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Critical Power and The Power-Duration Relationship

Paper Type: Free Essay Subject: Physiology
Wordcount: 3096 words Published: 8th Feb 2020

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The power output of an athlete and the duration they can maintain the effort for has a hyperbolic relationship (Burnley and Jones, 2018; Poole et al., 2016). The asymptote of this hyperbola is critical power (CP) whilst the curvature constant is W’.

CP, a model introduced by Monod and Scherrer (1965), is representative of the highest sustainable power output an individual can produce whilst remaining in a stable metabolic state (Bergstom et al., 2014; Poole et al. 2018). It represents a boundary above which an exercise intensity will become unsustainable (Morton and Billat, 2004). This intensity is known as severe intensity exercise, causing VO2, heart rate (HR) and blood lactate (BLa) levels to rise to their maximum values, making exercise intolerable if prolonged (Jones and Vanhatalo, 2017).

The total work an individual can perform above their CP level is known as W’ (Murgatroyd and Wylde, 2011; Vanhatalo, Doust and Burnley, 2007). Bergstrom et al., (2014) suggest the time to intolerance (Tlim) is directly influenced by the energy stored in active muscles.

If time is known, CP and W’ can be used to predict the highest average power output (PO)  an individual can maintain (Morton and Billat, 2004). These two parameters can also be insightful into the physiological responses and fatigue mechanisms during intense exercise, giving them practical application in enhancing athletes training programmes. (Jones and Vanhatalo, 2017; Poole et al., 2016).

The aim of this study was to calculate subjects’ CP and discover why this may be useful to performers, whilst also exploring the power-duration relationship and the physiological mechanisms involved.



14 undergraduate University students (6 males and 8 females) participated in this study. All subjects provided informed written consent and filled out a health questionnaire before undertaking the test. The mean mass of the participants was 73.58 ± 11.58 kg, measured with weighing scales (Seca, Germany) and the mean height was 172.70 ± 10.35 cm, measured using a stadiometer (Seca, Germany).


Prior to testing, each participants’ height and mass were recorded and they had a heart rate (HR) monitor (Polar, Finland) attached. The MetaSoft online gas analyser (Cortex, Germany) was set up whilst the participant was fitted with the correct sized mask. The cycle ergometer (Monark, Sweden) saddle was also set to the correct height so the subject could fully extend their legs, before they completed a warm up, cycling at 60 Watts (W) for 5 minutes.

Once the warm up was completed, a load was added to the ergometer. The amount of load was based on the mass, preferred cadence and fitness of the participant, equating to ~2-3 W per kg of body mass.

Each participant then completed two time-trials on the ergometer. A 12-minute maximum effort time-trial, preceding a 3 maximal time-trial (Simpson and Kordi, 2016). Researchers offered regular verbal encouragement throughout both trials to try to ensure a maximum effort (Andreacci et al., 2010).

Cadence and HR were recorded every 15 seconds whilst the load stayed constant so was recorded once at the beginning of each trial. After finishing the 12-minute trial, participants were given 30 minutes to rest (Simpson and Kordi, 2016), in which time all equipment was cleaned.

The participant then completed the 3-minute time trial. The load was slightly increased, but the test protocols remained the same as the first trial. During both time trials, the online gas analyser was recording VO2, VCO2 and minute ventilation (VE) throughout. HR was also recorded from the polar watch linked to the HR monitor every 15 seconds.

Data Analysis

Data analysis was completed using both group data and an individuals’ data. When reporting on individual data, the same participant is used, whilst for group data mean values were used for calculations and standard deviation is represented in graphs and tables.

A mean of the participants’ cadence recorded every 15 seconds and the load on the ergometer were multiplied together to calculate the mean power output (PO). However, this produces a non-linear relationship with time so once PO was known, total work was determined as PO x time. This results in a linear relationship between work (J) and time, which can be plotted on a graph (Bergstrom et al., 2014). The slope represents CP whilst the y-intercept represents W’ (Vandewalle et al., 1997).

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The online gas analyser was used to measure oxygen consumption (VO2). It recorded every breath the participant took and exported data every 15 seconds. Analysis of all data produced allowed the identification of the highest figure for VO2, thus giving the value for peak VO2.  The same procedure was used to calculate peak carbon dioxide expiration (VCO2)and peak minute ventilation (VE). As aforementioned, HR was measured every 15 seconds, the highest value during the trial was recorded for peak HR.


Figure 1 displays the work-duration relationship. The total work completed increased from 40821.37 ± 10328 Joules (J) during the 3-minute trial to 121152.80 ± 28978.45 J in the 12-minute time trial. The mean CP for all participants was 148.76  ± 37.75 W and the W’ value was 14044 J.

Figure 1. The relationship between the mean total work and duration. The slope represents CP.

As shown in table 1, peak VO2 and VCO2 values didn’t vary significantly between the 3-minute and 12-minute trials. Similarly, peak HR figures varied by less than a beat per minute on average. The mean VE was greater during the 3-minute trial with participants expiring 123.11 ± 32.87 L/min compared to 109.15 ± 46.48 L/min in the 12-minute trial.

Table 1. The parameters influencing the power-duration relationship

3 Minute Time-Trial

12 Minute Time-Trial

Peak VO2 (L.min-1)

Peak VCO2 (L.min-1)

Peak VE (L/min)

Peak HR (BPM)

Peak VO2


Peak VCO2


Peak VE


Peak HR




















Figure 2. The power-duration relationship of a single participant in the 3 and 12-minute time trials. Series 1 is the 3-minute trial, series 2 is the 12-minute trial.

Figure 2 represents the PO of single participant during the 3-minute time trial and the 12-minute trial. The participants’ PO increased from 222 W in the first minute to 279 W in the final minute of the 3-minute trial. Their PO during the 12-minute trial fluctuated, starting at 214.4 W at the first minute, dropping to 156 W at 6 minutes before increasing back up to 210 W after 12 minutes.

Figure 3. The VO2 response to severe-intensity exercise for a single participant. Series 1 is the 3-minute trial, series 2 is the 12-minute trial.

Figure 3 shows how the individuals’ oxygen consumption (VO2)failed to reach a steady state during the 3-minute trial as the values continue to rise. VO2 appears to  reach a plateau during the 12-minute time trial as the value stays consistently within 0.1 L/min of 2.5 L/min between 330 S and 660 S of the trial.

The individual who is analysed had their CP calculated as 165.17 W using the same method as in figure 1.


The purpose of this study was to calculate CP and explore the physiological components involved in the power-duration relationship. The mean CP of a group of participants was successfully calculated. A key finding was that although peak VO2 and peak HR remained constant between the 3 and 12-minute trials, mean PO was much higher during the 3-minute trial. This supports previous research into the power-duration relationship where findings have shown a PO above ones’ CP cannot be endured for long (Morton and Hodgson, 1996; Burnley and Jones, 2016).

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Simpson and Kordi (2016), completed a study to calculate CP, also using 2 trials of 3 and 12-minute durations. The 8 subjects, who were trained competitive cyclists, had a mean CP of 283 ± 66 W. When compared to the CP predicted from using a three-trial model, there was no difference found, suggesting the two-trial model is an affective and time effective model to predict CP. Simpson and Kordi (2016) predicted significantly higher CP in their subjects than found in this study. The study Simpson and Kordi completed used self-pacing trials, which have been shown to produce higher estimates of CP than fixed PO imposed trials which may explain why the results were higher (Black et al. 2015). Another factor in the differing findings could be their used trained competitive cyclists as their subjects, whereas the subjects in the present study were a mix of trained and untrained individuals from a range of sports.

Working above ones CP has been linked with a loss of metabolic homeostasis within muscles, leading to fatigue (Burnley and Jones, 2016). They found increases in VO2  to be one of the physiological responses to try to regain homeostasis, as found in our research with all participants experiencing increases in their VO2 during our trials. This increase is known as the VO2 slow component (Jones and Burnley, 2009). The VO2 slow component represents a decrease in the efficiency the body uses oxygen to maintain an exercise intensity, thus increasing VO2 (Whipp, 1994; Jones and Burnley, 2009). Jones et al. (2011), found the VO2 slow component to be linked with the recruitment of additional type II muscle fibres which are less efficient. The VO2 slow component concept can help explain the increase in VO2 in the 3-minute trial and in the first 4-minutes of the 12-minute trial shown in figure 3.

As displayed in table 1, there is no significant difference between the mean peak VO2 values in the 3 or 12-minute time trial, nor the peak HR, suggesting the subjects were working at or close to their VO2 max. This would mean they were working at a severe intensity, above their CP (Poole et al., 2016). The VO2 peaks in figure 3 correlate with the PO peaks in figure 2, representing a final unsustainable push. This PO becomes unsustainable because energy provision can no longer be wholly oxidative (Poole et al., 2016). As a result, intramuscular stores of phosphorylcreatine depleted and VO2 is no longer in a steady state. Alongside this, intramuscular inorganic phosphate (Pi) and hydrogen ions accumulate which have been shown to cause muscle fatigue (Murgatroyd et al., 2011). These are the physiological factors determining the W’, and therefore the power-duration relationship. The larger the disparity between PO and CP, the faster the Tlim and the faster the slow component develops (Poole et al., 2016).  This can be seen in the data recorded when the individual’s PO increases steeply in figure 2, their VO2 increases in the same manner.

The use of prediction models such as the one in the present study have practical application to performance modelling of both endurance and intermittent sports (Jones and Vanhatalo, 2017). CP defines the regions of physiological intensity, making it an important tool for setting training zones (Simpson and Kordi, 2016). Knowledge of the combination of CP and W’ allow performance to be simulated enabling the prediction of necessary changes to CP or W’ to improve performance (Simpson and Kordi, 2016). Jones et al. (2011), suggest that the magnitude of the VO2  slow component can be reduced through endurance and inspiratory muscle training, increasing performers’ oxygen uptake efficiency and therefore increasing their CP.

One limitation of the research completed is that although the use of 2 trials has been shown to be accurate, any individual mistake on either trial will have a large impact (Simpson and Kordi, 2016). Simpson and Kordi (2016), suggest a 3rd 5-minute trial could be used to improve the reliability of results if the findings fit into the linear relationship predicted. In addition, some subjects may have completed vigorous physical activity the day before participating in the study. This could’ve increased the fatigue experienced during the time-trials and reduced their PO. In future participants will be instructed to refrain from completing physical activity in the 24 hours before the study.

To conclude, the use of a 3-minute and 12-minute constant effort time trial is a time effective and valid method of determining CP. An understanding and knowledge of CP can prove useful to exercise performers and coaches alike when creating pacing strategies and implementing training zones. This will benefit an athlete’s ability to produce higher amounts of power over a longer duration.


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