Int J Sports Med 2004; 25(5): 357-361
DOI: 10.1055/s-2004-815838
Training & Testing

© Georg Thieme Verlag KG Stuttgart · New York

The Relationship between Power and Time to Fatigue in Cycle Ergometer Exercise

D. W. Hill1
  • 1Department of Kinesiology, Health Promotion, and Recreation, University of North Texas, Denton, Texas USA
Further Information

Publication History

Accepted after revision: September 15, 2003

Publication Date:
18 May 2004 (online)


The purpose of this study was to evaluate three critical power (Pcritical) models. Ten university students performed tests that elicited fatigue in > 2 min to ∼ 10 min. Power and time data were fit to a 2-parameter hyperbolic model, a 3-parameter hyperbolic model, and a 3-parameter exponential model. Models described the power-time relationship well (R2 ≥ 0.995). However, Pcritical (209 ± 51 W; SEE: 20 ± 47 W) and the time constant (198 ± 87 s; SEE: 103 ± 246 W) from the exponential model have no obvious meaning. The 2-parameter model produced Pcritical (187 ± 38 W) and anaerobic work capacity (20.4 ± 9.0 kJ) that have known physiological meaning, with excellent confidence (SEE: 2 ± 2 W and 1.0 ± 1.0 kJ, respectively). Addition of a maximal power parameter to the 2-parameter model did not improve description of the relationship, and the third parameter was superfluous. The 2-parameter model was preferred because, for the range of exercise durations used in this study, it describes the power-relationship adequately and in a most parsimonious fashion.


David W. Hill

Department of Kinesiology, Health Promotion, and Recreation · University of North Texas

P.O. Box 310469

Denton, Texas 76203-0769


Phone: + 9405652252

Fax: + 94 05 65 49 04

Email: [email protected]