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First published online March 2, 2007
Journal of Experimental Biology 210, 971-982 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02728
Limitations to maximum running speed on flat curves
1 Comparative Neuromechanics Laboratory, School of Applied Physiology,
Georgia Institute of Technology, Atlanta, GA 30332-0356, USA
2 Locomotion Laboratory, Department of Integrative Physiology, University of
Colorado, Boulder, CO 80309-0354, USA
* Author for correspondence (e-mail: yh.chang{at}gatech.edu)
Accepted 17 January 2007
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Key words: turning, maneuverability, curve, sprinting, running, locomotion, biomechanics
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; Usherwood and Wilson,
2005) and natural predator avoidance
(Alexander, 1982;
Howland, 1974), but more
detailed biomechanical data such as ground contact forces generated by the
limbs are lacking. Such data are difficult to obtain in non-human animals.
Studying curve sprinting in humans provides a more tractable experimental
system for gaining insights into the fundamental principles that limit sprint
speed along curved paths.
The maximum human running speed along a flat curved path is significantly
slower relative to a straight path. Records from track and field meets were
examined (Jain, 1980) and it
was found that 200 m sprinters were up to 0.4 s slower on curved tracks
compared to straight tracks. This decrease in maximum speed is related to the
curvature of the track lane and can potentially result in one sprinter gaining
an advantage of up to 0.12 s over a competitor in an adjacent inside lane
(Harrison and Ryan, 2000;
Jain, 1980). The attenuation
of sprint speed is more pronounced as the radius of curvature is reduced. The
mechanism for this speed reduction, however, is not firmly established.
Several studies have attempted to explain this phenomenon by modeling the
sprinter as a point mass and using classical physics principles for objects
moving in a circular path (Keller,
1973; Mureika,
1997). Along a curved path, the sprinter must generate centripetal
forces by applying lateral force on the ground with each step
(Fig. 1). This centripetal
force is required to change the direction of the momentum vector of the
sprinter. Few studies, however, have attempted to combine the physics with the
biomechanical limitations of the body to explain the mechanism for sprint
speed attenuation during flat curve sprinting.
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) based on the
primary assumption of a physiological limit to the maximum leg extension
force. According to Greene, a theoretical limit to peak resultant force
exerted on the ground must result in a vectorial decrease in the peak vertical
component due to the concomitant increase in the lateral component
(Fig. 1). A smaller peak
vertical force would require an increase in ground contact time to generate
sufficient vertical impulse to support body weight over the entire stride.
Running velocity can be calculated as the distance traveled during foot
contact (LC) divided by the contact time of the foot
(tC). Given that LC does not change
substantially with speed (McMahon and
Greene, 1979; Weyand et al.,
2000), an increase in tC would reduce forward
sprinting velocity. With these basic assumptions, Greene derived a
relationship between forward sprint velocity and radius of curvature for small
and large radii.
Although his empirical data on maximum running speeds agree with the
theory, Greene stated "there was a significant degree of scatter to
[the] data...[making it] possible that other theoretical models [could]
predict the data as successfully"
(Greene, 1985). A similar
model was developed using the same assumption of a constant leg force to
predict human sprint speeds from kinematics data
(Usherwood and Wilson, 2006).
Yet, in the 20 years since Greene's study, no ground reaction force (GRF) data
have been published to test this primary assumption that maximum leg extension
forces (i.e. peak resultant ground reaction forces) limit sprint speed on flat
curves.
Greene's data were collected on tracks of relatively large radii (11 m and
19 m) (Greene, 1985;
Greene, 1987). Although these
are realistic dimensions for indoor track events, they are not realistic for
predator/prey contexts where much tighter turns are common
(Howland, 1974). We reasoned
that the general principles of how curvature affects maximum speed running
would be more clearly observed at extremely small radii. It is often at these
limits of performance that we can gain the greatest insight into the design
and function of the locomotor apparatus
(Full and Koditschek,
1999).
The primary goal of this project was to directly test the hypothesis that the maximum physiological leg extension force observed during straight path sprinting is also generated during flat curve sprinting. We define `maximum physiological leg extension force' as being the maximum extension force that an individual is capable of generating and is estimated by the peak resultant ground reaction force measured during straight path sprinting. `Peak resultant ground reaction force' is defined as the peak force generated by the legs on the ground during a given sprint trial on either a straight or curved path. If the ability of a sprinter to exert a leg extension force on the ground is the limiting factor in maximum velocity, then the peak resultant ground reaction force should remain constant at all curvatures. To gain further insight into what limits maximum speed during curve sprinting, we separated the effects of generating the lateral GRF component from the effects of the curved path itself. According to Greene's theory, if a person were able to sprint along a curved path without having to generate centripetal forces, the sprint speed should not be slower than on a straight path. Specifically, we measured: (i) the constancy of peak resultant GRF for sprinters along curved paths of various radii; and (ii) sprint velocity on curved paths when centripetal forces were supplied by a tether rope secured at the center of a circular track.
A secondary goal of this study was to test the hypothesis that both legs
act symmetrically during sprinting on flat turns. The symmetrical action of
the legs is an implicit assumption in Greene's theory and other curve
sprinting theories that treat the runner as a point-mass
(Keller, 1973;
Mureika, 1997). Given the
differences in muscle activity, limb and joint dynamics observed between legs
during discrete `cutting' maneuvers (Besier
et al., 2003; Besier et al.,
2001a; Besier et al.,
2001b; Ohtsuki and Yanase,
1989; Ohtsuki et al.,
1987; Ohtsuki et al.,
1988; Rand and Ohtsuki,
2000), we predicted that the biomechanical constraints placed on
the inside leg would be different from those placed on the outside leg. We
specifically tested for asymmetries in the forces generated on the ground and
in the stride kinematics. Asymmetrical biomechanics might suggest that one leg
preferentially limits sprint speed on flat curves.
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Subjects sprinted on circular tracks of 1, 2, 3, 4 and 6 m radii. All five tracks were drawn with paint on flat, clean, paved asphalt so that they were cotangential with a strategically placed force platform (Advanced Mechanical Technology, Watertown, MA, USA; Fig. 2). The force platform was mounted flush with the surface of the ground and was covered with a rubber matting to prevent slipping. The track was kept clean of debris and subjects wore rubber-soled running shoes to allow maximal effort with no slipping. Subjects also wore safety wrist guards and knee pads for protection and to reduce fear of injury due to slips. We collected ground reaction forces as subjects sprinted on all five curved tracks and also on a straight 30 m runway leading up to the force platform. A 200 Hz high-speed video camera (J.C. Labs, Inc., Mountain View, CA, USA) provided a lateral view of the sprinters as they crossed the force platform. Video records were used to calculate the sprint speeds (Fig. 2).
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Protocol
After a 30 min warm up and practice session, subjects began by sprinting on
the straight path. We measured sprint speed for the last 5 m of the sprint.
Subjects then sprinted along the circular tracks alternating between the
normal curve sprinting condition and the tethered condition at each radius.
Subjects ran between 3–5 trials at each condition. Three subjects
started with the largest radius and ended with the smallest radius. Two
subjects performed the order in reverse and due to time constraints completed
their trials over multiple days. Subjects were given sufficient time to rest
between trials. We again measured straight path sprint speeds for each subject
at the end of each session to verify that fatigue had not affected their
sprint speeds over the course of the trials. No significant differences were
found between beginning and end sprint speed measurements (paired
t-test, P>0.05).
Velocity calculations
For straight sprinting trials, velocities were measured by two observers
with stopwatches and also by a set of infrared sensors in the last 5 m of the
runway before subjects reached the force platform. The averaged stopwatch
values compared well with the sensor data. For curved sprinting trials, the
sensors were used along secants of the track. Due to sunlight interference,
however, we found the infrared sensor measurements to be less reliable on the
curved tracks and we discarded them in favor of velocities calculated from
video. For the 1 m and 2 m radii, velocity was calculated over one complete
revolution (6.3 m and 12.6 m circumference, respectively) starting and ending
when the subject's hip marker crossed the center of the force platform, which
could be easily identified by the tether pole placed at the center of each
circular track. For the 3, 4 and 6 m radii, velocity was calculated over half
of a revolution (9.4, 12.6, 18.9 m half circumference, respectively), starting
when the subject's hip marker crossed on the exact opposite side of the track
from the middle of the force platform as indicated by the tether pole. Each
subject's fastest velocity trial was used for maximum sprint speeds at each
condition and radius.
Force calculations
We sampled ground reaction force data from the force platform at 1 kHz per
channel for the z, y and x components. Vertical,
fore–aft and lateral components were then calculated by transforming the
global force platform coordinate system (z, y, x) to a local,
anatomical coordinate system with its origin based at the center of pressure
underneath the foot. The fore–aft direction was defined as tangential to
the curved path and the medial–lateral direction was defined as radial
to the curved path. In this way, all fore–aft and lateral components of
force are relative to the curved path and did not depend on where the foot
landed on the force platform. We collected force data for 2–4 steps per
sprint trial depending upon the circumference of the track (fewer laps for
larger radii resulted in fewer steps). In no trials was the last step the
fastest; indicating that we had likely captured the subject's maximum velocity
for that condition. We filtered the data with a 4th-order recursive, zero
phase-shift, Butterworth low-pass filter with a 25 Hz cut-off. We have
previously determined that 99% of the integrated power content of the vertical
GRF signal during running is at frequencies <10 Hz and 98% of the
horizontal GRF signal is at frequencies <17 Hz
(Kram et al., 1998). We also
collected and averaged the tether force data.
For each trial, we calculated the peak resultant GRF magnitude, the peak GRF components, and the average force applied on the sprinter by the tether. For each condition, peak resultant forces were averaged across subjects for the outside and inside legs. We determined step length (LSTEP, distance from heel-strike to contralateral heel-strike), step frequency (fSTEP, inverse of time from heel-strike to contra-lateral heelstrike), and time of ground contact (tC) from the ground reaction force data. The instant of heel-strike was determined from the vertical force record by finding the closest local minimum before the vertical GRF reached a threshold of 100 N. The instant of toe-off was determined by finding the nearest local minimum after the vertical ground reaction force dropped below 100 N.
Statistical analyses
Due to our limited sample size for each condition, performing a multifactor
analysis of variance (ANOVA) would result in the presence of singularities.
Instead, we performed a single-factor ANOVA on our sprint speed, peak
resultant ground reaction force and stride parameter data. This provided a
much more conservative test for differences across all trial conditions since
each was treated as an independent observation. When we detected a significant
effect, we performed a Tukey's honestly significant difference
post-hoc test (P=0.05) to further test each radius condition
to the straight path, normal curve sprinting to tethered curve sprinting and
inside leg to outside conditions. Although this approach put us at risk for a
type II error (false negatives), any significant differences found should be
quite robust. As an additional test, we pooled our speed and ground reaction
force data across all radius conditions and performed a linear regression on
the log-transformed data plotted against a log-transformed dimensionless
radius (inverse Froude number). We then calculated the 95% confidence
intervals (C.I.) of these regression slopes to test for significant trends in
the force data across legs or to test if the sprint velocities predicted by
Greene's theory fell within the 95% C.I. of our log-transformed velocity
data.
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Ground reaction forces
Typical ground reaction force data sets from one representative subject are
shown for each tether, track radius and leg condition
(Fig. 4). Ensemble averages for
peak ground reaction force components across all subjects are shown in
Fig. 5.
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Peak propulsive ground reaction forces (Figs 4ii, 5ii) decreased at smaller radii during all sprint conditions on the curve compared to the straight path. In normal flat curve sprinting, the outside legs consistently generated greater propulsive forces than the inside legs. In contrast, with a tether, there was no consistent difference between legs with regard to generation of peak propulsive ground reaction forces.
Absolute magnitudes for peak braking ground reaction forces for normal curve sprinting also decreased at smaller radii, with the outside legs generating greater braking forces than the inside legs at each radius. In the tethered condition, however, the outside leg did not show a strong trend with radius, in contrast to the inside leg, which decreased in magnitude with smaller radii.
Peak lateral ground reaction forces (Figs 4iii, 5iii) were significantly greater for normal curve sprinting compared to straight path sprinting, but for all the curve conditions, values did not change substantially with radius. The outside leg always generated greater peak lateral ground reaction forces at each radius compared to the inside leg. In contrast, with tethered sprinting, we observed a decreasing trend in lateral force at smaller radii but no substantial difference in peak lateral ground reaction forces between the two legs.
Leg extension force
We observed a significant effect of our experimental curve and tether
conditions on the peak resultant ground reaction forces generated
(F(20,75)=4.83, P<0.001). Upon further
post-hoc analysis, we saw that the outside leg did not generate
statistically different forces from those generated during straight path
sprinting at any radius for the normal untethered condition
(P>0.05). In contrast, the inside leg generated significantly
lower peak resultant ground reaction forces at the 1 m and 2 m radius
conditions (P<0.05, Fig.
6A, Table 1). For
tethered curve sprinting, only the outside leg at the 1 m radius condition
showed significantly lower peak resultant ground reaction forces compared to
the straight path sprinting. Although a post-hoc test (Tukey HSD,
=0.05) did not reveal any significant differences between inside and
outside legs at matched radii, we likely lacked the statistical power in the
ground reaction force data to resolve any true differences between legs due to
the limited number of samples collected at each tether and leg condition. This
is supported by the consistent trends in the ground reaction force vs
radius data (Fig. 6) and the
fact that we saw more significant differences in the forces generated by the
inside leg compared to the straight path condition.
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Normal curve sprinting:
Inside leg:
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Outside leg:
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Tethered curve sprinting:
Inside leg:
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Outside leg:
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Greene's predictions
Although our velocity data qualitatively support Greene's predictions for
the relationship between maximum sprint speed and radius
(Fig. 3), they predict a
significantly greater exponent for the power fit of the data. Greene predicted
a relationship with an exponent of 0.258 for large radii [from equation 12 in
Greene (Greene, 1985)] and an
exponent of 0.333 for small radii [from equation 42 in Greene
(Greene, 1985)]. Our data
indicate a power relationship with an exponent of 0.363±0.012 (0.012
represents the 95% C.I. of our data; Eqn 5 and
Fig. 7):
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)]. This assumed
that the physiological limit to leg force would be generated on the ground at
every radius during sprinting. Our empirical evidence disputes that
assumption. Our direct measurements during curve sprinting indicated that the peak resultant ground reaction forces generated during maximal effort straight path sprinting were never reached for the inside leg at the smaller radii tested (Fig. 6, Table 1). Peak resultant ground reaction force decreased more with decreasing radius for the inside leg compared to the outside leg. When sprinting on the smallest curve radius (1 m radius), peak resultant ground reaction forces decreased to 69% (inside leg) and 83% (outside leg) of those generated on the straight path, though the outside leg difference was not statistically significant. This is direct evidence against the primary assumption that the peak resultant ground reaction forces generated during straight path sprinting are generated on flat curves.
An additional test of the constant leg force assumption was to examine whether our data relating sprint velocity and radius significantly differed from Greene's model. Our maximum velocity data provided a power curve fit with an exponent of 0.363 (95% C.I. for exponent is 0.351–0.375; Eqn 1, Fig. 7). This exponent was substantially greater than either exponent predicted by Greene for small or large radii tracks (P<0.05). In 1987, Greene revised his theory to incorporate sprinting on banked tracks. We further compared two predictions made from his later model for the velocity–radius relationship assuming no bank angle. We found that these predicted exponents again fell outside of the 95% C.I. of our fitted data (Fig. 7).
The constant leg extension force hypothesis predicts that time of foot
contact would increase at smaller radii to maintain the necessary vertical
impulse "to compensate for the vectorial decrease of available
vertical force" (Greene,
1985). Time of contact generally increased in our study with
smaller radii and correlated with slower sprint velocities. Our empirical data
suggest, however, that the vertical ground reaction forces decreased more than
would be predicted by a simple redistribution of the resultant force vector
from vertical to lateral components. In other words, the decrease in peak
vertical ground reaction force was not constrained by a physiological limit
for maximum force production by the leg. In fact, as indicated by the smaller
peak resultant forces generated during curve sprinting, each subject had ample
leg extension force available to generate the necessary vertical impulses for
a shorter ground contact time. We propose that the generation of ground
reaction forces was constrained instead by one or more other limiting factors.
To gain insight into what these limiting factors might be, we tested another
simplifying assumption made by these generalized curve sprinting models, which
is the symmetrical function of the legs. By investigating the function of each
individual leg in greater detail, we can come closer to elucidating the
mechanisms that limit performance during a complex behavior like curve
sprinting and generate additional hypotheses about the nature of speed and
maneuverability in legged locomotion.
Leg asymmetry
The use of the tether to externally supply the centripetal force necessary
to sprint along a curved path increased maximum tangential velocity by 12% on
average over the normal, untethered conditions
(Fig. 3,
Table 1). It also provided
insight into the asymmetrical function of the legs during curve sprinting. An
implicit assumption in many curve sprinting models is that both legs act
symmetrically (Alexander, 1982;
Howland, 1974;
Keller, 1973;
Mureika, 1997). We showed that
the peak resultant ground reaction forces generated by the inside leg were
more sensitive to track radius compared to those of the outside leg during
normal curve sprinting (Eqn 1, 2). This suggests that each leg was
experiencing substantially different biomechanical constraints during normal
curve running with the inside leg being more severely affected. The addition
of the tether eliminated these differences between legs and we observed a
significant increase in sprint speed.
Just as the weakest link in a chain limits the overall performance of the
chain, a force limitation in one leg can result in a reduction of maximum
performance of the entire locomotor system. Given that force generation is
correlated with straight path sprint speed
(Weyand et al., 2000), the
critical limit to curve sprinting speed is likely found in the forces
generated by the inside leg. It appears that the inside leg reached some
critical biomechanical threshold and limited the overall sprint speed.
Studies of discrete `cutting' turns may shed light on the asymmetric
constraints placed on the legs during human curve sprinting. Data from running
(Ohtsuki and Yanase, 1989;
Ohtsuki et al., 1987;
Ohtsuki et al., 1988;
Rand and Ohtsuki, 2000) and
walking (Hase and Stein, 1999;
Orendurff et al., 2006) reveal
functional differences during discrete turns made on either the outside leg or
the inside leg. For discrete turns, the inside leg is less effective at making
quick changes in running direction
(Ohtsuki and Yanase, 1989;
Ohtsuki et al., 1987;
Ohtsuki et al., 1988;
Rand and Ohtsuki, 2000). The
inside leg also generates smaller force impulses
(Ohtsuki et al., 1988) and
exhibits reduced muscle activation levels
(Rand and Ohtsuki, 2000)
compared to the outside leg during discrete turns. Our curve sprinting study
supports these previous studies. At maximal effort, a reduction in peak
resultant ground reaction forces by the inside leg likely plays a significant
role in limiting speed during curve sprinting.
What limits peak force generation by the inside leg?
The difficulty of understanding the limits to curve sprinting is apparent
when one considers it's complex nature, where significant movements are
simultaneously performed in all three anatomical planes (sagittal, frontal,
transverse). Different biomechanical constraints exist in each plane of motion
and can also interact with one another in a complex manner. In comparison,
straight path sprinting by humans, other cursorial mammals and birds generally
involves movements largely restricted to the sagittal plane, where any out of
plane constraints are not likely to play an important role in determining
maximum speed.
We propose that the need to optimize the alignment of the resultant ground
reaction force with the long axis of the leg during sprinting is a superseding
principle that guides the coupling of force constraints in all planes of
motion. This has been observed in a variety of running animals under different
straight path running conditions (Biewener,
1989; Chang et al.,
2000; Full et al.,
1991; Full and Tu,
1991; Gunther et al.,
2004). Aligning the resultant force vector with the leg generally
leads to a favorable minimization of joint moments, musculoskeletal stresses
and associated metabolic costs (Alexander,
1991) and has been hypothesized to be a fundamental behavioral
template for diverse locomotor systems
(Full and Koditschek, 1999).
Although we did not have sufficient 3-D kinematic data to quantify the
alignment of the resultant ground reaction force with the leg, this represents
a logical next step and testable hypothesis that deserves further attention.
This leg alignment principle may act to couple biomechanical constraints
across planes such that non-sagittal plane force constraints that were
negligible during straight path sprinting are likely to significantly limit
peak resultant ground reaction forces during curve sprinting.
The average vertical ground reaction force over an integral number of steps
must be equal to the body weight of the sprinter. Because of this constraint,
faster sprint speeds correlate with greater peak vertical ground reaction
forces and less time of foot contact with the ground, as demonstrated by
Weyand and colleagues (Weyand et al.,
2000). We have shown here that vertical ground reaction forces
were smaller at smaller radii and resulted in slower sprint speeds. But, we
saw that vertical ground reaction forces decreased more than could be
explained by a simple reallocation (or change in orientation) of the resultant
ground reaction force vector to generate lateral, centripetal forces. Rather,
the magnitude of the peak resultant ground reaction force also decreased
during curve sprinting.
Muscles acting primarily to stabilize joints in the frontal plane may be
inhibiting this leg extension force in the sagittal plane. Changing the angle
of hip adduction has been shown to change knee extensor activity during
squatting exercise (Coqueiro et al.,
2005). Also, studies on submaximal discrete running turns found a
discrepancy in the how non-sagittal plane joint stabilization demands
increased at the knee joints, depending on which leg was used for making the
turn (Besier et al., 2003;
Besier et al., 2001a;
Besier et al., 2001b). With no
substantial change in net knee extension moments between legs in the sagittal
plane, Besier and colleagues found substantial differences between the legs in
frontal plane and transverse plane moments. The inside leg consistently
generated greater varus moments and external rotation moments compared to the
outside leg. At maximal effort, these non-sagittal plane knee joint moments
may have reached critical limits, constraining the ability to increase
sagittal plane extension moments. We are not aware of any similar studies of
the ankle joint stabilizers. However, based on the ratios of our ground
reaction force components, we would expect lean angles (as a proxy for ankle
inversion angle) to be 35–40°. At these high ankle inversion angles,
the inside leg ankle stabilizer muscles may have been operating near or at
their critical limits as well. Stabilizing the different joints in the frontal
and transverse planes during curve sprinting is a likely mechanism that limits
leg extensor forces.
For example, at a given curve radius, sagittal plane leg extensor forces and frontal plane joint stabilization forces likely increase in proportion with increasing sprint speed until a physiological limit is reached in one or more muscle groups. The ratio of sagittal plane extensor muscle force to frontal plane joint stabilization muscle force is likely greatest during straight path sprinting, where speed is limited solely by the forces generated by extensor muscles. On increasingly tighter curves, this ratio probably decreases such that the absolute limit of muscle stress of the frontal plane joint stabilizers is reached at proportionately slower speeds while the extensor muscles remain well within their maximum force generating capacity. This hypothetical scenario is illustrated in Fig. 8. This could explain why we observed significantly smaller peak resultant ground reaction forces during curve sprinting compared to straight path sprinting.
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;
Alexander, 2002). Our subjects
wore rubber-soled running shoes and sprinted on a clean asphalt track. In
addition, the force platform surface was covered with a rubber matting to
eliminate the risk of slipping. Although we did not measure the static
coefficient of friction of our subjects' shoes on the track, typical values
for rubber on asphalt range from 0.5–0.8 with running shoes in
particular being on the upper end of this scale at approximately 0.75
(Tanaka et al., 2001). We did
not observe any slipping during our trials nor did any of our subjects report
any fear of slipping during trials or practice sessions.
The static coefficient of friction is a ratio of shear force to normal
force just before slipping occurs. `Required coefficient of friction' or RCOF
is a ratio of the shear force to normal force generated during normal
locomotion without slipping and provides a relative measure of slip potential
(Redfern et al., 2001). We
calculated ensemble averages of RCOF across subjects at times of peak force
generation (peak lateral force:peak vertical force) and found it was generally
less than 0.60 in all but one condition: the outside leg at 2 m radius
condition (RCOF=0.63). These ratios spanned a range of 0.45–0.63 across
all radii for both legs, which were well within the range of non-slip
conditions suggested in the literature.
Our subjects were likely modulating their fore–aft braking forces to
control body rotation and heading direction. The necessity to control body
rotation while sprinting on a curved track has received relatively little
attention. Since a sprinter must perform one complete rotation of the body for
each lap around the track, the angular velocity of the center of mass around
the track must equal the angular velocity of the body in the transverse plane.
Therefore, a sprinter's rotational velocity in the transverse plane is
directly related to their sprint speed. Recently, Jindrich and colleagues
suggested that braking forces generated during discrete turns in human running
may serve to control rotation of the body in the transverse plane
(Jindrich et al., 2006). This
supports their previous findings that running insects also use this general
mechanism for controlling over-rotation
(Jindrich and Full, 1999).
This may explain the consistent multiphasic pattern of fore–aft braking
forces observed between normal and tethered curve sprinting conditions
(Fig. 4). This is another
example of a coupling mechanism that can add to a multi-faceted system of
force generating constraints during curve sprinting.
The generation of forces on the ground by the legs during curve sprinting is a complex three-dimensional task bounded by several coupled biomechanical constraints. Maximizing the peak vertical ground reaction forces will minimize time spent on the ground and increase forward speed, as previously discussed. Lateral ground reaction forces must also be maximized to provide the centripetal force to change the momentum vector of the body and maximize forward (tangential) sprint speed, since centripetal force is proportional to the square of velocity. Fore–aft braking and propulsion forces must provide a delicate balance of maximizing forward acceleration and sprint speed while also controlling body rotation in the transverse plane. It is likely that during curve sprinting, these biomechanical constraints become inexorably coupled and cause sprinters to reach a critical limit at slower sprint speeds. To our knowledge, these speed-limiting mechanisms have not been considered in this light and warrant further study.
These multiplanar constraints are necessarily coupled for a bipedal
sprinter that has only one leg to generate forces on the ground. In
quadrupeds, it is possible that these constraints may become decoupled through
a delegation of biomechanical tasks to different limbs. For example, trotting
dogs have an asymmetric distribution of function with forelimbs performing
more of the braking in the fore–aft direction while the hindlimbs
perform most of the acceleration (Lee and
Bertram, 1999). Six-legged runners also exhibit this
specialization of tasks for each of the legs with the front legs performing
most of the braking function (Full et al.,
1991) while also controlling for rotation in the transverse plane
(Jindrich and Full, 1999).
Decoupling of the force-generating roles of the front and hind limbs during
curve sprinting has been suggested as a major mechanism that allows mice
(Walter, 2003) and dogs
(Usherwood and Wilson, 2005)
to reach greater relative curve sprint speeds compared to human curve
sprinters. In this sense, bipedal sprinters such as humans and birds may be
relatively slower than quadrupeds or hexapods during curve sprinting, due to
an inability to decouple the additional constraints placed on them by this
more complex behavior.
In summary, we have shown that maximum sprint velocity on curves is not only limited by a physiological limit to axial leg force since: (1) direct evidence indicates that maximal physiological force generation is not achieved during maximal effort sprinting at all radii; (2) externally supplying centripetal forces did not increase maximum velocities on the curve to expected values and revealed the importance of the underlying asymmetry between inside and outside legs; and (3) the power fit exponent of our empirical velocity data was significantly different from Greene's theoretical predictions. Instead, we propose that several coupled biomechanical constraints placed on the stance leg during curve sprinting make the inside leg particularly ineffective at generating the forces necessary to achieve straight path sprint velocities. The ability to decouple these constraints through the redistribution of function across multiple legs in quadrupeds may explain their superior curve sprint performance compared to bipedal sprinters.
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Acknowledgments |
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References |
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