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Updated: Jun 2, 2026

Comparative Analysis of Lower Limb Kinematics between the Initial and Terminal Phase of 5km Treadmill Running
Published on: July 17, 2020
Relationship between speed and time in running
D W Hill1, J L Vingren, F Y Nakamura
1University of North Texas, Kinesiology, Health Promotion and Recreation, Denton 76203, USA. david.hill@unt.edu
Abstract:
The purpose of this study was to evaluate the effect of using different mathematical models to describe the relationship between treadmill running speed and time to exhaustion. All models generated a value for an aerobic parameter (critical speed; S (critical)). 35 university students performed 5-7 constant-speed 0%-slope treadmill tests at speeds that elicited exhaustion in ∼3 min to ∼10 min. Speed and time data were fitted using 3 models: (1) a 2-parameter hyperbolic model; (2) a 3-parameter hyperbolic model; and (3) a hybrid 3-parameter hyperbolic+exponential model. The 2-parameter model generated values for S (critical) (mean (± SD): 186 ± 33 m·min (-1)) and anaerobic distance capacity (ADC; 251 ± 122 m) with a high level of statistical certainty (i.e., with small SEEs). The 3-parameter models generated parameter estimates that were unrealistic in magnitude and/or associated with large SEEs and little statistical certainty. Therefore, it was concluded that, for the range of exercise durations used in the present study, the 2-parameter model is preferred because it provides a parsimonious description of the relationship between velocity and time to fatigue, and it produces parameters of known physiological significance, with excellent confidence.
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