A Coaches Introduction to Critical Power

Mathematically Modeling The Power-Duration Relationship for Beginners

For something so familiar that everyone has experienced it, fatigue is paradoxically challenging to define. This is partly due to the limits of language and the fact that different fields of science define fatigue differently. But, it’s also due to the complexity of all of the underlying processes that lead to fatigue. For much of the time that ‘fatigue science’ has been a field, the ‘catastrophic’ model of fatigue was used to describe what occurs when an athlete reaches the absolute limit of their physical performance. Proponents of this model assert that the body either runs out of key nutrients or is ‘poisoned’ due to metabolite accumulation in the working skeletal muscles. However, as early as the dawn of the twentieth century, some individuals challenged these assumptions, one such example being Angelo Mosso, who stated, “At first sight [fatigue] might appear an imperfection of our body, is on the contrary one of its most marvelous perfections. The fatigue increases more rapidly than the amount of work done saves us from the injury which lesser sensibility would involve for the organism” [1]. In this view, fatigue is an immensely complex derivative of a number of functions, behaviors, and psychological processes. As a result, exercise limitations involve a wide range of systems working together in harmony to maintain homeostasis.

While these descriptive views of fatigue and exercise limitations can be useful, they don’t improve practitioners’ ability to predict or manage fatigue in athletes. As a result, the link between fatigue and performance has always been elusive. However, in recent years compelling evidence has indicated that the relationship between fatigue and performance is enshrined in the concept of critical power.

At it’s core, Critical power represents the highest power-output that can be sustained indefinitely, and the total amount of work that can be performed above this ‘critical power’ is referred to as W’ (pronounced “W Prime”). Traditionally W’ has been described as an ‘aerobic work capacity’, yet there is a lot of compelling evidence that suggests that W’ is sensitive to oxygen delivery. When we view Critical Power and W’ through the len s of oxygen delivery and utilization, which are two of the major components of exercise capacity, we can gain a new perspective that allows us to better model and predict time to fatigue in athletes.

Critical power is mathematically defined as the power-asymptote of the hyperbolic relationship between power output and time to exhaustion . In essence, critical power describes the duration that an individual can sustain a fixed power output in the severe exercise intensity domain, and physiologically critical power represents the boundary between steady-state and non-steady-state exercise. As a result, critical power may provide a more meaningful fitness index over more well-known performance metrics such as VO2max or lactate balance point.

The equation which describes the relationship between power output and exercise duration within the severe exercise intensity domain is as follows:

Time to Exhaustion = (W’) / (Power - Critical Power)

This equation creates a two-parameter model where critical power represents the asymptote for power, and the W’ represents a finite amount of work that can be done above critical power . Taken together, these two parameters can be used to predict the tolerable duration of exercise above critical power. The hyperbolic equation describing the power-duration relationship is rigorous and conserved across different forms of exercise, individual muscles, and modalities, thus establishing it as an important fatigue threshold for athletes in a range of sporting disciplines.

Figure 1: The power-duration curve defines the limit of tolerance for whole-body exercise and individual muscle exercise. The curve is constructed by the subject exercising at constant power or speed to the point of exhaustion, represented by points 1–3 on the chart. Typically these bouts are performed on different days and result in exhaustion within between two and twenty minutes. Two parameters define this hyperbolic relationship: the asymptote for power and the curvature constant W′ denoted by the rectangular boxes above critical power. Note that critical power defines the upper boundary of the heavy intensity domain and represents the highest power sustainable without drawing continuously upon W′. Above critical power, exhaustion occurs when W′ has been expended.

There are currently two validated methods for determining critical power and the fixed amount of work that can be done above critical power, termed W’. Traditionally critical power and W’ were calculated after having an individual perform three to seven all-out work bouts where they hold a fixed power-output until failure. These test results are then plotted on a chart where the x,y variables represent time to failure and power for each trial. Critical power is then determined as the slope of the work-time relationship, whereas W’ is determined from the y-intercept. More recently, though, investigators have introduced a 3-minute all-out exercise test, known as the 3MT, that has enabled the determination of critical power and W’ from a single exercise bout. The idea behind the 3-minute all-out test is that when a subject exerts themselves fully and expends W’ wholly, their power output equals their critical power. This idea can be summarised and expressed with the following equation:

Power = (W’ / Time to exhaustion) + Critical Power

Using these methods, critical power was originally defined as the external power output that could be sustained ‘indefinitely’. However, it should be understood that this definition is mainly theoretical as no bout of exercise can be sustained for an indefinite period regardless of the intensity. As a result, we can better understand critical power as the highest power output that can be sustained for a very long period of time without fatigue. In contrast to the historical definition, critical power is now considered to represent the greatest metabolic rate that results in ‘wholly oxidative’ energy provision, where wholly-oxidative considers the active organism as a whole. This means that energy supply through substrate-level phosphorylation reaches a steady-state and that there is no progressive accumulation of blood lactate or progressive breakdown of intramuscular phosphocreatine.

Figure II.

Given that HbO2 saturation, as measured with near-infrared spectroscopy, approximates phosphocreatine kinetics measured with magnetic resonance spectroscopy, we can conclude that a relationship between critical power and HbO2 saturation exists. As a result, the balance of oxygen supply and demand, which are two of the major determinants of exercise performance, can be used as a means of understanding CP & W’.

In the video below I outline a method for calculating critical power If you have any questions with this process or would like to see more content about this topic please let me know in the comments below. Additionally, if you enjoy this article please share it with a friend.

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