04/06/2026
The Spring-Mass Model and Ground Reaction Force Vector of Running
Modelling is used in science in an attempt to make an activity easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. For human running, the preferred model within the international biomechanics community for the past three decades is the Spring-Mass Model (Blickhan R: The spring-model for running and hopping. J Biomech, 22(11/12):1217-1227, 1989).
In the spring-mass model of running, the center of mass (CoM) of the individual is represented as a single mass that is attached to a leg-spring that contacts the ground with each running footstrike. The spring-mass model, like actual running, has the foot contact the ground in front of the CoM. Then, as the CoM progresses forward over the planted foot, the leg-spring compresses in the first half of the running support phase, then elongates in the second half of the running support phase. [The support phase in running is the phase in which the foot is on the ground and is analogous to the stance phase in walking.]
During the first half of the support phase, the leg-spring uses the kinetic energy of the falling CoM to compress and store potential energy as elastic strain energy within the tendons, ligaments and muscles of the lower extremity, or, in this model, the leg-spring. Then, in the second half of support phase, the leg-spring elongates, releasing the stored potential energy (i.e. elastic strain energy) as kinetic energy that then propels the CoM upwards and forwards.
This transfer of potential energy to kinetic energy, using the kinetic energy of a falling mass contacting the ground to first store potential energy to then be released next as kinetic energy, is the same potential-kinetic energy transfer mechanism used by bouncing balls and by a child bouncing along the ground on a pogo-stick.
In the spring-mass model, the ground reaction force (GRF) peaks when the CoM is directly over the planted foot. The GRF represents the mechanical interaction of the mass of the individual with the ground and the accelerations-decelerations of that mass relative to the ground at each instant of the support phase of running.
Note, in my video below, the GRF vector is illustrated at each phase of running gait, showing how the GRF vector will always align closely with the CoM of the body during running. This alignment of the GRF vector with the CoM of the runner causes the anterior-posterior shearing forces in running during the first half of support phase to be in a posterior direction, sometimes known as a "braking force".
This posteriorly-directed shear force during the first half of support phase does not necessarily slow down the runner as the name "braking force" suggests. Rather, this posteriorly-directed shear force is a necessary result of the foot needing to land in front of the CoM of the runner in order to allow the lower extremity (and foot) to have the time to store energy by "compressing the spring", as the body moves forward over the foot, which, in turn, allows the most metabolically-efficient running stride.
At the middle of the support phase, the anterior-posterior shearing force is at a magnitude of zero since the CoM is directly over the foot. With the CoM over the planted foot, the GRF vector is at its maximum. This phase of running gait, when shown on the GRF vs time curve from a force plate, is called the "active peak" or "propulsive peak".
In the second half of support phase, there will now be an anteriorly-directed shearing force on the foot (i.e. "propulsion force") since the CoM is now forward of the foot and the GRF vector always points toward the CoM of the runner. During the second half of the support phase of running, the foot and lower extremity is releasing its stored elastic strain energy within the leg-spring and converting it into a kinetic energy that now pushes the CoM of the runner upwards and forwards.
These posteriorly-directed shear forces in the first half of support phase and anteriorly-directed shear forces in the second half of support phase seen while running on a force plate are present during all forward running velocities, from a slow jog to an all-out sprint. The spring mass model of running predicts these anterior-posterior shear forces need to occur with running in order for proper potential-kinetic energy exchange to occur to optimize the metabolic efficiency of the runner and for the individual to be able to maintain upright balance during running.
Unfortunately, there is still a small number of vocal barefoot running-minimalist shoe wearing-anti-heel striking running zealots that teach that runners should have their foot under their CoM at the instant of footstrike in running. "Chi-Running" is one such example of a "running form" that teaches this running technique, "landing with your feet under your hips". In fact, it is impossible to run at a constant, non-zero forward velocity over level ground without the foot first striking the ground ahead of the CoM.
All in all, runners have their foot strike ahead of their CoM during running since this is the only way for the human body to maintain upright balance during all velocities of running and to use the potential-kinetic energy exchange within their feet and lower extremities to optimize the metabolic efficiency of running. Overall, the spring-mass model nicely predicts this experimental observation seen in runners over the five decades in which force plates have been able to accurately measure the three-dimensional GRF vector under the feet of runners during scientific running studies.
Podiatrists, and other foot-health professionals, should warn the public and their patients of the misinformation often taught by self-proclaimed "experts on running form" to avoid having them becoming injured by trying to run in a fashion that does not optimize their own running biomechanics. We need to ensure that accurate information is being relayed to our patients, and the running public in general, so that runners can better enjoy their activity, with less chance of becoming injured.
See less