Running Critical Power: A Comparison Of Different Theoretical Models

Abstract

This study aimed (i) to compare the critical power (CP) and work capacity over CP (W´) values reported by the different CP models available in current analysis software packages (Golden Cheetah and Stryd platform), (ii) to locate the CP values in the power-duration curve (PDC), and (iii) to determine the influence of the CP model used on the W´ balance. Fifteen trained athletes performed four time trials (i. e., 3, 5, 10, 20 minutes) to define their PDC through different CP models: work-time (CP_work), power-1/time (CP_1/time), Morton hyperbolic (CP_hyp), Stryd platform (CP_stryd), and Bioenergetic Golden Cheetah (CP_Cheetah). Three additional time trials were performed: two to locate the CP values in the PDC (30 and 60 minutes), and one to test the validity of the W’ balance model (4 minutes). Significant differences (p<0.001) were reported between models for the estimated parameters (CP, W´). CP_cheetah was associated with the power output developed between 10 to 20 minutes, CP_1/time, CP_stryd CP_work and CP_hyp. The W´ reported by the three-parameter CP models overestimated the actual 4 minutes time to exhaustion, with CP_work (0.48 [− 0.19 to 1.16] minutes); and CP_1/time (0.40 [− 0.13 to 0.94] minutes) being the only valid models (p≥0.240).

Key words

exercise testing - endurance training - endurance performance

Publication History

Received: 19 January 2023

Accepted: 11 March 2023

Article published online:
29 September 2023

• References

• 1 Ruiz-Alias SA, Olaya-Cuartero J, Ñacupil-Andrade A. et al. 9/3-Minute running critical power test: mechanical threshold location with respect to ventilatory thresholds and maximum oxygen uptake. Int J Sports Physiol Perform 2022; 1: 1-8
• 2 Vandewalle H. Modelling of running performances: Comparisons of power-law, hyperbolic, logarithmic, and exponential models in elite endurance runners. Biomed Res Int 2018; 2018: 8203062
• 3 Kirby BS, Winn BJ, Wilkins BW. et al. Interaction of exercise bioenergetics with pacing behavior predicts track distance running performance. J Appl Physiol 2021; 131: 1532-1542
• 4 Galbraith A, Hopker J, Passfield L. Modeling intermittent running from a single-visit field test. Int J Sports 2015; 36: 365-370
• 5 Moritani T, Ata AN, Devries HA. et al. Critical power as a measure of physical work capacity and anaerobic threshold. Ergonomics. 1981; 24: 339-350
• 6 Whipp BJ, Huntsman DJ, Storer TW. et al. A constant which determines the duration of tolerance to high-intensity work. FASEB J 1982; 41: 1591
• 7 Skiba PF, Clarke DC. The W′ balance model: Mathematical and methodological considerations. Int J Sports Physiol Perform 2021; 16: 1561-1572
• 8 Morton RH, Billat L. The critical power model for intermittent exercise. Eur J Appl Physiol 2004; 91: 303-307
• 9 Maturana FM, Fontana FY, Pogliaghi S. et al. Critical power: How different protocols and models affect its determination. J Sci Med Sport 2018; 21: 742-747
• 10 Housh TJ, Cramer JT, Bull AJ. et al. The effect of mathematical modeling on critical velocity. Eur J Appl Physiol 2001; 84: 469-475
• 11 Cerezuela-Espejo V, Hernández-Belmonte A, Courel-Ibáñez J. et al. Are we ready to measure running power? Repeatability and concurrent validity of five commercial technologies. Eur J Sport Sci 2021; 21: 341-350
• 12 García-Pinillos F, Latorre-Román P, Roche-Seruendo LE. et al. Prediction of power output at different running velocities through the two-point method with the Stryd^TM power meter. Gait Posture 2019; 68: 238-243
• 13 Imbach F, Candau R, Chailan R. et al. Validity of the Stryd power meter in measuring running parameters at submaximal speeds. Sports 2020; 8: 103
• 14 Taboga P, Giovanelli N, Spinazzè E. et al. Running power: lab based vs. portable devices measurements and its relationship with aerobic power. Eur J Sport Sci 2021; 22: 1555-1568
• 15 McKay AK, Stellingwerff T, Smith ES. et al. Defining training and performance caliber: A participant classification framework. Int J Sports Physiol Perform 2022; 17: 317-331
• 16 Morton H. A 3-parameter critical power model. Ergonomics 1996; 39: 611-619
• 17 Dearing CG, Paton CD. Is Stryd critical power a meaningful parameter for runners?. Biol Sport 2022; 40: 657-664
• 18 Skiba PF, Fulford J, Clarke DC. et al. Intramuscular determinants of the ability to recover work capacity above critical power. Eur J Appl Physiol 2015; 115: 703-713
• 19 Bland JM, Altman D. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986; 327: 307-310
• 20 Ludbrook J. Statistical techniques for comparing measurers and methods of measurement: A critical review. Clin Exp Pharmacol Physiol 2002; 29: 527-536
• 21 Ludbrook J. Linear regression analysis for comparing two measurers or methods of measurement: but which regression?. Clin Exp Pharmacol Physiol 2010; 37: 692-699
• 22 Gaesser GA, Carnevale TJ, Garfinkel A. et al. Estimation of critical power with nonlinear and linear models. Med Sci Sports Exerc 1995; 27: 1430-1438
• 23 Poole DC, Ward SA, Gardner GW. et al. Metabolic and respiratory profile of the upper limit for prolonged exercise in man. Ergonomics 1988; 31: 1265-1279
• 24 Jones AM, Wilkerson DP, DiMenna F. et al. Muscle metabolic responses to exercise above and below the “critical power” assessed using 31P-MRS. Am J Physiol Regul Integr Comp Physiol 2008; 294: 585-593
• 25 Hill DW, Poole DC, Smith JC. The relationship between power and the time to achieve VO2max. Med Sci Sports Exerc 2002; 34: 709-714
• 26 Bergstrom HC, Housh TJ, Zuniga JM. et al. Differences among estimates of critical power and anaerobic work capacity derived from five mathematical models and the three-minute all-out test. J Strength Cond Res 2014; 28: 592-600
• 27 Triska C, Karsten B, Beedie C. et al. Different durations within the method of best practice affect the parameters of the speed–duration relationship. Eur J Sport Sci 2018; 18: 332-340
• 28 Triska C, Karsten B, Nimmerichter A. et al. Iso-duration determination of D′ and CS under laboratory and field conditions. Int J Sports Med 2017; 38: 527-533
• 29 Girardi M, Gattoni C, Sponza L. et al. Performance prediction, pacing profile and running pattern of elite 1-h track running events. Sport Sci Health 2022; 18: 1457-1474