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European Journal of Applied Physiology (2022) 122:301–316
https://doi.org/10.1007/s00421-021-04833-y
INVITED REVIEW
Power profiling andthepower‑duration relationship incycling:
anarrative review
PeterLeo1 · JamesSpragg2· TimPodlogar3,4· JustinS.Lawley1· IñigoMujika5,6
Received: 2 June 2021 / Accepted: 14 October 2021 / Published online: 27 October 2021
© The Author(s) 2021
Abstract
Emerging trends in technological innovations, data analysis and practical applications have facilitated the measurement of
cycling power output in the field, leading to improvements in training prescription, performance testing and race analysis.
This review aimed to critically reflect on power profiling strategies in association with the power-duration relationship in
cycling, to provide an updated view for applied researchers and practitioners. The authors elaborate on measuring power
output followed by an outline of the methodological approaches to power profiling. Moreover, the deriving a power-duration
relationship section presents existing concepts of power-duration models alongside exercise intensity domains. Combining
laboratory and field testing discusses how traditional laboratory and field testing can be combined to inform and individual-
ize the power profiling approach. Deriving the parameters of power-duration modelling suggests how these measures can be
obtained from laboratory and field testing, including criteria for ensuring a high ecological validity (e.g. rider specialization,
race demands). It is recommended that field testing should always be conducted in accordance with pre-established guide-
lines from the existing literature (e.g. set number of prediction trials, inter-trial recovery, road gradient and data analysis). It
is also recommended to avoid single effort prediction trials, such as functional threshold power. Power-duration parameter
estimates can be derived from the 2 parameter linear or non-linear critical power model: P(t) = W′/t + CP (W′—work capacity
above CP; t—time). Structured field testing should be included to obtain an accurate fingerprint of a cyclist’s power profile.
Keywords Racing· Training· Analysis· Performance· Prediction· Power output
Abbreviations
%
̇
V
O2max Fractional utilization of the maximum oxygen
uptake
2-P CP Two-parameter critical power model
3-P CP Three-parameter critical power model
APR Anaerobic power reserve
ATP Adenosine tri phosphate
BMX Bicycle motocross
CT Critical torque
CP Critical power
CPTTF Time to task failure at critical power
e Basis of the natural logarithm (e = 2.178)
EVA Exposure variation analysis
FPCA Functional principal component analysis
FTP Functional threshold power
GET Gas exchange threshold
GXT Laboratory incremental graded exercise test
k The rate of the exponential decline in power
output
LT Lactate threshold
MAP Maximum aerobic power
Communicated by Michael Lindinger.
* Peter Leo
peter.leo@uibk.ac.at
1 Division ofPerformance Physiology & Prevention,
Department ofSport Science, University Innsbruck,
Innsbruck, Austria
2 Health Physical Activity Lifestyle Sport Research
Centre (HPALS), University ofCape Town, CapeTown,
SouthAfrica
3 Faculty ofHealth Sciences, University ofPrimorska, Izola,
Slovenia
4 Department ofAutomatics, Biocybernetics andRobotics,
Jožef Stefan Institute, Ljubljana, Slovenia
5 Department ofPhysiology, Faculty ofMedicine andNursing,
University oftheBasque Country, Leioa, BasqueCountry,
Spain
6 Exercise Science Laboratory, School ofKinesiology, Faculty
ofMedicine, Universidad Finis Terrae, Santiago, Chile
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302 European Journal of Applied Physiology (2022) 122:301–316
1 3
MLSS Maximum lactate steady state
MMP Maximal mean power output
OmPD Omni power duration model
P&T Peronnet and Thibault model
P(t) Power output
Pmax Peak power over 1s
SEE Standard error of the estimate
TT Cycling time trial
TTF Time to task failure
̇
V
O2 Oxygen uptake
̇
V
O2max Maximum oxygen uptake
W′ Work capacity above critical power
WEP Work above end test power
Introduction
Since the invention of the first mobile power meter for
cycling in the late 1980s training and racing with this tool
has become standard practice in multiple cycling disciplines
including road, track, mountain bike, cyclo-cross, bicycle
motocross (BMX) and triathlon. Mechanical power output
measured by strain gauges, most commonly mounted in the
bike’s crank spindle, crank arm or pedal spindle and con-
nected to a head unit mounted in the handlebar allows power
output data to be accurately recorded in field conditions in
real time (Maier etal. 2017). This enables an in-depth analy-
sis of a cyclist’s mechanical power output during training
and/or competition, and the assessment of an athlete’s endur-
ance capacity outside of a laboratory setting (Passfield etal.
2017).
These aforementioned technological innovations have
allowed applied scientific research to be undertaken in
cycling, including real-time measurements of internal (e.g.
heart rate) and external (e.g. power output) workloads (van
Erp and de Koning 2019; Mujika 2017; Muriel etal. 2021;
Padilla etal. 2000; Padilla etal. 2008). This in turn allows
the demands of racing to be described (Ebert etal. 2005,
2006; van Erp etal. 2021b; Menaspà etal. 2015; Menaspà
etal. 2013; Vogt etal. 2007b), training/racing performance
analysis to be conducted (Leo etal. 2021c; Lucia etal. 2001;
Mujika and Padilla 2001; Pinot and Grappe 2011) and train-
ing prescription to be quantified (Leo etal. 2020; Sanders
etal. 2020; Sanders and Heijboer 2019a).
Power profiling in cycling is most commonly defined as
the assessment of field derived power outputs, i.e. values
obtained during training and racing (Coggan 2003; Leo etal.
2020). Power profiling can be used for the tracking of longi-
tudinal changes in performance and race analysis (Leo etal.
2021b). There is a growing interest in the theoretical and
practical implications of power profiling. However, to date,
there is no consensus on what constitutes the best practice
for power profiling, especially given that there are numerous
methodological issues and approaches. Therefore, the aim
of this narrative review is to present and discuss existing
practices and methods, their implementation, interpreta-
tion, and practical applications, provide recommendations
to unify power profiling approaches for both practice and
research, and suggest future directions for research.
Measuring power output
Before analysing power output data, it is important to under-
stand how power output is measured during cycling and any
associated methodological issues. In cycling, when a force
is created by the muscles and applied perpendicular to the
bicycle crank arm, one crank arm revolution creates two
angular impulses (one per leg); this results in forward drive.
Optimal force production, and as a result optimal forward
drive, is a complex interplay of innervation, muscle recruit-
ment patterns, the contractile function of muscle as well
as an elastic tendon–muscle interaction and metabolic pro-
cesses occurring in these tissues. The properties of force
generation are often described using physics expressions
such as mean torque or mean power output; the former
describing the force and the latter the amount of work pro-
duced in a given time (Winter etal. 2016). Power output is
often expressed as a steady-state value (e.g. 100W), but this
value is a product of many impulses over a given period of
time or a given proportion of the pedal stroke. Some have
argued that ‘mean power output’ is therefore a more accurate
descriptor (Winter etal. 2016). Notwithstanding the validity
of this argument, for the purposes of this review the authors
will employ the customarily used term ‘power output’
throughout. However, it should be noted that power output
does not include the energy used to accelerate the cyclist’s
limbs nor forces applied in non-propulsive directions.
Mechanical (or external) power output can either be meas-
ured by strain gauges or calculated mathematically (Maier
etal. 2017; Martin etal. 1998). Depending on the position of
the strain gauge (e.g., pedal spindle, crank, bottom bracket),
the recorded power output is expected to deviate slightly as
some energy is lost via drivetrain inefficiencies (Coyle etal.
1991; Maier etal. 2017; Martin etal. 1998). This highlights
that power output values derived from different strain gauge
positions may not be comparable. Likewise, different power
meter brands and models have different levels of trueness
and precision. Maier etal (2017) found that while on average
commercially available power meters record at a trueness of
− 0.9 ± 3.2% some units will deviate by more than 5%. The
authors also reported that some power meter brands have
significantly greater precision than others.
On average Maier etal. (2017) found that the small-
est worthwhile change for the accuracy of commercially
available power meters was 1.1–2.8%. This implies that
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303European Journal of Applied Physiology (2022) 122:301–316
1 3
any performance improvements of less than 1.1% cannot
be accurately quantified by commercially available power
meter devices. However, this value may differ from brand to
brand and model to model. Validation studies have been con-
ducted for most commercially available power meters, but
there is no agreed-upon gold standard to which power meters
should be compared. Therefore, researchers and practitioners
should take note of the comparative measure when assess-
ing the validity of any power output measuring device. We
draw the reader’s attention to the aforementioned study by
Maier and colleagues (2017) for a broader discussion of the
methodological issues surrounding power meter validation.
To ensure high data quality the authors strongly recommend
accurate calibration according to the manufacturer’s recom-
mendations prior to the collection of any power meter data.
Additionally, dynamic (Gardner etal. 2004), static (Wooles
etal. 2005), and day-to-day calibration, known as ‘zero-
offsetting’ are all recommended before data derived from
power meters are used for power profiling purposes.
Methodological approaches topower
proling
Numerous methodologies have been applied in the field
of power profiling. The most basic of these is simply the
reporting of average power output values for a given race or
event (Ebert etal. 2005; Vogt etal. 2007a, b). While this is
the starting point in understanding the demands of a given
event, it fails to fully utilise the full potential of power pro-
filing. Another disadvantage is that unless data are derived
from cyclists with differing performance levels within an
event, this approach does not provide any information on the
demands of peak performance, instead it merely describes
the demands of participation.
A more advanced approach is to describe the power out-
put by time at a given intensity. This approach is normally
described as ‘binning’. Binning is where each power output
value is categorized into a bin; each bin represents a range
of intensities (for example 100–200W). The resulting cat-
egorization of each output value can then be expressed as
either total cumulative time in each bin or as a percentage of
total time. (Abbiss etal. 2010; Ebert etal. 2006; Leo etal.
2021b; Metcalfe etal. 2017). Typically, but not always, the
bins are defined by normalizing the power output to body
mass (for example 4–5W kg−1). However, the suitability of
this approach can be questioned; for example, in some events
aerodynamic drag is a far more important factor than body
mass (Pringle etal. 2011). Besides scaling power output
relative to the frontal area (Padilla etal. 1999), to the best
of the authors’ knowledge no studies have been published
where the bins represent ranges of power output values nor-
malised to aerodynamic drag (W CdA−1).
Binning has advantages in that it can describe the range
of intensities that are required to compete or perform in a
given event. Typically, cycling events are not completed
at a fixed power output; instead, power output is stochas-
tic in nature, even in individual time trials (Gordon 2005).
Whilst binning allows the total time at different intensities
to be described, there are weaknesses with this approach.
Firstly, the choice of the range of intensities for a given bin
will influence the results. Often arbitrary bins are chosen,
based on a given power output normalized to body mass,
for example 5.9–7.9W kg−1. If the range of intensities is
too wide the granularity of the power output data cannot be
captured. Another problem is that binning gives no insight
into the length of individual efforts. The cumulative time
in each power output bin may represent one long effort or
multiple short efforts. Finally, if arbitrary bins are used then
it may be that the range of intensities covered by a single
bin includes power outputs that are both sustainable and
unsustainable from a physiological point of view. A solu-
tion to this problem is to use physiological thresholds to
define the bins (Abbiss etal. 2010; Passfield etal. 2013).
For example, the submaximal physiological thresholds that
define the exercise intensity domains could be determined
during laboratory testing and used to define the bins. While
this approach does give a greater insight into the physiology
of a given event for individual athletes, problems occur when
data from multiple athletes are amalgamated, as the bins,
while representing consistent physiological responses, do
not necessarily represent the same absolute or relative power
output for all athletes.
As previously mentioned, one of the main problems with
binning is that duration of individual efforts are not rep-
resented within the data. However, there is a small body
of work that uses exposure variation analysis (EVA) to try
and overcome this limitation (Abbiss etal. 2010; Passfield
etal. 2013). This approach uses a two-bin system; one set of
bins is used in the traditional manner to describe the inten-
sity. Bins can be associated with either arbitrary values or
physiological thresholds. The second set of bins is used to
describe the duration of individual efforts. Here arbitrary
durations are used, for example 0–5s, 5–10s or > 1min.
The intensity bins are plotted on the x-axis, the duration of
individual efforts is plotted on the z-axis and the percentage
of total race time is plotted on the y-axis (see sample data
in Fig.1).
Whilst the exact power output of individual efforts is
still not displayed, EVA is a very powerful tool to show the
pacing strategy and stochastic nature of power output in a
given event. This approach may be especially powerful to
describe events where lots of short submaximal sprints are
interspersed by periods of recovery, for example cyclo-cross
or Olympic cross country mountain biking. EVA is an effec-
tive way to describe the duration of efforts and recovery
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304 European Journal of Applied Physiology (2022) 122:301–316
1 3
bouts. This information can be valuable for coaches and
practitioners when prescribing interval training sessions to
replicate the demands of an event.
A major limitation of the approaches discussed thus far is
that they fail to describe power outputs for individual efforts.
To do this the mean maximal power output (MMP) approach
can be used (van Erp and Sanders 2020; Puchowicz etal.
2020; Quod etal. 2010; Vogt etal. 2007b). MMP values
represent the highest average power that was recorded for a
given (arbitrary) duration, during an event. For example, the
highest average power output recorded over a 5min duration
in a race would be the 5min MMP. Such MMP data are very
valuable because they make it possible to identify the power
output and duration that a cyclist is required to produce to
be competitive in an event. For example, MMP data analysis
shows that a top male general classification contender in a
grand tour is required to produce 5.8W kg−1 for 20min on
key mountain climbs (van Erp etal. 2020a, b). For coaches
and practitioners this is very valuable information.
There are however some fundamental issues with MMP
data. Firstly, it is not known if the recorded MMP values
were derived from a maximal effort. This contrasts with
values derived from formal testing where the maximality
of an effort can be verified. For example, in a traditional
laboratory incremental graded exercise test (GXT) a given
perception of effort and respiratory exchange ratio need to be
obtained for the test to be considered maximal in nature and
therefore a valid maximum oxygen uptake (
̇
V
O2max) value to
be obtained (Jones etal. 2016). It is hypothesised that almost
none of the MMP values derived from races are maximal
in nature. If a rider were to produce a maximal effort at
any point other than at the finish of a race, it may compro-
mise their ability to subsequently follow their competitors
in bunch events or compromise their pacing strategy in indi-
vidual events (Leo etal. 2021b, c). Secondly, MMP data
from a specific (arbitrary) duration could be the result of
the bracketing of a subsection of a longer effort, or a shorter
duration effort and a subsequent recovery (Leo etal. 2021a,
b). For example, it is very unlikely that a 5-min MMP value
derived from a race represents a maximal effort of exactly
5min in duration. As a result, there is a high probability of
an inherent underestimation of maximal power output when
using MMP values alone. MMP data are only indicative of
what a cyclist did, not what the cyclist is capable of.
Another issue with MMP data in research is that there is
no agreed-upon set of (arbitrary) durations that are being
applied. This means that when trying to compare data from
various studies coaches and practitioners cannot perform
like for like comparisons. This situation has improved some-
what as research groups have started to incorporate a wider
range of MMP durations from ~ 5 to ~ 1800s. This allows a
power-duration curve to be developed using the MMP val-
ues, allowing for some comparisons between studies. A final
issue with MMP analysis is that it may not actually define
‘race winning efforts’. Recent work by Leo and colleagues
(2021b) and van Erp and colleagues (2021a; b) showed that
the power output that cyclists produce falls throughout an
event; and that MMP values are not predictive of race per-
formance. Instead, it is the power output that riders produce
at key moments in the race that is predictive of performance.
For example, in the case of a sprinter in road cycling it is
the power that they can produce in the final moments of the
race that is important, but this is not necessarily the same
as their 10s MMP. This means that MMP analysis may
be missing the very efforts that it is trying to identify. To
better identify these race-winning efforts an approach has
been taken in research whereby the event is broken down
into segments and MMP values in each segment have been
reported (van Erp etal. 2021a; Leo etal. 2021b; Sanders and
van Erp 2021). To date, these segments have been defined
Fig. 1 EVA—exposure varia-
tion analysis in the final hour of
a race in six U23 cyclists (N = 6)
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305European Journal of Applied Physiology (2022) 122:301–316
1 3
via accumulated work, either absolute values or normal-
ized to body mass, for example MMP values after 2.500kJ
of work. However, this approach, which has thus far only
been applied in road cycling has introduced some further
limitations. Road cycling is a team sport in which riders
perform individual tasks such as sheltering a team leader or
collecting nutrition from a following car. It is not the goal of
every rider to try and win the race. Therefore, the reported
decrease in MMP values, as accumulated work increases,
may partially be a product of the fact that some riders have
simply finished their tasks and are therefore no longer pro-
ducing maximal efforts.
To alleviate the problem of arbitrary MMP durations not
matching actual effort durations, some studies have selected
specific sections of the event and identified power output
exclusively in that section (Jobson etal. 2008; Leo etal.
2021c; Padilla etal. 2008). For example, Leo and colleagues
(2021a; b) looked at MMP values exclusively on classified
climbs. This approach, while potentially beneficial in certain
circumstances, does require researchers to identify the key
moments in races for analysis. While this may be possible
for some events, such as a road race stage that starts out flat
and concludes with a mountain top finish, it is not always
possible to accurately identify the key moment in a race. A
possible solution to this is to seek the input of athletes when
identifying the key periods in the race. Whilst an attrac-
tive proposition, to the best of the authors’ knowledge this
approach has not been used in published research.
As mentioned before, the major issue with MMP analysis
is the uncertainty surrounding whether an effort was maxi-
mal in nature, and whether the MMP duration is equal to the
effort duration. To counter this problem, the authors recom-
mend using power output values derived from formal test-
ing to provide a comparative measure to MMP values. This
approach has particular benefits for coaches and practition-
ers as comparisons between MMP data and formal testing
data can be used to monitor changes in the power profile;
and if a rider records a MMP value which exceeds the pre-
diction from formal testing a new formal performance test
can be scheduled. This is particularly useful when analysing
performance in timed events where the in-competition power
output and event duration can be compared to the theoreti-
cal power-duration relationship. This example highlights
the importance of developing a power-duration relationship
rather than simply using standard duration performance
tests, as the likelihood of the test and competition durations
being identical is low. For methodological issues surround-
ing the development of theoretical power duration relation-
ships please see the section ‘Deriving a power-duration
relationship’ below.
Unfortunately, this approach (i.e. comparing MMP
against a pre-established theoretical power-duration relation-
ship derived from prior formal testing) was only undertaken
by a few research groups (Leo etal. 2020; Leo etal. 2021b;
Nimmerichter etal. 2020; Quod etal. 2010). However, all
research has shown good to very good agreement between
power output values from formal testing and MMP values.
Of particular interest is work by Leo and colleagues (2020,
2021a) that shows the formal testing values are only predic-
tive of race performance for a 6-month period before formal
re-testing is required.
Methodological issues
Thus far we have discussed methodological approaches in
power profiling, however, there are also methodological
issues that are pertinent to all approaches. Recorded power
output values can be highly influenced by the topography of
the event (Padilla etal. 2000, 2008; Sanders and Heijboer
2019a), differences between single day and multi-day stage
racing (van Erp and de Koning 2019; van Erp and Sanders
2020; Lucía etal. 2003) and race category (Sanders and
van Erp 2021). In professional road cycling race category
was found to influence power output: higher power outputs
over shorter durations (< 2min) were reported in lower-
ranked races, and higher power outputs over longer durations
(> 10min) were observed in races with higher difficulty.
Another important consideration when performing power
profiling are environmental factors. Altitude, temperature,
and humidity can all influence the power output athletes can
produce. Therefore, from a research perspective the authors
recommend that the environment and race conditions should
be reported whenever possible.
Recent research has also shown that power profiling anal-
ysis conducted exclusively on either training or racing data
produces different results in the same participants (Leo etal.
2020). This is an important factor and further highlights
the need to provide adequate information on the context in
which any power profiling data were collected.
Finally, in competition settings, alongside the aforemen-
tioned issues surrounding team roles there is an influence of
other team-mates and competitors on power output due to
drafting, which lowers the power output requirement for a
given speed (Ouvrard etal. 2018, van Druenen and Blocken
2021). Research has also suggested that competition may
influence the pacing strategy adopted by cyclists (Bossi etal.
2018).
Deriving apower‑duration relationship
When power output is plotted against time to task failure
(TTF) a consistent power-duration relationship emerges
(Burnley and Jones 2018). The first researchers to math-
ematically describe this relationship were Monod and
Scherrer (1965) who analysed muscle fatigue during static
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306 European Journal of Applied Physiology (2022) 122:301–316
1 3
and dynamic work (knee extension exercise) and created a
mathematical model describing the hyperbolic relationship
between completed work and TTF. Due to the strong scien-
tific evidence over decades (Burnley and Jones 2018; Jones
etal. 2010; Poole etal. 2016) the power-duration relation-
ship can be considered to represent an integrative approach
to the limits of tolerable exercise in humans.
From a physiological perspective the power-duration
relationship is comprised of four distinct exercise intensity
domains; namely, moderate, heavy, severe, and extreme
(Burnley and Jones 2007), which are characterised by dis-
tinct whole-body physiological responses (Jamnick etal.
2020; Vanhatalo etal. 2016; Whipp 1996). While a complete
physiological background on the systemic and mechanistic
bases of the power-duration relationship would be beyond
the scope of this narrative review, interested readers are
referred to the following review articles: Burnley and Jones
(2018), Jones etal. (2010), Poole etal. (2016), Poole etal.
(2021), Vanhatalo etal. (2016).
Various models are available to coaches and practitioners
to model the power-duration relationship for use in power
profiling (Sreedhara etal. 2019). However, most models only
cover a specific section of the power-duration relationship
(see Fig.2).
Modelling power output intheextreme exercise
intensity domain
Previous research (Bundle etal. 2003; Bundle and Wey-
and 2012; Weyand etal. 2006) has demonstrated that the
anaerobic power reserve (APR) is capable of predicting
short duration (< 3min) power outputs within the extreme
exercise intensity domain, where
̇
V
O2max may not be attained
before task failure occurs. The APR approach was initially
developed in laboratory settings where the maximum aero-
bic power (MAP) recorded during a GXT and the maximal
power an athlete can produce over one pedal revolution or
over one second (Pmax) are used as parameter inputs. How-
ever, Sanders etal. (2017, 2019b) developed a field testing
method where 3min MMP can be used as a surrogate for
MAP. In this approach the time constant (k), which can be
defined as the rate of the exponential decline in power out-
put (i.e. the reciprocal of the corresponding time constant:
k = 1/τ), can be varied between values of 0.024–0.027 to best
Fig. 2 An illustration of the spectrum of physiological responses
across the power-duration relationship using arbitrary power output
values. Pmax 1s peak power, W′ work above critical power, CP criti-
cal power, LT lactate threshold, GET gas exchange threshold, APR
anaerobic power reserve model, 2-P CP two-parameter critical power
model, 3-P CP three-parameter critical power model, P&T Peronnet
and Thibault Model, OmPD omni power duration model
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307European Journal of Applied Physiology (2022) 122:301–316
1 3
fit the MMP data. This allows for an individualisation of the
power-duration relationship modelling, which may provide
a better fit (Sanders and Heijboer 2019b) [see sample data
in Fig.3 and Table1 (Eq.1)].
Alongside the APR model, power output in the extreme
exercise intensity domain can also be predicted using the
three-parameter critical power (3-P CP) (Morton 1996), the
Peronnet and Thibault model (P&T) (1989) and Puchow-
icz’s omni power duration model (OmPD) (Puchowicz etal.
2020). It should be noted that in the P&T model, Pmax is pro-
vided as a parameter estimate, whereas in the APR model,
3-P CP model and the OmPD model Pmax is required as an
input parameter. These different modelling approaches con-
siderably influence power output predictions in the extreme
exercise intensity domain (see Fig.4).
Modelling power output inthesevere exercise
intensity domain
Multiple approaches based on the CP concept have been
proposed to predict power outputs within the severe exercise
intensity domain. Although all CP models are equivalent
from a mathematical perspective (i.e. they can be derived
mathematically from one another) they produce different sta-
tistical parameter estimates for CP and work above CP (W′)
(Jones etal. 2010; Muniz-Pumares etal. 2019), and there-
fore slightly different predictions within the severe exercise
intensity domain; particularly at the extremes of the domain.
The 3-P CP model (Morton 1996) aimed to overcome these
limitations for short duration power outputs toward the upper
end of the severe and into the extreme exercise intensity
domain by incorporating Pmax as a model parameter, but it
still overestimates power outputs in the moderate exercise
intensity domain (see Fig.4).
Modelling power output belowthecritical power
The CP represents the theoretical asymptote of the power-
duration curve, suggesting that a given power output is infi-
nitely sustainable. However, this is clearly not the case for
real-world performances where exercise at the CP is limited
to 20–40min (Poole etal. 2016). For this reason, previ-
ous research (Peronnet and Thibault 1989; Puchowicz etal.
0306090120 150 180
0
500
600
900
1200
1500
Time (s)
PowerOutput (W)
Fig. 3 Sample data for the anaerobic power reserve model, black
dots—record power output over 5, 10, 15, 30, 60, 90, 120 and 150s
durations; horizontal black dashed line:—anaerobic power reserve;
green, blue and red dashed lines representing the power duration
curve with the rate constant (k) of the exponential decline in power
output (k = 0.024, k = 0.026, k = 0.027) according to Sanders and Hei-
jboer (2019b)
Table 1 Power-duration models corresponding to the respective exercise intensity domains
Equation1: P(t) power output, P(3-min) 3min field test, P(max) 1s peak power, e base of the natural logarithm (2.718), k the rate constant of the
exponential decline in power output, t time in seconds
Equation2: t time in seconds, Wʹ work above critical power, P power output, CP critical power, P(max) 1s peak power
Equation3: P(t) power output, Wʹ work above critical power, CP critical power, t time in seconds
Equation4: Pmap(t) power output at maximum aerobic power, MAPTTF time to task failure at maximum aerobic power, t time in seconds, A rep-
resents a fixed constant for the decline in power output over time, Ln natural logarithm to the base of e (2.718)
Equation5: P(t) power output, Wʹ work above critical power, CP critical power, t time in seconds, CPTTF time to task failure at critical power, A
represents a fixed constant for the decline in power output over time, Ln natural logarithm to the base of e (2.718)
Exercise intensity domains Model Equation
extreme Anaerobic power reserve
P(t)
=P
(
3
−min)
+
(
P
(max)
−P
(
3
−
min
))
×e(−k×t
)
(1)
extreme and severe 3-parameter critical power model
t
=
W�
P
−
CP
+
W�
CP
−
Pmax
(2)
Severe 2-parameter critical power model
P
(t)=
W�
t
+
CP
(3)
extreme, severe and heavy Peronnet and Thibault model
Pmap
(t)=MAP −A×Ln
(
t
MAPTTF )
;t>MAP
TTF
(4)
Omni power duration model
P
(t)=W�
t
×
(
1−e−t×
P
max−
CP
W�
)
+CP;t≤CP
TTF
P
(t)=W�
t×
(
1−e−t×
P
max
−CP
W�
)
+CP −A×Ln
(
t
CP
TTF )
;t>CP
TTF
(5)
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308 European Journal of Applied Physiology (2022) 122:301–316
1 3
2020) has suggested an exponential decay term below the
CP to predict power outputs in the heavy exercise intensity
domain (see Fig.2 and Eqs.4 and 5). However, these decay
terms are not necessarily routed in the underlying physiol-
ogy of fatigue in the heavy and moderate exercise intensity
domains (see Black etal. (2017), Clark etal. (2019) and
Amann (2011) for overviews of possible fatigue mecha-
nisms at these intensities). They do however represent the
best models to date for estimating exercise tolerance below
the CP (see equations in Table1).
Choosing amodelling approach
The authors recommend that coaches and practitioners refer
to the physiological demands of a given discipline or train-
ing modality to guide their choice. They should then select
the model that best predicts the power-duration relationship
across the range of intensities in which athletes will train and
race. For example, the two-parameter CP model (Moritani
etal. 1981; Whipp etal. 1982) overestimates both short-
and long-duration power outputs outside the severe exer-
cise intensity domain (see Fig.4), thus potentially limiting
its utility. To give some practical examples; power outputs
in the team sprint falls exclusively in the extreme exercise
intensity domain, whereas power outputs in the individual
pursuit falls within both the extreme and severe exercise
intensity domains (Gardner etal. 2005). In road cycling a
large proportion of the power output falls within the heavy
and moderate exercise intensity domains (van Erp and de
Koning 2019); however, power outputs in the extreme and
severe exercise intensity domains are more important in
predicting race performance (Menaspà etal. 2017). Longer
duration (ultra) endurance events, for example, ironman dis-
tance triathlons (Laursen 2011) or the ‘Race Across Amer-
ica’ (Hulton etal. 2010) fall within the moderate exercise
intensity domain, as do extensive training sessions in cycling
or triathlon (van Erp etal. 2020b; Laursen 2011). A differ-
ent modelling approach may be required for each of these
examples.
Interestingly some of the aforementioned models are able
to predict exercise tolerance in multiple exercise intensity
domains. Whilst there is a considerable body of evidence
indicating that the physiological responses in each exercise
intensity domain is unique (Burnley and Jones 2007), it
should be noted that most research is derived from exer-
cise intensities that are not in close proximity to the thresh-
olds that define a given exercise intensity domain. Work
by Pethick and colleagues (2020) looking at responses in
proximity to the critical torque (CT) during isolated knee
extension exercise, a proxy for CP, showed that above the
CT participants displayed physiological responses consist-
ent with the severe exercise intensity domain. Likewise,
slightly below the CT physiological responses associated
with the heavy exercise intensity domain were recorded.
Another pertinent example is that research has shown that
although the
̇
V
O2 slow component is a defining characteris-
tic of the heavy exercise intensity domain, a variant of the
slow component, albeit smaller in magnitude, also occurs in
the moderate exercise intensity domain (Davies and Thomp-
son 1986). Whilst a proportion of the change in
̇
V
O2 uptake
may be due to a shift in substrate utilisation, this change
wouldn’t account for the entire increase in
̇
V
O2, suggesting
altered or additional muscle recruitment (Burnley and Jones
2018). Together, these findings suggest that rather than each
exercise intensity domain inducing distinct physiological
responses, there is instead a spectrum of responses across the
power-duration relationship (see Fig.2). Indeed, this would
explain why the power-duration curve is smooth in nature
and doesn’t contain ‘turn-points’ as would be expected if
the thresholds between exercise intensity domains were
indeed ‘hard’ in nature. It may also explain why some of
the aforementioned models are able to predict exercise toler-
ance across intensities in multiple exercise intensity domains
(Fig.2 and Table1).
Combining laboratory andeld testing
Both laboratory and field testing have been used in isola-
tion and in conjunction with each other to investigate physi-
ological and performance capacity in cycling (Gardner etal.
0
200
300
600
900
1200
1500
1800
Power Output (W)
0
5s
30s
1-min
2-min
15-min
40-min
1-h
2-h
4-h
MMPOmPD P&T
2-PCP3-PCP
Fig. 4 Various power duration modelling approaches applied to
the same MMP data. MMP Mean Maximum Power, OmPD Omni
Power Duration model, P&T Peronnet and Thibault model, 2-P CP
two-parameter critical power model, 3-P CP three-parameter critical
power model; horizontal dashed line—critical power asymptote; ver-
tical dashed lines represent the approximate transitions between the
exercise intensity domains (extreme, severe, heavy and moderate)
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309European Journal of Applied Physiology (2022) 122:301–316
1 3
2007; Jobson etal. 2009; Jones and Vanhatalo 2017; Lucia
etal. 2001; Paton and Hopkins 2001).
In cycling, the most commonly reported measures from
laboratory testing include peak power output from sprint-
ing or graded incremental exercise tests,
̇
V
O2max, %
̇
V
O2max,
MAP, fractional utilization of MAP, first and second lactate
or ventilatory thresholds, maximum lactate steady state and
cycling efficiency (Laurent etal. 2007; Lucia etal. 2000;
Mujika and Padilla 2001). Although good agreement exists
between some of these laboratory measures and cycling per-
formance, none of the aforementioned physiological vari-
ables can be used to create a power-duration relationship
as recommended by the authors for the purposes of power
profiling.
As demonstrated before, a critical component of the
power-duration relationship is the border between the
heavy and severe exercise intensity domains; power outputs
at which a steady state can and cannot be achieved (Poole
etal. 2016; Poole etal. 1988). The physiological bound-
ary between these domains has been most associated with
endurance performance (Burnley and Jones 2007; Poole
etal. 1988). For a long time, the maximum lactate steady
state (MLSS) was considered as the gold standard for this
boundary (Billat etal. 2003; Keir etal. 2015; Kilding and
Jones 2005). However, recent work (Galán-Rioja etal. 2020;
Jamnick etal. 2020; Jones etal. 2019; Nixon etal. 2021) has
suggested that CP better estimates the maximal metabolic
steady state, the highest power output where a steady state
in the oxygen uptake (
̇
V
O2) response can still be observed,
despite increasing blood lactate values (Bräuer and Smekal
2020). There is still some debate as to which method (if any)
is superior for differentiating between metabolic steady state
and non-steady state exercise, and whether both MLSS and
CP can actually be used interchangeably (Jones etal. 2019;
Keir etal. 2015; Nixon etal. 2021; Poole etal. 1988).
In applied settings, it has been suggested that an alter-
native approach, namely the functional threshold power
(FTP), can be used as a surrogate for the maximal meta-
bolic steady state: (Mackey and Horner 2021). FTP was
first described as the cycling power output that can be sus-
tained for one hour in a “quasi physiological steady-state”
(Bassett etal. 1999; Coggan 2003; Mackey and Horner
2021). FTP is therefore a surrogate of the 60min MMP.
It has been proposed that FTP can also be predicted either
by taking 95% of the power output in a 20-min maximal
field test (Borszcz etal. 2018; Morgan etal. 2019; Valen-
zuela etal. 2018) or by taking 90% of the power output
in a 8-min maximal field test (Sanders etal. 2020); the
former being commonly used (Valenzuela etal. 2018). In
contrast to CP and MLSS, where multiple determination
trials are required, FTP can be predicted from a single trial
and is, therefore, less time consuming. This time efficient
approach may explain why the concept has been widely
adopted in cycling (Mackey and Horner 2021). However,
whilst CP and MLSS can be considered as estimates of the
maximal metabolic steady state (Keir etal. 2015; Poole
etal. 1988), this cannot be confirmed for FTP (Morgan
etal. 2019). Whilst both MLSS and FTP are single-param-
eter estimates, the CP concept can be used to predict TTF
for a range of power values within the severe exercise
intensity domain and provides an estimate of the border
between metabolic steady state and non-steady state exer-
cise. The same cannot be said for either MLSS or FTP,
which can only predict a single point on the power-dura-
tion relationship, or a border between exercise intensity
domains, but not TTF for a range of power output values.
Physiologically speaking, CP has been shown to represent
the highest power output at which there is no progressive
derangement in the muscle metabolite milieu (Burnley and
Jones 2018); however, instead of a ‘hard’ border, the CP
represents a phase transition between the heavy and severe
exercise intensity domains (Pethick etal. 2020). Mitchell
and colleagues (2018) also reported a strong relationship
between CP and muscle capillary density, underpinning the
aerobic component of CP. Similarly, Vanhatalo etal. (2016)
demonstrated that CP was strongly associated with the per-
centage of highly oxidative type I muscle fibres. Above CP,
in the severe exercise intensity domain a non-metabolic
steady state occurs, characterized by a reduction in intra-
muscular creatine phosphate stores, continuously increasing
concentrations of inorganic phosphate, hydrogen ions and
blood lactate, which are all associated with a reduced con-
tractile function of the working muscle (Allen etal. 2008;
Burnley and Jones 2007, 2018; Jones etal. 2010; Poole etal.
2016, 1988).
Although a strong relationship exists between FTP and
CP estimates (Denham etal. 2020; Karsten etal. 2020; Mor-
gan etal. 2019, Mackey and Horner 2021), and FTP and
MLSS (Borszcz etal. 2019), the cited studies have demon-
strated that the limits of agreement between parameters are
too large for them to be used interchangeably. This ques-
tions the relevance of FTP (Borszcz etal. 2018; Karsten
etal. 2020; Morgan etal. 2019; Valenzuela etal. 2018).
Furthermore, Borszcz and colleagues (2018) demonstrated
that the 95% of 20min power output overestimates 60min
power output, and recommended that 20min power output
alone should be used for training prescription and perfor-
mance monitoring, rather than trying to make estimates
of 60min power output (i.e. FTP). After all, both 20 and
60min power output are arbitrary in nature. However, whilst
FTP might represent an arbitrary value, rather than a physi-
ological threshold, it may still have practical utility in terms
of informing the training process (Valenzuela etal. 2018).
However, to the best of the authors’ knowledge no studies
exist that compare performance outcomes when prescribing
training based on different concepts, i.e. FTP, CP and MLSS.
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310 European Journal of Applied Physiology (2022) 122:301–316
1 3
That said, for the reasons outlined above the authors
consider CP the most useful concept in terms of deriving a
power-duration relationship, and therefore recommend the
use of the CP concept in the field of power profiling.
Deriving theparameters ofpower‑duration
modelling
There is currently no consensus on how best to derive the
parameters that are needed to model the power-duration rela-
tionship; namely Pmax, CP and W′. Likewise, there is consid-
erable debate on which mathematical model should be used
to derive CP and W′ (Maturana etal. 2018; Muniz-Pumares
etal. 2019; Nimmerichter etal. 2020).
Traditionally, performing three to five prediction trials
between 2 and 15min of duration (Karsten etal. 2015; Mat-
urana etal. 2018; Muniz-Pumares etal. 2019) allows CP and
W′ to be derived through weighted least square or geometric
mean linear and nonlinear regression analysis (Vinetti etal.
2017; Vinetti etal. 2020). Prediction trials shorter than 2min
do not ensure the attainment of
̇
V
O2max (i.e. they fall outside
the severe intensity domain) (Hill and Smith 1994; Maturana
etal. 2018; Muniz-Pumares etal. 2019; Nimmerichter etal.
2020), while prediction trials longer than 15min are not
recommended due to the influence of glycogen depletion and
psychological factors (i.e. motivation) (Karsten etal. 2015;
Maturana etal. 2018). To avoid any skewness during the
mathematical modelling and reduce errors in the calculation
of CP and W′ the shortest prediction trial should last between
2 and 5min and the longest prediction trial between 12 and
15min (Karsten etal. 2015; Maturana etal. 2018; Muniz-
Pumares etal. 2019). Inter-trial recovery between prediction
trials should be set to a minimum of 30min during a single
visit or 24h during multiple days (Karsten etal. 2017). The
benefit of multiple days if that any fatigue induced by the
initial prediction trial does not affect the subsequent one, but
possible error due to day-to-day variation in power output
is introduced.
Once the performance trials have been completed the
respective power output and trial duration values can be
used to derive CP and W′. Computing CP and W′ estimates
from a nonlinear two- or three-parameter models requires
access to statistical software to perform a weighted least
square or geometric mean regression analysis (Vinetti
etal. 2017, 2020). To simplify this process for coaches
and practitioners there are two options available to lin-
earize the hyperbolic power-duration relationship (see
Fig.5). Practitioners can either use a) the linear work time
CP model (see Eq.3 and Fig.5c or b) the linear power
inverse of time CP model (see Eq.3 and Fig.5b), where
CP and W′ can be derived as the slope and intercept of
the linear relationship (Clarke and Skiba 2013; Sreedhara
etal. 2019). All mathematical models from Fig.5 provide
a high accuracy for the model fit, but there is a possibility
that the power-duration parameter estimates (CP and W′)
diverge somewhat depending on which fitting method is
used (Muniz-Pumares etal. 2019). As a result, Hill (1993)
suggested that the best fit mathematical model could be
more objectively selected, where the model producing the
lowest standard error of the estimate (SEE) should be the
0200 400600 800
0
300
400
500
600
Time (s)
Poweroutput(W)
0.0000.002 0.0040.006 0.0080.010
0
300
400
500
600
1/Time
Poweroutput(W)
0200 400600 800
0
100000
200000
300000
Time (s)
Work (J)
a
b
c
Fig. 5 Graphical illustration of the power-duration relationship for the
hyperbolic (a), inverse of time (b) and linear work time (c). Model
adopted from Clarke and Skiba (2013)
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311European Journal of Applied Physiology (2022) 122:301–316
1 3
preferred way to derive CP (Hill 1993; Muniz-Pumares
etal. 2019).
CP and W′ parameter estimates can also be derived using
only two prediction trials (Parker Simpson and Kordi 2017).
While this can be seen as a time-efficient testing protocol,
the limitation of this approach is that the linear relation-
ship always results in a perfect fit (R2 = 1.0). In addition, no
parameters for the goodness of fit (i.e., SEE) can be derived.
Therefore, it is recommended to use at least three prediction
trials to ensure a low standard error for CP (2–5%) and W′
(< 10%) (Black etal. 2016; Dekerle etal. 2015). Performing
three prediction trials and using a two-parameter CP model
to fit the data results in one degree of freedom. For instance,
a standard error of 5W for a cyclist with a CP of 385W
would then need to be multiplied by 12.7 to calculate the
95% confidence limits (± 64W) in both directions. Adding a
fourth prediction trial would reduce the CP standard error to
3W and the 95% confidence limits (± 38W) thus improving
the CP predictive ability.
The 3-min all out test has also been proposed as a more
time efficient way to derive CP and W′ (Vanhatalo etal.
2007, 2008). The principal assumption in this test is that W′
or more accurately WEP (work above end test power) as it is
known in this test, is fully depleted within the first 150s and
therefore during the last 30s only CP (end test power) can
be sustained. Despite showing good reliability and validity
compared with traditional CP testing in some circumstances
(Wright etal. 2017), other research in elite cyclists shows
significantly higher CP estimates are derived from the 3-min
all out test than traditional protocols (McClave etal. 2011)
which can lead to overestimation of performance capacity
in the severe exercise intensity domain (Nicolò etal. 2017).
This finding brings into question whether the 3-min all out
test can be used in the field of power profiling.
In some power-duration models (see Table1) Pmax is
an additional input parameter when modelling the power-
duration relationship. Extensive research (Douglas etal.
2021; Driss and Vandewalle 2013; McCartney etal. 1983,
1985) was conducted on the assessment and mechanisms of
Pmax in cycling (Sargeant etal. 1981). Assessing Pmax in the
laboratory or field settings requires a thoughtful reflection
on testing protocols. Recent research used the highest 1s
power output within 4s, 10s and 15s sprints to derive Pmax
(Driss and Vandewalle 2013; Ferguson etal. 2021; Gardner
etal. 2007; Sanders and Heijboer 2019b). If efforts longer
than 10s are used Pmax could be negatively influenced as the
cyclist may apply a pacing strategy (Driss and Vandewalle
2013; Gardner etal. 2007). Practitioners should also be
aware of a “learning effect” during all-out sprint efforts, and
it is therefore recommended that adequate familiarization is
undertaken prior to formal testing of Pmax. Additional impor-
tant factors to consider when testing Pmax in a laboratory
setting are; the torque factor setting (Forbes etal. 2014) and
whether the expected Pmax is within the range of validity of
the power measuring device. For example, a commercially
available smart trainer is only valid up to 700W, which is
much lower than the expected Pmax for some populations
(Zadow etal. 2016).
Ecological validity
Cadence, body position as well as topography, i.e. level
ground or uphill conditions, have also been shown to influ-
ence model parameter estimates due to different biomechani-
cal recruitment patterns (Bertucci etal. 2005; Kordi etal.
2019; Nimmerichter etal. 2012). Therefore, rider specializa-
tion (for example climber vs. time trial specialist) and race
demands (uphill vs. flat, on-road vs. off-road, etc.) need to
be considered in the selection of testing environments (Nim-
merichter etal. 2012). The testing conditions should mirror
the conditions in which athletes are expected to perform.
For example, it is recommended that time trial specialists
perform prediction trials on a time trial bike on level ground,
while climbing specialists conduct testing in uphill condi-
tions on a road bike.
Previous research has also investigated whether time
trials or TTF trials should be favoured as prediction trials
(Coakley and Passfield 2018; Karsten etal. 2018). Tradi-
tionally, TTF trials have been based on a fixed percentage
(i.e. 80–105%) of the power output in a GXT. The main
limitation with this approach being that inter-individual dif-
ferences could influence the trial duration (Jamnick etal.
2020). In contrast, maximum effort time trialling requires a
high level of pacing ability and may therefore only be suit-
able for use with experienced cyclists (Karsten etal. 2018).
However, time trials are inherently easier to perform in field
settings, as Simpson and Kordi (2017) have shown a particu-
larly time-effective protocol using time trials in elite athletes
can produce valid CP and W´ estimates. However, in less
trained participants higher power output values have been
reported in TTF trials resulting in higher CP and W´ estima-
tions (Coakley and Passfield 2018).
As mentioned above, environmental factors should be
considered whenever performing any formal testing. Testing
conditions during formal testing should therefore aim to mir-
ror as closely as possible the competition settings to ensure
environmental validity. To illustrate this point, CP has been
shown to decline significantly as altitude increases, while
W′ only decreased above 4.000m of altitude (Townsend
etal. 2017); heat and humidity have been shown to influ-
ence power outputs in formal testing (Racinais etal. 2015).
Previous research also investigated the influence of
cadence on time trial performance and power-duration
parameter estimates. While CP estimates were higher at
cadences 60 vs. 100 revolutions per minute in recreation-
ally trained individuals (Barker etal. 2006; Carnevale and
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312 European Journal of Applied Physiology (2022) 122:301–316
1 3
Gaesser 1991), no statistically significant differences in
physiological determinants (gross efficiency, energy turno-
ver) were reported at cadences between 80 vs. 100 revolu-
tions per minute in elite cyclists during cycling time trials
(Foss and Hallén 2005). Although higher power outputs can
be achieved at lower cadences, elite cyclists tend to prefer
higher cadences around ~ 90 revolutions per minute despite
reductions in cycling efficiency.
Agreement betweenmodelled
power‑duration relationship andMMP
values
Good agreement between CP estimates derived from for-
mal testing and MMP values has been reported (Leo etal.
2020, 2021a; b; Nimmerichter etal. 2020; Quod etal. 2010).
While a good agreement between CP derived from formal
testing and racing has been shown, the same cannot be
confirmed for W′. Both Leo etal. (2020) and Karsten etal.
(2015) reported low agreement between W´ derived from
formal testing and MMP data. This low agreement may be
due to cyclists not performing maximal efforts in race situ-
ations apart from very specific circumstances (i.e., during
time trials or at the finish of races). If cyclists were to fully
deplete W´ in any other circumstance (i.e. uphill mountain
finish, lead out or tine trial), there is a chance that they may
subsequently not be able to match the power requirement to
follow the peloton. These scenarios have direct implications
on the recorded MMP values thereafter, as they are not as
high as the MMP values recorded earlier in the race (Leo
etal. 2021b). Thus, these efforts are not being captured via
basic MMP analysis per se.
Good agreement has been reported between power out-
puts predicted by the APR model and race-derived MMP
data for short duration power outputs (< 2min) in profes-
sional male cyclists (Sanders etal. 2017; Sanders and Heij-
boer 2019b). However, only limited research exists to verify
if this approach could also be applied to other populations.
Future directions
Although many approaches concerning power profiling have
been developed in the literature, it remains unclear which
approach provides the greatest insight. Arguably, the most
convenient way for practitioners to create a power profile
would be to retrospectively use field derived MMP data
from training and racing over pre-defined durations (Ebert
etal. 2005; Menaspà etal. 2017; Sanders and van Erp 2021;
Vogt etal. 2007b). Although this kind of data may provide
valuable insights into racing demands in highly trained
cyclists, little information can be retrieved in terms of the
power-duration relationship due to the arbitrary selection of
MMP values.
Deriving a comparative measure allows longitudinal
analysis: for example, if a rider records a MMP value in
racing which exceeds the prediction from formal testing,
practitioners can use that information to monitor changes
in the power profile. However, deriving W´ from racing or
field testing has shown poor predictive ability (Karsten etal.
2015; Leo etal. 2021a) questioning the practical utility of
W′ for power profiling purposes. When creating a theoreti-
cal power-duration curve from formal testing, care should
be taken that the appropriate models are used. For example,
application of the CP concept outside the severe exercise
intensity domain involves an overestimation in short MMP
(< 2min) ability and long duration MMP (> 40min) sus-
tainability. For this reason, the APR model provides a use-
ful concept to predict the power-duration relationship in the
extreme exercise intensity domain.
While the power-duration relationship in the severe exer-
cise intensity domain has been well investigated based on
the CP concept (Jones etal. 2010; Poole etal. 2016), limited
research exists on deriving the power-duration relationship
in the moderate and heavy exercise intensity domains (Black
etal. 2017). Hence Puchowicz etal. (2020) and Peronnet
and Thibault (1989) proposed mathematical models with an
aerobic decay term, but limited research exists to assess if
these concepts have a high predictive ability for the power-
duration relationship in the moderate and heavy exercise
intensity domains in relation to the muscle bioenergetic sys-
tem (Korzeniewski 2019; Korzeniewski and Rossiter 2020,
2021; Vanhatalo etal. 2016).
Recent work (van Erp etal. 2021b; Leo etal. 2021b) has
shown a reduction in MMP values as prior work increases.
However, future research is needed to better understand the
mechanisms which lead to alterations in the power-dura-
tion due to fatigue, especially the influence of the exercise
intensity and if work in different exercise intensity domains
induce the same degree of downward shift in the power-
duration curve. This is important as improved performance
capacity, i.e. smaller alterations in the power-duration rela-
tionship, has been positively related to race success (van Erp
etal. 2021b; Leo etal. 2021b).
In the era of big data science a novel approach intro-
duced by Puchowicz (2018) on the Golden Cheetah open
data project (Liversedge 2020) could provide novel insights
into power profiling. Functional principal component anal-
ysis (FPCA) enables an in-depth view of the components
of variability in MMP data between cyclists via eigenfunc-
tions which classify riders on their phenotype (sprinter vs.
climber) and performance level. Currently, however, the use
of FPCA for the purposes of power profiling still requires
adequate scientific validation before any potential findings
can be applied by coaches and practitioners.
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313European Journal of Applied Physiology (2022) 122:301–316
1 3
Practical recommendations inapplied
settings
Based on the current literature and the authors’ experience
conducting power profiling in applied settings, the fol-
lowing recommendations can be made as a starting point
for coaches and practitioners: to derive the parameters
to model a power-duration curve a formal test protocol
should include one sprint effort (i.e. ~ 10–15s) and at least
three maximum efforts between 2 and 15min (Karsten
etal. 2015; Leo etal. 2021a; Muniz-Pumares etal. 2019;
Sanders and Heijboer 2019b). These efforts can be com-
pleted in a single testing session, though it is recom-
mended to divide field testing into two sessions over two
consecutive days. The order of efforts should preferably be
randomized for scientific research or follow the cyclist’s or
coach’s individual preference in applied settings. Inter-trial
recovery between efforts should be set to a minimum of
30min of active recovery (< 2 rating of perceived exer-
tion) (Karsten etal. 2017). CP and W′ should be derived by
the non-linear two-parameter CP model (Muniz-Pumares
etal. 2019), while Pmax should be referred to the 1s peak
power during the ~ 10–15s sprint effort (Sanders and Hei-
jboer 2019b). This protocol will allow coaches and practi-
tioners to derive valid Pmax, CP and W′ estimates. Coaches
can then choose the best modelling approach based on the
exercise intensity domain(s) that are important for race
analysis and training prescription in a given discipline.
Power meters should be verified for accurate and reli-
able measurement and a zero-offset or re-calibration
according to the manufacturer’s recommendations is
recommended.
The authors do not recommend using single effort field
tests (i.e. 8min or 20min TT) to derive the FTP estimate
because it lacks physiological background and only rep-
resents a single point on the power-duration curve. Nor
do they recommend the use of the 3- min all-out test as
this may lead to an overestimation of the power-duration
relationship in the severe exercise intensity domain.
To increase the ecological validity of power profiling
we recommend a careful selection of the power-duration
modelling approach, based on biomechanical and physi-
ological principles. Standardized laboratory and field test-
ing should be conducted in line with performance analysis
from training and racing to increase the practical utility of
performance prediction and training related consequences.
In addition, any formal testing should consider the envi-
ronmental and topographical conditions in which the power
profile information is to be applied in. Therefore, the dura-
tion of the effort, gradient, inter-trial recovery, rider type
specialization (climbers vs. flat specialist) and race demands
(climb vs. time trial) should be replicated as best possible.
Collectively, power profiling provides an advanced
opportunity for performance modelling based on power
output data from training and racing in combination with
traditional laboratory and field-testing methods to maximize
cycling performance.
Acknowledgements We would like to thank Dr. Richard Ferguson and
Mag. Dieter Simon for their theoretical input and assistance in real-
izing this project.
Author contributions PL, JS and IM had the idea of the article. PL, JS
and TP performed the literature search and writing and and graphical
illustration. JS, TP, JL and IM critically revised the manuscript.
Funding Open access funding provided by University of Innsbruck
and Medical University of Innsbruck. No funding was received for the
preparation of this manuscript.
Availability of data and material Not applicable.
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