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UNCORRECTED PROOF
Gait & Posture xxx (2018) xxx-xxx
Contents lists available at ScienceDirect
Gait & Posture
journal homepage: www.elsevier.com
Prediction of power output at di`erent running velocities through the two-point
method with the Stryd™power meter
Felipe García-Pinillosa, ⁎, Pedro Á. Latorre-Románb, Luis E. Roche-Seruendoc, Amador García-Ramosd, e
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ARTICLE INFO
*=;36)7
Endurance runners
Linear regression
Power output
Two-Velocity method
ABSTRACT
'(/,6392) The force- and power-velocity (F–V and P–V, respectively) relationships have been extensively stud-
ied in recent years. However, its use and application in endurance running events is limited.
!*7*'6(- 59*78.32 This study aimed to determine if the P–V relationship in endurance runners ^ts a linear model
when running at submaximal velocities, as well as to examine the feasibility of the “two-point method”for esti-
mating power values at different running velocities.
*8-3)7 Eighteen endurance runners performed, on a motorized treadmill, an incremental running protocol to
exhaustion. Power output was obtained at each stage with the Stryd™power meter. The P–V relationship was
determined from a multiple-point method (10, 12, 14, and 17 km·h−1) as well as from three two-point methods
based on proximal (10 and 12 km·h−1), intermediate (10 and 14 km·h−1) and distal (10 and 17 km·h−1) velocities.
!*79087 The P–V relationship was highly linear ( 6= 0.999). The ANOVAs revealed significant, although gener-
ally trivial (effect size < 0.20), differences between measured and estimated power values at all the velocities
tested. Very high correlations ( 6= 0.92) were observed between measured and estimated power values from the
4 methods, while only the multiple-point method ( 62 = 0.091) and two-point method distal ( 62 = 0.092) did not
show heteroscedasticity of the error.
".,2.B('2(* The two-point method based on distant velocities (i.e., 10 and 17 km·h−1) is able to provide power
output with the same accuracy than the multiple-point method. Therefore, since the two-point method is quicker
and less prone to fatigue, we recommend the assessment of power output under only two distant velocities to
obtain an accurate estimation of power under a wide range of submaximal running velocities.
1. Introduction
Testing endurance athletes is essential for determining how they
are adapting to their training program, understanding individual re-
sponses to training, assessing fatigue and the associated need for re-
covery, and minimizing the risk of nonfunctional overreaching, in-
jury, and illness [1,2]. The use of incremental tests for detecting adap-
tations to training, predicting performance and determining training
zones (i.e., thresholds) in endurance runners is quite ex
tended [2]. The term ‘threshold’refers to the level at which abrupt
changes in the dynamic of any parameter occur in response to a stim-
ulus. For instance, the blood lactate threshold concept has been used
to de^ne the exercise intensity at which there is a non-linear increase
in lactate concentration [3]. Likewise, the heart rate during incre-
mental exercise is sigmoidal, with a linear component in the mid-
dle and a plateau close to the maximal workloads [4]. The non-lin-
ear dynamic of these commonly used parameters makes dif^cult its
prediction and utilization for prescribing training intensity. The iden-
ti^cation of variables that change linearly together with the in
⁎Corresponding author at: Department of Physical Education, Sports and Recreation, Universidad de La Frontera, Calle Uruguay, 1980, Temuco, Chile.
1'.0 '))6*77*7 fegarpi@gmail.com (F. García-Pinillos); platorre@ujaen.es (P.Á. Latorre-Román); leroche@usj.es (L.E. Roche-Seruendo); amagr@ugr.es (A. García-Ramos)
https://doi.org/10.1016/j.gaitpost.2018.11.037
Received 22 May 2018; Received in revised form 22 July 2018; Accepted 29 November 2018
Available online xxx
0966-6362/ © 2018.
Full length article
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'6(@' .2.0037*8'0 '.8 37896* <<< <<<<<<
crease in intensity might facilitate the prescription of training intensity.
The force-velocity (F–V) and load-V (L–V) are two important rela-
tionships that follow a linear ^t (the higher the force and load, the lower
the velocity) [5,6]. The assessment of the F–V relationship allows to de-
termine the athletes force and velocity de^cits [7,8], while the L–V rela-
tionship enables to estimate the one-repetition maximum [9,10]. There-
fore, both relationships provide valuable information that can be used to
prescribe individualized resistance training programs. The typical pro-
cedures used to determine the F–V and L–V relationships are based on
the application of multiple loads (at least 4), which provide a wide
range of force and velocity data that can be modelled through a lin-
ear regression [11,12]. However, since this procedure is time consuming
and prone to fatigue, Jaric [13] proposed that, due to the high linear-
ity of the F–V and L–V relationships, the application of only two loads
could be enough to accurately determine these relationships. The name
“two-point method”has been proposed to describe the testing proce-
dure in which an individual linear relationship is modelled from only
two data points (e.g., two different loads or velocities), while the name
“multiple-point method”is used when more than two loads or velocities
are applied [14].
Such a time-ef^cient method (i.e., ‘two-point method') has been
proved to be valid and accurate for determining the F–V and L–V re-
lationships during a variety of resistance training exercises [9,15,16],
cycling [17–19] and running [11,12,20]. Of note, in all the aforemen-
tioned studies subjects were required to exert maximum values of force
against all the tested loads, obtaining a linear F–V relationship and a
parabolic power-V (P–V) relationship. However, during an incremental
running test (i.e. submaximal intensities), the resistance (i.e. runners´
body mass) is constant and, therefore, a linear P–V is expected. If this
rationale is con^rmed (i.e. the P–V relationship obtained from differ-
ent treadmill velocities turns out to be approximately linear), a simpli-
^ed method for its assessment might be used (i.e., ‘two-point method'
[20]), but no data is available regarding the feasibility of the two-point
method during submaximal efforts.
Once discussed the importance of the information provided by the
F–V and P–V relationships, now the point is how to measure them.
Traditionally, force data during running has been obtained using spe-
ci^c instrumented treadmills [21]. Despite the high accuracy of instru-
mented treadmills, most coaches do not have easy access to such expen-
sive equipment. In an attempt to provide an easier access to the F–V
and P–V relationships, Samozino et al. [12] proposed a method to es-
timate them from only anthropometric and spatiotemporal data during
an overground sprint acceleration, but this method is not applicable to
submaximal velocities. Fortunately, the development of inertial motion
units to quantify performance have been considerably developed in re-
cent years and, today, some devices provide power data during running
(e.g. Stryd™or Runscribe™).
To ^ll the aforementioned gaps in the literature, an incremental run-
ning protocol to exhaustion was performed by trained endurance run-
ners and power output recorded with the Stryd™power meter was av-
eraged at each stage to determine the P–V relationship using a multi-
ple-point method (10, 12, 14, and 17 km·h−1) as well as three two-point
methods based on proximal (10 and 12 km·h−1), intermediate (10 and
14 km·h−1) and distal (10 and 17 km·h−1) velocities. This study aimed to
determine if the power-velocity (P–V) relationship in endurance runners
^ts a linear model when running at submaximal velocities, as well as to
examine the feasibility of the “two-point method”for estimating power
values at different running velocities.
2. Methods
'68.(.4'287
Eighteen recreationally trained male endurance runners (age range:
19–46 years; age: 34 ± 7 years; height: 1.76 ± 0.05 m; body mass:
70.5 ± 6.2 kg) voluntarily participated in this study. All participants
met the inclusion criteria: (1) older than 18 years old, (2) able to run
10 km in less than 40 min, (3) training on a treadmill at least once per
week, (4) not suffering from any injury (points 3 and 4 related to the last
6 months before the data collection). After receiving detailed informa-
tion on the objectives and procedures of the study, each subject signed
an informed consent form in order to participate, which complied with
the ethical standards of the World Medical Association’s Declaration of
Helsinki (2013). It was made clear that the participants were free to
leave the study if they saw ^t. The study was approved by the Institu-
tional Review Board.
63(*)96*7
Subjects were individually tested on one day. The testing session
started with the collection of anthropometric data. Then, participants
performed an incremental running test on a motorized treadmill (HP
cosmos Pulsar 4 P, HP cosmos Sports & Medical, Gmbh, Germany). The
initial speed was set at 8 km.h−1, and speed increased by 1 km.h−1every
3 min until exhaustion [22]. The slope was maintained at 1% in order
to reproduce the effects of air resistance and try to obtain results as sim-
ilar as possible to ^eld conditions [23]. The treadmill protocol was pre-
ceded by a standardized 10-min accommodation program (5 min walk-
ing at 5 km.h−1, and 5 min running at 10 km.h−1). Participants were ex-
perienced in running on a treadmill but anyway, previous studies on hu-
man locomotion have shown that accommodation to a new condition
occurs in ~6-8 min [24,25].
'8*6.'07 '2) 8*78.2,
For descriptive purposes, body height (cm) and body mass (kg) were
determined using a precision stadiometer and weighing scale (SECA 222
and 634, respectively, SECA Corp., Hamburg, Germany). All measure-
ments were taken with the participants wearing underwear. Body mass
index (BMI) was calculated from the subjects' body mass and height
(kg. m−2).
Power output (in W) was estimated with the Stryd™power me-
ter (Stryd Power meter, Stryd Inc. Boulder CO, USA). Stryd™is a rel-
atively new carbon ^bre-reinforced foot pod (attached to the shoe)
that weights 9.1 g. Based on a 6-axis inertial motion sensor (3-axis gy-
roscope, 3-axis accelerometer), this device provides twelve metrics to
quantify performance: pace, distance, elevation, running power, form
power, cadence, ground contact time, vertical oscillation, leg sti`ness.
To the best of the authors´ knowledge, just one study has examined
its validity and reliability (in this case, to measure spatiotemporal gait
characteristics [26]), with no data to demonstrate validity and relia-
bility of this device to measure power and related variables. For this
study, only two out of twelve metrics (running velocity and power out-
put) were used. Those variables were obtained from Stryd´s website
(https://www.stryd.com/powercenter/analysis) into the. ^t ^le. Then,
data were analyzed using the publically available software (Golden
Cheetah, version 3.4) and exported as. csl ^le. Those ^les were im-
ported from Excel® (2016, Microsoft, Inc., Redmond WA) and laps
were done every 3 min. Twenty seconds were removed from each stage
(10 s at the beginning and 10 s at the end) in order to avoid data
close to changes in running velocity. Mean and
2
UNCORRECTED PROOF
'6(@' .2.0037*8'0 '.8 37896* <<< <<<<<<
standard deviation (SD) were calculated for those variables at each
stage. Therefore, power output was obtained at each stage from
8 km·h−1to exhaustion (range: 16-20 km·h−1). Four methods were con-
sidered in the present study to estimate power output at different run-
ning velocities: (1) multiple-point method (10, 12, 14, and 17 km·h−1),
(2) two-point method proximal (10 and 12 km·h−1), (3) two-point
method intermediate (10 and 14 km·h−1), and (4) two-point method dis-
tal (10 and 17 km·h−1) (Fig. 1). Velocities lower than 10 km·h-1 were ex-
cluded from the models because resulted uncomfortable for trained en-
durance runners, while velocities higher than 17 km·h−1were excluded
from the models because some runners did not reach those levels during
the protocol.
"8'8.78.('0 '2'0=7.7
Descriptive data are presented as means and standard deviation,
while the Pearson's correlation coef^cient ( 6) are presented through
their median values and ranges. Normal distribution for all variables
(Shapiro–Wilk test) and the homogeneity of variances (Levene's test)
were con^rmed (4> 0.05). The 6coef^cient was used to evaluate the
strength of the individual P–V relationships. A 1-way repeated-mea-
sures analysis of variance (ANOVA) with Bonferroni post hoc tests
was applied at each velocity condition to compare the measured val-
ues of power against the values of power obtained from the 4 es-
timation methods (i.e., multiple-point method, two-point method
Fig. 1. Power-velocity relationship obtained for a representative participant. The individ-
ual points represent the power values recorded against 10 different velocities. The black
points denote the velocities that were used for the 4 estimation methods (multiple-point
method: 10, 12, 14, and 17 km·h−1, two-point method proximal: 10 and 12 km·h−1,
two-point method intermediate: 10 and 14 km·h−1, and two-point method distal: 10 and
17 km·h−1). Note that the regression lines of the two-point method distal are not easily ap-
preciated due to their high overlap with the multiple-point method.
proximal, two-point method intermediate, and two-point method dis-
tal). To further explore the validity of the 4 estimation methods, the 6
coef^cient and the Cohen's )effect size (ES) were calculated between
the measured power and the values of power obtained from the 4 es-
timation methods. The scale used to interpret the magnitude of the ES
was speci^c to training research: negligible (<0.2), small (0.2–0.5),
moderate (0.5–0.8), and large (≥0.8) [27]. Finally, Bland-Altman plots
were constructed to examine the presence of systematic and propor-
tional bias between the measured and estimated values of power. Het-
eroscedasticity of error was de^ned as an 62 > 0.1 [28]. Significance
was accepted at 4≤0.05. All statistical analyses were performed using
the software package SPSS (IBM SPSS version 22.0, Chicago, IL, USA).
3. Results
The strength of the P–V relationship was very high (6= 0.999
[0.994, 1.000]). The ANOVAs revealed significant differences between
the measured and the estimated values of power at all the velocities
analysed (Table 1). However, most of the ES comparing the measured
and estimated values of power were trivial (ES < 0.2) with the only
exception of the two-point method proximal that overestimated power
outputs at high velocities (see Fig. 2; lower panel). The magnitude of
the correlations between the measured power and the power values es-
timated from the 4 methods was very high for the individual velocities
(Fig. 2) as well as when the data of all velocities were pooled (Fig. 3).
Bland–Altman plots revealed heteroscedasticity of error for the
two-point method proximal ( 62 = 0.139) and for the two-point method
intermediate ( 62 = 0.128) with increasing differences in favour of the
estimated power at higher running velocities, while heteroscedasticity
of error was not observed for the multiple-point method ( 62 = 0.091)
and two-point method distal ( 62 = 0.092) (Fig. 4).
4. Discussion
This study explored the possibility of predicting power outputs at
different running velocities from the recording of power values un-
der only two velocity conditions ("two-point method"). The use of the
two-point method to estimate power output at different running veloc-
ities is justi^ed by the strong linearity observed in the current study
for the P–V relationship. Despite that the three two-point methods ex-
amined in this study were able to provide valid estimations of power
output, the two-point method based on distant veloci
Table 1
Comparison of the measured values of power against the values of power obtained from the 4 estimation methods.
Velocity
(km·h−1)
ANOVA
(Snedecor's
F)
Measured power
(W)
Multiple-point method
(W)
Two-point method proximal
(W)
Two-point method intermediate
(W)
Two-point method distal
(W)
11
(n = 18)
10.3* 217.1 ± 18.8 216.1 ± 19.1 216.1 ± 19.0 215.7 ± 19.1* 215.4 ± 19.1*
13
(n = 18)
7.9* 252.2 ± 22.3 250.4 ± 22.0* 251.9 ± 22.0 250.7 ± 22.2* 249.7 ± 22.1*
15
(n = 18)
5.5* 285.2 ± 25.6 284.6 ± 25.1 287.6 ± 25.1 285.7 ± 25.4 284.0 ± 25.2
16
(n = 18)
6.0* 301.8 ± 27.0 301.7 ± 26.7 305.5 ± 26.7 303.2 ± 27.1 301.1 ± 26.7
18
(n = 17)
5.7* 334.4 ± 30.5 334.9 ± 30.5 340.2 ± 30.5 337.0 ± 31.0 334.4 ± 30.6
19
(n = 11)
5.0* 339.1 ± 31.4 340.5 ± 29.8 347.7 ± 30.6 344.2 ± 31.2 339.7 ± 29.7
20 (n =6) 3.6* 343.3 ± 26.8 346.7 ± 29.0 349.4 ± 27.1 347.3 ± 27.8 346.7 ± 29.3
Mean ± standard deviation.
*denotes a signi^cant F value and signi^cant di`erences respect to the measured power (4< 0.05).
3
UNCORRECTED PROOF
'6(@' .2.0037*8'0 '.8 37896* <<< <<<<<<
Fig. 2. Pearson's correlation coef^cients (upper panel) and Cohen's )effect size (lower
panel) between the measured and the estimated values of power from the multiple-point
method (^lled circle), two-point method proximal (empty circle), two-point method inter-
mediate (^lled triangle) and two-point method distal (empty triangle) at different running
velocities. Effect size = (estimated power mean –measured power mean) / SDboth.
ties (i.e., 10 and 17 km·h−1) provided the most accurate estimations,
especially at high running velocities. It is important to note that the
two-point method distal was able to provide power output with the
same accuracy than the multiple-point method.
As we earlier mentioned, the validity and reliability of the two-point
method has been tested during a wide variety of resistance training ex-
ercises [9,15,16]. Zivkovic et al. [15] tested twelve participants during
functional movement tasks against multiple loads, and an almost perfect
level of agreement between the routinely used “multiple-point method”
and a simple “two-point method”was reported. Some previous stud-
ies also used the two-point method during cycling [18,19,29]. In a re-
cent work, García-Ramos et al. [29] aimed to determine the two opti-
mal resistive forces for testing the F–V relationship in cycling. The ex-
periment involved twenty-six men, who were tested on maximal sprints
performed on a leg cycle ergometer against 5 _ywheel resistive forces
(R1–R5), and the authors concluded that the two-point method in cy-
cling should be based on 2 distant resistive forces (R1-R4). This ^nd-
ing, consistent with the current study, was reinforced by an interven-
tion study from the same research group [19]. In this case, the au-
thors reported that speci^c changes on the F–V parameters during a cy-
cling-based training program can be accurately monitored by applying
just two distinctive resistances during routine testing. Despite method-
ological differences, these previous studies are in line with the current
^ndings, showing that the two-point method (with distant loads) accu-
rately predicts the F–V and P–V relationships in protocols and exercises
where variables are linearly, or close to, related.
Despite the bene^ts attributed to the two-point method, in terms
of time and effort [13,14], limited evidence has examined the possi-
bility to apply this method to running. Some previous studies have
applied the multiple-load method to determine the F–V relationship
during maximal runs (i.e. sprints) [11,12]. Cross et al. [11] deter-
mined the F–V relationship from the velocity recorded against a range
of sled-resisted sprints [11], whereas Samozino et al. [12] used
Fig. 3. Relationship between the measured and the estimated values of power from the multiple-point method (upper-left panel), two-point method proximal (upper-right panel),
two-point method intermediate (lower-left panel) and two-point method distal (lower-right panel). The regression equation and the Pearson's coef^cient of determination ( 62) are depicted.
4
UNCORRECTED PROOF
'6(@' .2.0037*8'0 '.8 37896* <<< <<<<<<
Fig. 4. Bland–Altman plots showing differences between the measured power and the values of power estimated from the multiple-point method (upper-left panel), two-point method
proximal (upper-right panel), two-point method intermediate (lower-left panel) and two-point method distal (lower-right panel). Each plot depicts the averaged difference and 95% limits
of agreement (dashed lines), along with the regression line (solid line) (n = 106). 62, Pearson's coef^cient of determination.
the anthropometric and spatiotemporal data recorded during an un-
loaded sprint [12]. Despite it seems well established that multi-joint
functional tasks typically reveal strong and approximately linear F–V re-
lationship patterns [5], a mistake would be committed if results from
the aforementioned studies were compared to those reported by the cur-
rent work. With maximum values of force against a tested load (i.e.
maximal sprint), the higher the force the lower the velocity, obtaining
a linear F–V relationship and a parabolic P–V relationship. However, in
the current study performed at submaximal intensity, the resistance (i.e.
runners´ body mass in this case) is constant and, therefore, the P–V re-
lationship is linear.
To the best of the authors´ knowledge, no previous studies have
tested the feasibility of using the two-point method to determine the
F–V or P–V relationship during running at submaximal intensities (com-
monly used for endurance runners in training and competition). Do-
brijevic et al. [20] tested 28 physically active subjects on their max-
imum pulling force exerted horizontally while walking or running on
a treadmill set to different velocities (5–12 km.h−1), and concluded
that the F–V relationship could be strong, linear, and reliable at ve-
locities tested, and the “two-velocity method”could provide reliable
and ecologically valid indices of force, velocity, and power. Before
comparing their ^ndings with the current study some points need to
be considered. First, based on the aforementioned rationale, the ap-
plication of their maximum pulling F while walking or running en-
sures a linear F–V relationship and a parabolic P–V relationship what
differs from our study, obtaining a linear P–V relationship. Second,
the methodological differences according to the population involved
(physically active vs. trained endurance runners) and the velocities
tested (~5-12 km·h-1 vs. ~8-21 km·h-1) makes the comparison dif^cult.
Despite those differences, the results reported provide sup
port to the feasibility of using the two-point method to estimate the
power output during running at a wide range of velocities. The current
study is focused on endurance runners and suggests that the assessment
of power output, easy-to-obtain data with new devices such as Stryd™
power meter, under only two distant velocities (i.e., 8 and 17 km·h-1)
provided the most accurate estimations - with the same accuracy than
the multiple-point method. From a practical standpoint, this informa-
tion might be crucial for coaches. Con^rmed the linear P–V relationship
during submaximal runs, any interval workout (including distant veloc-
ities) might be enough to update the P–V pro^le during running and,
therefore, give coaches information about adaptations to the training
program (monitoring) and work capacity almost on a daily basis (peri-
odization and training design).
Finally, some limitations must be addressed. The validity and reli-
ability of the power output data from the Stryd™system is still un-
known. However, a recently published book [30] indicated that the
external mechanical power (W/kg) reported by this system is highly
correlated (R2 = 0.96) with metabolic cost (VO2 in ml/kg/min). It
is a relatively new device and more research is clearly needed to de-
termine its potential. Other point to consider, though not necessar-
ily a limitation, is related to the protocol itself. This is an incremen-
tal test to exhaustion, which means that high levels of fatigue are en-
sured at the end of the protocol. Since the duration that exercise can
be maintained decreases as the power requirements increase, and vice
versa [31], the fatigue induced might in_uence on the power out-
put if compared with data from just two-point methods (i.e., 10 and
17 km·h−1as proposed in the current study). Notwithstanding these
limitations, the current work highlights the linear P–V relationship
during running in a wide range of submaximal intensities (typically
performed in training and competition contexts), as well as con^rms
5
UNCORRECTED PROOF
'6(@' .2.0037*8'0 '.8 37896* <<< <<<<<<
the effectiveness of the two-point method based on distant velocities
(i.e., 10 and 17 km·h−1) for accurately estimating P–V pro^le.
In conclusion, the results obtained in the current study show that the
two-point method based on distant velocities (i.e., 10 and 17 km·h−1) is
able to provide power output with the same accuracy than the multi-
ple-point method. The data reported also indicate a strong linearity for
the P–V relationship. Therefore, since the two-point method is quicker
and less prone to fatigue, we recommend the assessment of power out-
put under only two distant velocities to obtain an accurate estimation of
power under a wide range of submaximal running velocities.
Authors' contributions
FGP: analysis and interpretation of data and drafting the article;
PALR: conception and study design, acquisition data, revising the manu-
script critically; LERS: conception and study design, acquisition data, re-
vising the manuscript critically; AGR: conception and study design, ac-
quisition data, revising the manuscript critically. All authors have read
and approved the ^nal version of the manuscript, and agree with the or-
der of presentation of the authors.
Con#ict of interests
The authors declare that they have no con_ict of interests.
Declarations of interest
None.
Acknowledgements
The authors would like to thank to all the participants.
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