The energetics of the trotgallop transition
1 Departments of Animal and Veterinary Science, California State
Polytechnic University, Pomona, CA 91768, USA
2 Biological Sciences and the Equine Research Center, California State
Polytechnic University, Pomona, CA 91768, USA
* Author for correspondence (e-mail: sjwickler{at}csupomona.edu)
Accepted 3 February 2003
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Summary |
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Key words: equine, horse, Equus caballus, oxygen consumption, time of contact, trotgallop transition, gait
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Introduction |
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The walktrot and trotgallop gait transitions were originally
explained on the basis of metabolic economy
(Hoyt and Taylor, 1981). In
ponies (Equus caballus), metabolism increased curvilinearly for
walking and trotting, and the gait transitions occurred at the speeds where
the metabolism curves intersected. This is referred to as the `energetically
optimal transition speed' (EOTS; Hreljac,
1993
) because, when the animals extended their gaits beyond the
normal transition speeds, the metabolic rate was higher in the extended gait
than in the normal gait. Hoyt and Taylor concluded that ponies changed gaits
to minimize energetic costs. However, one limitation of this study was that
gait transition speeds were not rigorously determined.
Subsequently, this explanation was challenged by the `force trigger'
hypothesis. Farley and Taylor
(1991) showed that the
transition from trotting to galloping in ponies is correlated with
musculoskeletal forces by demonstrating that the transition occurs at a slower
speed when a pony carries a load. Measurements of oxygen consumption (again
observed to be a curvilinear function of speed) indicated that the ponies were
making the transition to a gallop at speeds where it is energetically more
expensive to gallop than to trot at speeds slower than the EOTS. In
some studies, the walkrun transition in humans occurs at the EOTS
(Mercier et al., 1994
;
Diedrich and Warren, 1995
) and
in others it does not (Hreljac,
1993
; Minetti et al.,
1994a
,b
).
Hreljac (1993
) ruled out
muscle stress as the trigger for the walkrun transition in humans and
suggested that the trigger is kinematic
(Hreljac, 1995
).
In a study of horses and preferred speed
(Wickler et al., 2000), the
energetics of trotting were measured on the level and up a 10% incline. In the
preliminary portion of this study, we determined the speeds at which the
horses would trot. We noted that, when trotting up an incline, the horses made
the transition to a gallop at a slower speed than they would when on the
level. Because forces are not expected to be higher when trotting up an
incline (Roberts et al.,
1997
), this observation appeared to be inconsistent with the force
trigger hypothesis. In the present study, we revisited the energetics of the
trotgallop transition and, based on the earlier work of Hoyt and Taylor
(1981
), hypothesized that
horses would make the transition at the energetically optimal speed. Our
second hypothesis was that, when trotting up an incline, horses would also
make the transition at the energetically optimal transition speed. Thirdly, we
hypothesized that, when trotting up an incline, the EOTS would be a slower
speed than on the level.
The majority of the cost of running gaits can be explained by the rate that
force must be applied during the support phase of the stride cycle
(Kram and Taylor, 1990). Kram
and Taylor's study reports that the metabolic rate when locomoting is
inversely proportional to the time of contact (the length of time the foot is
in contact with the ground): the shorter the time of contact, the greater the
metabolic cost. Given these observations, we measured time of contact and
stride frequency to determine how these change at the trotgallop
transition.
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Materials And Methods |
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Gait transition speeds
Horses were warmed up on the treadmill for a minimum of 8 min (3 min of
walking and 5 min of trotting at 3.5 m s1). Speeds were then
either increased from 3.75 m s1 or decreased from 6.75 m
s1. The result was that, at the beginning of a transition
speed trial, all the horses were either trotting (increasing speed) or
galloping (decreasing speed). The speed was then changed in 0.25 m
s1 increments and held for 1 min. The gait or number of gait
transitions was recorded for each speed. It soon became obvious that there was
a range of speeds where the animals switched repeatedly between gaits; below
this range of speeds they trotted consistently, and at faster speeds they
galloped consistently. Thus, two transition speeds were defined: the maximum
sustained trotting speed was the fastest speed at which the horse trotted
continuously for 1 min, and the minimum sustained galloping speed was the
slowest speed at which the horse galloped continuously for 1 min. It should be
emphasized that these terms, maximum sustained trotting speed and minimum
sustained galloping speed, are defined as the speeds at which a horse normally
exhibits these behaviors because, subsequently, we trained our horses to
extend their gaits beyond these speeds (e.g. to gallop for several minutes at
speeds below minimum sustained galloping speed). This procedure for
determining maximum sustained trotting speed and minimum sustained galloping
speed was followed for horses on the treadmill on the level or with the
treadmill inclined 10% (inclination calibrated with a transit). The condition
(level or incline) and the direction of speed change (increasing or
decreasing) were randomized on different days.
Extended gaits
After the data for gait transition speeds had been collected and analyzed,
horses were trained to extend their gait: to trot consistently at speeds 0.5 m
s1 faster than the minimum sustained galloping speed and to
gallop at speeds 1.0 m s1 below the maximum sustained
trotting speed. This procedure involved using voice and visual cues or gentle
pressure on the animal's halter to either maintain the gait or to switch. Only
positive reward was used to train the horses.
Oxygen consumption
After the training to extend the horses' gaits, metabolic measurements were
made using techniques described previously
(Wickler et al., 2000).
Briefly, an open-flow system was used with flow continuously monitored during
metabolism trials and calibrated at the end of each day using a nitrogen
dilution technique. Tread speed was measured optically using a sensor to
detect rotation of the non-drive axle. The tread speed was checked every week
by timing a minimum of 10 tread revolutions, with the horse on the
treadmill.
Speeds (in 0.25 m s1 increments between 3.75 m
s1 and 6.75 m s1) and conditions (level or
incline) were all randomized. A maximum of three speeds were run per day. The
initial gait that the horse would maintain was determined at random for each
speed, and the rate of oxygen consumption
(O2) was
measured for 3 min. After 3 min, the horse was instructed to change gaits and
metabolic rate was measured for another 3-min period without changing tread
speed. Before metabolic measurements were made at the next speed and
condition, the horses walked for 5 min. Calculations of oxygen consumption
were made from the average of the last minute (a total of 12 points), because
2 min is a sufficient time to reach steady-state rate of oxygen consumption in
horses at these speeds (Wickler et al.,
2000
,
2001
).
Stride parameters
In a separate series of experiments, accelerometers (model # CXL25M1;
Crossbow Technology, San Jose, CA, USA; ±25 g) were
taped to the lateral aspect of each hoof, and horses were run on the treadmill
at speeds around the transition speeds to determine how stride frequency and
time of contact changed with gait transition. To facilitate statistical
analysis of these data, the speeds studied were defined relative to the
minimum sustained galloping speed because this was the speed defined as the
trotgallop transition speed by Farley and Taylor
(1991). This was necessary
because the transition speeds varied by almost 1 m s1 among
animals. Accelerometry trials (Hoyt et
al., 2000
) were run at the minimum sustained galloping speed, 0.5
m s1 faster and slower than this speed, and 1.0 m
s1 below this speed for each individual horse. For each
trial, the horse was brought to speed for 45 s, and then a 15-s recording was
made (Labview®; National Instruments, Austin, TX, USA; sampling at 4000
Hz). The horse was then instructed to change gaits and another 15-s recording
was made after 45 s at the new gait. Speeds, conditions (level or incline) and
the sequence of gaits were randomized. Stride frequencies and contact times
for each speed and condition were averaged over 10 strides. Time of contact of
each individual limb was determined from the accelerometer record. Because the
time of contact of the fore and hindlimbs in trotting horses differ (S. J.
Wickler, D. F. Hoyt, E. A. Cogger and G. Myers, unpublished data), we
calculated the mean of one pair of contralateral fore and hindlimbs. In
galloping horses, the time of contact of all four limbs differed (S. J.
Wickler, D. F. Hoyt, E. A. Cogger and G. Myers, unpublished data), so we
calculated the mean time of contact for all four limbs. These are the same
methods used by Kram and Taylor
(1990
). The points from the
accelerometry records chosen for contact and heel lift were validated using a
force plate (9287BA; Kistler, Winterhur, Switzerland; 600 mmx900 mm).
For these validation trials, a portable computer (MS-4002; Maxwell
Microsystems, Inc., Denver, CO, USA) mounted on a pack frame (total mass,
approximately 28 kg) carried by the horse sampled accelerometry data while the
horses were trotted over the force plate. Accelerometer records for both the
fore and hindlimbs were validated.
Data analysis
Gait transition speeds, maximum sustained trotting speed and minimum
sustained galloping speed, on the level and on the incline, were analyzed
using a repeated-measures analysis of variance (ANOVA) of mean values from
each horse to determine the effects of three variables: gait (trot or gallop),
direction of speed change on the treadmill (increasing or decreasing) and
slope of the treadmill (level or inclined 10%).
Data for O2
versus speed were also analyzed using an analysis of covariance
(ANCOVA; with speed as the covariate) to test if there was an effect of gait
(Statview® v.5.0; SAS Institute, Cary, NC, USA). In each instance in which
there was a difference with gait, the relationship between
O2 and speed was
tested with step-wise regression analysis (Statview®) to determine the
best-fit relationship. For each animal and condition, the energetically
optimal transition speed (EOTS), the speed where metabolism at a trot equaled
that at a gallop, was determined from the intersection of the regression
equations. The EOTSs were compared with the maximum sustained trotting speed
and the minimum sustained galloping speed using paired t-tests. When
no difference was found between the EOTS and the maximum sustained trotting
speed, a simple, linear regression analysis between them was performed to see
if they were correlated.
Stride frequency and time of contact data were analyzed by a two-way, repeated-measures ANOVA with gait, condition (level and incline) and speed as the independent variables. A means separation comparison test was used to test for the effect of gait at different speeds. Significance was set at P<0.05 for all analyses.
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Results |
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For each horse at each condition (level and incline), the relationship between metabolic rate and speed was different for trotting and galloping. The slope for the regression line (Fig. 1) for trotting was larger than for galloping (with the exception of the horse Anakin on the incline).
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In the group of five horses for which all the necessary data have been
determined on the level, the mean minimum sustained galloping speed was 0.63 m
s1 greater (P=0.010) than the EOTS. Similarly, an
unpaired t-test of the data on an incline (required because EOTS was
not determined on an incline for one of the five horses) showed that the
minimum sustained galloping speed was also 0.63 m s1 greater
(P=0.032) than the EOTS. Therefore, under both conditions, at the
minimum sustained galloping speed on the level (the speed used by
Farley and Taylor, 1991) the
metabolic rate when galloping was lower than when trotting. There was no
difference in the EOTS and the maximum sustained trotting speed on the level
(difference = 0.07; P=0.597) or on the incline (difference =
0.03; P=0.912). A regression analysis of maximum sustained
trotting speed versus EOTS indicated that there was a strong
correlation (r2=0.60, P=0.014) and that the slope
(0.93) was not different from 1.
On the level, stride frequency (Fig. 2) increased linearly with speed in trotting horses up to the minimum sustained galloping speed. At faster speeds, there was no further increase in stride frequency (P=0.950; power = 0.0531). When a horse made a transition to the gallop, stride frequencies increased by approximately 7% (P=0.0008). Over the limited range of speeds measured in this study, galloping stride frequency was independent of speed (P=0.816; power = 0.0502). The striking difference on the incline was that trotting stride frequencies became constant at a slower speed and frequency than on the level. As on the level, when horses made a transition to the gallop on the incline, stride frequencies increased (approximately 14%). Because the transition occurred at a slower speed on the incline, the increase in stride frequency between trotting and galloping was greater than on the level (14% versus 7%).
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The time that the hoof is in contact with the ground (tc; Fig. 3) decreased with increasing speed. On the level, there were no differences in the tc between trotting and galloping for the limited range of overlapping speeds (P=0.69 and power = 0.2134 for the lowest speed, and P=0.53 and power = 0.1356 for the next higher speed). On the incline, tc was also not different from that on the level over the range of speeds measured. However, tc was shorter at a gallop than at a trot on the incline (P=0.0095 for 4.5 m s1 and P=0.003 for 4.0 m s1).
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Discussion |
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The results of the present study are consistent with those of Hoyt and
Taylor (1981) but lead to the
opposite conclusion to those of Farley and Taylor
(1991
) regarding the metabolic
consequences of the trotgallop transition. The energetically optimal
transition speed (EOTS), the speed where metabolic costs were identical for
the trot and gallop, always occurred near the range of speeds at which the
horses switched back and forth between gaits. The maximum sustained trotting
speed was not different from the EOTS
(Table 1) and, in fact, was
correlated. The minimum sustained galloping speed was always faster than the
EOTS. Farley and Taylor (1991
)
defined the trotgallop transition as the lowest speed at which their
ponies would gallop for one minute (equivalent to our minimum sustained
galloping speed) and reported that this speed was slower than the EOTS. This
led them to conclude that the animals made the transition from trot to gallop
in spite of the fact that the gallop was less economical than the trot. At the
minimum sustained galloping speed in our study, the gallop was more economical
than the trot.
When the treadmill was inclined 10%, there was a 13% decrease in transition
speed. This was true for both maximum sustained trotting speed and minimum
sustained galloping speed. Metabolism increased substantially on the incline
as expected (Eaton et al.,
1995; Wickler et al.,
2000
); however, the EOTS decreased on the incline. As on the
level, the EOTS was significantly slower than the minimum sustained galloping
speed and not different from the maximum sustained trotting speed. Hence, when
moving up an incline, the horses chose the gait that was metabolically the
most economical.
The discrepancy between the present study and Farley and Taylor's is puzzling. One difference was in the breed studied and the correlated substantial differences in mass (140 kg for the ponies) and perhaps differences in behavior that may have influenced the gait transition trigger. Another difference in the methodology was the paradigm for changing treadmill speed. In the study by Farley and Taylor, treadmill speed was changed continuously at 0.33 m s1 every minute and then held constant for one minute after the pony changed gait. If the animal switched gait again, treadmill speed was again continuously increased until another gait change occurred. In our study, we rapidly changed speed in 0.25 m s1 increments and then held it constant for one minute and recorded what gait(s) the horses used. These small differences in our methods were ones we could identify, but it seems unlikely that they can account for the very different results.
There are also conflicting conclusions about the metabolic consequences of
the walkrun transition, although walking is fundamentally different
from either trotting or galloping. Mercier et al.
(1994) found that humans made
the transition from the walk to the run at the EOTS. However, in other human
studies, the trigger to switch from the walk to the run does not appear to be
metabolic minimization (Brisswalter and
Mottet, 1996
; Hreljac,
1993
; Minetti et al.,
1994a
,b
).
These studies identified other possible triggers: the maximal angle in the
limbs (Grillner et al., 1979
),
increases in internal work (Minetti et
al., 1994b
) or the maximal angular velocity of the ankle
(Hreljac, 1995
). It has also
been suggested that the trigger is a function of the dynamics of an
inverted-pendulum system that characterizes the walk
(Kram et al., 1997
).
Forces acting on the bones have been identified as a potential trigger for
the trotgallop transition in several studies. In vivo
recordings of bone strain from the radius and tibia of goats showed a marked
decrease when the animals made a transition from the trot to the gallop
(Biewener and Taylor, 1986).
These results were consistent with similar observations made in the dog
(Rubin and Lanyon, 1982
) and
the horse (Biewener et al.,
1983
). In the Farley and Taylor
(1991
) study, when the ponies
made the transition from the trot to the gallop, peak forces on the limbs
decreased. When the ponies carried additional weight, the transition speed was
reduced but occurred at the same `critical level of force'. They concluded
that musculoskeletal forces trigger the trotgallop transition.
Our observation that the trotgallop transition occurs at a slower
speed on the incline than on the level appears to be inconsistent with the
force trigger hypothesis; however, this depends on the assumption that forces
are not elevated on an incline. This assumption is based on the physical fact
that total vertical impulse per stride is determined by body mass (which is
not elevated on the incline) and the observation that forces in the tendon of
the lateral gastrocnemius are not elevated when a turkey runs up an incline
(Roberts et al., 1997). The
fact that stride frequency and time of contact are not changed when a horse
trots up an incline (Figs 2,
3) suggests that impulse and
peak forces are the same on the level and on the incline.
Even though total forces are expected to be the same on the level and on
the incline, there is evidence that the forces under the fore and hindlimbs of
a quadruped may not change in the same way with speed or incline, and this has
some interesting implications for the trigger. One kinematic analysis
(Sloet van Oldruitenborgh-Oosterbaan et
al., 1997) shows that, when trotting up an incline, there is
increased hyperextension of the metacarpophalangeal joint (MCP) on the
hindlimb and decreased hyperextension of the MCP joint on the forelimb when
compared with level locomotion. Because the MCP joint is primarily controlled
by ligaments, these changes in the kinematics suggest that smaller forces act
on the forelimb and larger forces act on the hindlimb when going up an
incline. This observation, combined with a lower transition speed on an
incline, suggests that the trigger on the incline might be elevated hindlimb
forces. However, this is probably not the case on the level based on
the observation that the tendon strain does not increase with speed in the
hindlimb on the level but does increase in the forelimb
(Biewener, 1998
). This suggests
that forces on the hindlimb do not increase with speed on the level,
indicating that the trigger on the level cannot be hindlimb forces but might
be forelimb forces. Thus, if forces are the trigger for the trotgallop
transition, it is possible that forelimb forces are the trigger on the level
and hindlimb forces are the trigger when going up an incline.
As complex as these conclusions are, our results indicate that there may be another signal that indicates to the animal that gait should be changed. In the range of speeds between the maximum sustained trotting speed and the minimum sustained galloping speed, the animal switches gait repeatedly. One possible interpretation of this behavior is that the animal is detecting conflicting signals one indicating that trotting is the preferred gait and another indicating that galloping is the preferred gait. However, neither of the triggers previously suggested (metabolism and force) can explain this behavior because, in this range of speeds, forces and metabolic rate are both lower when galloping. Thus, it seems likely that some other signal causes the animal to switch from galloping to trotting. The only stride parameter we studied that might be implicated is the duration of the swing phase, which is 10% shorter when galloping at the same speed.
Additionally, different triggers may be required to explain the transition
from trotting to galloping when speed is increasing and the transition from
galloping to trotting when speed is decreasing
(Kram et al., 1997). The fact
that forces decrease when a horse changes from trotting to galloping means
that forces increase when making the transition from galloping to trotting. It
seems unlikely that the change from the gallop to the trot is triggered by
increasing strain and forces. However, it is also difficult to provide a link
between metabolism and a trigger for the gait transition. The maximum
sustained trotting speed was not different to the EOTS, but, at speeds between
the maximum sustained trotting speed and the minimum sustained galloping
speed, where the horses were making a transition after only a couple of
strides, it seems unlikely that the animals could detect very small
differences in metabolic rate, and at the minimum sustained galloping speed,
metabolic rate is usually higher when trotting. Again, the only parameter that
decreases when a horse switches from galloping to trotting is stride
frequency, resulting in a longer swing phase. Similar conclusions have come
from studies of the walkrun transition in humans
(Prilutsky and Gregor, 2001
);
the transition from the walk to the run was correlated with increased activity
of muscles to swing the leg, whereas the runwalk transition was
correlated with increased activity of muscles used in supporting the body.
The present study expands our understanding of the relationship between
stride frequency and speed. Stride frequency increased as a linear function of
speed at the trot up to the minimum sustained galloping speed. At speeds
faster than the minimum sustained galloping speed, stride frequency in the
extended trot did not change. When the horses made a transition to the gallop,
there was a sudden increase in frequency, and stride frequency was independent
of speed at all galloping speeds. Using allometric equations from Heglund and
Taylor (1988), the stride
frequency and speed at the trotgallop transition (on the level) were
calculated to be 100 strides min1 and 5.8 m
s1, respectively (using a mean mass of 467 kg). Stride
frequency at the minimum sustained galloping speed in the present study was
109 strides min1, and the transition speed was 5.7 m
s1. The calculation of transition speeds in the Heglund and
Taylor (1988
) study was based
on the assumption that this speed occurred at the intersection of separate
regression lines fitted to stride frequency versus speed for trotting
and for galloping; they did not note the sudden increase in stride frequency
that occurs when trotting and galloping at the same speed. This phenomenon
occurs in horses but it is not known if it occurs in other quadrupeds. In the
present study (Fig. 2), this
intersection would occur at a speed of approximately 6.7 m
s1 and a stride frequency of 118 strides
min1.
The present analysis is the first examination of time of contact at speeds
near the transition speed. In a seminal paper, Kram and Taylor
(1990) compared metabolic
costs and time of contact as a function of speed in a group of mammals with
body masses ranging from 30 g to 140 kg. They concluded that the majority of
the cost of transport is determined by the cost of supporting the animal's
mass and the time course of the application of force during contact. A shorter
time of contact would result in the requirement for a faster application of
force that would, in turn, increase metabolic costs. In the horses, time of
contact was shorter during galloping than trotting on the level at speeds
slower than the EOTS, and that is consistent (based on
Kram and Taylor, 1990
) with
the higher metabolic costs of galloping at those speeds. At the EOTS, the time
of contact was not different between trotting and galloping; again, an
observation consistent with Kram and Taylor
(1990
). On an incline, the
time of contact at the maximum sustained trotting speed is not the same when
trotting and galloping in spite of the fact that this is the EOTS on an
incline. We do not consider this to be inconsistent with Kram and Taylor
(1990
) because their
hypothesis did not address the cost of locomotion on an incline.
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Acknowledgments |
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