A general relationship links gait mechanics and running ground reaction forces

The relationship between gait mechanics and running ground reaction forces is widely regarded as complex. This viewpoint has evolved primarily via efforts to explain the rising edge of vertical force-time waveforms observed during slow human running. Existing theoretical models do provide good rising-edge fits, but require more than a dozen input variables to sum the force contributions of four or more vague components of the body's total mass (m_b). Here, we hypothesized that the force contributions of two discrete body mass components are sufficient to account for vertical ground reaction force-time waveform patterns in full (stance foot and shank, m₁=0.08m_b; remaining mass, m₂=0.92m_b). We tested this hypothesis directly by acquiring simultaneous limb motion and ground reaction force data across a broad range of running speeds (3.0-11.1 m s^-1) from 42 subjects who differed in body mass (range: 43-105 kg) and foot-strike mechanics. Predicted waveforms were generated from our two-mass model using body mass and three stride-specific measures: contact time, aerial time and lower limb vertical acceleration during impact. Measured waveforms (N=500) differed in shape and varied by more than twofold in amplitude and duration. Nonetheless, the overall agreement between the 500 measured waveforms and those generated independently by the model approached unity (R²=0.95±0.04, mean±s.d.), with minimal variation across the slow, medium and fast running speeds tested (ΔR²≤0.04), and between rear-foot (R²=0.94±0.04, N=177) versus fore-foot (R²=0.95±0.04, N=323) strike mechanics. We conclude that the motion of two anatomically discrete components of the body's mass is sufficient to explain the vertical ground reaction force-time waveform patterns observed during human running.