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Muniz-Pumares, D, Karsten, B, Triska, C, and Glaister, M. Methodological approaches and related challenges associated with the determination of critical power and W'. J Strength Cond Res 33(2): 584-596, 2019-The relationship between exercise intensity and time to task failure (P-T relationship) is hyperbolic, and characterized by its asymptote (critical power [CP]) and curvature constant (W'). The determination of these parameters is of interest for researchers and practitioners, but the testing protocol for CP and W' determination has not yet been standardized. Conventionally, a series of constant work rate (CWR) tests to task failure have been used to construct the P-T relationship. However, the duration, number, and recovery between predictive CWR and the mathematical model (hyperbolic or derived linear models) are known to affect CP and W'. Moreover, repeating CWR may be deemed as a cumbersome and impractical protocol. Recently, CP and W' have been determined in field and laboratory settings using time trials, but the validity of these methods has raised concerns. Alternatively, a 3-minute all-out test (3MT) has been suggested, as it provides a simpler method for the determination of CP and W', whereby power output at the end of the test represents CP, and the amount of work performed above this end-test power equates to W'. However, the 3MT still requires an initial incremental test and may overestimate CP. The aim of this review is, therefore, to appraise current methods to estimate CP and W', providing guidelines and suggestions for future research where appropriate.