A Comparison Of Four Methods Of Calculating Vertical Stiffness In Distance Running

Abstract

Vertical stiffness is a useful method for characterizing distance running. It has been correlated with stride frequency, surface, speed, and aerobic demand. 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. Another approach was recently introduced measuring a stiffness that begins relatively high, and then drops to a lower stiffness around the heel strike (variable stiffness). This method matches reproduced force very well. PURPOSE This study compares the benefits and drawbacks of the variable stiffness method to three different constant stiffness methods. METHODS Four methods of calculating vertical stiffness were compared by their correlations with measured versus modeled vertical ground reaction forces. 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. 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. This is a constant stiffness method using a stiffness that provides the best fit between measured and modeled vertical ground reaction forces. 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. RESULTS Fisher's z-tests investigated differences between all groups using an adjusted alpha level of 0.0083. Differences were detected between all groups (p<0.001). However, the first three methods described above were very close to each other. The variable stiffness method was practically and statistically improved over all other methods investigated. CONCLUSION The variable stiffness method provides the most accurate fit. The body reacts very stiff to the ground at initial contact. Then, 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.