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

Abstract

The purpose of this study was to evaluate three critical power (P_critical) 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, P_critical (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 P_critical (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.

Key words

Aerobic - anaerobic - critical power - exercise - modeling

References

• 1 Bishop D, Jenkins D G, Howard A. The critical power function is dependent on the duration of the predictive exercise tests chosen.  Int J Sports Med. 1998;  19 125-129
• 2 Bull A, Housh T J, Johnson G O, Perry S R. Effect of mathematical modeling on the estimation of critical power.  Med Sci Sports Exerc. 2000;  32 526-530
• 3 Gaesser G A, Carnevale T J, Garfinkel A, Walter D O, Womack C J. Estimation of critical power with nonlinear and linear models.  Med Sci Sports Exerc. 1995;  27 1430-1438
• 4 Gaesser G A, Poole D C. The slow component of oxygen uptake kinetics in humans. Holloszy JO Exercise and Sport Sciences Reviews. Baltimore, MD; Williams & Wilkins 1996: 35-70
• 5 Hill D W, Poole D C, Smith J C. The relationship between power and the time to achieve V·O_2max.  Med Sci Sports Exerc. 2002;  34 709-714
• 6 Hill D W, Smith J C. A method to ensure the accuracy of estimates of anaerobic capacity derived using the critical power concept.  J Sports Med Phys Fitness. 1994;  34 23-37
• 7 Hill D W, Smith J C. Determination of critical power by pulmonary gas exchange.  Can J Appl Physiol. 1999;  24 74-86
• 8 Hill D W, Smith J C, Leuschel J L, Chasteen S D, Miller S A. Effect of pedal cadence on parameters of the hyperbolic power-time relationship.  Int J Sports Med. 1995;  16 82-87
• 9 Hill D W, Steward Jr R P, Lane C J. Application of the critical power concept to young swimmers.  Pediatric Exerc Sci. 1995;  7 281-293
• 10 Hopkins W G, Edmund I M, Hamilton B H, MacFarlane D J, Ross B H. Relation between power and endurance for treadmill running of short duration.  Ergonomics. 1989;  32 1565-1571
• 11 Housh T J, Cramer J T, Bull A J, Johnson G O, Housh D J. The effect of mathematical modeling on critical velocity.  Eur J Appl Physiol. 2001;  84 469-475
• 12 Jenkins D G, Quigley B M. Blood lactate in trained cyclists during cycle ergometry at critical power.  Eur J Appl Physiol. 1990;  61 278-283
• 13 Jenkins D G, Quigley B M. The influence of high-intensity exercise training on the Wlim-Tlim relationship.  Med Sci Sports Exerc. 1993;  25 275-282
• 14 MacIntosh B R, Neptune R R, Horton J F. Cadence, power, and muscle activation in cycle ergometry.  Med Sci Sports Exerc. 2000;  32 1281-1287
• 15 Monod H, Scherrer J. The work capacity of a synergic muscle group.  Ergonomics. 1965;  8 329-338
• 16 Morton R H. A 3-parameter critical power model.  Ergonomics. 1996;  39 611-619
• 17 Poole D C, Ward S A, Whipp B J. The effects of training on the metabolic and respiratory profile of high-intensity cycle ergometer exercise.  Eur J Appl Physiol. 1990;  59 421-429
• 18 Smith J C, Dangelmaier B S, Hill D W. Critical power is related to bicycle time trial performance.  Int J Sports Med. 1999;  20 374-383