Draft:Critical Power Concept

Critical Power

Critical Power (CP) is a concept in exercise physiology that represents the threshold at which cyclists can sustain a certain power output for an extended period without fatiguing. CP is a measure of the highest power output that can be maintained over a prolonged period, typically ranging from 20 to 60 minutes, depending on the individual's fitness level and the methodology used to determine CP. CP also exists within the exercise domain paradigm as the delineator between 'heavy' and 'severe' domains.

Theoretical Background

The concept of Critical Power is based on the hyperbolic relationship between power output and time to exhaustion. It divides the power-duration relationship into two parts:
 * Above Critical Power (Non-Sustainable Work): Power outputs that can be sustained only for short periods, leading to rapid peripheral fatigue due to the accumulation of metabolic byproducts.
 * Below Critical Power (Sustainable Work): Power outputs that can be maintained over longer durations without significant accumulation of fatigue.

Mathematical Model

The power-duration relationship can be modelled in several ways. Permitting that at least three exhaustive exercise tests were completed by the cyclist, the standard error of the estimate indicates the fit of the model to the data. It is customary to run the power-duration data points through the big-three models (Work-Time, Inverse Time-Power, and Hyperbolic) and select the parameters from the model with the lowest standard error of the estimate (citation needed). It is possible that two different models will produce lower standard errors of the estimate for the two parameters (CP and W'), in this case, the practitioner should decide whether a more reliable CP or W' is sought since the parameter estimates for CP and W' should not be taken from separate models.

Linear work-time model.

The work-time model is described by the equation:

$$Work = (CP \bullet T) + W\prime $$

Where:
 * (CP) is the Critical Power.
 * (W') (pronounced "W prime") is the finite amount of work that can be performed above CP before fatigue occurs.

Linear power-time model.

$$P = \frac{W\prime}{T} + CP$$

where P is mean power output.

Nonlinear power-time model.

$$T = \frac{W\prime}{(P+CP)} $$

3-parameter CP model

$$Time = \frac{W\prime}{(P-CP)} + \frac{W\prime}{(CP - P_{max})} $$

where Pmax is the maximal 1-second power output.

3-minute All-Out model.

burnley

The 3-minute all-out model determines that mean power output achieved in the final 30-seconds of the trial format is the CP, whereas the W' is the total accumulated work above the CP. There is no error indicated in the 3-minute all-out test. Also, the test is ideally performed on specialised ergometry equipment that can keep pedalling frequency (cadence) at a specified value, thus preventing the effect of cadence impacting the parameters of the power-duration relationship.

Power-Law

Maximal Mean Power Output.

Measurement and Testing

Critical Power can be determined through various testing protocols, typically involving multiple maximal efforts of differing durations. Common methods include:
 * Two-to-five all-out efforts lasting between 2 to 15 minutes.
 * 3-minute all-out test.

The data of power output and duration from the tests are used to derive the Critical Power and (W') parameters.

Applications in Training and Performance

Understanding an athlete's CP provides insights into aerobic conditioning, while (W') describes an athlete's capacity for work above CP (often thought of as the anaerobic capacity). The uses of CP and (W') testing are:
 * Training Prescription: Designing workouts that target specific energy systems.
 * Pacing Strategies: Developing race strategies to avoid early fatigue and maximize performance.
 * Monitoring Fitness: Tracking changes in CP over time to assess the effectiveness of training programs.

Comparison with Other Metrics

CP is often compared with other endurance performance metrics such as Functional Threshold Power (FTP) and Maximal Lactate Steady State (MLSS), or Maximal Metabolic Steady State (MMSS):
 * FTP: Often defined as the highest power output a cyclist can maintain for approximately one hour. While power output at FTP is similar to CP, CP is determined through a different methodology and can yield different results. The main criticism of FTP is the assumption of identical adjustments necessary for predicting 1-hour power from 20-minute power. The CP model addresses this limitation by individualizing the power output decay.
 * MLSS: The highest power output at which lactate production and clearance are balanced. CP and MLSS are closely related but not identical; MLSS is typically determined through lactate measurements, while CP is derived from power-duration tests.

The concept of Critical Power was first introduced in the 1960s by Monod and Scherrer. It has since evolved with advancements in exercise physiology, sports science, and technology. Ongoing research continues to refine CP models and explore its implications for different types of athletes and sports.