Quantifying sprint force-velocity elasticity: implications for individualized training decisions
Year: 2026
Type: preprint
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 ( ν 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 ( ν e ), the elasticity of sprint time to ν 0 ; the force-velocity elasticity norm capturing the combined sprint time sensitivity to proportional changes in F 0 and ν 0 ; and the force-velocity elasticity ratio, (F −V ER = F e ÷ ν e ), indicating which variable dominates the sprint time response. Model simulations showed that F e decreased with rising F 0 and increased with rising ν 0 , while ν e showed the opposite pattern. With increasing sprint distance, F e decreased and ν e increased. Given its negligible effect on sprint time, ignoring air resistance yields a conservation law (2 F e , + ν e ≡ 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 F − V ER = 2, where F−V EN is minimized 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 ν 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.
Language: English
Subfield: Orthopedics and Sports Medicine
Field: Medicine
Domain: Health Sciences
Open Access status: green
OpenAlex ID: W7204927886