Purpose To compare linear and curvilinear models describing the force–velocity relationship obtained in lower-limb acyclic extensions, considering experimental data on an unprecedented range of velocity conditions.

Methods Nine athletes performed lower-limb extensions on a leg-press ergometer, designed to provide a very broad range of force and velocity conditions. Previously inaccessible low inertial and resistive conditions were achieved by performing extensions horizontally and with assistance. Force and velocity were continuously measured over the push-off in six resistive conditions to assess individual force–velocity relationships. Goodness of fit of linear and curvilinear models (second-order polynomial function, Fenn and Marsh’s, and Hill’s equations) on force and velocity data were compared via the Akaike Information Criterion.

Results Expressed relative to the theoretical maximal force and velocity obtained from the linear model, force and velocity data ranged from 26.6 ± 6.6 to 96.0 ± 3.6% (16–99%) and from 8.3 ± 1.9 to 76.6 ± 7.0% (5–86%), respectively. Curvilinear and linear models showed very high fit (adjusted r2 = 0.951–0.999; SEE = 17-159N). Despite curvilinear models better fitting the data, there was a ~ 99–100% chance the linear model best described the data.

Conclusion A combination between goodness of fit, degrees of freedom and common sense (e.g., rational physiologically values) indicated linear modelling is preferable for describing the force–velocity relationship during acyclic lower-limb extensions, compared to curvilinear models. Notably, linearity appears maintained in conditions approaching theoretical maximal velocity. Using horizontal and assisted lower-limb extension to more broadly explore resistive/assistive conditions could improve reliability and accuracy of the force–velocity relationship and associated parameters.