Ground reaction forces in horses trotting up an incline and on the level over a range of speeds
1 Department of Kinesiology and Health Promotion, California State
Polytechnic University, Pomona 91768, USA
2 Department of Biological Sciences, California State Polytechnic
University, Pomona 91768, USA
3 Department of Animal and Veterinary Science, California State Polytechnic
University, Pomona 91768, USA
* Author for correspondence (e-mail: ddutto{at}csupomona.edu)
Accepted 5 July 2004
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Summary |
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On the level, forelimb peak forces increased with trotting speed, but hindlimb peak force remained constant. On the incline, both fore- and hindlimb peak forces increased with speed, but the sum of the peak forces was lower than on the level. On the level, over the range of speeds tested, total force was consistently distributed between the limbs as 57% forelimb and 43% hindlimb, similar to the weight distribution of the horses during static weight tests. On the incline, the force distribution during locomotion shifted to 52% forelimb and 48% hindlimb.
Time of contact and duty factor decreased with speed for both limbs. Time of contact was longer for the forelimb than the hindlimb, a finding not previously reported for quadrupeds. Time of contact of both limbs tended to be longer when traveling up the incline than on the level, but duty factor for both limbs was similar under both conditions. Duty factor decreased slightly with increased speed for the hindlimb on the level, and the corresponding small, predicted increase in peak vertical force could not be detected statistically.
Key words: ground reaction force, limb, horse, biomechanics, force, locomotion, trotting, incline
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Introduction |
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Even though total vertical forces are expected to be the same on the level
and an incline, there is evidence that the forces under the fore- and
hindlimbs of a quadruped may not change in the same way when trotting up an
incline. One kinematic analysis (Sloet van
Oldruitenborgh-Oosterbaan et al., 1997) showed that, when trotting
up an incline, there was increased hyperextension of the metatarsophalangeal
(MTP) joint on the hindlimb and decreased hyperextension of the
metacarpophalangeal (MCP) joint of the forelimb. Because the MCP and MTP are
primarily controlled by ligaments and increases in MCP range of motion have
been found to positively correlate with increased ground reaction force
(McGuigan and Wilson, 2003
),
we hypothesized that there will be smaller forces acting on the forelimb and
increased forces acting on the hindlimb. Additionally, we asked whether these
changes in force would produce concomitant changes in the temporal stride
characteristics.
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Materials and methods |
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Experimental set-up
Two runways, each 30 m in length, were built for data collection. The first
runway was level and the second was sloped with a 10% gradient (5.7°
relative to horizontal as measured using a transit). The cement runways (10 cm
thick, 1.25 m wide) were covered by a 10 mm-thick, high density, black
rubberized mat (All Weather Rollout Runway, Dodge Regupol, Lancaster, PA,
USA). A 0.6 mx0.9 m force plate (model 9287BA, Kistler Instruments,
Winterthur, Switzerland) was located approximately in the middle of each
runway supported by a 0.9 m-thick pedestal of cement, isolated from the rest
of the runway by vibration-dampening material. The same force measuring plate
was used for all data collection. The top of the force plate was covered with
a rubberized mat of material identical to that covering the rest of the runway
to provide a continuous visual field for the animal. With the mat glued to the
surface of the force plate, the natural frequency of the force plate was 384
Hz in the z-axis and 500 Hz in the two horizontal directions. These
frequencies are somewhat lower than the original natural frequency of the
plate (520 Hz and 750 Hz, respectively) but the observed decrements are within
the tolerances recommended by the manufacturer. Three-dimensional force data
were sampled at 1000 Hz for all tests, but only the horizontal (representing
the foreaft direction) and vertical forces were included in the
study.
Data analysis
Normal and parallel forces were recorded for each trial. For the level
trials, the normal force corresponded to Fz (true
vertical) and the parallel force to Fy (the foreaft
force or true horizontal). For the data collected during the inclined trials,
the normal and parallel forces were rotated 5.7° relative to the level
condition. In order to compare level and incline data, force data recorded
during the incline trials were converted to represent true vertical (parallel
to the gravitational vector) and horizontal (orthogonal to the gravity vector)
force. Thus, data referred to as Fz and
Fy are representations of forces parallel and orthogonal
to the gravitational vector. Fbrake and
Fprop are used in subsequent analysis of the horizontal
force, where Fbrake is indicative of a braking force, and
Fprop of a propulsive force, and these are also orthogonal
to the gravitational vector.
From each trial, the following variables were calculated: peak vertical force (Fz,peak), vertical impulse (Impz), peak braking and propulsive forces (Fbrake, Fprop), and the total (net) horizontal impulse (Imph). The distribution of vertical forces between the fore- and hindlimbs was determined by calculating the average force over a stride for both the fore- and hindlimbs, and then the percentage distribution of force is simply the ratio of the average force over the stride for a particular limb and the sum of the fore- and hindlimb average forces over the stride. Time of contact (tc) was also measured from the recorded force data. From video recordings obtained simultaneously with the force recordings, stride time was measured. Duty factor (DF) was calculated as the ratio of time of contact to stride time.
It would not have been statistically valid to treat all of the ca. 120
values obtained for a given limb and condition as independent observations
because they were obtained from four individual animals. Therefore, the data
obtained from an individual animal were subjected to regression analysis and
then the resulting regression coefficients were subjected to analysis of
variance (ANOVA). For each animal, the best-fit regression line was determined
for the variable of interest using speed as the independent variable. For
three variables (tc, DF and Impz), the
best-fit lines were power functions. A log transform was applied to both speed
and the variable (tc, DF or Impz) to
create a linear relationship, from which a linear regression was calculated.
From all regression lines, two values were used for statistical analysis: the
slope of the line and the predicted value at 3.5 m s1. The
predicted value at 3.5 m s1 was used, rather than intercept,
to assess the magnitude of difference between limbs and between level and
incline, because it represents a datum in the mid-range of speeds tested, and
is relatively close to the preferred trotting speed of horses of this mass
(Wickler et al., 2000).
Differences between the fore- and hindlimb (leg) and the differences between
the level and incline (condition) were assessed by a 2x2 ANOVA
(P=0.05), with repeated measures used for the leg but not for the
condition comparison. Repeated measures were not used for condition because
only one horse was tested on both the level and incline conditions; each of
the remaining six horses performed either the level or the incline test. An
ANOVA was used to assess each variable of interest (one for the slope of the
regression line and the second for the value at 3.5 m s1).
To determine whether speed affected a particular variable, under a particular
condition, the 95% confidence interval for the slope was determined. The speed
effect was present if the 95% confidence interval did not include zero.
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Results |
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Temporal characteristics as a function of speed
Time of contact (tc) for both limbs decreased with
speed for level and incline, and the tc for the forelimb
decreased at a faster rate than the hindlimb
(Table 1). At the higher speeds
(>4.5 m s1), tc tended to converge
for both limb and condition (Fig.
2A,B), indicating that both limbs were spending roughly equivalent
time periods on the ground at higher speeds. Because the stride times were
essentially the same for fore- and hindlimbs, duty factor exhibited the same
pattern as time of contact. Duty factor also decreased with speed for both
limbs during level and incline trotting
(Table 1), and duty factor of
the forelimb decreased at a greater rate than that of the hindlimb. At higher
speeds, the DF of the fore- and hindlimbs converged.
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Forces as a function of speed
Peak vertical ground reaction force (Fz,peak) generated
under the forelimb increased with speed for both the level
(Fig. 3A) and incline
conditions (Fig. 3B). The
Fz,peak under the hindlimb did not change with speed on
the level, but did on the incline (Table
1). As speed increased, the decreasing tc
counteracted the increasing Fz,peak and resulted in a net
decrease in Impz for both limbs and both conditions
(Fig. 4A). Forces tended to be
distributed consistently between the limbs with increased speed, with a
57%/43% split to fore/hindlimbs, respectively, on the level and 52%/48% on the
incline (Fig. 4B). The average
force produced by the limbs was not significantly different than 9.8 N
kg1, for individual animals at all speeds tested
(Fig. 4B), despite the
appearance from the regression line that the total average force might be
less, particularly at lower speeds.
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Peak braking force tended to increase with speed for both limbs and both conditions (Table 1). Peak propulsive force increased with speed for both limbs on the level but only for the hindlimb on the incline (Table 1). The total horizontal impulse remained essentially unchanged with speed for both limbs under both conditions (Table 1). While average slopes different from zero were found for the horizontal impulse of the hindlimb on the level and the forelimb on the incline, the magnitude of these slopes is so close to zero that they probably have no biological significance.
Comparison of temporal characteristics on the level and incline
On the incline, tc of the forelimb was no different
from the value on the level both in terms of the relationship with speed and
in the average magnitude at 3.5 m s1
(Table 1). For the hindlimb on
the incline, however, tc decreased at a greater rate with
speed (Fig. 2), and tended to
be longer (than on the level) at 3.5 m s1. As speed
increased tc tended to converge, regardless of condition
or limb. Duty factor of the hindlimb decreased at a greater rate with speed on
an incline (Table 1). The
magnitude of the duty factor of both limbs at 3.5 m s1 was
not different between conditions (Table
1), but it was for the hindlimb at 2.75 m s1
(level, 0.392±0.008; incline, 0.409±0.008).
Forces on the level and incline
Fz,peak when trotting up an incline was reduced on the
forelimbs when compared to the level (Fig.
3), but increased with speed in a similar manner for both
conditions (Table 1,
Fig. 3). On the incline,
Fz,peak for the hindlimb was higher than that of the
forelimb at the low speeds (<3.0 m s1) and increased with
speed, in contrast to a constant hindlimb peak force on the level. The effect
of incline was to make the Fz,peak of the two limbs more
similar. Impz (Fig.
4) was lower for the forelimb and higher for the hindlimb on the
incline.
Comparing conditions, the forelimb tended to apply less braking force and the hindlimb more braking force on the incline, as indicated by Fbrake at 3.5 m s1 (Table 1). Fprop was greater for the hindlimb and less for the forelimb on the incline. On the level, Imph for the forelimb was slightly negative and for the hindlimb was slightly positive (Table 1). On the incline, the Imph became larger for both limbs, with the forelimb creating a net braking and the hindlimb a net propulsive impulse. The net effect is that horizontal impulse across both limbs was slightly positive on both the level and the incline.
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Discussion |
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The decrease in time of contact with speed was similar to observations
recorded from previous studies on horses
(Hoyt et al., 2000;
McLaughlin et al., 1996
;
Robert et al., 2002
), other
quadrupeds (Kram and Taylor,
1990
) and bipeds (Munro et
al., 1987
; Roberts et al.,
1997
). Interestingly, the time of contact was longer for the
forelimb than the hindlimb, a fact not previously reported for quadrupeds.
Duty factor decreased as speed increased, similar to bipeds
(Gatesy and Biewener, 1991
) and
horses (Biewener, 1983
;
Hoyt et al., 2000
). Contact
time and duty factor for the fore- and hindlimbs converged and decreased less
rapidly at higher speeds (Fig.
2).
On the level, the contact time and duty factor of the hindlimb decreased
with increasing speed, but there was no change in peak vertical force. The
relatively small changes in DF were not of sufficient magnitude to effect a
change in hindlimb peak force. The observation in the present study that
hindlimb peak forces are independent of speed is not consistent with reported
increased stress on both the tibia and metatarsus
(Biewener et al., 1988), but is
consistent with observations of an absence of change in muscletendon
stresses in the hindlimb (Biewener,
1998
) and constant tibial compressive strain
(Rubin and Lanyon, 1982
). On
the incline, peak forces in the hindlimb were greater and they increased with
increasing speed due to the greater decrease in duty factor of the hindlimb
and a rearward distribution of force compared to the level. That forces on the
incline were increased is consistent with the reported increased
hyperextension of the metatarsophalengeal joint on the incline
(Sloet van Oldruitenborgh-Oosterbaan et
al., 1997
; McGuigan and
Wilson, 2003
).
Because of the inversely proportional relationship between duty factor and
speed, one might expect peak force to increase due to the requirement of
maintaining a consistent vertical impulse over the stride
(Alexander et al., 1979). This
relationship certainly holds true for the forelimb and the increases in peak
force with speed were consistent with measured stress increases on the
muscletendon units with speed of trotting in horses
(Biewener, 1998
). However, on
the incline, due to the shift of force distribution to hindlimb (from 57%/43%
on the level to 52%/48% on the incline, fore/hind, respectively), peak forces
were decreased. This decrease in measured peak force is consistent with the
kinematic data of Sloet van Oldruitenborgh-Oosterbaan et al.
(1997
). They observed that
hyperextension of the metacarpophalangeal joint decreased when trotting up an
incline and the extension of this joint is a function of the amount of force
placed on the limb (McGuigan and Wilson,
2003
). Also, the increased peak force generated by the forelimb
with increased speed was not consistent with an absence of change in radial
compressive strain (Rubin and Lanyon,
1982
), but was with measured stress increases on the
muscletendon units with increased speed of trotting
(Biewener, 1998
).
Based on the observations that, as a function of speed on the level,
contact time for both limbs decreased, contact time was lower for the hindlimb
and force was higher for the forelimb, one might conclude that the
distribution of force used to support the mass of the animal against gravity
might shift forward. However, the distribution of total force remained the
same (57% fore, 43% hind) across all speeds
(Fig. 4B). The 57% of total
force under the forelimb on the level was slightly less than that reported by
Jayes and Alexander (1978) for
sheep and dogs (which was 60%/40%), but the same as reported by Knill et al.
(2002
) for horses. The
measured 57%/43% force distribution during locomotion was also consistent with
subsequent static weight measurements of each animal. When trotting on an
incline, support shifted slightly to the hindlimb (52% fore/48% hind). This
redistribution of force to the hindlimb may seem plausible since the long axis
of the horse becomes oriented to an angle similar to that of the slope.
However, later static measurements of several of the horses on the incline
revealed that each animal's posture (slightly leaning into the slope) was such
that a 57%/43% fore/hind distribution of weight was maintained, so that the
observed force distribution (52%/48% fore/hind) during trotting up the hill
was different from that during standing. Kinematic analysis of the hindlimb
(Hoyt et al., 2002
) suggests
very little change in hindlimb positioning during trotting up an incline, and
the small changes that were found may be due to a slight backward or downward
shift of the torso of the animal on the incline, which is consistent with the
changes in force distribution observed in the current study.
Horizontal forces increased in magnitude with speed on the level, and peak braking forces increased more than peak propulsive forces (Table 1). These increases in horizontal forces produced slight increases in the braking and propulsive impulses and this resulted in a small, net positive horizontal impulse at lower speeds and a net horizontal impulse of zero at higher speeds. Using the regression equations to predict the net horizontal impulse at 2.0 m s1 indicates the change in velocity will be 0.06 m s1, a 3% increase in speed, and at more intermediate speeds the net positive impulse would increase velocity by only 0.8% (0.03 m s1 at a trotting speed of 3.5 m s1). This small acceleration at intermediate speeds may not be biologically significant given the variability around the regression lines; however, it was beyond the resolution of our system of monitoring speeds and would not have caused trials to be excluded, because our standard was to exclude trials in which speed changed by more than 10% between the two timing zones. Increases in braking and propulsive peak forces and impulse were more pronounced on the incline so that the forelimb produced greater braking and the hindlimb greater propulsion when trotting up an incline.
The mechanics of the fore- and hindlimbs appeared to be different and speed-dependent. Despite differences in temporal and force measures, the horse maintained a consistent distribution of weight. Trotting up an incline was produced through increased propulsive and vertical force of the hindlimb, while force decreased for the forelimb. Both duty factor and time of contact are different between the limbs, which may have implications for previous research relating force and energy cost of locomotion to these parameters.
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Acknowledgments |
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References |
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