Jones AM, Vanhatalo A (2017) The, “critical power” concept: applications to sports performance with a focus on intermittent high-intensity exercise. Sports Med 47:65–78
Joyner MJ (2017) Physiological limits to endurance exercise performance: influence of sex. J Physiol 595:2949–2954
Katz JS, Katz L (1999) Power laws and athletic performance. J Sports Sci 17:467–476
Tucker R, Lambert MI, Noakes TD (2006) An analysis of pacing strategies during men’s world-record performances in track athletics. Int J Sports Physiol Perform 1:233–245
Jones AM, Kirby BS, Clark IE, Rice HM, Fulkerson E, Wylie LJ et al (2021) Physiological demands of running at 2-hour marathon race pace. J Appl Physiol 130:369–379
Billat LV, Koralsztein JP, Morton RH (1999) Time in human endurance models. Sports Med 27:359–379
Bosquet L, Duchene A, Lecot F, Dupont G, Leger L (2006) Vmax estimate from three-parameter critical velocity models: validity and impact on 800 m running performance prediction. Eur J Appl Physiol 97:34–42
Bundle MW, Hoyt RW, Weyand PG (2003) High-speed running performance: a new approach to assessment and prediction. J Appl Physiol 95:1955–1962
Poole DC, Burnley M, Vanhatalo A, Rossiter HB, Jones AM (2016) Critical power. Med Sci Sports Exerc 48:2320–2334
Jones AM, Vanhatalo A, Burnley M, Morton RH, Poole DC (2010) Critical power: implications for determination of VO2max and exercise tolerance. Med Sci Sports Exerc 42:1876–1890
Smyth B, Muniz-Pumares D (2020) Calculation of critical speed from raw training data in recreational marathon runners. Med Sci Sports Exerc 52:2637–2645
Gamelin FX, Coquart JM, Ferrari N, Vodougnon H, Matran R, Leger L et al (2006) Prediction of one-hour running performance using constant duration tests. J Strength Cond Res 20:735–739
Bosquet L, Léger L, Legros P (2002) Methods to determine aerobic endurance. Sports Med 32:675–700
Vandewalle H (2018) Modelling of running performances: comparisons of power-law, hyperbolic, logarithmic, and exponential models in elite endurance runners. Biomed Res Int 2018:8203062
Casado A, Hanley B, Jiménez-Reyes P, Renfree A (2020) Pacing profiles and tactical behaviors of elite runners. J Sport Health Sci. https://doi.org/10.1016/j.jshs.2020.06.011
Díaz JJ, Fernández-Ozcorta EJ, Torres M, Santos-Concejero J (2019) Men vs. women world marathon records’ pacing strategies from 1998 to 2018. Eur J Sport Sci 19:1297–1302
Kennelly AE (1906) An approximate law of fatigue in the speeds of racing animals. Proc Am Acad Arts Sci 42:275–331
Savaglio S, Carbone V (2000) Scaling in athletic world records. Nature 404:244
Zinoubi B, Vandewalle H, Zbidi S, Driss T (2019) Estimation of running endurance by means of empirical models: a preliminary study. Sci Sports 34:24–29
Vandewalle H (2017) Mathematical modeling of the running performances in endurance exercises: comparison of the models of Kennelly and Péronnet-Thibaut for World records and elite endurance runners. Am J Eng Res 6:317–323
Kosmidis I, Passfield L (2015) Linking the performance of endurance runners to training and physiological effects via multi-resolution elastic net. arXiv preprint arXiv:150601388. http://arxiv.org/abs/1506.01388
Zinoubi B, Vandewalle H, Driss T (2017) Modeling of running performances in humans: comparison of power laws and critical speed. J Strength Cond Res 31:1859–1867
Muniz-Pumares D, Karsten B, Triska C, Glaister M (2019) Methodological approaches and related challenges associated with the determination of critical power and curvature constant. J Strength Cond Res 33:584–596
Abbiss CR, Laursen PB (2008) Describing and understanding pacing strategies during athletic competition. Sports Med 38:239–252
Tucker R (2009) The anticipatory regulation of performance: the physiological basis for pacing strategies and the development of a perception-based model for exercise performance. Br J Sports Med 43:392–400
Hanley B (2015) Pacing profiles and pack running at the IAAF World Half Marathon Championships. J Sports Sci 33:1189–1195
Thiel C, Foster C, Banzer W, De Koning J (2012) Pacing in Olympic track races: competitive tactics versus best performance strategy. J Sports Sci 30:1107–1115
Padulo J, Annino G, Migliaccio GM, D’ottavio S, Tihanyi J (2012) Kinematics of running at different slopes and speeds. J Strength Cond Res 26:1331–1339
Clermont CA, Osis ST, Phinyomark A, Ferber R (2017) Kinematic gait patterns in competitive and recreational runners. J Appl Biomech 33:268–276
Ogueta-Alday A, Morante JC, Gómez-Molina J, García-López J (2018) Similarities and differences among half-marathon runners according to their performance level. PLoS ONE 13:e0191688
Schache AG, Blanch PD, Rath DA, Wrigley TV, Starr R, Bennell KL (2001) A comparison of overground and treadmill running for measuring the three-dimensional kinematics of the lumbo–pelvic–hip complex. Clin Biomech 16:667–680
Bishop D, Gjenkins D, Howard A et al (1998) The critical power function is dependent on the duration. Int J Sports Med 19:125–129
Gorostiaga EM, Sánchez-Medina L, Garcia-Tabar I (2021) Over 55 years of critical power: fact or artifact? Scand J Med Sci Sports. https://doi.org/10.1111/sms.14074
Triska C, Karsten B, Beedie C, Koller-Zeisler B, Nimmerichter A, Tschan H (2018) Different durations within the method of best practice affect the parameters of the speed–duration relationship. Eur J Sport Sci 18:332–340
Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Quart Appl Math 2:164–168
Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math 11:431–441
Jones AM, Burnley M, Black MI, Poole DC, Vanhatalo A (2019) The maximal metabolic steady state: redefining the “gold standard.” Physiol Rep 7:e14098
Krouwer JS (2008) Why Bland–Altman plots should use X, not (Y+X)/2 when X is a reference method. Stat Med 27:778–780
Bland JM, Altman DG (1999) Measuring agreement in method comparison studies. Stat Methods Med Res 8:135–160
García-Manso JM, Martín-González JM, Vaamonde D, Silva-Grigoletto MED (2012) The limitations of scaling laws in the prediction of performance in endurance events. J Theor Biol 300:324–329
Vandewalle H, Vautier JF, Kachouri M, Lechevalier JM, Monod H (1997) Work-exhaustion time relationships and the critical power concept. A critical review. J Sports Med Phys Fit 37:89–102
Mitchell EA, Martin NRW, Bailey SJ, Ferguson RA (2018) Critical power is positively related to skeletal muscle capillarity and type I muscle fibers in endurance-trained individuals. J Appl Physiol 125:737–745
Péronnet F, Thibault G (1989) Mathematical analysis of running performance and world running records. J Appl Physiol 67:453–465
Chinnasamy C, St Clair Gibson A, Micklewright D (2013) Effect of spatial and temporal cues on athletic pacing in schoolchildren. Med Sci Sports Exerc 45:395–402
Williams KR, Snow R, Agruss C (1991) Changes in distance running kinematics with fatigue. J Appl Biomech 7:138–162
Hanley B, Mohan AK (2014) Changes in gait during constant pace treadmill running. J Strength Cond Res 28:1219–1225
Hunter I, Smith GA (2007) Preferred and optimal stride frequency, stiffness and economy: changes with fatigue during a 1-h high-intensity run. Eur J Appl Physiol 100:653–661
Enomoto Y, Kadono H, Suzuki Y, Chiba T, Koyama K (2008) Biomechanical analysis of the medalists in the 10,000 metres at the 2007 World Championships in Athletics. New Stud Athl 3:61–66
Azevedo RDA, Silva-Cavalcante MD, Lima-Silva AE, Bertuzzi R (2021) Fatigue development and perceived response during self-paced endurance exercise: state-of-the-art review. Eur J Appl Physiol 121:687–696
Krzysztof M, Mero A (2013) A kinematics analysis of three best 100 m performances ever. J Hum Kinet 36:149–160
Weyand PG, Sternlight DB, Bellizzi MJ, Wright S (2000) Faster top running speeds are achieved with greater ground forces not more rapid leg movements. J Appl Physiol 89:1991–1999
Weyand PG, Sandell RF, Prime DNL, Bundle MW (2010) The biological limits to running speed are imposed from the ground up. J Appl Physiol 108:950–961