defined as the ability to turn in a limited space
(Norberg and Rayner, 1987).
Maneuverability is most commonly measured as the minimum radius of the turning
path [denoted as R (Howland,
1974)]. For R, performance is considered to increase as
turning radii decrease. Thus, maximal turning performance is attained through
superior values of both agility and maneuverability (i.e. high values of
and low values of R).
Over the past few decades, several studies have investigated the effects of
particular morphologies on turning performance
(Norberg and Rayner, 1987;
Carrier et al., 2001;
Fish, 2002;
Walter and Carrier, 2002).
Among aquatic animals, studies of turning performance have focused primarily
on actinopterygian fishes (Webb and Keyes,
1981; Webb, 1983;
Blake et al., 1995;
Schrank and Webb, 1998;
Gerstner, 1999;
Walker, 2000;
Webb and Fairchild, 2001),
though a few studies have also examined turning performance in chondrichthyans
(Kajiura et al., 2003;
Domenici et al., 2004),
cetaceans (Fish, 2002),
pinnipeds (Fish et al., 2003),
penguins (Hui, 1985), squid
(Foyle and O'Dor, 1988) and
beetles (Fish and Nicastro,
2003). For aquatic taxa, morphological attributes that are
correlated with turning performance include: body shape, the position and
mobility of propulsors and control surfaces (e.g. fins, flippers and limbs),
and body flexibility (Blake et al.,
1995; Fish, 1999;
Fish, 2002;
Walker, 2000;
Fish and Nicastro, 2003). Body
flexibility varies substantially among different aquatic animals, ranging
along a continuum from animals that are highly flexible to those that are
unable to bend their body axis. Along this continuum, three broad categories
of body design can be recognized: flexible, stiff and rigid. Animals with
flexible bodies can bend their body axis easily; examples include many
ray-finned fishes, especially those inhabiting complex environments
(Domenici and Blake, 1997).
Animals with stiff bodies have a more limited capacity to bend the body axis
and include many pelagic swimmers, such as thick-skinned tuna and many
cetaceans (Blake et al., 1995;
Fish, 2002). Finally, animals
with rigid bodies are completely inflexible and have no capacity to bend the
body axis. Rigid body designs can be found in many animals with exoskeletons,
shells, or other forms of body armor
(Walker, 2000;
Fish and Nicastro, 2003).
Flexibility of the body is thought to enhance turning performance for
several reasons (Fish, 1999;
Fish, 2002;
Walker, 2000). First, having a
flexible body allows an organism to turn in a circular space with a radius of
less than 0.5 body lengths (L), the theoretical minimum for a rigid
structure turning with no translation
(Walker, 2000). Second,
flexibility of the body allows animals to reduce their second moment of area
about the rotational axis, thereby decreasing rotational inertia
(Walker, 2000;
Walter and Carrier, 2002).
Conversely, a rigid body should impair both of these advantages of body
flexibility. Although turning performance has been studied in a large number
of diverse flexible- and stiff-bodied species, explicit evaluations of turning
performance among rigidbodied animals have been limited to one invertebrate
and one vertebrate: whirligig beetles
(Fish and Nicastro, 2003) and
boxfish (Walker, 2000). The
results of these studies have led to differing conclusions as to whether rigid
body designs actually constrain turning performance. In particular, boxfish
can turn with a very small radius (i.e. are highly maneuverable), but turn
fairly slowly [i.e. have low agility
(Walker, 2000)]. In contrast,
whirligig beetles display high angular velocities (i.e. high agility) during
turns, but also have large turning radii [i.e. low maneuverability
(Fish and Nicastro,
2003)].
Because examinations of aquatic turning performance in rigid-bodied animals
have had a limited taxonomic scope, the effects of many body shapes and
designs on aquatic maneuverability and agility have yet to be evaluated. One
group of vertebrates that provides an ideal system in which to evaluate the
effects of rigid bodies on aquatic turning performance is the turtles. Turtles
represent the oldest extant group of rigid-bodied vertebrates and the only
such group of tetrapods (Rieppel and
Reisz, 1999; Santini and
Tyler, 2003). The chelonian bauplan represents an evolutionary
novelty that has remained relatively unchanged for over 200 million years
(Burke, 1989;
Gaffney, 1990). In turtles,
the vertebrae are fused dorsally with a bony carapace, precluding movement of
the axial skeleton between the base of the neck and the tail. As a result of
their immobilized axial skeleton and reduced tail, thrust in swimming turtles
is generated exclusively by the movements of fore- and hindlimbs
(Pace et al., 2001). Despite
the potential constraints of a rigid body on locomotion in turtles, over 100
species currently live in freshwater and marine habitats. Freshwater species
in particular have adapted to life in a diverse array of aquatic flow regimes,
ranging from ponds and lakes to fast flowing rivers, while also maintaining
the ability to move efficiently on land
(Ernst et al., 1994). Although
morphological data suggest that the shells of freshwater turtles are highly
suited for movement through aquatic habitats
(Aresco and Dobie, 2000;
Claude et al., 2003),
examinations of swimming performance in freshwater turtles have been limited.
Knowledge of aquatic locomotion in freshwater turtles consists mainly of
studies of limb kinematics during rectilinear swimming or underwater walking
(Zug, 1971;
Davenport et al., 1984;
Pace et al., 2001;
Willey and Blob, 2004). No
study has yet evaluated how turtles generate turns, or quantified any aspect
of turning performance for species in this lineage. Because they possess a
very different body design than that of boxfish (with a dorsoventrally
flattened body shape and jointed limbs, rather than flexible fins, as
propulsors) turtles provide an important comparison for evaluating the effects
of morphological design on hydrodynamic performance in vertebrates.
To gain insight into the effects of body design on aquatic turning
performance, we measured the performance of aquatic turns by painted turtles
(Chrysemys picta), a freshwater species that exhibits a generalized
morphology typical of the emydid turtle clade
(Ernst et al., 1994). The
specific objectives of this work were twofold. First, we measured limb
kinematics in turning turtles in order to evaluate the mechanisms used by
turtles to produce turns. Second, we compared the turning performance of
painted turtles with that previously measured from other taxa in order to
further evaluate the effects of different body designs on aquatic locomotor
performance.
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Materials and methods |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Turns that each turtle executed as it chased fish were filmed (150 Hz)
simultaneously in ventral and lateral views using two digitally synchronized
high-speed video cameras (Phantom V4.1,Vision Research, Inc., Wayne, NJ, USA).
The ventral view was captured using a mirror placed at 45° to the tank
bottom, which allowed a camera to be focused on a central 25 x25 cm area
that was delineated on the transparent bottom of the test arena. As a result,
turns that occurred within 2.5 cm of the sides of the arena (
0.5
L; body length) were not entirely within the field of view and were
excluded from analysis; this allowed us to ensure that turtles conducted turns
without contacting the sides of the arena. A 1 cm square grid filmed in the
ventral view for each trial provided a distance calibration for video analyses
(see below). Lateral view videos for each trial were reviewed to ensure that
turtles were not in contact with the bottom of the tank, and that they
remained level (less than ±15°) and in a horizontal plane
throughout the turn. Any turn that did not conform to these criteria also was
excluded from analysis. Acceptable trials were downloaded to a computer as
proprietary format CINE (.cin) files and converted to AVI format for
analysis.
Turning data analysis
To begin quantifying aquatic turning kinematics and performance in turtles,
the positions of landmarks on their bodies were first digitized from
ventral-view AVI video files using a modification of the public domain NIH
Image program for Macintosh, developed at the US National Institutes of Health
and available on the internet at
http://rsb.info.nih.gov/nih-image/
(the modification, QuickImage, was developed by J. Walker and is available
online at
http://www.usm.maine.edu/~walker/software.html).
Nineteen points were digitized on every other video frame, yielding effective
framing rates of 75 Hz. These points were located on the head (tip of snout),
plastron (six points along the midline: anterior edge, humeral-pectoral
suture, pectoral-abdominal suture, abdominal-femoral suture, femoral-anal
suture and posterior edge), forelimbs (shoulder, elbow and distal tip of
manus) and hindlimbs (hip, knee and distal tip of pes;
Fig. 1).
To evaluate the kinematic patterns that turtles used to produce aquatic turns, coordinate data were input into a custom Matlab (Ver. 7, Mathworks, Inc.; Natick, MA, USA) routine that calculated the movements of each of the four limbs throughout the course of each trial. Each limb was defined as a vector marked by the endpoints of its proximal segment (forelimb: shoulder and elbow; hindlimb: hip and knee). The position of each limb was calculated using standard equations for the angle between two vectors, with the proximal limb segment (humerus or femur) forming the first vector, and the midline axis of the body forming the second. Angles were calculated from the ventral-view videos as two-dimensional projections onto the horizontal plane. A limb segment parallel to the midline axis and oriented cranially was assigned an angle of 0°, whereas one parallel to the midline and oriented caudally was assigned an angle of 180°.
To evaluate maneuverability for each turn, the software QuicKurve
(Walker, 1998a) was used to
interpolate 100 equidistant points along the line of best fit through the six
midline landmarks of the plastron for each digitized frame of every trial. For
each turn, these coordinate data (100 midline points per frame) were input
into a custom Matlab routine, which calculated the position of the turtle's
center-of-rotation (COR) as it moved along the curved turning path. The COR
was calculated as the point along the turtle's midline that traveled the
smallest cumulative distance throughout the turn (sensu
Walker, 2000) and is used to
define the turning path. We then used QuicKurve
(Walker, 1998a) to fit a
quintic spline to the x-y coordinates of the COR along the turning
path (Woltring, 1986;
Walker, 1998b), smoothing the
data and allowing us to compute the local (i.e. instantaneous)
curvature,
, along the path using the parametric function:
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where ' and '' reflect the first and second derivative of
x and y, respectively. Finally, the instantaneous radius of
the curved turning path is obtained by calculating the reciprocal of ;
the smallest of these values is the minimum instantaneous radius, R.
For each turn, R was used as an index of maneuverability.
Length-specific turning radii (R/L) were calculated to
adjust for differences in size of individual turtles, and between turtles and
other taxa. In addition, the average and maximum tangential velocity of the
COR (Uavg and Umax, respectively) were
calculated for each trial to examine the relationship between tangential
velocity (i.e. velocity along the curved turning path) and the length-specific
minimum radius of the turning path, R/L. Tangential velocity
(U, in L s-1) was calculated from differentiation
of the cumulative displacement of the COR along the turning path (based on the
positional data). Differentiation was performed using QuickSAND software
(available online at
http://www.usm.maine.edu/~walker/software.html).
Prior to differentiation, data were smoothed in QuickSAND using a quintic
spline and the generalized cross validation smoothing option
(Walker, 1998b). The largest
value during a trial represented Umax, whereas
Uavg represents the mean of all values during a trial.
Midline coordinate data from each turn were also input into a custom Matlab
routine to calculate, (1) cumulative angular rotation of the midline from its
initial orientation (i.e. at the beginning of the turn), and (2) the maximum
angle of the turn. Angular rotation was calculated using standard equations
for the angle between two vectors, with the vectors defined by the positions
of the anterior and posterior edges of the plastron in the initial frame of
the turn and in each digitized frame thereafter. Using the values obtained for
cumulative angular rotation, the instantaneous angular velocity ()
(i.e. the angular velocity between each pair of sequentially digitized frames)
was calculated in QuickSAND software using the procedures described above for
measures of tangential velocity (U). The largest value during a trial
represented the maximum instantaneous turning rate, max,
whereas the mean of all values during a trial was the average turning rate,
avg.
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Limb kinematics
Forward and backward turns showed distinct kinematic patterns. In order to
describe the movement of limbs during forward swimming we will follow the
terminology used by Fish and Nicastro
(Fish and Nicastro, 2003) and
use `inboard' to describe the side of the turtle facing toward the center of
the turn, and `outboard' to refer to the side facing away from the center of
the turn. In forward turns, turtles maintain velocity while executing turns by
alternating movements of the hindlimbs, similar to the pattern of hindlimb
movement employed during rectilinear swimming
(Fig. 2A,B). However, during
rectilinear swimming, synchronous movements of contralateral fore- and
hindlimbs appear to help maintain a straight trajectory. In forward turns the
pattern of forelimb motions is modified. During forward turns, the inboard
forearm is held in a protracted position throughout the turn
(Fig. 2B); this should increase
drag on the inboard side, allowing the forelimb to function as a pivot
(Fish and Nicastro, 2003). The
outboard forelimb continues to move as in rectilinear swimming, producing
torque (i.e. a turning moment) about the inboard pivot and effecting the turn.
The outboard forelimb moves in alternation with the ipsilateral hindlimb and
synchronously with the contralateral hindlimb (i.e. maintains the pattern of
movement seen in rectilinear swimming; Fig.
2B).
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Turning performance
The smallest R/L was 0.0018 L
(Table 1) and occurred during a
forward turn with an average tangential velocity (Uavg) of
1.26 L s-1 and an average turning rate
(avg) of 134.4 deg. s-1. The second smallest
R/L for a forward turn was 0.0083 L and had a
Uavg of 1.40 L s-1 and a
avg of 166.9 deg. s-1. These two turns were
performed by two different individuals. The smallest R/L for
a backward turn was 0.0091 L with a Uavg of 0.86
L s-1 and a avg of 115.1 deg.
s-1. All seven backward turns had R/L less than
0.1 L. In contrast, only 13 of the 43 forward turns (30.2%; with each
of the five turtles performing at least one) had R/L less
than 0.1 L. The maximum avg for all turns was 247.1
deg. s-1 and was attained during a forward turn of 79.1° with
an R/L of 0.2846 L.
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In addition to showing different kinematic patterns, forward and backward
turns also exhibited considerable differences in performance. Unless otherwise
stated, results are reported as the mean ± s.e.m. Turn angles ranged
from 76.2° to 243.6° (mean, 118.0±5.1°) for forward turns,
and from 113.0° to 200.0° (mean, 162.0±12.4°) for backward
turns. The average center-of-rotation (COR) for forward turns was positioned
at 30.9±2.4% of the body length, whereas for backward turns it was
66.7±3.6%. There was a significant relationship between tangential
velocity (Uavg) and the COR for both forward and backward
turns. Leastsquares regressions indicated that the COR moved farther anterior
as speed increased for forward turns, whereas for backward turns the COR moved
farther posterior as speed increased (r2=0.295 and
r2=0.772, respectively; P<0.01). Forward turns
showed a weak, but significant, relationship (r2=0.420;
P<0.001; Fig. 3)
between the average tangential velocity through the turn
(Uavg) and the length-specific minimum instantaneous
radius of the turning path (R/L); this relationship for
backward turns was even stronger (r2=0.863;
P<0.01; Fig. 3).
However, no relationship was found between angular velocity
(avg) and R/L for forward
(r2=0.001; P=0.878) or backward
(r2=0.259; P=0.244) turns
(Fig. 4).
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To further compare performance differences between forward and backward
turns, for each of the six primary performance variables we calculated the
extreme 20% (N=9) values for forward turns
(Table 1). These extreme values
included the minimum nine values for R and R/L and
the maximum nine values for U and [following published
precedents (Webb, 1983;
Gerstner, 1999;
Fish and Nicastro, 2003;
Fish et al., 2003;
Maresh et al., 2004)]. These
values of R and R/L for forward turns were much
more similar to those of backward turns; however, values of U and
became substantially greater for forward turns than backward turns in
this comparison.
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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). One focus of this study was to determine how painted
turtles use their limbs to execute turns. Turns require an asymmetry in forces
between the inboard and outboard sides of the animal, which could be produced
through any of several different patterns of limb movement. Using a simplified
descriptive framework, each individual limb might show one of four basic
patterns of movement during a turn: (1) continue to move as in rectilinear
swimming, (2) exhibit movements modified from the pattern used during
rectilinear swimming, (3) fold along the body to stop contributing to
propulsion, but minimize additional drag, or (4) project out from the body to
increase drag and act as a pivot. For example, either one or both inboard
limbs might show pattern 3 (fold along the body) while the outboard limbs show
pattern 1 or 2 (standard-rectilinear or modified rowing). Alternatively,
either one or both inboard limbs might show pattern 4 (outward projection as a
pivot) while the outboard limbs show patterns 1 or 2 (standard-rectilinear or
modified rectilinear rowing; powered turns) or 3 (fold along the body;
unpowered turns). Our data show that, during forward turns, painted turtles
consistently combine patterns 4 and 1, protracting the inboard forelimb and
holding it stationary into the flow, while continuing to move the outboard
forelimb and both hindlimbs as in rectilinear swimming. This combination of
limb movements during forward turns is a fairly basic modification of the limb
movements used for rectilinear swimming, which may simplify their neural
control (Macpherson, 1991;
Earhart and Stein, 2000).
Moreover, the functional consequence of this movement pattern is that swimming
freshwater turtles execute forward turns by increasing inboard drag while
still producing thrust, a combination of limb movements that should allow them
to execute turns more quickly than alternative patterns (e.g. if any of the
limbs were folded against the body). These patterns of turning kinematics are
similar to those of another rigid-bodied species, the whirligig beetle
(Fish and Nicastro, 2003), in
which inboard limbs appear to function as a pivot about which the body rotates
due to both initial forward momentum and forward thrust generated by the
outboard limbs. In addition, because the left and right hindlimbs of turtles
show similar patterns of motion during forward turns, it is the movements of
the forelimbs in particular that appear to be responsible for generating the
asymmetric forces required for turtles to execute turns. These findings
support the conclusion of Pace et al.
(Pace et al., 2001) that
swimming freshwater turtles (except Carettochelys and possibly
trionychid softshells) use their forelimbs primarily for balance and
controlling orientation. Evaluations of the forces produced by each limb
during turns [e.g. using techniques such as particle image velocimetry
(Drucker and Lauder, 1999;
Blob et al., 2003)] could
further test this hypothesis.
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observed that sliders (Emydidae) often swept both hindlimbs forward in unison
to achieve rapid braking, so it is likely that the initial protraction of the
hindlimbs during backward turns by painted turtles functions to stop forward
momentum (rather than contribute to the turn) and that subsequent synchronous
protractions generate the forward thrust used to reverse direction. Once
turtles were moving backward, turns were initiated by near simultaneous
retraction of one forelimb and protraction of the contralateral hindlimb,
producing a turning moment that rotated the body.
In addition to differences in kinematics, several parameters of turning
performance also differed between forward and backward turns
(Table 1). For both forward and
backward turns the COR moved closer to the leading edge of the body with
increasing velocity. This resulted in a cranially positioned COR for forward
turns and a caudally positioned COR for backward turns. Backward swimming was
slower than forward swimming and also resulted in much lower angular
velocities. In addition, the R/L for backward turns
generally were much smaller than those for forward turns. However, when only
the minimum 20% of values for forward turns are compared to values for
backward turns these differences are minimized. In fact the two smallest
turning radii were from forward turns. Still, the performance of backward
turns was much less variable than that of forward turns, with the range of
R/L spanning only one order of magnitude (0.0091-0.0950
L), whereas for forward turns R/L spanned four
orders of magnitude (0.0018-1.0442 L). Similar comparisons of forward
and backward turning performance in other aquatic taxa are available for only
one other species, the angelfish [Pterophyllum scalare
(Webb and Fairchild, 2001)].
In contrast to turtles, angelfish showed significantly larger length-specific
turning radii (R/L) during backward turning (0.71) than
during forward turning (0.41), a result that may relate to the differing
positions of propulsive appendages in these species.
Comparisons with other taxa
Another focus of this study was to compare the turning performance of
turtles with that of other taxa, particularly those with rigid bodies.
Rigid-bodied animals that have been examined to date have excelled in one of
the two parameters of turning performance (agility or maneuverability), but
not both. For example, boxfish are highly maneuverable (small
R/L), but have low agility
(Walker, 2000); in contrast,
whirligig beetles can rotate with high agility (high angular velocities), but
are not very maneuverable [i.e. they have large R/L
(Fish and Nicastro, 2003)].
Our analysis of turning performance in painted turtles shows that when
compared to other rigid-bodied taxa, rather than excelling at one of the two
performance parameters, painted turtles display intermediate values for both
(Fig. 5). For each of the four
measurements of R/L, the same pattern of performance was
identified for the three species: boxfish<turtle<beetle. Although the
values for the painted turtles overlapped with both those of boxfish and the
whirligig beetle, the maximum R/L of boxfish (0.1121
L) was smaller than the minimum R/L for the beetle
(0.24 L). The pattern is the same for avg, with
boxfish<turtle<beetle, for all but the minimum values.
If comparisons are expanded beyond rigid-bodied taxa, differences in
maneuverability between painted turtles and other taxa vary considerably
depending on the criteria used. Table
2 shows R/L (maneuverability) values from 18 studies that
have measured turning performance in a wide range of aquatic animals. These
values are most often published as an average of all trials for a given
species. However, other values are also frequently reported, either as a
complement to overall means or in place of them, such as the average of the
minimum 20% R/L values, or single, overall minimum values
(e.g. Webb, 1976;
Webb, 1983;
Fish, 2002;
Fish et al., 2003). The most
conservative comparisons rely on the average of all trials. In this case,
painted turtles have an average R/L (0.25 L) that
is smaller than only four previously studied taxa: whirligig beetles [0.86
L (Fish and Nicastro,
2003)], squid [0.5 L
(Foyle and O'Dor, 1988)], tuna
[0.47 L (Blake et al.,
1995)] and angelfish [0.41 L
(Webb and Fairchild, 2001)].
However, because the goal of our study was to examine maximal turning
performance in turtles (in the context of predator-prey encounters),
comparisons of minimum R/L values are also justified. In
these comparisons, the mean-minimum 20% R/L for painted
turtles (0.0423 L) was smaller than the reported values for all but
four previously examined species: damselfish (0.04 L), wrasse (0.02
L), surgeonfish (<0.01 L) and boxfish (0.0015 L)
(Gerstner, 1999;
Walker, 2000). Moreover, when
single minimum R/L values are compared, only the boxfish
(0.0005 L) and possibly surgeonfish (<0.01 L; reported as
mean-min 20%) have turning radii smaller than painted turtles (0.0018
L). As seen with boxfish, these comparisons indicate that the rigid
bodies of painted turtles do not appear to severely limit their
maneuverability.
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) also varies considerably among taxa
(Fig. 6). The maximum
avg for turtles (247 deg. s-1) is greater than
the values for boxfish [147 deg. s-1
(Walker, 2000)] and squid [90
deg. s-1 (Foyle and O'Dor,
1988)], but less than those for beetles [4438 deg. s-1
(Fish and Nicastro, 2003)],
stiff-bodied tuna [426 deg. s-1
(Blake et al., 1995)] and
penguins [576 deg. s-1 (Hui,
1985)]. In addition, because body size appears to be an important
underlying determinant of agility (Fish
and Nicastro, 2003), the fact that much larger stiff-bodied
cetaceans can turn at comparable rates suggests that they are much more agile
than rigid turtles. Similarly, the fact that flexible fish of similar size are
able to turn at rates much higher than turtles
(Fig. 6) suggests that agility
may be constrained by a rigid design.
Modes of turning and performance
That two of the three smallest reported R/L values are
from rigid-bodied taxa, boxfish (Walker,
2000) and turtles (this study), suggests that rigid-bodied taxa
use modes of turning that increase maneuverability. In fact, having small
turning radii may be of particular importance to rigid taxa because it is the
only way to decrease the space required for them to complete a turn. In
contrast, flexible taxa can reduce the area required to turn simply by bending
their bodies (Walker, 2000).
However, rigid-bodied whirligig beetles turn with relatively large radii
(Fish and Nicastro, 2003).
Reasons for these differences between low and high R among
rigid-bodied taxa, as well as for the discrepancy in agility between flexible-
and rigid-bodied taxa, may be based on the modes of turning used by these
different groups.
Aquatic organisms can generate turning forces (i.e. torque) by two
mechanistically different methods: (1) actively, by motion of control
surfaces, or (2) passively, from flows produced by movements of the body or
external flow fields (Fish,
2004). Passively powered turns rely on the kinetic energy of a
translating body or extended hydrofoil moving through local flow, and
therefore require that turning path (R) and tangential velocity
(U) be greater than 0. The effectiveness of passively powered turns
should vary with speed, with torque production increasing with the square of
velocity (Weihs, 1981). As a
result, at low U, passive maneuvering becomes more difficult
(Weihs, 1981;
Fish, 2002). In contrast,
actively powered turns are generated by oscillating limbs, and although
R and U may be greater than 0, this is not required.
Oscillating limbs have a distinct advantage over passive maneuvering when
U=0, as oscillating limbs produce hydrodynamically derived drag
without movement of the body (Blake,
1986). This allows turns to be composed of pure rotational
movements with no body translation
(Walker, 2000). As a result,
it seems that oscillating limbs are a better design for maneuverability (lower
R). However, there are several reasons why actively powered turns
should reduce agility compared to passively powered turns regardless of
whether the turn involves body translation. The first is that an object
turning in place (R and U=0) will have higher pressure drag
resisting rotation because the angle of attack between the body and the local
flow is close to 90° along the entire length of the body
(Walker, 2000). As long as an
organism is designed to reduce drag while moving in a longitudinal direction,
the angle of attack between the body and the local flow (and thus drag) will
be reduced as R increases, being lowest while moving in a straight
line. This is particularly the case for rigid-bodied taxa that cannot bend
their bodies in the direction of the turn
(Walker, 2000). A second
reason that actively powered turns might suffer reduced agility is that for
turns with translation (R and U>0), the rate of rotation
is dependent on the speed of the oscillating limbs, the latter of which is
reduced overall as a result of having distinct power and recovery strokes. In
addition, paddling is inefficient at high U because the speed
differential between the body and the paddle becomes smaller with less
propulsive force being generated (Blake,
1986; Fish, 1996).
In contrast, passively powered turns utilize much higher tangential speeds and
have the advantage that turning forces can be generated without incurring a
large decelerating drag.
These ideas help to explain the patterns of maneuverability and agility that are observed for the three rigid-bodied taxa examined to date. Turtles and boxfish are able to turn with a small R because their use of oscillating appendages does not depend on tangential velocity. In addition, although velocity is generated by oscillating limbs in whirligig beetles, their high angular velocity is achieved by having very high tangential velocity (U) while traveling along a large R. Lastly, flexiblebodied organisms can have high levels of maneuverability and agility, but they also have the ability to mix styles of turning, whereas most rigid-bodied taxa appear to be limited to actively powered turns using oscillating limbs.
Morphological correlates of turning performance
Differences in agility between painted turtles and boxfish may not relate
exclusively to their differences in body size
(Fig. 6). Walker
(Walker, 2000) gives three
reasons why the rigid bodies of boxfish should limit agility: (1) an inability
to bend the cranial end of the body into the turn, (2) an inability to bend
and reduce the body's second moment of area about the rotational axis,
resulting in high inertial resistance to rotation
(Carrier et al., 2001;
Walter and Carrier, 2002), and
(3) high pressure drag resisting rotation because the angle of attack between
the body and the local flow is close to 90° along the entire length of the
body. Because turtles are also unable to bend their bodies, they must also
face the same constraints on agility posed in points 1 and 2. However, painted
turtles are more dorsoventrally flattened and have more rounded dorsal
profiles than boxfish, both of which should reduce the pressure drag to which
turtles are exposed.
Despite having rigid bodies, painted turtles may also be able to reduce
second moments of area through mechanisms unavailable to boxfish. First, with
very few exceptions (e.g. snapping turtles), most extant turtles have highly
reduced tails (Willey and Blob,
2004). The presence of a long tail in swimming turtles would
increase both the second moment of area and rotational inertia, which would
result in decreased agility (Carrier et
al., 2001). Therefore, tail reduction in turtles may be a factor
contributing to their greater agility in comparison to boxfish. In this
context, it is perhaps not surprising that those turtles that possess long
tails (chelydrines) are primarily benthic scavengers or ambush predators that
do not actively pursue evasive prey, for which high turning performance might
be required (Ernst et al.,
1994).
Other morphological features of turtles that may help enhance their agility
compared to boxfish relate to the propulsors, or control surfaces. The fins of
boxfish are supported by flexible rays, whereas the limbs of turtles are
supported by more robust, stiffer limb bones that can extend farther from the
body than boxfish fins. These differences in structure may help make turtle
limbs a more effective brake or pivot on the inboard side, and a more powerful
propulsor on the outboard side. In addition, the position of the limbs in
turtles, with all four located near and approximately equidistant from the
center of rotation, might also enhance maneuverability
(Fish, 2002). Furthermore,
because all four limbs in turtles lie within the same horizontal plane, thrust
and drag forces used to generate torque are all directed within the plane of
rotation. Boxfish also achieve enhanced maneuverability by using multiple
control devices [i.e. five fins (Gordon et
al., 2000; Walker,
2000; Hove et al.,
2001)], but multiple fins located outside a single plane of
rotation may be less effective contributors to horizontal (i.e. yawing)
turns.
Directions for further study
As noted by Walker (Walker,
2000), morphologies that might facilitate or limit turning have
been widely discussed, but the effects of many design features on turning
performance remain unresolved. Numerous studies have examined the effect of
body and fin shape on turning performance among fishes and have identified
morphological features correlated with turning performance
(Gerstner, 1999;
Schrank and Webb, 1998;
Schrank et al., 1999).
Similarly, it is possible that interspecific variation in the morphology of
turtles could also produce substantial differences in turning performance.
Although the general body plan of turtles has changed little over 200 million
years (Gaffney, 1990;
Rieppel and Reisz, 1999),
extant freshwater turtles exhibit considerable morphological diversity. For
example, softshell turtles of the genus Apalone are dorsoventrally
flattened to an even greater degree than the painted turtles examined in this
study, and possess extensive webbing on the forefeet
(Webb, 1962;
Pace et al., 2001). As a
result, these highly aquatic species might be expected to exhibit turning
performance superior to that of painted turtles. In contrast, many species of
the riverine genus Graptemys (map turtles) have prominent mid-dorsal
keels (Ernst et al., 1994). It
is possible that, like the keels of boxfish
(Bartol et al., 2003;
Bartol et al., 2005), the keels
of map turtles may aid in stabilization during rectilinear swimming, which in
turn could negatively affect turning performance. Correlating parameters of
turning performance (maneuverability and agility) with predator-prey
interactions and habitat characteristics (e.g. flow velocity and turbulence)
could help to determine the factors that have influenced the diverse
morphologies seen within turtles as well as the broad impact of rigid body
designs.
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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