Estimating the Preferred Walking Speeds Based on the Center of Mass Work Analysis

Abstract This study investigates the role of optimal push-off impulses in minimizing the total mechanical work dissipation per step, aiming to achieve passive single support work performance for a variety of walking conditions. By optimizing push-offs to cover the entire step’s energy demands, the single support work may become only storage and release of mechanical energy through tendons and tissues. Our simulations indicate that for each walking speed, there is an optimal push-off impulse that ensures energy balance without the need for additional energy input or dissipation during the subsequent single support phase when the soft tissue dissipation is negligible. For this circumstance, the step total dissipation is minimum. For level ground (even terrain), the estimated preferred walking speeds align closely with literature values for young adult (∼ 1.2 m.s −1 )and older adult (∼ 1.0 m.s −1 ) self-selected speeds, with a reduction observed for the restricted view of oncoming irregularities in the substrate terrain (15%). For walking on uneven surfaces, terrain amplitude was shown to impact walking costs quadratically, with optimal speeds declining by approximately 20% per unit increase in terrain amplitude. Key findings include evidence that net single support work remains near zero when push-off optimally covers collision and gravity work, confirming the passive nature of single support work under this condition. We also observed that the preferred speeds for older adults tend to be 12-15% lower than for younger adults, likely due to biomechanical adaptations. Beyond certain terrain amplitudes, no preferred walking speed allowed fully passive single support work, highlighting a possible biomechanical threshold where ankle push-off alone becomes insufficient and hip torque compensation may be necessary. This approach provides a framework for estimating preferred walking speeds across different terrain amplitudes (continuous parameter), varying conditions and demographics, with potential applications in designing assistive devices and gait rehabilitation protocols that reduce metabolic cost through optimal mechanical work management.

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