A 3-parameter critical power model

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Abstract
The critical power test is a well-established procedure that provides estimates of two important parameters characterizing work performance; anaerobic work capacity (AWC) and critical power (CP). The concept proscribes a hyperbolic relationship between power output (P) and time to exhaustion (t), given by (P − CP)t = AWC. Since evidence now exists that the procedure overestimates CP and underestimates AWC, this study was undertaken to investigate the effect of relaxing the requirement that the time asymptote necessarily be at zero. Using data from a previous study, it is shown that in so doing, (1) a time asymptote significantly less than zero is obtained, (2) significantly smaller estimates of CP and larger estimates of AWC are obtained, (3) a third parameter is introduced that theoretically represents maximal instantaneous power, (4) it implies that the maximal power that could be developed at any instant is proportional to the amount of AWC remaining at that instant, which in turn implies that (5) at exhaustion not necessary all of AWC is consumed.