Abstract
Damping is a vital mechanical feature for a dynamic system like shoe that is a specialized sports equipment designed to protect and enhance human movement performance. This study aimed to investigate the damping characteristics of adaptable shoe configurations to simulate the real-world cutting effects. To achieve this, repetitive cyclic torsional loading tests were conducted at different angular velocities (25°/s, 50°/s, 75°/s, 100°/s, 125°/s, and 150°/s) with a torsion angle range of 0–30°. Experimental conditions were: (a) control shoe (CS), which are adaptable air cushion shoe, (b) midpart adapted shoe (MAS), and (c) forepart adapted shoe (FAS), both altered in sole construction with adjustable elastomeric spacers. A torsion testing machine with a specially designed fixture system held the test shoes. Then, the shoes underwent repetitive torsional loading and unloading with angular displacements from 0° to 30° to simulate inversion motion. Results revealed an inverse correlation between damping coefficient (DCoeff) and angular velocities. Notably, at the highest angular velocity 150⁰/s, all shoe conditions demonstrated the lowest DCoeff, indicating that shoes retained most of their energy during twisting motion, resulting in relatively low energy dissipation. This might result in higher twisting forces on foot-shoe system and ankle, might impact on ankle stability. Similarly, low mechanical damping at higher velocity in the shoe forepart may reduce energy dissipation. This could exert greater force on the metatarsophalangeal (MTP) joint of the forefoot, potentially compromising its stability. Study findings may provide preliminary insights into the damping behavior of shoes at increasing angular velocities to assist in the development of athletic footwear for sports performance, and further studies are needed optimized damping.
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Acknowledgements
The authors are thankful to Dr. Ying-Chun Huang of Dr. aiR Inc. for providing shoe samples for this study.
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**MSA** : Conceptualization, methodology, formal analysis, investigation, resources, data curation, writing original draft, writing review & editing, visualization, project administration. **CJL** : Methodology, writing review & editing. **HFC** : Methodology, writing review & editing. **KNA** : Methodology, writing review & editing. **YCH** : Methodology, writing review & editing. **FCS** : Conceptualization, methodology, writing review & editing, supervision.
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Arefin, M.S., Lin, CJ., Chieh, HF. et al. Damping behavior of adaptable shoe under torsional loading at varying angular velocities: replicating the effects on cutting maneuvers. Sci Rep (2026). https://doi.org/10.1038/s41598-026-41715-9
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DOI: https://doi.org/10.1038/s41598-026-41715-9
