Analysis of Mean Maximal Power in cycling with a modified Critical Power model allowing for a non-constant Anaerobic Work Capacity

Abstract

Introduction : Since its introduction by Monod and Sherrer 1 the Critical Power model has been applied to the analysis of cycling performances. In this model the Critical Power CP is the highest power that can be sustained without fatigue, and the total amount of work that can be produced until fatigue at any level above CP is indicated as the anaerobic work capacity W’. As yet W’ is considered to be a constant quantity. However Mean Maximal Power data, indicated by MMP, or a (t lim ,P lim ) data set can by described adequately by this CP-model only in a limited time range, typically between t lim =20’ and t lim =60’. Although the model can also formally be applied to short efforts, the relevant parameters CP and W’ as obtained from short and long efforts will differ significantly. Therefore we propose a modified CP-W’ model that will describe the MMP curve for the full relevant time range. Theory and results: The standard critical power model is expressed as 𝑃 ð‘i = 𝐶𝑃 + where t is the limiting time that a power P can be sustained until exhaustion. This equation is valid for all values of P(t) > CP but it leads to a catastrophe for short sustainable times because lim → 𝑃 ð‘i = ∞ Therefore some authors have proposed a general modification 𝑃 ð‘i = 𝐶𝑃 + 𝑓 ð‘i wherethefunction 𝑓 ð‘i hastobechosensuchthat lim → 𝑃 ð‘i = 𝑃 !# and P max is the zero-extrapolated maximal power. The effective work that can be delivered above CP is then ð‘S ! = ð‘S 𝑓 ð‘i . Examination of a number of MMP curves have lead us to consider 2 sustainable time zones, each zone being described with an appropriate correction function f(t). The full MMP curve is described as 𝑃 ð‘i = 𝐶𝑃 + 1 − 1 − ð‘i 𝑈 ( 𝑇 − ð‘i ) 𝑈 ð‘i − ð‘i𝑠𝑤 + 𝑀𝐴𝑃 + ( 1 − 𝑒 / ) 𝑈 ( ð‘i𝑠𝑤 − ð‘i ) 𝑇 !# !# Where U(t) is the unit step function i.e. U(t ≥ 0)=1 and U(t SCP the available W eff is much lower than the saturation value. This indicates that for this cyclist any test at sustainable times shorter than Tscp = 22 minutes will inevitably lead to anomalously high values of CP and low values of W’. Conclusions : We have presented a new model describing the full MMP-curves. Detailed analysis of the MMP and the [P,W’] data yield a set of field-based power parameters CP, W’,SCP,T SCP , MAP, P max , I„ . This model lifts the long standing discrepancy between the determinations of CP from short or from long efforts. CP from short test is closely related to MAP, while CP from long times is related to Maximal Lactate Steady State. CP test should be performed in the exhaustive time interval where W eff ’ has a constant value, i.e. for times higher than T SCP . Further research may focus on the relevance of these objective parameters for qualifying the strengths of sprinters, punchers, time trialists and climbers.