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Journal of Sports Sciences
ISSN: 0264-0414 (Print) 1466-447X (Online) Journal homepage: http://www.tandfonline.com/loi/rjsp20
The anaerobic power reserve and its applicability
in professional road cycling
Dajo Sanders & Mathieu Heijboer
To cite this article: Dajo Sanders & Mathieu Heijboer (2018): The anaerobic power reserve and its
applicability in professional road cycling, Journal of Sports Sciences
To link to this article: https://doi.org/10.1080/02640414.2018.1522684
Published online: 13 Oct 2018.
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The anaerobic power reserve and its applicability in professional road cycling
Dajo Sanders
a,b
and Mathieu Heijboer
c
a
Physiology, Exercise and Nutrition Research Group, University of Stirling, Stirling, UK;
b
Sport, Exercise and Health Research Centre, Newman
University, Birmingham, UK;
c
Team LottoNL-Jumbo professional cycling team, Amsterdam, Netherlands
ABSTRACT
This study examined if short-duration record power outputs can be predicted with the Anaerobic Power
Reserve (APR) model in professional cyclists using a field-based approach. Additionally, we evaluated if
modified model parameters could improve predictive ability of the model. Twelve professional cyclists
(V
O
2max
75 ± 6 ml∙kg
−1
∙min
−1
) participated in this investigation. Using the mean power output during
the last stage of an incremental field test, sprint peak power output and an exponential constant
describing the decrement in power output over time, a power-duration relationship was established for
each participant. Record power outputs of different durations (5 to 180 s) were collected from training
and competition data and compared to the predicted power output from the APR model. The originally
proposed exponent (k = 0.026) predicted performance within an average of 43 W (Standard Error of
Estimate (SEE) of 32 W) and 5.9%. Modified model parameters slightly improved predictive ability to a
mean of 34–39 W (SEE of 29 –35 W) and 4.1 –5.3%. This study shows that a single exponent model
generally fits well with the decrement in power output over time in professional cyclists. Modified
model parameters may contribute to improving predictability of the model.
ARTICLE HISTORY
Accepted 6 September 2018
KEYWORDS
Performance; endurance;
cycling; power output
Introduction
Competitive road cycling is predominantly an endurance-
based aerobic sport (Lucia, Hoyos, & Chicharro, 2001).
However, it’s conceivable that decisive moments within a
competition also require the cyclists to possess a high anae-
robic capacity. The ability to generate high power outputs
over a short period of time is a decisive performance para-
meter in cycling to close a gap, break away from the pack or
win a sprint (Abbiss, Menaspa, Villerius, & Martin, 2013;
Rønnestad & Mujika, 2013). High-intensity interval training
(HIT) has been shown to improve both indices of aerobic
and anaerobic capacity in well-trained cyclists (Laursen,
Shing, Peake, Coombes, & Jenkins, 2005; Lindsay et al., 1996).
Therefore, besides low-intensity aerobic training, HIT is also an
important part of cyclists’training programme to prepare
optimally for key moments in the race and to improve the
physiological potential of the athlete (Laursen & Jenkins,
2002). There are several measures proposed in the literature
with which to prescribe exercise intensity for intervals during
HIT such as a power output, heart rate or rating of perceived
exertion (Buchheit & Laursen, 2013b). Given the well-known
lag in heart rate response at the onset of exercise, and the
decreased heart rate recovery response during accumulated
intervals (Buchheit & Laursen, 2013b), heart rate may be less
applicable as a measure to monitor and/or prescribe intensity
during HIT, especially for short duration intervals (< 3 min). In
contrast, power output provides a direct and objective mea-
sure of exercise intensity (Sanders, Myers, & Akubat, 2017).
Ranges in power output for supramaximal HIT intervals (i.e.
training at intensities > power output at VO
2max
) are typically
estimated based on functional threshold power (FTP) or power
output at VO
2max
(Allen & Coggan, 2010; Billat, 2001; Laursen &
Jenkins, 2002). However, two cyclists with a similar power
output at VO
2max
can have significantly different sprint peak
power outputs (Sanders, Heijboer, Akubat, Meijer, & Hesselink,
2017; Weyand, Lin, & Bundle, 2006). As such, if the intensity of
a HIT session is exclusively based on an “aerobic marker”(e.g.
intervals at 130% of power output at VO
2max
) the athlete with
the higher sprint peak power output has to work at a lower
percentage of their maximal capacity, potentially resulting in a
different physiological demand and exercise tolerance
(Buchheit & Laursen, 2013b).
The anaerobic reserve could be useful in individualising
exercise intensity for HIT. In cycling, the anaerobic power
reserve (APR) is defined as the difference between maximal
sprint peak power output and power output at VO
2max
(Weyand et al., 2006). Studies have used the anaerobic reserve
range to set out the minimal and maximal values of a short-
duration power-duration curve (Bundle, Hoyt, & Weyand, 2003;
Sanders et al., 2017; Weyand & Bundle, 2005; Weyand et al.,
2006). Subsequently, an exponential decay model is used to
describe the decrement in power output over time. The
obtained power-duration curve can be used to predict
power output over all-outs efforts lasting from a few seconds
to a few minutes (Sanders et al., 2017; Weyand et al., 2006).
This is a similar approach to the critical power (CP) model
(Poole, Burnley, Vanhatalo, Rossiter, & Jones, 2016), however,
the CP model mainly applies to longer duration performances
(approximately 3 –45 min) while the APR model focuses on
short-duration performance (5 –300 s). The APR model is
based on the assumption that the decrement in (cycling)
CONTACT Dajo Sanders. dajosanders@gmail.com Physiology, Exercise and Nutrition Research Group, University of Stirling, Stirling, United Kingdom
JOURNAL OF SPORTS SCIENCES
https://doi.org/10.1080/02640414.2018.1522684
© 2018 Informa UK Limited, trading as Taylor & Francis Group
power output over time in humans, irrespective of between-
individual differences in absolute power outputs, is the same
when this is expressed in relation to their anaerobic reserve
(Bundle et al., 2003; Weyand et al., 2006).
Bundle and colleagues (Bundle et al., 2003; Bundle &
Weyand, 2012; Weyand & Bundle, 2005; Weyand et al., 2006)
used the anaerobic reserve model to predict performance
during all-out efforts of different durations in runners and
cyclists. To date, most studies have used recreationally active
runners (Bundle et al., 2003; Bundle & Weyand, 2012; Weyand
& Bundle, 2005) or cyclists (Weyand et al., 2006) in a laboratory
setting. However, in elite environments, field-testing is more
representative of the athlete’s environment and often more
valued by coaches and practitioners as field tests are easier to
implement in to daily practice. Recently, in a preliminary pilot
study, we presented four case studies on the applicability of
the APR model in professional cyclists using a field-based
approach (Sanders et al., 2017). It was shown that the power
output predicted by the model was very largely to nearly
perfectly correlated to the actual power output obtained dur-
ing all-out time trials for each cyclist (r = 0.88 –0.97). Even
though these results should be considered promising, it still
remains questionable how well the model would fit a larger
group of (elite) athletes. However, the implementation of
multiple all-out time trials to a professional cyclists’training
plan would be too intrusive and would limit the possibility to
collect data with a larger pool of athletes. Therefore, the
record power outputs (Allen & Coggan, 2010; Pinot &
Grappe, 2011) over short-durations (5 –180 s) achieved during
training and competitions can be assessed and would provide
the possibility to collect a substantial dataset that provides an
indication of short-duration performance of the cyclists.
Therefore, the aim of this study was to test the ability of
the APR model in predicting record power outputs achieved
during training and racing in professional cyclists using a field-
based approach. In addition, this study aims to evaluate if
modifications to the previously established exponential con-
stant (k = 0.026) (Weyand et al., 2006) or modifications in the
parameters used to determine the anaerobic power reserve
could improve predictive ability of the APR model in this
cohort of professional cyclists.
Methods
Participants
Twelve professional cyclists from a Union Cycliste
Internationale (UCI) World-Tour professional cycling team par-
ticipated in this investigation (mean ± SD:age 29 ± 5 y, height
1.81 ± 0.06 m, body mass 72.3 ± 5.3 kg, V
O
2max
74.6 ± 5.9 ml∙kg-
−1
∙min
−1
). Participants were informed of the purpose and pro-
cedures of the investigation. Institutional ethics approval was
granted and in agreement with the Helsinki Declaration.
Testing
Every cyclist performed an incremental field test protocol
(Sanders et al., 2017) during a January training camp. The
protocol consisted of 6 times 6 min blocks on uphill terrain
(mean gradient of 4.8%). The cyclists were advised to main-
tain a set power output during the 6 min intervals with the
defined power output increasing with every interval (mean
increment of 23 ± 9 W per interval). The absolute power
output and stage increments were based on pre-season
laboratory testing (data not shown). After the 6 min interval
the riders had 6–10 min active recovery (< 55% of power
output at 4 mmol∙L
−1
) before starting the next interval. The
last effort was a 6 min all-out performance; mean power
output during this 6 min bout was used as the lower bound
of the anaerobic power reserve (PO
incr
). Previous research
has typically used power output at V
O
2max
as the lower
bound of the anaerobic reserve, however since we used a
field-basedprotocol,weadoptedadifferentapproach.
Nevertheless, studies have shown that all-out performances
of ~ 5 min largely correlates to power at V
O
2max
as time to
exhaustion at V
O
2max
varies between 4–8 min (Berthon et al.,
1997; Hill & Rowell, 1996). Power output and cadence were
measured (1 Hz) using a mobile ergometer system (Pioneer
Power Meter, Kawasaki, Kanagawa, Japan). Riders were
instructed to perform zero-offset procedures prior to each
training session or stage according to manufacturers’
instructions. Sprint power output (PO
sp
) was defined as the
peak power output the cyclists could achieve during all-out
sprints in the field during training sessions, measured as a 1-
second peak power output. The sprints were performed as
10 s “flying sprints”with the cyclist already riding at
30–35 km· h
−1
and the sprints were performed with a self-
selected cadence.
Original anaerobic power reserve approach
With PO
sp
and PO
incr
as the maximal and minimum values of
the curve, a power-duration relationship was established for
each subject individually (Bundle & Weyand, 2012). This rela-
tionship was set using the following formula (Equation (1);
Bundle et al., 2003):
POt¼POincrþPOsp POincr
eðktÞ(1)
Where tis the duration of the all-out trial, PO
t
is the power
output maintained for that trial with a duration of t,PO
incr
is
the mean power output during the last stage of the incre-
mental test, PO
sp
is the sprint peak power output, eis the base
of the natural logarithm and kis the exponent that describes
the decrement in power output over time. The exponential
time constant (k= 0.026) is based on the previously estab-
lished exponential power-duration curve fitted through data
in recreationally active cyclists (Weyand et al., 2006) and tested
in professional cyclists (Sanders et al., 2017).
Modified approaches
In addition to the original modelling approach described
above, four modified approaches were adopted to evaluate
if predictive ability could be improved with modified model
parameters. In “Modified Approach 1”, the lowest bound of
the anaerobic reserve (PO
incr
) was replaced with record power
output over 3 min (PO
3min
) achieved during the study period
(Equation (2)).
2D. SANDERS AND M. HEIJBOER
POt¼PO3minþPOsp PO3min
eðktÞ(2)
In “Modified Approach 2”, the original exponential decay con-
stant (k
1
= 0.026) was replaced with a modified exponent (k
2
).
In order to evaluate if the previously established exponential
time decay constant could be optimised, an iterative best-fit
approach was adopted for every participant using their mea-
sured record power outputs, assessed values for PO
incr
and
PO
sp
and Equation (1). The iterative best-fit approach was
performed using a least-squares analysis in which an optimal
time decay constant could be determined for every individual
by aiming to minimise the residual sum of squares (RSS; sum
of the squared differences) between predicted power output
by the model and record power outputs. Based on the optimal
individual exponential decay constants, a general time decay
constant was established by taking the mean of the individual
constants, a similar approach to previous studies (Weyand &
Bundle, 2005; Weyand et al., 2006). The modified constant
calculated using this approach was k
2
= 0.0244 ± 0.0053. In
addition, this procedure was repeated for Equation (2) with
PO
3min
as the lowest anchor point in the iterative process
instead of PO
incr
. The modified constant (k
3
) calculated using
this approach was k
3
= 0.0277 ± 0.0061. In “Modified Approach
3”, both the modified lowest bound of the anaerobic reserve
(PO
3min
) as well as exponential decay constant k
2
were
adopted. Lastly, “Modified Approach 4”used PO
3min
as the
lower bound of the anaerobic reserve and exponential decay
constant k
3
.
Record power outputs
In the four months following the incremental exercise test
protocol, record power outputs of different durations achieved
during training and competitions were obtained for each
cyclist, using previously described methods (Allen & Coggan,
2010; Pinot & Grappe, 2011). The chosen durations for the
record power outputs were: 5, 10, 15, 30, 45, 60, 90, 120, 150
and 180 seconds, respectively. Measured record power out-
puts were compared with the power output predicted by the
APR modelling approaches.
Statistical analysis
Record power outputs achieved over the different durations
during training and racing was compared to the predicted
power outputs by the original approach and Modified
Approach 1,2,3 and 4 using a multilevel random intercept
model with Tukey’s method for pairwise comparisons, using
the statistical package R (R: A Language and environment for
statistical computing, Vienna, Austria). To account for indivi-
dual differences in absolute power outputs, random effect
variability was modelled using a random intercept for each
individual participant. Level of significance was established at
P< 0.05. Standardised effect size is reported as Cohen’sd,
using the pooled standard deviation as the denominator.
Qualitative interpretation of dwas based on the guidelines
provided by Hopkins, Marshall, Batterham, and Hanin (2009): 0
–0.19 trivial; 0.20 –0.59 small; 0.6 –1.19 moderate; 1.20 –1.99
large; ≥2.00 very large. Standard Error of Estimate (SEE) was
calculated to evaluate the accuracy of the predictions between
modelled and record power output provided by the regres-
sion. Bland-Altman plots including mean bias and 95% limits
of agreement were used to visually represent the differences
between record power outputs and predicted power outputs.
The limits of agreement were calculated according to the
recommendations by Bland and Altman (2007).
Results
Absolute and relative mean power output during the last
stage of the incremental test (PO
incr
), PO
3min
and sprint peak
power output (PO
sp
) as well as the anaerobic reserve can be
found in Table 1. Mean and maximal cadence during the 10 s
sprints was 103 ± 10 rev∙min
−1
and 113 ± 12 rev∙min
−1
.PO
sp
were achieved at a cadence of 103 ± 9 rev∙min
−1
.
A total of 1647 training and race files were analysed for the
12 participants, averaging 137 ± 22 sessions per participant.
Record power outputs varying from 5 up to 180 seconds were
collected for every individual over the course of the study
period. Mean cadence during the 5 and 10 s record power
outputs (102 ± 7 and 101 ± 7 rev∙min
−1
, respectively) was
moderately to largely higher (d= 0.95 –1.88) compared to
cadences during the 30 –180 s record power outputs (mean
cadence ranging between 87 –93 rev∙min
−1
). Trivial to small
differences were observed for most cadences achieved
between 30 –180 s record power outputs (d= 0.01 –0.58)
with only the cadence for 45 s record power output (93 ± 9
rev∙min
−1
) being moderately higher (d= 0.80) compared to
cadence at the 150 s record power output (85 ± 11 rev∙min
−1
).
The predictive ability of the APR model using the original
approach and the four modified approaches proposed in this
study are presented in Table 2. Using the previously estab-
lished exponential decay constant (k=0.026), record power
outputs remained within an average of 5.9% and an average
of 43 W of the predicted power output by the model (SEE
32 ± 19 W, R
2
= 0.97). Figure 1 presents the record power
outputs compared to the predicted line of identity (i.e. pre-
dicted power output = actual power output) by the APR
model using the original approach as well as the respective
Bland-Altman plot. Predictive ability of the APR model was
slightly improved using the modified approaches with mean
deviation between predicted power output and record power
output being lower in the modified approaches (d=0.22 –
0.56, ES = small). Figure 2 presents the record power outputs
Table 1. The field-derived mean power output during the last stage of the
incremental test, record power output over 3 min and sprint peak power output
achieved by the participants.
n = 12 Mean ± SD Range
Mean PO during the last stage of
incremental test (PO
incr
) (W)
458 ± 29 401 –505
Mean PO during the last stage of
incremental test (PO
incr
)(W∙kg
−1
)
6.35 ± 0.39 5.69 –7.05
Record PO over 3min (PO
3min
) (W) 500 ± 43 440 –563
Record PO over 3min (PO
3min
)(W∙kg
−1
) 6.92 ± 0.26 6.56 –7.36
Sprint peak PO (PO
sp
) (W) 1254 ± 153 1064 –1635
Sprint peak PO (PO
sp
)(W∙kg
−1
) 17.37 ± 1.84 15.80 –22.71
APR for PO
incr
(W) 796 ± 141 622 –1150
APR for PO
3min
(W) 753 ± 111 602 –1141
Abbreviations: PO, power output; APR, anaerobic power reserve
JOURNAL OF SPORTS SCIENCES 3
Table 2. Predictive ability of the Anaerobic Power Reserve model with the original and modified approaches.
Original model
PO
incr
PO
sp
k
1
= 0.026
Modified Approach 1
→PO
3min
PO
sp
k
1
= 0.026
Modified Approach 2
PO
incr
PO
sp
→k
2
= 0.0244
Modified Approach 3
→PO
3min
POsp
→k
2
= 0.0244
Modified Approach 4
→PO
3min
POsp
→k
3
= 0.0277
Participant
Mean deviation
(W) SEE (W) Mean deviation (W) SEE (W)
Mean deviation
(W) SEE (W)
Mean deviation
(W) SEE (W)
Mean deviation
(W) SEE (W)
1 4816 25 15381622164416
2 4932 29 29423630323027
3 6724 30 22562021183927
4 6223 28 19542840242017
5 2322 27 21292635262017
6 1717 14 16161822171017
7 6476 80 71728285697166
8 3352 33 52335736573248
9 4651 47 51395036494552
10 42 14 31 13 33 18 33 18 38 12
11 30 36 32 34 30 41 41 40 25 29
12 33 19 31 18 30 23 33 22 33 16
Mean ± SD 43 ± 16 32 ± 19 34 ± 16 30 ± 18 39 ± 15 35 ± 20 36 ± 17 32 ± 18 34 ± 16 29 ± 17
Mean deviation 5.9% ± 2.5% 4.3% ± 2.0% 5.3% ± 2.2% 4.6% ± 2.1% 4.1% ± 1.9%
Abbreviations: PO
incr
, mean power output over the last 6 min stage of the incremental field tests; PO
sp
, maximal sprint peak power output; PO
3min
, record power output over 3 min; SEE, standard error of estimate; SD, standard
deviation; k
1
, exponential decay constant proposed by Weyand et al. (2006); k
2
, modified exponential decay constant determined with the individual best fits to the record power outputs using Equation (1); k
2
, modified
exponential decay constant determined with the individual best fits to the record power outputs using Equation (2)
4D. SANDERS AND M. HEIJBOER
compared to the predicted line of identity (i.e. predicted
power output = actual power output) (R
2
= 0.96 –0.97) by
the APR model using the four modified approaches (A –D) as
well as their respective Bland-Altman plots (E -H).
Record power outputs achieved during the training and
races and predicted power outputs by different modelling
approaches are presented in Table 3 and the respective plots
of predicted and actual power output for a participant are
presented in Figure 3. The multilevel model analysis revealed
no significant differences (P> 0.75) between record power
outputs and predicted power output by the modelling
approaches, for all durations. Trivial to small differences
(d= 0.03 –0.56) were observed when comparing predicted
power output by the original approach to record power out-
put over durations varying from 5 to 60 s, whilst these differ-
ences were moderate (d= 0.59 –1.01) for power outputs over
durations from 90 to 120 s. Trivial to small differences (d= 0.08
–0.30) were observed when comparing record power output
to predicted power output by Modified Approach 1, over all
durations. For Modified Approach 2, trivial to small differences
(d= 0.09 –0.29) were observed for durations from 5 to 90 s,
whilst the difference were moderate (d= 0.75 –0.93) for
durations 120 to 180 s. For Modified Approach 3, a moderate
difference (d= 0.65) was observed between record power
output and predicted power output over a duration of 45 s,
whilst all the other durations showed trivial to small differ-
ences (d= 0.04 –0.52). For Modified Approach 4, trivial to
small differences (d= 0.03 –0.30) were observed comparing
record power output to predicted power output, over all
durations.
Discussion
This study aimed to test the ability of the APR model in
professional cyclists in predicting record power outputs
achieved during training and competitions over different
durations (5 –180 s). In addition, it was examined if mod-
ified model parameters could improve predictive ability of
the APR model. Firstly, it was shown that in professional
cyclists, short-duration performance achieved in training
and competitions can be predicted from field-based mea-
surements of the maximal sprint peak power and mean
power output during the last stage of an incremental test,
using the original APR model (k= 0.026). The single expo-
nent model generally fits well with the decrement in power
versus duration for this elite athlete population. In addition,
it was shown that adjusting model parameters, such as a
modified exponential constants or modified lowest bound of
the anaerobic reserve (i.e. PO
3min
), led to slight improve-
ments in predictive ability.
Using the originally proposed exponential constant
(k= 0.026) the APR model predicted the short-duration per-
formances within an average of 43 W and 5.9%. The predictive
ability of the model in this study is found to be slightly better
than our previously reported predictive ability of 6.6% and
53 W in a smaller cohort of professional cyclists (Sanders
et al., 2017). Furthermore, its predictive ability is lower com-
pared to the previously determined predictive ability of the
model in running (3.7% and 2.6%) (Bundle et al., 2003;
Weyand & Bundle, 2005) and slightly higher compared to
predictability previously reported for cycling performance
(6.6%) (Weyand et al., 2006). The described accuracy of the
model is within an average of 43 W whilst Weyand et al. (2006)
showed a slightly lower mean deviation of 34 W. In addition,
the proposed modified exponential constant (k
2
= 0.0244),
based on an iterative best-fit procedure, improved overall
predictive ability of the model slightly. The modified constant
predicted performance within a mean of 34 W and 4.3%
suggesting that the methods used to obtain a modified expo-
nential constant can improve the overall predictability of the
APR model. Interestingly, it was shown that using different
lower bounds of the anaerobic reserve (i.e. PO
3min
vs PO
3min
)
resulted in different “optimal”exponents (k
3
= 0.0277 vs
k
2
= 0.0244) when applying the iterative best-fit procedures,
with one being higher and one being lower than the originally
proposed exponent (k
1
= 0.026). This suggests that the expo-
nent may vary depending on what measure as the lowest
bound of the anaerobic reserve is used. When applying
Modified Approach 4, which uses both a modified lowest
bound of the anaerobic reserve (i.e. PO
3min
) and the modified
exponent (k
3
= 0.0277) based on Equation (2), predictive
ability was also improved (34 W, 4.1%) compared to the
original model (43 W, 5.9%).
Modifying the lowest bound of the anaerobic reserve
from PO
incr
to PO
3min
had the biggest impact on improving
the predictive ability of the model. Expectedly, this occurred
Figure 1. Record power output versus those predicted by the APR model using the original approach (a) and Bland-Altman plot (b), displaying bias (black line) and
95% limits of agreement (grey lines), comparing record power output for the different durations versus those predicted by the APR model using the original
approach.
JOURNAL OF SPORTS SCIENCES 5
at the lower intensity end of the power duration curve (90 –
180 s). Whilst moderate differences were observed between
record power output achieved over durations of 90 to 180 s
and power output predicted by the original model (d=0.59
–1.01) these differences were trivial to small when PO
3min
was used as the lowest anchor point (d=0.13–0.29)
(“Modified Approach 1”). These results may suggest that
using PO
3min
as the lowest bound of the anaerobic reserve
in the APR model could be preferred in professional cyclists.
This further suggests that the applicability of the APR model
in predicting power outputs over durations longer than
180 s is most likely minimal. Therefore, the APR model
should be considered as a potential tool for predicting and
monitoring performance (progression) within the investi-
gated durations (5 –180 s). When aiming to predict perfor-
mance of durations longer than 3 min, the CP model might
be considered favourable.
Substantial between-individual differences in mean devia-
tion between predicted power output by the APR model and
the record power outputs achieved in competition were
observed (Table 2). It must be recognised that using a general
exponential value for the decrement in power output over
Figure 2. Record power output versus those predicted by the APR model using modified approach 1 (a), modified approach 2 (b), modified approach 3 (c) and
modified approach 4 (d) and Bland-Altman plots, displaying bias (black line) and 95% limits of agreement (grey lines), comparing record power output for the
different durations versus those predicted by modified approach 1 (e), modified approach 2 (f), modified approach 3 (g) and modified approach 4 (h).
6D. SANDERS AND M. HEIJBOER
time across multiple individuals will always result in the model
suiting one individual better than the other based on indivi-
dual differences in power-duration decrement. Similar to the
methodology used in this study, predictive ability could be
improved with an exponential decay constant specific to the
individual, determined using a least squares analysis. However,
such an approach would only be possible if a substantial
amount of (recent) data is available for that cyclist on their
record power outputs over a variety of durations. It is also
important to acknowledge that, as shown within the results,
the exponent may change depending on what lowest bound
of the anaerobic reserve is used. If no data is available for a
particular athlete, it would be advised to use a general expo-
nential constant (e.g. k= 0.026) first and adjust the exponent,
if needed, when a substantial amount of data on their record
power outputs has been collected.
There are some limitations that need to be considered with
this study. Firstly, the record power outputs achieved during the
competitions are assumed to be all-out performances, it is how-
ever hard to determine if that is really the case. Race tactics and
Table 3. Record and predicted power outputs over different durations as well as the predicted power outputs by the original model and four modified approaches.
Original model
PO
incr
PO
sp
k
1
= 0.026
Modified Approach 1
→PO
3min
PO
sp
k
1
= 0.026
Modified Approach 2
PO
incr
PO
sp
→k
2
= 0.0244
Modified Approach 3
→PO
3min
POsp
→k
2
= 0.0244
Modified Approach 4
→PO
3min
POsp
→k
3
= 0.0277
Record power output
(W)
Predicted power output
(W)
Predicted power output
(W)
Predicted power output
(W)
Predicted power output
(W)
Predicted power output
(W)
5 s 1210 ± 134 1173 ± 132 1177 ± 133 1179 ± 134 1183 ± 134 1170 ± 135
10 s 1110 ± 116 1086 ± 118 1095 ± 120 1096 ± 120 1105 ± 121 1083 ± 120
15 s 1013 ± 107 1009 ± 105 1023 ± 107 1023 ± 107 1030 ± 105 1008 ± 106
30 s 831 ± 69 831 ± 75 853 ± 80 849 ± 78 871 ± 82 835 ± 78
45 s 714 ± 66 711 ± 56 739 ± 63 729 ± 59 756 ± 66 722 ± 61
60 s 661 ± 69 629 ± 44 662 ± 54 646 ± 45 677 ± 55 646 ± 52
90 s 560 ± 47 536 ± 33 574 ± 46 548 ± 35 584 ± 46 563 ± 45
120 s 529 ± 44 494 ± 30 533 ± 43 501 ± 30 539 ± 44 528 ± 42
150 s 508 ± 44 474 ± 29 514 ± 43 479 ± 29 518 ± 43 512 ± 42
180s 500 ± 42 465 ± 29 506 ± 43 468 ± 29 508 ± 43 506 ± 42
Abbreviations: PO
incr
, mean power output over the last 6 min stage of the incremental field tests; PO
sp
, maximal sprint peak power output; PO
3min
, record power
output over 3 min; k
1
, exponential decay constant proposed by Weyand et al. (2006); k
2
, modified exponential decay constant determined with the individual best
fits to the record power outputs using Equation (1); k
2
, modified exponential decay constant determined with the individual best fits to the record power outputs
using Equation (2)
Figure 3. Power-duration curves of participant 2 showing the predicted power outputs (line) by the modelling approaches using modified approach 1 (a), modified
approach 2 (b), modified approach 3 (c) and modified approach 4 (d) compared to record power outputs achieved in training and racing (open dots).
JOURNAL OF SPORTS SCIENCES 7
pacing strategy as well as the influence of fatigue (e.g. during
multiday stage races; Rodriguez-Marroyo, Villa, Pernia, & Foster,
2017) play an important role in the performance capability ofthe
cyclists. However, by analysing a large number of training and
competitions and determining the record power outputs they
achieved over all those sessions, the influence of some of these
limitations will be minimised. In addition, record power outputs
were collected in the four months following the assessment of
PO
sp
and PO
incr
. It must be acknowledged that shifts in these
parameters can be expected (e.g. increase in PO
incr
or suppres-
sion of PO
sp
due to heavy training and/or racing) over the course
of this period. However, within this current framework, irrespec-
tive of potential changes in the model parameters, the APR
modelling approaches were able to predict record power out-
puts within a reasonable accuracy in the four months following
the testing. After this period, retesting would be advised to
potentially adjust model parameters and predict power output
in the months following this retesting.
Practical applications
More research is needed regarding the actual practical appli-
ance of this model in elite cycling, however the possible
advantages that could come with the use of this model with
regards to HIT prescription are promising. The lower (e.g.
PO
3min
) and upper bound (PO
sp
)oftheanaerobicreserve
can be determined using two rather simple field test.
Subsequently, using the APR model, a power-duration
curve from 5 to ~ 180 s can be established for each athlete
individually. When applying HIT, a consideration should be
made with regards to different work to rest ratios and the
impact these may have on adaptation (Buchheit & Laursen,
2013a,2013b). For example, a professional cyclist could be
preparing for a hilly one-day race which is characterised by
short hills of durations varying from 60 to 180 s and the
coach would like to implement specific intervals at these
durations to optimally prepare the athletes for the demands
of the race. The APR model could be used to predict record
power output over the interval durations, if not known for
this athlete, and interval intensity could be based on a
certain proportion of that record power output. Especially
when the aim is to remain a steady performance over every
interval (i.e. no big decreases in power output comparing
the first and last interval due to fatigue) and when wanting
to individualise the demand of the HIT sessions across the
team, such an approach could be valuable. Especially in
cycling, with multiple specialities (Lucia et al., 2001;Padilla,
Mujika, Cuesta, & Goiriena, 1999) and varying competition
elements (Mujika & Padilla, 2001;Padillaetal.,1999), the
APR model may contribute to help coaches set the correct
intensities and work to rest ratios to achieve differing com-
petition goals.
Conclusion
To conclude, this study builds on the promising evidence of using
the APR model as a tool to predict short duration (5 –180 s)
cycling performance. The decrement in all-out performance dur-
ing high-intensity cycling seems to conform to a general
relationship with a single exponent appearing to be sufficient to
describe the decrement in power versus duration. It is also shown
that by using record power output over 3 min as a model para-
meter in the model, predictive ability of the model can be
improved. In addition, by using an iterative least-squares method,
modified exponents for a specific population of athletes can be
identified to improve overall predictive ability of the model. The
determination of an APR-range may contribute to the individuali-
sation of training intensity and demand during HIT.
Acknowledgments
No sources of funding were used to compose this article. The authors
have no conflicts of interest that are related to the described content of
this manuscript. We would like to thank the cyclists for their participation
in this investigation.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
No sources of funding were used for this study.
References
Abbiss, C. R., Menaspa, P., Villerius, V., & Martin, D. T. (2013). Distribution of
power output when establishing a breakaway in cycling. International
Journal of Sports Physiology and Performance,8(4), 452–455.
Allen, H., & Coggan, A. R. (2010). Training and racing with a power meter
(2nd ed.). Boulder, CO: Velopress.
Berthon, P., Fellmann, N., Bedu, M., Beaune, B., Dabonneville, M., Coudert,
J., & Chamoux, A. (1997). A 5-min running field test as a measurement
of maximal aerobic velocity. European Journal of Applied Physiology and
Occupational Physiology,75(3), 233–238.
Billat, L. V. (2001). Interval training for performance: A scientific and
empirical practice. Special recommendations for middle- and long-dis-
tance running. Part II: Anaerobic interval training. Sports Medicine,31(2),
75–90.
Bland, J. M., & Altman, D. G. (2007). Agreement between methods of
measurement with multiple observations per individual. Journal of
Biopharmaceutical Statistics,17, 571–582.
Buchheit, M., & Laursen, P. B. (2013a). High-intensity interval training,
solutions to the programming puzzle. Part II: Anaerobic energy, neuro-
muscular load and practical applications. Sports Medicine,43(10), 927–
954.
Buchheit, M., & Laursen, P. B. (2013b). High-intensity interval training,
solutions to the programming puzzle: Part I: Cardiopulmonary empha-
sis. Sports Medicine,43(5), 313–338.
Bundle, M. W., Hoyt, R. W., & Weyand, P. G. (2003). High-speed running
performance: A new approach to assessment and prediction. Journal of
Applied Physiology,95(5), 1955–1962.
Bundle, M. W., & Weyand, P. G. (2012). Sprint exercise performance: Does
metabolic power matter? Exercise and Sport Sciences Reviews,40(3),
174–182.
Hill, D. W., & Rowell, A. L. (1996). Significance of time to exhaustion during
exercise at the velocity associated with VO2max. European Journal of
Applied Physiology and Occupational Physiology,72(4), 383–386.
Hopkins, W. G., Marshall, S. W., Batterham, A. M., & Hanin, J. (2009).
Progressive statistics for studies in sports medicine and exercise
science. Medicine and Science in Sports and Exercise,41(1), 3–13.
Laursen, P. B., & Jenkins, D. G. (2002). The scientific basis for high-intensity
interval training: Optimising training programmes and maximising per-
formance in highly trained endurance athletes. Sports Medicine,32(1),
53–73.
8D. SANDERS AND M. HEIJBOER
Laursen, P. B., Shing, C. M., Peake, J. M., Coombes, J. S., & Jenkins, D. G.
(2005). Influence of high-intensity interval training on adaptations in
well-trained cyclists. Journal of Strength and Conditioning research/
National Strength & Conditioning Association,19(3), 527–533.
Lindsay, F. H., Hawley, J. A., Myburgh, K. H., Schomer, H. H., Noakes, T. D., &
Dennis, S. C. (1996). Improved athletic performance in highly trained
cyclists after interval training. Medicine and Science in Sports and
Exercise,28(11), 1427–1434.
Lucia, A., Hoyos, J., & Chicharro, J. L. (2001). Physiology of professional
road cycling. Sports Medicine,31(5), 325–337.
Mujika, I., & Padilla, S. (2001). Physiological and performance character-
istics of male professional road cyclists. Sports Medicine,31(7), 479–
487.
Padilla, S., Mujika, I., Cuesta, G., & Goiriena, J. J. (1999). Level ground and
uphill cycling ability in professional cycling. Medicine and Science in
Sports and Exercise,31(6), 878–885.
Pinot, J., & Grappe, F. (2011). The record power profile to assess perfor-
mance in elite cyclists. International Journal of Sports Medicine,32(11),
839–844.
Poole, D. C., Burnley, M., Vanhatalo, A., Rossiter, H. B., & Jones, A. M. (2016).
Critical power: An important fatigue threshold in exercise physiology.
Medicine and Science in Sports and Exercise,48(11), 2320–2334.
Rodriguez-Marroyo, J. A., Villa, J. G., Pernia, R., & Foster, C. (2017).
Decrement in professional cyclists’performance after a grand tour.
International Journal of Sports Physiology and Performance,1–23.
[Epub ahead of print]. doi:10.1123/ijspp.2016-0294
Rønnestad, B. R., & Mujika, I. (2013). Optimizing strength training for
running and cycling endurance performance: A review. Scandinavian
Journal of Medicine & Science in Sports,24(4), 603–612.
Sanders, D., Heijboer, M., Akubat, I., Meijer, K., & Hesselink, M. K. (2017).
Predicting high-power performance in professional cyclists.
International Journal of Sports Physiology and Performance,12(3), 410–
413.
Sanders, D., Myers, T., & Akubat, I. (2017). Training-intensity distribution in
road cyclists: Objective versus subjective measures. International
Journal of Sports Physiology and Performance,12(9), 1232–1237.
Weyand, P. G., & Bundle, M. W. (2005). Energetics of high-speed running:
Integrating classical theory and contemporary observations. American
Journal of Physiology. Regulatory, Integrative and Comparative
Physiology,288(4), 956–965.
Weyand, P. G., Lin, J. E., & Bundle, M. W. (2006). Sprint performance-
duration relationships are set by the fractional duration of external
force application. American Journal of Physiology. Regulatory,
Integrative and Comparative Physiology,290(3), 758–765.
JOURNAL OF SPORTS SCIENCES 9
