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Differences Among Estimates of Critical Power and Anaerobic Work Capacity Derived From Five Mathematical Models and the Three-Minute All-Out Test

Bergstrom, Haley C.1; Housh, Terry J.1; Zuniga, Jorge M.2; Traylor, Daniel A.1; Lewis, Robert W. Jr1; Camic, Clayton L.3; Schmidt, Richard J.1; Johnson, Glen O.1

Journal of Strength & Conditioning Research: March 2014 - Volume 28 - Issue 3 - p 592–600
doi: 10.1519/JSC.0b013e31829b576d
Original Research

Abstract: Bergstrom, HC, Housh, TJ, Zuniga, JM, Traylor, DA, Lewis, RW Jr, Camic, CL, Schmidt, RJ, and Johnson, GO. 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 28(3): 592–600, 2014—Estimates of critical power (CP) and anaerobic work capacity (AWC) from the power output vs. time relationship have been derived from various mathematical models. The purpose of this study was to examine estimates of CP and AWC from the multiple work bout, 2- and 3-parameter models, and those from the 3-minute all-out CP (CP3min) test. Nine college-aged subjects performed a maximal incremental test to determine the peak oxygen consumption rate and the gas exchange threshold. On separate days, each subject completed 4 randomly ordered constant power output rides to exhaustion to estimate CP and AWC from 5 regression models (2 linear, 2 nonlinear, and 1 exponential). During the final visit, CP and AWC were estimated from the CP3min test. The nonlinear 3-parameter (Nonlinear-3) model produced the lowest estimate of CP. The exponential (EXP) model and the CP3min test were not statistically different and produced the highest estimates of CP. Critical power estimated from the Nonlinear-3 model was 14% less than those from the EXP model and the CP3min test and 4–6% less than those from the linear models. Furthermore, the Nonlinear-3 and nonlinear 2-parameter (Nonlinear-2) models produced significantly greater estimates of AWC than did the linear models and CP3min. The current findings suggested that the Nonlinear-3 model may provide estimates of CP and AWC that more accurately reflect the asymptote of the power output vs. time relationship, the demarcation of the heavy and severe exercise intensity domains, and anaerobic capabilities than will the linear models and CP3min test.

1Department of Nutrition and Health Sciences, Human Performance Laboratory, University of Nebraska-Lincoln, Lincoln, Nebraska;

2Department of Exercise Science, Creighton University, Omaha, Nebraska; and

3Department of Exercise and Sport Science, University of Wisconsin-La Crosse, La Crosse, Wisconsin

Address correspondence to Haley C. Bergstrom,

Copyright © 2014 by the National Strength & Conditioning Association.