Giant Galápagos tortoises walk without inverted pendulum mechanical-energy exchange
Department of Integrative Physiology, University of Colorado, Boulder, Colorado 80309-0354, USA
* Author for correspondence (e-mail: zani{at}colorado.edu)
Accepted 23 February 2005
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Summary |
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We studied five adult giant Galápagos tortoises Geochelone elephantopus (mean mass=142 kg; range= 103196 kg). Walking speed was extremely slow (0.16±0.052 m s1; mean ± 1 S.D.). The fluctuations in kinetic energy (8.1±3.98 J stride1) were only one-third as large as the fluctuations in gravitational potential energy (22.7±8.04 J stride1). In addition, these energies fluctuated nearly randomly and were only sporadically out of phase. Because of the dissimilar amplitudes and inconsistent phase relationships of these energies, tortoises conserved little mechanical energy during steady walking, recovering only 29.8±3.77% of the mechanical energy (range=1352%). Thus, giant Galápagos tortoises do not utilize effectively an inverted-pendulum mechanism of energy conservation. Nonetheless, the mass-specific external mechanical work required per distance (0.41±0.092 J kg1 m1) was not different from most other legged animals. Other turtle species use less than half as much metabolic energy to walk as other terrestrial animals of similar mass. It is not yet known if Galápagos tortoises are economical walkers. Nevertheless, contrary to biomechanical convention, poor inverted-pendulum mechanics during walking do not necessarily correspond to high mechanical work and may not result in a high metabolic cost.
Key words: biomechanics, locomotion, ground-reaction forces, mechanical-energy recovery, Geochelone elephantopus
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Introduction |
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It is well known that mechanical-energy conservation is influenced by
walking speed. Cavagna et al.
(1977) found that among
species, the greatest energy recovery occurs over a narrow range of
intermediate walking speeds for that species. At slow speeds, KE is
insufficient to lift substantially the COM. Previous studies of the mechanics
of relatively slow animals include geckos
(Farley and Ko, 1997
),
penguins (Griffin and Kram,
2000
), and alligators (Willey
et al., 2004
). While lizards and alligators exhibited fairly low
values of mechanical-energy conservation, penguins have the highest recovery
values. Willey et al. (2004
)
suggested that alligators conserve little mechanical energy due to frequent
dragging of their feet, tail dragging and imprecise coordination of their
feet. However, it also seems likely that their inherently slow speed precludes
substantial energy conservation.
We chose to study the mechanical-energy recovery during walking by giant
Galápagos tortoises Geochelone elephantopus because of their
extremely slow speeds, especially when expressed relative to body size (up to
200 kg). As Darwin (1839, p.
464) noted, "one large tortoise...walked... sixty yards in ten
minutes", or about 0.09 m s1. Unlike lizards and
alligators, the tails of turtles do not play an important role in locomotion,
except possibly on inclines (see Finkler
and Claussen, 1997
). Therefore, tortoises are an ideal group to
test the importance of absolute speed on mechanical-energy recovery without
being confounded by the presence of a substantial tail as in other non-avian
reptiles.
Due to their slow walking speed, we anticipated that these tortoises would have small fluctuations in KE. If this prediction is correct, to have an effective exchange of mechanical energy using the inverted-pendulum mechanism tortoises would need to walk with unreasonably small changes in GPE corresponding to vertical COM fluctuations of <0.5 mm. Thus, we hypothesized that giant Galápagos tortoises would not conserve substantial mechanical energy using the inverted-pendulum mechanism.
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Materials and methods |
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We calculated the COM mechanical-energy fluctuations of these tortoises from ground-reaction force (GRF) data. We sampled GRFs (Fig. 1) at 1000 Hz from an AMTI model ZBP7124 force platform (1.83 mx0.61 m). To accommodate the width of the tortoises, we attached a rigid metal frame to the top of the force platform, covered it with a 0.04 m thick plywood surface (1.83 mx1.22 m), and glued noncompressible rubber matting to this surface to provide traction. This rigid top had a mass of approximately 100 kg. The force platform is designed for loads up to 2000 N. We calibrated the force platform with known loads.
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Video recordings (60 fields s1) allowed for determination of limb phases and duty factors. We calculated limb phases as the proportion of the total stride time elapsed between the limb contact times. We calculated duty factors as the proportion of the total stride time that each limb was in contact with the ground. Paint marks on the shell enabled determination of average velocity for each step from video. We calibrated the video field from markers placed on the tortoise's shell a known distance apart. In addition, we used video to determine hip height during walking from a marker on the shell, placed with aid of hip palpation. Hip height (l) was then used to calculate Froude numbers (dimensionless velocity) as v2 g1 l1, where v is velocity (m s1) and g is gravitational force, 9.81 m s2.
To calculate the mechanical energies of the COM, we integrated the GRF
values as per Cavagna (1975),
modified for three dimensions (Griffin and
Kram, 2000
; Donelan et al.,
2002
). Force integration was conducted over an integral number of
steps, during which all stance limbs were on the force platform. One step =
half a stride or the time between one foot contact and its following
contralateral pair (e.g. left front to right front). We calculated the %
mechanical energy recovered during a step following Cavagna et al.
(1977
). This traditional method
of calculating mechanical-energy recovery is not perfect and overlooks the
substantial loss of energy at each footground contact as the COM is
redirected and accelerated (Donelan et al.,
2002
). However, it was not feasible to obtain the individual
leg-force measurements needed for calculating mechanical work with the
individual-limbs method. We determined the mechanical work per distance by
calculating the external work of the COM per step, multiplying by step
frequency, and dividing by speed and mass.
Statistical analyses were performed in SuperANOVA 1.11
(Abacus Concepts Inc., 1991)
for Macintosh.
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Results |
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The fluctuations in COM KE (8.1±3.98 J stride1;
Fig. 3) were only a third as
large as the fluctuations in COM GPE (22.7±8.04 J
stride1). Much of this difference was due to the fact that
tortoises walked extremely slowly (0.16±0.052 m s1;
within-stride vforeaft=0.03±0.054 m
s1), with KE occasionally reaching zero during normal steady
locomotion. This slow speed in tortoises equates to a Froude number
(dimensionless velocity) of 0.008±0.0040
(Table 1). Surprisingly, the
medio-lateral movements accounted for about two-thirds of the total KE
fluctuations. This percentage of total KE fluctuation is even greater than the
30% reported for waddling penguins
(Griffin and Kram, 2000
).
However, in mass-specific terms the medio-lateral KE fluctuations for
tortoises (0.07±0.019 J kg1 m) are slightly less than
those of penguins (0.10±0.059 J kg1 m; T. M. Griffin,
personal commication).
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The average COM vertical amplitude was 1.6±0.37 cm within a stride.
Considering that the leg length of these tortoises (0.33 m) was approximately
one-third that of humans (0.9 m), these COM fluctuations (and hence GPE
fluctuations) are proportionally similar to the fluctuations of humans
(typically 5 cm; Inman et al.,
1994
).
Tortoises did not systematically utilize an inverted-pendulum mechanism of
energy recovery while walking (Fig.
3). When we calculated the mechanical-energy recovery
(sensu Cavagna et al.,
1977) we found that tortoises recovered just 29.8±3.77% of
the total mechanical energy (range=1352%;
Fig. 4). This value of
mechanical-energy recovery is very near the lowest average reported for any
legged terrestrial animal during walking (frogs: mean=32%, range=2044%,
Ahn et al., 2004
; alligators:
mean=20%, range=632%, Willey et
al., 2004
; see also Cavagna et
al., 1977
). The low values of mechanical-energy recovery were due
to dissimilar amplitudes and inconsistent phase fluctuations of KE and GPE. In
addition, we calculated the amount of energy converted from GPE to KE as well
as from KE to GPE. We found essentially no difference in the direction of
energy exchange: GPE to KE was 48.5% of total energy exchange; KE to GPE was
51.5%. Because we were unable to identify a consistent pattern of peaks or
troughs in mechanical energies in many cases
(Fig. 3), we felt it
unwarranted to calculate the relative phase fluctuations of KE and GPE. Unlike
other species (Cavagna et al.,
1977
; Willey et al.,
2004
), tortoises did not recover more mechanical energy with
increasing speed (Fig. 4A) and
even had a slight negative trend to this relationship. External mechanical
work per distance (sensu Cavagna
et al., 1977
) averaged 0.41±0.092 J kg1
m1 (Fig. 4B)
and also had a slight negative trend.
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Discussion |
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The extremely slow walking speed of these animals is a major factor
contributing to their poor mechanical-energy recovery. Previous studies have
concluded that walking speed affects mechanical-energy recovery in general,
with intermediate speeds resulting in the greatest percent recovery
(Cavagna et al., 1977). Giant
Galápagos tortoises are certainly slow, especially for their size,
walking at an average of just 0.16 m s1. As a result, their
KE fluctuations are much smaller than their GPE fluctuations
(Fig. 3). In order to utilize
the inverted-pendulum mechanism of energy recovery, tortoises would need to
walk either with smaller fluctuations in GPE or larger fluctuations in KE. We
estimate that their COM fluctuations would need to be <0.5 mm to match
their KE fluctuations. In order to match their GPE fluctuations, tortoises
would need velocity fluctuations roughly 23 times their current
fluctuations. Tortoises simply do not have sufficient KE to lift their COM up
and over the stance limbs during each step. In addition to the dissimilar
magnitude of energies, their relative phase relationship appears to allow for
only intermittent exchange of mechanical energy.
Despite the poor mechanical-energy exchange, the mass-specific total
external mechanical work required to travel a given distance in these
tortoises is similar to other legged animals. Previous studies of walking have
found that the mass-specific mechanical work to travel a given distance ranges
from about 0.20.5 J kg1 m1
(Cavagna et al., 1977;
Willems et al., 1995
;
Griffin and Kram, 2000
;
Griffin et al., 2004
). Our
data show that tortoises require 0.42±0.083 J kg1
m1, which is not exceptional.
Compared to other terrestrial animals of similar mass
(Full, 1989), some turtles use
half as much metabolic energy to walk. However, the metabolic cost of walking
is known for only two relatively small species of turtles
(Baudinette et al., 2000
;
Zani et al., 2004
). To test
critically the causal link between mechanical-energy conservation and
metabolic costs, we need metabolic data on Galápagos tortoises or
mechanical and metabolic data on other turtle species. Tortoise walking may be
metabolically inexpensive due to (1) extremely efficient muscles
(Woledge, 1968
;
Nwoye and Goldspink, 1981
;
Rall, 1985
), (2) extremely
slow muscles that generate force economically
(Kram and Taylor, 1990
) or (3)
the unique pectoral articulation between the scapula and carapace (top shell;
Walker, 1986
), which
eliminates the `muscular sling' (Goslow et
al., 1981
) used by mammals.
There are reasons to question the link between mechanical-energy recovery
and metabolic cost of transport. For example, penguins recover up to 80% of
their mechanical energy (Griffin and Kram,
2000), but have a metabolic cost of walking twice as expensive as
other walking birds of the same mass
(Pinshow et al., 1977
). In
contrast, lizards have relatively low mechanical-energy recovery during
walking (
238%; Farley and Ko,
1997
), but are remarkably economical
(Autumn et al., 1997
).
Alligators have poor mechanical-energy recovery (
632%, mean=20%,
Willey et al., 2004
). However,
based on data from Emshwiller and Gleeson
(1997
; T. T. Gleeson, personal
communication) we have calculated the metabolic cost of transport to be 13.2 J
kg1 m1, which is similar to other 300 g
animals (Full, 1989
). Because
alligators rely on oxidative and non-oxidative metabolism to provide energy
for walking, we combined rates of oxygen consumption during walking and
subsequent recovery to estimate the cost of transport. This may overestimate
the steady-state metabolic costs. Hence, contrary to biomechanical convention,
there are clear examples where there is not a strong link between
inverted-pendulum recovery and the metabolic cost of walking.
New approaches to understanding the mechanical determinants of the
metabolic cost of walking are needed. Donelan et al.
(2002) pointed out important
flaws with measuring the mechanical work performed on the center of mass from
the summed GRF values of all limbs. During the stance phase some limbs are
performing negative work at the same time that other limbs are performing
positive work. Donelan et al.
(2002
) proposed that it is
important to measure the individual limb work performed to restore and
redirect the COM velocity during step-to-step transitions. Alternatively,
Griffin et al. (2003
) provided
evidence that in humans the metabolic cost of walking is more closely related
to the cost of muscular force generation than the individual limb work that
muscles must perform. Most recently, Grabowski et al.
(2005
) showed that supporting
weight and performing work on the center of mass each have a distinct
metabolic cost. Though developed for human bipedal walking, these new
approaches may help to link the mechanics and energetics of locomotion in all
animal species.
In summary, Galápagos tortoises walk extremely slowly, without systematic inverted-pendular mechanics, but with normal mechanical power outputs. Studies of the metabolic cost of locomotion in turtles are needed to determine how these unusual mechanics affect the energetics of walking.
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Acknowledgments |
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Footnotes |
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