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First published online August 9, 2007
Journal of Experimental Biology 210, 2811-2818 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.004267
Death roll of the alligator: mechanics of twist feeding in water
1 Department of Biology, West Chester University, West Chester, PA 19383,
USA
2 Department of Physics, West Chester University, West Chester, PA 19383,
USA
* Author for correspondence (e-mail: ffish{at}wcupa.edu)
Accepted 14 May 2007
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Summary |
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 TOP Summary IntroductionMaterials and methodsResultsDiscussionReferences |
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Key words: death roll, alligator, Alligator mississippiensis, feeding, maneuverability
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; Cleuren and De Vree,
1992; Cleuren and De Vree,
2000; Erickson et al.,
2003). Although small prey are swallowed whole, large prey are
subdued and dismembered with a spinning maneuver
(McIlhenny, 1935;
Neill, 1971;
Guggisberg, 1972;
Pooley and Gans, 1976;
Ross, 1989). This maneuver is
dramatically termed the `death roll'. The death roll is an example of a
behavioral strategy referred to more generally as rotational feeding.
Body-rolling inertial feeding or rotational feeding is used by elongate
vertebrates that lack specialized cutting dentition
(Gans, 1974;
Helfman and Clark, 1986;
Davenport et al., 1990; Maesey
and Herrel, 2006). The inability to cut food into smaller portions requires
such species to use mechanisms to remove manageable pieces from prey that are
too large to consume whole. Large crocodiles and alligators will grab a limb
or lump of flesh with their jaws and then rotate around the longitudinal axis
of their body until the piece is torn free
(Guggisberg, 1972;
Cleuren and De Vree, 2000).
While there have been numerous observations of the spinning behavior for prey
reduction, there is only one description of the gross motions of the body
components for the alligator (McIlhenny,
1935). McIlhenny reported that an alligator would immediately roll
when it caught an animal that was too large to be instantly killed. The
alligator would initiate the roll by throwing its tail up and sideways. The
body and tail would turn simultaneously in the same direction. The feet were
not used as they were folded against the body. Observations from a second
crocodilian species, large (>3 m) Nile crocodiles, Crocodylus
niloticus, reported spin rates of 0.55–1.11 rotations
s–1 (Helfman and Clark,
1986).
The mechanics of the spinning maneuver in crocodilians have not been previously examined. The goal of this study was to understand how the alligator is able to initiate and sustain a spinning maneuver in an aquatic medium and to construct a model to describe the relevant dynamics. In this study, we were able to elicit juvenile alligators in the laboratory to spin in the manner of the death roll. By using high-speed video recordings of the rolling maneuver, we detailed the movements of body components and measured spinning performance. From this information, a mathematical model was produced that satisfactorily described the dynamics of the rolling maneuver, allowing the model to predict the torque and shear forces produced at the snout during this feeding behavior.
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Materials and methods |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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Experiments on spinning were conducted in a 38 l aquarium (0.51 mx0.26 mx0.32 m). Water depth was 100 mm, which was sufficient to keep the alligator from touching the bottom of the aquarium with any part of its body. Water temperature was 20–23°C. Alligators were placed singly in the test aquarium and allowed to acclimate for a minimum of 10 min. Immediately upon entry into the aquarium, the alligator would dive and swim. The alligator would eventually return to the water surface where it would float quiescently. The alligator would be presented with a small (approximately 50 mm) strip of meat held with tongs at the water surface. Once the animal grasped the meat, one to several small, sharp tugs were given to induce it to spin.
To determine if motions or orientation of the tail were associated with spinning, the tails of the alligators were restrained. Two test groups of four animals each were chosen. Strips of duct tape were used to bind a wooden stick (180 mmx6 mmx1 mm) to the dorsum of the alligators in one group (Fig. 1) and the venter of alligators in the other group. The neck and legs were free to move in all animals. The alligators were able to float at the water surface. As with unrestrained alligators, these animals were presented with a strip of meat to bite in order to initiate spinning. Restrained alligators were tested for no longer than 10 min.
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The spinning maneuver was recorded with a high-speed video camera (Redlake Imaging MotionMeter, Morgan Hill, CA, USA) at 250 frames s–1 with a 6 mm lens (Cosmicar Television Lens, Japan). The camera was mounted on a tripod 1.6 m above the aquarium. Video recordings from the camera were played back at 60 frames s–1 and stored on videotape using a Panasonic AG-7300 video recorder. Two 250 W halogen lamps supplied lighting at water level.
Sequential frames of videotape were viewed using a Panasonic CT 2600 M monitor and Panasonic AG 7300 video recorder. Video records were chosen for analysis only if the animal displayed at least one full rotation, the animal was not pushing off the walls or floor of the aquarium, and the entire animal was in the field of view. Each spinning sequence was analyzed frame-by-frame. Data were collected on the duration of a complete spin, number of spins, and angular displacements of the head and tail relative to the longitudinal axis of the body. Angular displacements were measured using a protractor on the video frame at the initiation of the spin when the animal's dorsum was directed toward the camera and the animal's head, body and tail were parallel to the plane of the water surface. These angular data were combined with the morphometrics data to construct a mathematical model that allowed calculation of torques and shear forces, resulting from death roll behaviors.
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Results |
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Sequential images of spins are shown in Figs 2 and 3. The spin was observed after limbs and tail were moved (Fig. 2). The head, body and tail were bent into a C-shape. The fore- and hindlimbs were appressed against the sides and venter of the body. The head and tail could be flexed laterally, dorsally, or ventrally. Once the spin was initiated, the body remained relatively straight from the pectoral region to the pelvic region (Fig. 3). The alligator maintained this shape throughout the maneuver. The head, body and tail rotated around their individual longitudinal axes. The tail was rotated at its base, maintaining its position throughout the spin. However, the relative orientation of the body parts change with respect to each other. In Fig. 2, the tail starts bent to the left side of the alligator, but is bent to the right side of the animal later in the spin. At the end of the spin, the head, body and tail straighten out. In all cases, the legs abduct from the body and return to a typical sprawled posture, thus ending with zero angular momentum. With this condition, there are no external torques or forces operating during the spinning maneuver. Drag from the interaction of the animal and the fluid is thus negligible. In a few cases, after the animal straightens at the end the maneuver, a slow residual spin remains. This small amount of angular motion was attributed to an inadvertent external torque applied in the feeding.
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The angle (
) between the longitudinal axes of the head and body at
the start of each maneuver ranged between 20° and 75° with a mean of
49±10° (Fig. 4). The
angle (
) between the body and tail at the same time ranged between
79° and 139° with a mean of 103±13°
(Fig. 4). There was no
significant correlation between head and tail angles (d.f.=50;
R=0.043). The mean rate of rotation was 1.5±0.5 rotations
s–1 or 560±170° s–1. The rotation
rate ranged from 0.7 to 2.7 rotations s–1 (257–978°
s–1) No significant correlations were found for head or tail
angle with rotation rate (head: d.f.=50; R=0.131; tail: d.f.=50;
R=0.184).
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Model
Based upon the observations and kinematics of the spinning maneuver, a
mathematical model was developed that was based on a spinning maneuver with a
zero not angular momentum. Such zero angular momentum turns have been analyzed
for some simple cases, such as a falling cat and aerial human maneuvers
(Kane and Scher, 1970;
Frohlich, 1979;
Edwards, 1986;
Galli, 1995). The dynamics of
our model permit a calculation of the torque and shearing force produced at
the snout.
The alligator was modeled as ellipsoidal head and body with a right
circular cone as a tail (Fig.
5). The head and body had circular cross sections. The joints at
the junctions of head and body and the body and tail can rotate freely without
slipping. As indicated above, the initial state is one of zero angular
momentum. The head and body sections each possess three principal moments of
inertia. For the model head with semi-major axis of aH and
semi-minor axes each of length bH, we denote the smallest
moment of inertia about the major axis as iH. The moments
about the two equal minor axes are each denoted by IH and
are larger than the moment about the major axis
(Table 1). The length of the
head lH is 2aH and the width and
thickness are each 2bH. In this case,
 | (1) |
 | (2) |
). Similarly for
the model ellipsoidal body (or trunk) with axes of length
aB and bB, the principal moments of
inertia iB and IB are given by:
 | (3) |
 | (4) |
 | (5) |
 | (6) |
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The model head, body and tail all roll without slipping with angular speeds
H=B=T= and
simultaneously revolve around the RR'-axis, the roll axis, with angular
speed rev (Fig.
5).
The rotating head, body and tail each possess angular momentum. To
determine the moments of inertia of the body parts and the resulting angular
momenta about the RR'-axis, we adopt the coordinate system shown in
Fig. 5. The unit vectors for
each body part are described in Cartesian coordinates of
and 
. The
axes lie along the spin axes of each body part and the
axes are perpendicular to the
axes. The angular momentum of the head is:
 | (7) |
 | (8) |
 | (9) |
In a zero angular momentum maneuver, the vector sum of these angular
momenta vanishes, that is,
.
For this case,
 | (10) |
 | (11) |
with lH the length of the head. After rearranging terms to
form the ratio /rev, we find:
 | (12) |
=45° and =90°, which are typical values for
these angles (Fig. 4), this
expression reduces to:
 | (13) |
It is important to note that the rev motion (i.e. the
motion of the animal revolving around the RR'-axis) is a reaction to the
rolling motions initiated by the animal after it fastens onto its prey. Before
the spin is initiated the angular momentum of the alligator is observed to be
zero, must remain zero during the spin, and is observed to be zero when the
spin terminates. The motion around the RR'-axis, which occurs at an
angular frequency approximately an order of magnitude slower than the rolling
motions, results purely from the conservation of angular momentum. This is
roughly analogous to how a figure skater controls spin rate
(Giancoli, 1985). By
voluntarily bringing both arms close to his or her body from an extended
position, a figure skater can increase angular speed to conserve angular
momentum. Rather than this one-dimensional case, the death roll is a
two-dimensional example.
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Discussion |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; Neill, 1971;
Guggisberg, 1972;
Pooley and Gans, 1976;
Ross, 1989). The conical teeth
of crocodilians are useful for grasping prey with a large bite force
(Erickson et al., 2003), but
not for tearing and cutting flesh
(Guggisberg, 1972). Spinning
is a mechanism that can tear apart large prey by subjecting the tissue to
torsional stresses. Animals and their tissues are weak in torsion
(Gordon, 1978;
Currey, 2002). The spinning
maneuver is used predominately by crocodilians with broad, short snouts, which
feed on large prey and on a more general diet
(Cleuren and De Vree, 2000).
This skull structure can resist the substantial forces associated with the
maneuver (Cleuren and De Vree,
1992). Inertia of the prey is required for the maneuver to be
effective. Spinning does not work with small prey animals, because as the
crocodile spins, the prey will also rotate. Thus, when groups of crocodilians
(e.g. Crocodylus niloticus) feed on a carcass at the same time
(Pooley and Gans, 1976;
Guggisberg, 1972;
Ross, 1989), the inertia added
by attached predators would facilitate the success of spin feeding by
individual crocodilians by helping to secure the prey.
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;
Pooley and Gans, 1976).
Hatchling (50 g) and juvenile (100–550 g) salt-water crocodiles
(Crocodylus porosus) feeding on carrion were observed to use
side-to-side head shaking, rather than spinning, to detach small pieces
(Davenport et al., 1990).
Side-to-side head shaking was used to detach small pieces of the carrion.
However, the carrion was a large fish, which may not have offered resistance
to tearing (Davenport et al.,
1990). The toughness of the food presented to the alligators in
this study provided sufficient resistance to initiate the spinning
behavior.
Conservation of angular momentum in crocodilian death rolls
The ferocity of the death roll of alligators and crocodiles is particularly
enhanced by the rapid speed of the spinning motions. How can the animal
generate these motions and still conserve angular momentum? From a
configuration where the symmetry axes of the head, body and tail are all
aligned, the animal quickly bends itself into a C-shape and commences
spinning. Consequently, each body part possesses a vector angular momentum
(Fig. 5). While the horizontal
components of the angular momenta of the head and tail largely cancel, the
vertical components add. This angular momentum vector, however, is canceled by
a more subtle motion of the entire animal. As a reaction to the spinning
motion, the animal also revolves around a roll axis roughly parallel to the
animal's trunk (body). The roll axis runs through its snout, which is fastened
onto meat, and a point approximately one-quarter of the distance from base of
the tail to its tip. The revolution of the animal's head, body and tail about
the roll axis also has an angular momentum, which is directly opposite to the
vector sum of the angular momentums of each body segment. Thus, the initial
angular momentum is zero, the total angular momentum during the roll is zero,
and when the maneuver terminates by the alligator straightening, it remains
zero.
The reason that the motion about the roll axis is less apparent than the spinning motions of the head, body and tail is because it takes place with an angular speed that is an order of magnitude smaller than the spinning motion (Fig. 6). When an animal executes a roll of one spin, it only completes a tenth of a revolution around the roll axis. This relatively small angular velocity is not measurable in this experiment. The relatively small magnitude of this compensatory rotation can ultimately be attributed to the large size of the moment of inertia of the alligator bent into a C-shape with the massive trunk relatively far from the roll axis.
The alligator is able to centralize its mass and its axis of rotation by
keeping its legs in close to its body. This also effectively helps reduce drag
and enables it to create a faster, more powerful spin. Similarly, human divers
create a central axis as they somersault from a diving board
(Frohlich, 1980). By drawing
their arms and legs in close to their body, they can isolate their axis of
rotation. The same principle applies when a person is spinning on ice skates.
When their arms are extended the spin is slowed down, but when tucked in, the
person is able to increase their speed of spinning. This can be seen in the
spinning alligator when the legs are tucked in close to its body. Because the
legs play no role in actually producing the torque of the spin, it appears
that the alligator relies completely on the axial components of its body. The
mechanics of the spinning behavior indicate that orientation between the body
and tail and, to a lesser extent, the head are important in the maneuver of
the alligator. The angular displacement between body parts changes the moment
of inertia, which is necessary to conserve angular momentum during the spin.
McIlhenny originally noted the reorientation of the tail and tucking of the
legs during the roll (McIlhenny,
1935).
The angular momentum balance and lack of external torques to maintain the
maneuver make spinning of the alligator a zero angular momentum maneuver. A
similar maneuver is observed in an inverted cat during free-fall
(Frohlich, 1980;
Galli, 1995). The cat in an
inverted position is able to twist its body in mid air to land on its feet.
The cat begins its free fall with no initial angular momentum
(Arabyan and Tsai, 1998). As it
falls, the cat bends at the waist. The anterior and posterior body sections
rotate in the same direction (Frohlich,
1980; Fredrickson,
1989). Each section has an angular momentum, whose vector sum
gives a counter-rotation to the entire body
(Edwards, 1986). This results
in no net change in angular momentum for the cat. The legs are positioned
close to the symmetry axis of each body section during the maneuver. This
orientation reduces the moment of inertia and increases the spin rate of the
body sections. When the cat has rotated 180°, it straightens its spine to
stop rotating and can land on its feet
(Fredrickson, 1989). The cat
then terminates its maneuver with no angular momentum. The alligator and the
cat both generate internal forces that enable these animals to spin.
Generation of shear force in the death roll
To tear apart its food using the death roll, the alligator needs to
generate large shear forces. Although data on the magnitude of shear forces
required to dismember bodies have not been collected, the shear force in a
death roll can be calculated over a range of sizes for the alligator. To
illustrate this computation, the morphometric data
(Table 1) of a model juvenile
(0.3 m) and adult (3 m) specimen of A. mississippiensis are used. The
calculation estimates the total rotational kinetic energy
(Krot) in the spinning maneuver. Krot
equals the work needed to remove that energy and bring the roll to a halt.
Krot of an alligator executing a spin possesses two
contributions: (1) the rotation at relatively high angular speed of each body
section about their individual symmetry axis, , and (2) the rotation of
the entire animal about the roll axis, rev, which occurs at
a relatively smaller angular speed. The ratio of to
rev is given by Eqn
13. For the model adult individual,
/rev=11.5 and for the juvenile,
/rev=12.2.
Using =1 rotation s–1 (=6.3 rad
s–1) for our sample calculation, rev=(6.3
rad s–1)/11.5=0.55 rad s–1 and the total
rotational kinetic energy Krot of an adult is:
 | (14) |
The work done by a constant external torque 
acting over an angle
in order to remove an energy Krot is
W=. For =1, rotation=2
rad, in our case,
=(78.1 J)/2=12.4 N m. Furthermore, the shear force produced by this
torque acting over a lever arm equal to one half the width (w) of the
distal portion of the snout equals the torque, i.e.
=Fs(0.5w), and therefore
Fs=2/w=(2)(12.1 N m)/(0.18 m)=138 N. This
analysis does not account for any reduction in the ultimate strength of the
prey's tissue due to perforation by the alligator's dentition, which would
serve to significantly lower the shear force required for dismemberment.
For comparison, results for the juvenile A. mississippiensis
executing a death roll with =2 rotations s–1 show that
/rev=12.2, which yields, along with relevant data
from Table 1,
Krot=4.1x10–4 J. The corresponding
torques and shear force are 6.5x10–5 N m and 0.015 N,
respectively. Thus, an adult having a mass 1800 times that of a juvenile can
produce 200 000 times the energy and torque, and approximately 1000 times the
shear force.
Force scaling relationships of alligators
The foregoing analysis permits the development of a scaling relation for
large adult individuals with lengths in the vicinity of 3 m. For 51
individuals ranging in length from 0.23 m to 3.75 m and in mass from 0.0318 kg
to 296.7 kg (Fig. 7), mass
M varies with length L according to the equation:
 | (15) |
|
 | (16) |
 | (17) |
). Using
Eqn 15,
Eqn 17 can be rewritten so that
the shear force is given in terms of mass:
 | (18) |
(rad s–1), an adult whose length is just 10%
larger than another whose length is 3 m produces a shear force 50% greater.
Helfman and Clark (Helfman and Clark,
1986) provide values for of 0.6–1.1 rotations
s–1 for large (>3 m) crocodiles. Using =1 rotation
s–1=6.3 rad s–1, the record alligator of 5.8
m (Wood, 1976) would have a
Fs of 2326 N! Thus, shear forces generated by the spinning
maneuver are predicted to increase disproportionally with alligator size,
allowing dismemberment of large prey.
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Along with crocodilians, spin feeding is used by other vertebrates with
elongate bodies (Gans, 1974;
Helfman and Clark, 1986;
Measey and Herrel, 2006).
Among these other species, spinning by eels occurs at higher rotation rates
than similarly sized alligators and the mechanics of spinning may be
different. A spinning force of 1.35 N was measured on rotationally feeding
caecilians (Measey and Herrel,
2006). Although this spinning force was greater than the shear
force calculated for alligators of approximately the same body length, these
forces are not equivalent. The caecilians were handheld and were presumably
pushing off the solid substrate during the maneuver, whereas alligators can
generate their own internal torques to spin in water.
Rolling has largely been ignored as a maneuver for animals. Analyses of
maneuverability and agility have been confined to examination of pitching and
yawing motions (Frey and Salisbury,
2000; Webb, 2002;
Fish, 2002;
Rivera et al., 2006). While
pitch and yaw are typically associated with directional changes during
locomotion, roll is used for more varied behaviors. Spinner dolphins
(Stenella longirostris) perform aerial leaps and rotate around their
longitudinal axis up to seven times. This behavior was believed to function in
the removal of remoras from the body surface
(Fish et al., 2006), but may
function in acoustic communication. Birds will roll to use a component of lift
generated by the wings to produce a centripetal force to effect turning in
flight (Norberg, 1990).
Similarly, turning in water is facilitated by rolling in marine mammals and
penguins (Hui, 1995; Fish and Battle,
1995; Fish, 2002;
Fish et al., 2003;
Cheneval et al., 2007). Kasapi
et al. (Kasapi et al., 1993)
considered roll to be an important kinematic parameter in escape maneuvers by
knifefish (Xenomystus nigri). Female dugongs (Dugon dugon)
and right whales (Eubalaena australis) will roll onto their backs at
the water surface to prevent mating with unwanted suitors
(Payne, 1995;
Marsh, 2002). Grooming by sea
otters (Enhydra lutris) utilizes rolling to wash the fur
(Kenyon, 1969). Rolling
maneuvers are also involved in feeding behaviors. Fin whales (Balaenoptera
physalus) and other rorquals make lateral lunges involving a 90° roll
(Goldbogen et al., 2006). Gray
whales (Eschrichtius robustus) consume benthic invertebrates
(Pivorunas, 1979) by laterally
orienting the body as they plow thorough the soft sediment. The varied nature
of these behaviors provide a fruitful avenue for future studies of maneuvering
performance.
List of symbols and abbreviations
,
rev
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Acknowledgments |
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