A COMPARISON OF FOUR METHODS OF CALCULATING VERTICAL STIFFNESS IN
DISTANCE RUNNING
Iain Hunter, Ty Hopkins, and Cindy A. Trowbridge
Department of Physical Education, Brigham Young University, Provo, UT, USA
E-mail: [email protected]
Web: www.byu.edu
INTRODUCTION
Vertical stiffness is a useful method for
characterizing distance running. It has been
correlated with stride frequency, surface,
speed, and aerobic demand (Arampatzis,
1999, Heise, 1998, Farley, 1996, Kerdok,
2002, McMahon, 1990, Dalleau, 1998).
However, there are limitations to the
traditional method of calculating stiffness.
The heel strike and initial slope compared
with the final slope are poorly matched
when reproducing force based upon the
calculated stiffness and initial conditions
(Figure 1).
Figure 2: The variable stiffness method of
calculating vertical stiffness demonstrating
how well measured force matches modeled
force.
This study compares the benefits and
drawbacks to three different constant
stiffness methods and the variable stiffness
method.
METHODS
Figure 1: The traditional method of
calculating vertical stiffness using a constant
stiffness with modeled force.
Another approach was recently introduced
measuring a stiffness that begins relatively
high, and then drops to a lower stiffness
around the heel strike (Hunter, 2002). This
method matches reproduced force very well
(Figure 2).
Four methods of calculating vertical
stiffness were compared by their
correlations with measured versus modeled
vertical ground reaction forces
Traditional: The traditional method of
calculating stiffness divides the maximum
vertical ground reaction force by the change
in vertical position of the center of mass
from foot contact to the maximum
displacement.
Constant low: This method differs from
the traditional method by dividing by the
maximum vertical displacement of the
center of mass from the lowest point to
takeoff.
Constant best fit: This is a constant
stiffness method using a stiffness that
provides the best fit between measured and
modeled vertical ground reaction forces.
Variable: This method uses a best fit model
with an initial high stiffness that drops to a
lower value around the heel strike. The drop
begins at the peak force of heel strike and
ends at the valley between heel strike and
the active peak.
While two variables are required to use the
vertical stiffness model (initial and final
stiffnesses), there may be cases where only
the initial or final stiffness may be of
importance in the model being considered.
SUMMARY
The variable stiffness method for calculating
vertical stiffness provides the best fit for
modeling vertical ground reaction forces.
However, there are two variables required to
use this method.
RESULTS AND DISCUSSION
REFERENCES
All methods were significantly different
from each other using an adjusted
significance level of 0.0083 for multiple
comparisons (Table 1). While the
differences between most methods were
practically non-significant, the variable
stiffness method appeared functionally
significant. It is clear visually and
statistically that the variable stiffness
method provides a much better fit than any
other method.
The variable stiffness method may be the
best fit for the following reasoning. The
body reacts very stiff to the ground at initial
contact. As the foot becomes flat to the
ground, the center of pressure progresses
forward, resulting in a lengthening of the leg
spring. Since the leg spring is slightly
increasing, the stiffness will decrease during
this time. Once the foot is flat with the
ground, the ankle becomes more involved in
the stance. With an additional joint
becoming a major part of the spring, the
overall stiffness may decrease.
Arampatzis, A., Bruggemann, G. P. and
Metzler, V. (1999) The effect of speed
on leg stiffness and joint kinetics in
human running. J Biomech, 32, 13491353.
Farley, C. T. and Gonzalez, O. (1996) Leg
stiffness and stride frequency in human
running. J Biomech, 29, 181-186.
Heise, G. D. and Martin, P. E. (1998) "Leg
spring" characteristics and the aerobic
demand of running. Med Sci Sports
Exerc, 30, 750-754.
Hunter, I. (2003). A new approach to
modeling vertical stiffness in heel-toe
distance runners. Journal of Sci and
Sports Med, 2, 139-143.
Kerdok, A. E., Biewener, A. A., McMahon,
T. A., Weyand, P. G. and Herr, H. M. (2002)
Energetics and mechanics of human running
on surfaces of different stiffnesses. J Appl
Physiol, 92, 469-478
Table 1: Correlations between measured and modeled vertical ground reaction forces using four
approaches to calculating stiffness (mean± SD) (all methods were significantly different from all
others, p<0.0083).
Method 1
Method 2
Method 3
Method 4
Stiffness method
0.948±0.026
0.940±0.028
0.960±0.020
0.994±0.004
Correlation