{
  "abstract": "This study aimed to (1) develop an elasticity framework for the sprint force-velocity (F-V) relationship and (2) examine how maximal force (F_{0}), maximal velocity (v_{0}), and sprint distance modulate the four derived elasticity metrics, and (3) explore these elasticity metrics' interrelation. After modelling the F-V relationship differential equation, four elasticity metrics were defined as force elasticity (F_{e}), the elasticity of sprint time to F_{0}; velocity elasticity (v_{e}), the elasticity of sprint time to v_{0}; the force-velocity elasticity norm {(\\mathrm{F}-\\mathrm{V}}_{\\mathrm{EN}}=\\sqrt{F_{e}^{2}+v_{e}^{2}}), capturing the combined sprint time sensitivity to proportional changes in F_{0} and v_{0}; and the force-velocity elasticity ratio {(\\mathrm{F}-\\mathrm{V}}_{\\mathrm{ER}}=F_{e}{\\div v}_{e}), indicating which variable dominates the sprint time response. Model simulations showed that F_{e} decreased with rising F_{0} and increased with rising v_{0}, while v_{e} showed the opposite pattern. With increasing sprint distance, F_{e} decreased and v_{e} increased. Given its negligible effect on sprint time, ignoring air resistance yields a conservation law (2F_{e}+v_{e}\\equiv 1), indicating that a gain in one elasticity metric necessarily diminishes the other in a fixed proportion. This framework also identifies a valley distance (d_{valley}) at {\\mathrm{F}-\\mathrm{V}}_{\\mathrm{ER}}=2, where {\\mathrm{F}-\\mathrm{V}}_{\\mathrm{EN}} is minimized (\\sqrt{0.2}) and sprint time is least responsive to changes in F-V relationship variables. Empirical data confirmed that the two theoretical laws still hold approximately when air resistance is considered. By linking changes in F_{0} and v_{0} to sprint time across different distances, the elasticity framework provides a quantitative basis for estimating the theoretical sprint time response to documented changes in F-V relationship variables.",
  "abstract_shown": true,
  "affiliations": [
    "Beijing Polytechnic College"
  ],
  "article_type": "New results",
  "arxiv": null,
  "author_total": 8,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Z. Li"
    },
    {
      "name": "J. Yan"
    },
    {
      "name": "X. Zhang"
    },
    {
      "name": "Z. Chen"
    },
    {
      "affs": [
        0
      ],
      "name": "Q. Li"
    },
    {
      "name": "P. Jimenez-Reyes"
    },
    {
      "name": "D. Janicijevic"
    },
    {
      "name": "A. garcia-ramos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09j5g0z47pp0f.bib",
  "cited_by": 0,
  "doi": "10.64898/2026.08.29.748040",
  "fulltext_url": "https://www.biorxiv.org/content/10.64898/2026.08.29.748040v1.full",
  "id": "09j5g0z47pp0f",
  "issns": [],
  "landing_url": "https://www.biorxiv.org/content/10.64898/2026.08.29.748040v1",
  "language": null,
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "biorxiv",
      "biophysics"
    ],
    [
      "openalex",
      "2732|Sports Performance and Training"
    ]
  ],
  "openalex": "W7204927886",
  "pdf_url": "https://www.biorxiv.org/content/10.64898/2026.08.29.748040v1.full.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09j5g0z47pp0f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:06Z",
      "native_id": "10.64898/2026.08.29.748040",
      "source": "biorxiv",
      "url": "https://www.biorxiv.org/content/10.64898/2026.08.29.748040v1"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "biorxiv:biophysics",
      "subfield": "biophysics"
    }
  ],
  "title": "Quantifying sprint force-velocity elasticity: implications for individualized training decisions",
  "title_text": "Quantifying sprint force-velocity elasticity: implications for individualized training decisions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:06Z",
  "url": "https://research.draconitic.com/paper/09j5g0z47pp0f",
  "venue": "bioRxiv",
  "versions": []
}