Citation: Bascuas, P.J.; Gutiérrez, H.;
Piedraﬁta, E.; Rabal-Pelay, J.; Berzosa,
C.; Bataller-Cervero, A.V. Running
Economy in the Vertical Kilometer.
Sensors 2023, 23, 9349. https://
doi.org/10.3390/s23239349
Academic Editor: Nicola Francesco
Lopomo
Received: 16 October 2023
Revised: 16 November 2023
Accepted: 17 November 2023
Published: 23 November 2023
Copyright:
© 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed
under
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terms
and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
sensors
Article
Running Economy in the Vertical Kilometer
Pablo Jesus Bascuas
, Héctor Gutiérrez
, Eduardo Piedraﬁta
, Juan Rabal-Pelay
, César Berzosa *
and Ana Vanessa Bataller-Cervero
Facultad de Ciencias de la Salud, Universidad San Jorge, Autov. A-23 Zaragoza-Huesca,
50830 Villanueva de Gallego, Spain; pbascuas@usj.es (P.J.B.); hgutierrez@usj.es (H.G.); epiedraﬁta@usj.es (E.P.);
jrabal@usj.es (J.R.-P.); avbataller@usj.es (A.V.B.-C.)
* Correspondence: cberzosa@usj.es
Abstract: New and promising variables are being developed to analyze performance and fatigue in
trail running, such as mechanical power, metabolic power, metabolic cost of transport and mechanical
efﬁciency. The aim of this study was to analyze the behavior of these variables during a real vertical
kilometer ﬁeld test. Fifteen trained trail runners, eleven men (from 22 to 38 years old) and four women
(from 19 to 35 years old) performed a vertical kilometer with a length of 4.64 km and 835 m positive
slope. During the entire race, the runners were equipped with portable gas analyzers (Cosmed K5)
to assess their cardiorespiratory and metabolic responses breath by breath. Signiﬁcant differences
were found between top-level runners versus low-level runners in the mean values of the variables of
mechanical power, metabolic power and velocity. A repeated-measures ANOVA showed signiﬁcant
differences between the sections, the incline and the interactions between all the analyzed variables,
in addition to differences depending on the level of the runner. The variable of mechanical power
can be statistically signiﬁcantly predicted from metabolic power and vertical net metabolic COT. An
algebraic expression was obtained to calculate the value of metabolic power. Integrating the variables
of mechanical power, vertical velocity and metabolic power into phone apps and smartwatches is a
new opportunity to improve performance monitoring in trail running.
Keywords: performance monitoring; energy expenditure; human movement; trail running
1. Introduction
Over the past decade, there has been a signiﬁcant increase in interest in sport ﬁeld
applications, driven by both users and technological companies. This interest has been
propelled by advancements in the development of wearable sensors based on micro-
electromechanical systems (MEMSs) [1]. These sensors ﬁnd application during training
sessions and sports competitions, serving the purpose of monitoring the internal training
load [2], scheduling workouts and tracking the athlete’s ﬁtness level progression. To
achieve this objective, it is essential to develop automated assessment methods that analyze
highly accurate variables capable of reﬂecting the physiological, metabolic, biomechanical
and neuromuscular state of the athlete. Additionally, these methods should be easily
implemented in low-cost sensors, such as inertial measurement units, linear transducers,
potentiometers and global navigation satellite systems, among others [3].
Trail running races have increasingly gained the interest of amateur and professional
runners around the world due to their great accessibility and low economic cost. Speciﬁcally,
the vertical kilometer is a trend in trail running. In this modality, the athletes must complete
a course of an approximately 1000 m vertical climb in a maximum of 5000 m total race
length, although these parameters could change between different races, according to the
rules of the International Skyrunning Federation [4].
Research on key performance parameters, both in road and trail running, has been
a growing target of analysis by numerous health and sport science researchers. The aim
of these studies is to understand in more depth those factors correlated with running
Sensors 2023, 23, 9349. https://doi.org/10.3390/s23239349
https://www.mdpi.com/journal/sensors
Sensors 2023, 23, 9349
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performance to later be able to apply this knowledge in the creation of personalized
trackers that can be implemented in phone apps and smartwatches. With technological
advances, many scientists have developed new promising concepts whose assessment
seems to be sensitive to physiological and biomechanical modiﬁcations during running
and which may be suitable real feedback measures of performance and training monitoring
in trail running and vertical kilometers. These concepts are the running economy, the
net metabolic power, the mechanical vertical center of mass power, the net mechanical
efﬁciency, the net metabolic cost of transport and the vertical net metabolic cost of transport.
Running economy is deﬁned as the oxygen uptake (VO2) required to run a given
distance or run at a given submaximal velocity [5]. This parameter can also be deﬁned and
calculated in energy terms as the amount of energy liberated per liter of oxygen, denomi-
nated in this case as net metabolic rate or power (Cmetab) (kcal·min−1·kg−1·or W·kg−1). It
is calculated by measuring the steady-state consumption of oxygen (VO2) and the respira-
tory exchange ratio [6] and is considered a physiological determinant of endurance running.
This variable is multifactorial, depending on metabolic, cardiorespiratory, biomechanical
and neuromuscular factors [7], such as heart rate, minute ventilation, substrate utilization,
muscle ﬁber type and core temperature, among many other variables, and is a new concept
that reﬂects the physiological and neuromuscular state of the athlete [8]. It is currently
considered more sensitive than VO2 itself when used to observe performance differences
between runners [7,9].
The mechanical vertical power of the center of mass (Cmec) is deﬁned as the external
mechanical work performed to lift the body mass at each running stride, calculated by
multiplying the vertical running velocity by the weight of the subject. Recent studies related
to running power have found a linear relationship between running power and aerobic
power (VO2 consumption) [10,11]. In addition, lower limb power is related to running
spatiotemporal improvements (increased contact time), reduction in the energy cost of
running [12] and reduction in the increase in energy cost of running due to fatigue in trail
running [13]. Speciﬁcally, in vertical kilometers, runners must overcome extreme uphill
running slopes, lifting the center of body mass in each step more than in level running
by increasing the net mechanical work. This mechanism entails an increase in energy
expenditure and a poorer mechanical advantage for producing force against the ground by
the hip extensors [14].
Finally, from the previous concepts, the parameters of net mechanical efﬁciency, net
metabolic cost of transport and vertical net metabolic cost of transport have emerged. The
ﬁrst authors to evaluate these parameters were Margaria et al., (1963) [15] and Minetti et al.,
(2002) [16]. They calculated the net metabolic cost of transport (both walking and running)
(cost of walking (Cw) and cost of running (Cr)) by dividing the metabolic power or rate
by running or walking velocity (vertical velocity for the vertical net metabolic cost of
transport (VCw and VCr)). This parameter is a key factor in road running [4] and describes
the amount of energy needed to transport a kilogram of body mass per unit of distance
covered (kcal·kg−1·km−1 or J·kg−1·m−1). In their studies, Margaria et al., (1963) [15] and
Minetti et al., (2002) [16] observed that the metabolic cost of running (Cr) was dependent
on gradient and independent of speed, except for the steepest positive slopes (above 15%
or 8.5◦).
Based on these data, subsequent studies have found a great increase in Cr between
slopes among runners, whose cause is still unknown, since uphill Cr correlates with neither
level Cr nor with biomechanical parameters, such as stride frequency, stride length and
body mass index [17]. Likewise, there is no correlation between either the initial Cr values
or the changes in Cr values before and after the trail running race with performance
time, in contrast to the observed correlation in road running [18]. The increase in Cr with
a positive incline is due to an increase in power output and greater muscular activity
at all joints, especially in the hip [19]. Unlike level running, where the center of mass
behavior oscillates cyclically and both potential and kinetic energy ﬂuctuation are in-phase
during the stride [20], in uphill running above 15% (8.5◦), positive work predominately
Sensors 2023, 23, 9349
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lifts the center of mass and decreases the use of elastic energy (the stretch–shortening cycle
mechanism disappears) and bouncing mechanisms [21,22]. Consequently, the metabolic
demand increases, coinciding with an increase in blood lactate values and cardiorespiratory
values [17,19,23].
In connection with the concepts of mechanical and metabolic power, Margaria et al.,
(1963) [15] and Minetti et al., (2002) [16] also introduced the concept of net mechanical
efﬁciency (Eff) by explaining the ratio of these two variables. In their analysis, they observed
that trained athletes were only 5–7% more efﬁcient than non-athletes [15]. They predicted
that mechanical efﬁciency was approximately 22–24% with positive slopes above 15%
(8.5◦) and 25% above 20% (11.3◦), corresponding to concentric muscle contraction [15,16].
Peyré-Tartaruga et al., (2018) [24] proposed that overall efﬁciency in locomotion (walking
and running) is determined by muscular efﬁciency, deﬁned as the fraction of metabolic
energy transformed into muscular mechanical work, and transmission efﬁciency, deﬁned
as the fraction of muscular mechanical work utilized as total work. However, for practical
purposes, the concept net mechanical efﬁciency (Eff) is considered the fraction of metabolic
power transformed into mechanical power or total work. These authors also contended
that if the efﬁciency value was close to 25% (indicating pure concentric muscle efﬁciency),
it would suggest good efﬁciency transmission. If the value exceeded 25%, it would indicate
that passive elastic elements in series within muscles (fascial tissues) and tendons provided
either the same or signiﬁcant negative work.
Based on the studies analyzed to date, most research has been conducted on a treadmill
in trail running, and any study of the vertical kilometer was executed through a ﬁeld test.
For these reasons, the present study aims to determine the correlation with performance in
the previously mentioned concepts (Cmec, Cmetab, Cw, Cr, Vcw, VCr and Eff), as well as
to observe the effect of fatigue on these concepts during the progress of a vertical kilometer
ﬁeld test.
2. Materials and Methods
2.1. Participants
Fifteen trained trail runners participated in the study (eleven males, four females).
Demographic, anthropometric and training level data are presented in Table 1. All runners
had been training regularly for more than 3 years, and none of them had a history of
musculoskeletal injuries in the last year. Before the experiment, all subjects were informed
about the objectives, beneﬁts and risks of the investigation, and they signed an informed
consent form. The experimental protocol received approval from the University Ethics
Committee (Ref 005-19/20), and all procedures adhered to the principle of the Declaration
of Helsinki.
Table 1. Demographic, anthropometric and training level data.
Men
Women
Age (years)
22–38 *
19–35 *
28.4 ± 5.11
27.7 ± 6.70
Height (cm)
174 ± 4.54
163 ± 2.36
Body mass (kg)
69.8 ± 5.56
54 ± 4.08
BMI (kg/m2)
22.8 ± 1.63
20.2 ± 1.01
Running training duration per session (min)
52 ± 7.58
60 ± 21.6
Running training frequency per week (days/week)
4.40 ± 1.14
4.75 ± 1.26
Pre-test heart rate (bpm)
73.8 ± 10.7
79.5 ± 3.31
HR change (%)
16.1 ± 4.99
61.2 ± 56.6
VO2 peak (mL/kg/min)
65.8 ± 7.00
57.9 ± 6.61
Values: Mean ± SD. BMI: body mass index. HR change: percentage change in heart rate during the vertical
kilometer test. VO2 peak achieved in the vertical kilometer test. *: age range of participants.
Sensors 2023, 23, 9349
4 of 19
2.2. Procedure
Each participant completed a vertical kilometer (VK) route spanning 4.64 km with a
positive slope of 835 m. The vertical kilometer entails a continuous uphill test, comprising
natural segments with varying positive inclinations ranging from 0◦ to 20◦ on this speciﬁc
route. To facilitate analysis, the route was divided into three equal parts, each measuring
1.58 km, as illustrated in Figure 1. Within each of these segments, ﬁve sections with a
constant slope were chosen (0◦, 5◦, 10◦, 15◦, and 20◦ positive slope). Each section had to
last a minimum of 30 s to extract stable physiological data. Furthermore, to ensure data
stability, only the central 20 s of each section were analyzed, excluding the initial and ﬁnal
portions of the positive slope.
Values: Mean ± SD. BMI: body mass index. HR change: percentage change in heart r
vertical kilometer test. VO2 peak achieved in the vertical kilometer test. *: age range o
2.2. Procedure 
Each participant completed a vertical kilometer (VK) route spanning 4.6
positive slope of 835 m. The vertical kilometer entails a continuous uphill test
natural segments with varying positive inclinations ranging from 0° to 20° on
route. To facilitate analysis, the route was divided into three equal parts, eac
1.58 km, as illustrated in Figure 1. Within each of these segments, ﬁve section
stant slope were chosen (0°, 5°, 10°, 15°, and 20° positive slope). Each section
minimum of 30 s to extract stable physiological data. Furthermore, to ensure d
only the central 20 s of each section were analyzed, excluding the initial and ﬁ
of the positive slope. 
 
Figure 1. Vertical kilometer track. Race course divided into 3 sections of 1.58 km. 
2.3. Measurements 
2.3.1. Metabolic Data 
Throughout the entire course, the runners were equipped with a porta
lyzer (Cosmed K5 (Rome, Italy)) to assess cardiorespiratory and metabolic re
breath-by-breath basis. This measurement was facilitated by a turbine ﬂowm
to a properly ﬁtted face mask. The gas analyzer was secured to the runner’s 
harness, and the entire system weighted 900 g. To ensure time alignment, t
parameters from the gas analyzer (including GPS data) were synchronized a
the data logger. Calibration of the Cosmed system was performed before ea
ment, using a calibration syringe (3L) for the turbine. The oxygen (O2) and ca
(CO2) sensors of the gas analyzer were also calibrated to ambient air condit
O2 and 0.03% CO2), along with delay calibration. Each experimental day comm
determining the metabolic rate during a 10-min standing trial. Subsequently
ygen consumption (VO2) and carbon dioxide production (VCO2) were measur
Cosmed K5 analyzer. For statistical analysis, the data for each slope and sect
d
th
l
t d 20
i t
l
1600 m
1400 m
1200 m
1000 m
800 m
Figure 1. Vertical kilometer track. Race course divided into 3 sections of 1.58 km.
2.3. Measurements
2.3.1. Metabolic Data
Throughout the entire course, the runners were equipped with a portable gas analyzer
(Cosmed K5 (Rome, Italy)) to assess cardiorespiratory and metabolic responses on a breath-
by-breath basis. This measurement was facilitated by a turbine ﬂowmeter attached to
a properly ﬁtted face mask. The gas analyzer was secured to the runner’s back using a
harness, and the entire system weighted 900 g. To ensure time alignment, the analyzed
parameters from the gas analyzer (including GPS data) were synchronized and stored in the
data logger. Calibration of the Cosmed system was performed before each measurement,
using a calibration syringe (3L) for the turbine. The oxygen (O2) and carbon dioxide
(CO2) sensors of the gas analyzer were also calibrated to ambient air conditions (20.93%
O2 and 0.03% CO2), along with delay calibration. Each experimental day commenced
with determining the metabolic rate during a 10-min standing trial. Subsequently, rates of
oxygen consumption (VO2) and carbon dioxide production (VCO2) were measured using
the Cosmed K5 analyzer. For statistical analysis, the data for each slope and section were
averaged over the selected 20-s intervals.
Sensors 2023, 23, 9349
5 of 19
2.3.2. Calculations
The calculation of mechanical vertical center of mass (COM) power (Watts/kg) utilized
GPS velocity and incline, as expressed in (Equation (1)):
Mechanical vertical COM power = g × v × sin (θ)
(1)
where θ represents the incline in degrees, and v is the instantaneous velocity in m/s.
Net metabolic power (Watts/kg) was calculated from running respiratory measure-
ments using the Peronnet and Massicot equation [6], adjusted by subtracting the standing
metabolic rate measured 10 min before the test. The calculation is outlined in (Equation (2)):
Net Metabolic power = ((16.89 × VO2 + 4.84 × VCO2)/kg) − standing metabolic rate
(2)
The net mechanical efﬁciency was derived by dividing the mechanical vertical COM
power by the net metabolic power, as illustrated in (Equation (3)) [25]:
Net mechanical efﬁciency = Mechanical vertical COM power/Net metabolic power (3)
The net metabolic cost of transport (J/kg/m) was computed by dividing the net
metabolic power by the running velocity, representing the mean net metabolic cost per unit
distance traveled parallel to the running surface. (Equation (4)) summarizes this calculation:
Net Metabolic COT = Net metabolic power/v
(4)
The vertical net metabolic cost of transport (J/kg/m) was determined by dividing the
net metabolic power by vertical velocity, factored by the mean net metabolic cost to ascend
a vertical meter. (Equation (5)) outlines this computation:
Vertical Net Metabolic COT = Net metabolic power/v × sin (θ)
(5)
2.4. Statistical Analysis
The following statistical analysis of the data was conducted:
•
Normality testing: the Shapiro–Wilk test was used to assess the normality of the variables.
•
Gender and performance level comparison: A T-student parametric test was employed
to compare gender and performance level differences. The sample was divided into
quartiles based on the ﬁnal test time, and values from the ﬁrst quartile were compared
to the remaining quartiles.
•
Comparison of assessed variables: A two-factor repeated-measures ANOVA was
utilized to compare means across multiple analyzed variables. The analysis compared
three sections and ﬁve positive slopes in each section. Before applying ANOVA, the
Mauchly’s sphericity test was performed. If sphericity was rejected, the univariated
F-statistic was used, adjusted with the Greenhouse–Geisser correction index. Bonfer-
roni’s post hoc analysis was performed when signiﬁcant differences were found for
pairwise comparison.
•
Statistical power and effect size determination: The statistical power (SP) and effect
size (partial eta squared, ηp2) were determined. The effect size was categorized as
trivial (ηp2 ≤ 0.01), small (0.01 ≤ ηp2 < 0.06), moderate (0.06 ≤ ηp2 < 0.14) or large
(ηp2 ≥ 0.14) [26].
•
Relationship analysis with ﬁnal uphill time: Multiple regression and correlation
models were calculated using an “intro” method. Mechanical vertical COM power
was considered the dependent variable, and net metabolic power and vertical net
metabolic cost of transport were the independent variables in the three VK sections.
The entry and exit criteria were set at F probabilities greater than 0.05 and 0.10, re-
spectively. The residual linearity and independence assumptions were checked with
the Durbin–Watson test. The homoscedasticity was studied in a partial standardized
Sensors 2023, 23, 9349
6 of 19
residual-standardized prediction plot. The method of Bland and Altman was used to
determine systematic bias and random error in the prediction model, as well as the
lower and upper limits of agreement (1.96 × SD). The multicollinearity was estimated
using a variance inﬂation factor (VIF), with values greater than 10 considered exces-
sive. Inﬂuential cases (Cook’s distance > 1) and atypical cases (residual > 3 standard
deviations) were removed from the analysis.
•
A signiﬁcance level of p < 0.05 was established. All statistical tests were conducted
using the statistical package SPSS version 25.0 (SPSS, Chicago, IL, USA).
3. Results
Mean values for the three sections and ﬁve slope conditions are presented in Table 2.
Regarding gender, no statistical differences were observed. Furthermore, when analyzing
the aforementioned variables based on runner performance level (vertical kilometer ﬁnal
time) (Table 3), signiﬁcant differences emerged between the ﬁrst quartile and the remaining
quartiles in the variables mechanical vertical COM power, net metabolic power, velocity
and vertical velocity. On the other hand, no signiﬁcant differences were identiﬁed in
the variables net mechanical efﬁciency, net metabolic cost of transport and vertical net
metabolic cost of transport.
A repeated-measures ANOVA revealed signiﬁcant differences between sections, in-
cline and the interaction of section x incline in all the variables presented in Table 4. These
ﬁndings indicate a “Large” effect size of fatigue on all variables as the VK progresses.
Additional distinctions are detailed in Table 5 through percentages.
Conducting a two-way ANOVA with performance level as a factor (ﬁrst quartile versus
remaining quartiles), signiﬁcant differences were only identiﬁed in mechanical vertical
COM power (incline p < 0.001, SP = 0.967, ηp2 = 0.320) and vertical velocity (incline p < 0.001,
SP = 0.972, ηp2 = 0.307). No signiﬁcant differences were observed in net metabolic power,
net mechanical efﬁciency, net metabolic COT, vertical net metabolic COT, and velocity. The
percentage of change with corresponding p-values is depicted in Figures 2 and 3.
Sensors 2023, 23, 9349
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Table 2. Descriptive data of values in the three sections and ﬁve slope conditions.
Section 1
Section 2
Section 3
0◦
5◦
10◦
15◦
20◦
0◦
5◦
10◦
15◦
20◦
0◦
5◦
10◦
15◦
20◦
Velocity (m/s)
3.42 ± 0.39
1.98 ± 0.34
1.52 ± 0.19
1.35 ± 0.21
1.00 ± 0.13
2.26 ± 0.38
1.95 ± 0.30
1.40 ± 0.24
1.03 ± 0.14
0.88 ± 0.14
2.39 ± 0.60
1.67 ± 0.27
1.33 ± 0.19
1.00 ± 0.22
0.73 ± 0.16
Vertical velocity
(m/s)
0 ± 0
0.17 ± 0.03
0.26 ± 0.03
0.35 ± 0.05
0.34 ± 0.05
0 ± 0
0.17 ± 0.03
0.24 ± 0.04
0.27 ± 0.04
0.30 ± 0.05
0 ± 0
0.14 ± 0.02
0.23 ± 0.03
0.26 ± 0.06
0.25 ± 0.06
RER
0.94 ± 0.08
0.82 ± 0.08
0.88 ± 0.10
0.90 ± 0.10
0.81 ± 0.08
0.82 ± 0.08
0.81 ± 0.09
0.81 ± 0.08
0.80 ± 0.08
0.80 ± 0.08
0.79 ± 0.08
0.80 ± 0.08
0.78 ± 0.08
0.79 ± 0.07
0.80 ± 0.08
Mechanical
vertical COM
power (W/kg)
0 ± 0
1.69 ± 0.29
2.58 ± 0.32
3.42 ± 0.54
3.38 ± 0.47
0 ± 0
1.67 ± 0.26
2.37 ± 0.40
2.62 ± 0.36
2.94 ± 0.48
0 ± 0
1.42 ± 0.23
2.25 ± 0.33
2.54 ± 0.55
2.46 ± 0.55
Net metabolic
power (W/kg)
17 ± 2.41
17.4 ± 3.10
18.8 ± 2.97
18.7 ± 2.80
17.5 ± 2.69
16.3 ± 2.89
16.4 ± 2.84
16.3 ± 2.93
16.5 ± 2.82
16.3 ± 2.97
15.1 ± 3.33
16 ± 2.92
16.3 ± 2.65
16.7 ± 2.77
16.8 ± 2.91
Net mechanical
efﬁciency
0 ± 0
9.88 ± 1.54
13.9 ± 2.15
18.6 ± 3.10
19.5 ± 2.83
0 ± 0
10.3 ± 1.66
14.8 ± 2.91
16 ± 1.92
18.1 ± 2.05
0 ± 0
9.03 ± 1.37
14.0 ± 1.75
15.6 ± 4.48
14.7 ± 2.23
Net metabolic cost
of transport
(J/kg/m)
5.01 ± 0.72
8.84 ± 1.37
12.4 ± 1.81
14.0 ± 2.36
17.4 ± 2.16
7.26 ± 0.97
8.47 ± 1.19
11.8 ± 2.15
16.0 ± 1.96
18.7 ± 2.03
6.77 ± 2.47
9.66 ± 1.39
12.3 ± 1.54
17.2 ± 4.19
23.4 ± 3.72
Vertical net
metabolic cost of
transport (J/kg/m)
0 ± 0
101.6 ± 15.7
71.9 ± 10.5
54.2 ± 9.15
51.0 ± 6.32
0 ± 0
97.3 ± 13.6
68.5 ± 12.4
62.1 ± 7.59
54.8 ± 5.93
0 ± 0
111.1 ± 15.9
71.3 ± 8.92
66.8 ± 16.2
68.5 ± 10.9
Values: mean ± standard deviation. RER: respiratory exchange rate; COM: center of mass.
Table 3. Differences in values in the three sections and ﬁve slope conditions between ﬁrst quartile and remaining quartiles.
Section 1
Section 2
Section 3
0◦
5◦
10◦
15◦
20◦
0◦
5◦
10◦
15◦
20◦
0◦
5◦
10◦
15◦
20◦
Vertical
velocity (m/s)
1st quartile (n = 5)
0 ± 0
0.20 ± 0.02 *
0.29 ± 0.02 *
0.39 ± 0.06 *
0.37 ± 0.02 *
0 ± 0
0.19 ± 0.01 *
0.26 ± 0.04
0.30 ± 0.02 *
0.35 ± 0.03 **
0 ± 0
0.16 ± 0.02 *
0.26 ± 0.03 *
0.28 ± 0.02 *
0.30 ± 0.01 **
Remaining
quartiles (n = 9)
0 ± 0
0.16 ± 0.02
0.26 ± 0.03
0.33 ± 0.04
3.33 ± 0.05
0 ± 0
0.16 ± 0.02
0.23 ± 0.04
0.25 ± 0.03
0.28 ± 0.03
0 ± 0
0.14 ± 0.02
0.21 ± 0.02
0.24 ± 0.06
0.22 ± 0.04
Velocity (m/s)
1st quartile
3.74 ± 0.23 *
2.26 ± 0.27 *
1.67 ± 0.15 *
1.53 ± 0.22 *
1.10 ± 0.07 *
2.64 ± 0.14 *
2.25 ± 0.15 *
1.52 ± 0.24
1.17 ± 0.09 **
1.02 ± 0.09 *
2.79 ± 0.24 *
1.90 ± 0.24 *
1.50 ± 0.20 *
1.10 ± 0.68 *
0.89 ± 0.03 **
Remaining
quartiles
3.33 ± 0.41
1.86 ± 0.28
1.49 ± 0.22
1.27 ± 0.15
0.96 ± 0.14
2.10 ± 0.32
1.83 ± 0.27
1.35 ± 0.22
0.98 ± 0.12
0.81 ± 0.09
2.22 ± 0.61
1.58 ± 0.23
1.23 ± 1.10
0.94 ± 0.25
0.65 ± 0.13
Mechanical
vertical COM
power (W/kg)
1st quartile
0 ± 0
1.92 ± 0.23 *
2.82 ± 0.25 *
3.87 ± 0.56 *
3.62 ± 0.23 *
0 ± 0
1.92 ± 0.13 *
2.58 ± 0.41 *
2.97 ± 0.24 *
3.43 ± 0.32 **
0 ± 0
1.62 ± 0.20 *
2.54 ± 0.35 *
2.77 ± 0.17
2.98 ± 0.12 **
Remaining
quartiles
0 ± 0
1.56 ± 0.24
2.44 ± 0.28
3.19 ± 0.37
3.25 ± 0.53
0 ± 0
1.53 ± 0.21
2.25 ± 0.37
2.43 ± 0.26
2.66 ± 0.30
0 ± 0
1.32 ± 0.18
2.09 ± 0.19
2.42 ± 0.65
2.17 ± 0.48
Net metabolic
power (W/kg)
1st quartile
19 ± 0.64 *#
20.1 ± 2.62 *#
22 ± 1.10 **#
21.6 ± 1.66 **#
20.1 ± 1.32 *#
19.5 ± 0.93 **#
19.6 ± 1.61 **#
19.7 ± 1.35 **#
19.7 ± 1.24 **#
19.8 ± 1.46 **#
18.6 ± 2.16 **#
19.4 ± 1.42 **#
19.3 ± 1.24 **#
19.9 ± 1.11 **#
20.2 ± 1.46 **#
Remaining
quartiles
15.9 ± 2.31
15.8 ± 2.21
17.1 ± 2.06
17.1 ± 1.81
16 ± 2.08
14.5 ± 1.75
14.6 ± 1.31
14.4 ± 1.28
14.8 ± 1.52
14.4 ± 1.19
13.1 ± 1.88
14.1 ± 1.13
14.6 ± 1.25
14.9 ± 1.42
14.9 ± 1.25
Values: mean ± standard deviation. COM: center of mass. * p-value < 0.05. ** p-value < 0.001. #: strong effect size (g Hedges > 0.8).
Sensors 2023, 23, 9349
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Table 4. Repeated-measures ANOVA results.
p-Value
Power (SP)
Effect Size (ηp2)
Vertical velocity
(m/s)
Section
<0.001
1
0.779
Large
Slope
<0.001
1
0.973
Large
Interaction
<0.001
1
0.463
Large
Velocity (m/s)
Section
<0.001
1
0.872
Large
Slope
<0.001
1
0.949
Large
Interaction
<0.001
1
0.654
Large
Mechanical
vertical COM
power (W/kg)
Section
<0.001
1
0.776
Large
Slope
<0.001
1
0.972
Large
Interaction
<0.001
1
0.452
Large
Net metabolic
power (W/kg)
Section
<0.001
0.993
0.600
Large
Slope
<0.001
1
0.489
Large
Interaction
<0.001
0.991
0.243
Large
Net mechanical
efﬁciency
Section
<0.001
1
0.626
Large
Slope
<0.001
1
0.969
Large
Interaction
<0.001
0.994
0.379
Large
Net metabolic
cost of transport
(J/kg/m)
Section
<0.001
1
0.706
Large
Slope
<0.001
1
0.952
Large
Interaction
<0.001
0.997
0.406
Large
Vertical net
metabolic cost of
transport (J/kg/m)
Section
<0.001
1
0.648
Large
Slope
<0.001
1
0.972
Large
Interaction
<0.001
0.964
0.304
Large
Table 5. Differences in values between sections and inclines.
Sections 1 vs. 2
Sections 1 vs. 3
Sections 2 vs. 3
Vertical velocity (m/s)
5◦
=0%
↓21.4% *
↓21.4% *
10◦
↓8.33%
↓13% *
↓4.35%
15◦
↓29.6% **
↓35.6% **
↓3.85%
20◦
↓13.3% *
↓36% **
↓20% *
Velocity (m/s)
0◦
↓51.3% **
↓43.1% **
↑5.75%
5◦
↓1.53%
↓18.6% *
↓16.8% *
10◦
↓8.6%
↓14.3% *
↓5.3%
15◦
↓31% **
↓35% **
↓3%
20◦
↓13.6% *
↓37% **
↓20.5% *
Mechanical vertical
COM power (W/kg)
5◦
↓1.19%
↓19% *
↓17% *
10◦
↓8.86%
↓14.7% *
↓5.33%
15◦
↓30.5% **
↓34.6% **
↓3.15%
20◦
↓15% *
↓37.4% **
↓19.5% *
Net metabolic power
(W/kg)
0◦
↓4.3%
↓12.6%
↓7.95%
5◦
↓6.10%
↓8.75%
↓2.50%
10◦
↓15.3% **
↓15.3% **
=0%
15◦
↓13.3% **
↓12% **
↑1.21%
20◦
↓7.36%
↓4.17%
↑3.07%
Net mechanical
efﬁciency
5◦
↑4.25%
↓9.41% *
↓14.1% *
10◦
↑6.47%
↓0.72%
↓5.71%
15◦
↓16.2% *
↓19.2% *
↓2.56%
20◦
↓7.73%
↓32.6% **
↓23.1% *
Sensors 2023, 23, 9349
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Table 5. Cont.
Sections 1 vs. 2
Sections 1 vs. 3
Sections 2 vs. 3
Net metabolic cost of
transport (J/kg/m)
0◦
↑44.9% **
↑35.1% *
↓7.24%
5◦
↓4.37%
↑9.28% *
↑14% *
10◦
↓5.08%
↓0.81%
↑4.24%
15◦
↑14.3% *
↑22.8% *
↑7.5%
20◦
↑7.47%
↑34.5% **
↑25.1% *
Vertical net metabolic
cost of transport
(J/kg/m)
5◦
↓4.42%
↑9.35% *
↑14.2% *
10◦
↓4.96%
↓0.84%
↑4.10%
15◦
↑14.6% *
↑23.2% *
↑7.57%
20◦
↑7.45%
↑34.3% **
↑25% *
% of change in mean values with p-values of Bonferroni post hoc. Up and down arrows correspond to increases
and decreases respectively; equal symbols indicate no change. * p-value < 0.05. ** p-value < 0.001.
Sensors 2023, 23, x FOR PEER REVIEW 
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velocity. The percentage of change with corresponding p-values is depicted in Figures 2 
and 3. 
(a) 
(b) 
Figure 2. Percentage of change in mechanical vertical center of mass power between slopes. * p-value 
< 0.05. ** p-value < 0.001. (a) Percentage of change in the runners of the ﬁrst quartile. The ﬁgures are 
arranged according to VK section (a1: ﬁrst section; a2: second section; a3: third section). (b) Percent-
age of change in the runners of the remaining quartiles (b1: First section; b2: second section; b3: third 
section). 
1.62
2.54
2.77
2.98
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
5º
10º
15º
20º
Section 3
1st Quartile
3
1.93
2.83
3.87
3.63
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
4,50
5º
10º
15º
20º
Section 1
1st Quartile
1
88%**
28%*
1.92
2.58
2.97
3.43
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
4,00
5º
10º
15º
20º
Section 2
1st Quartile
2
46%**
100%**
37%*
34%*
55%**
79%**
33%*
57%**
71%**
84%**
9%
17%
7%
− 7%
15%
15%
1.65
2.45
3.19
3.25
0,00
0,50
1,00
1,50
2,00
2,50
3,00
3,50
5º
10º
15º
20º
Section 1
Remaining Quartiles
1
1.53
2.25
2.43
2.67
0,00
0,50
1,00
1,50
2,00
2,50
3,00
5º
10º
15º
20º
Section 2
Remaining Quartiles
2
1.32
2.09
2.42
2.18
0,00
0,50
1,00
1,50
2,00
2,50
3,00
5º
10º
15º
20º
Section 3
Remaining Quartiles
3
48%**
93%**
97%**
30%*
33%*
8%
47%**
59%**
74%**
2%
19%
10%
− 11%
4%
16%
65%**
83%**
58%**
5°
10°
15°
20°
5°
10°
15°
20°
5°
10°
15°
20°
5°
10°
15°
20°
5°
10°
15°
20°
5°
10°
15°
20°
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
3.50
0.00
3.00
2.50
0.50
2.00
1.50
1.00
3.50
4.00
3.00
2.50
2.00
1.50
1.00
0.50
0.00
3.00
2.50
2.00
1.50
1.00
0.50
0.00
3.00
3.50
2.50
2.00
1.50
1.00
0.50
0.00
3.00
2.50
2.00
1.50
1.00
0.50
0.00
Figure 2.
Percentage of change in mechanical vertical center of mass power between slopes.
* p-value < 0.05. ** p-value < 0.001. (a) Percentage of change in the runners of the ﬁrst quartile.
The ﬁgures are arranged according to VK section (a1: ﬁrst section; a2: second section; a3: third sec-
tion). (b) Percentage of change in the runners of the remaining quartiles (b1: First section; b2: second
section; b3: third section).
Sensors 2023, 23, 9349
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Sensors 2023, 23, x FOR PEER REVIEW 
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(a) 
(b) 
Figure 3. Percentage of change in vertical velocity between slopes. * p-value < 0.05. ** p-value < 0.001. 
(a) Percentage of change in the runners of the ﬁrst quartile. The ﬁgures are arranged according to 
VK section (a1: ﬁrst section; a2: second section; a3: third section). (b) Percentage of change in the 
runners of the remaining quartiles (b1: ﬁrst section; b2: second section; b3: third section). 
A multiple regression analysis was conducted to predict mechanical vertical COM 
power from the remaining variables. The analysis revealed that the variable mechanical 
vertical COM power can be statistically signiﬁcantly predicted using net metabolic power 
and vertical net metabolic cost of transport. This relationship held true across all sections 
and slopes. 
The resulting model can be expressed algebraically as follows (Equation (6)): 
Mechanical Vertical COM power = 𝛼𝐶𝑚𝑒𝑡𝑎𝑏 +  𝛽𝑉𝐶𝑟 +  𝛾 
(6) 
where Cmetab represents net metabolic power (Equation (2)) and VCr stands for vertical 
net metabolic cost of transport (Equation (5)). 
0.16
0.26
0.28
0.30
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
5º
10º
15º
20º
Section 3
1st Quartile
3
0.20
0.29
0.39
0.37
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
5º
10º
15º
20º
Section 1
1st Quartile
1
0.20
0.26
0.30
0.35
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
5º
10º
15º
20º
Section 2
1st Quartile
2
45%**
− 5%
95%**
85%**
30%*
34%*
27%*
50%**
75%**
15%
35%*
17%
62%**
75%**
7%
87%**
8%
15%
0.16
0.26
0.33
0.33
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
5º
10º
15º
20º
Section 1
Remaining Quartiles
1
0.16
0.23
0.25
0.28
0,00
0,05
0,10
0,15
0,20
0,25
0,30
5º
10º
15º
20º
Section 2
Remaining Quartiles
2
0.14
0.21
0.24
0.22
0,00
0,05
0,10
0,15
0,20
0,25
0,30
5º
10º
15º
20º
Section 3
Remaining Quartiles
3
106%**
106%**
62%**
27%*
27%**
0%
44%**
56%**
75%**
9%
22%*
12%
50%**
71%**
57%**
14%
5%
− 9%
5°
10°
15°
20°
5°
10°
15°
20°
5°
10°
15°
20°
5°
10°
15°
20°
5°
10°
15°
20°
5°
10°
15°
20°
0.00
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.00
0.00
0.00
0.00
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.30
0.25
0.20
0.15
0.10
0.05
0.35
0.30
0.25
0.20
0.10
0.15
0.05
0.30
0.20
0.25
0.15
0.10
0.05
Figure 3. Percentage of change in vertical velocity between slopes. * p-value < 0.05. ** p-value < 0.001.
(a) Percentage of change in the runners of the ﬁrst quartile. The ﬁgures are arranged according to VK
section (a1: ﬁrst section; a2: second section; a3: third section). (b) Percentage of change in the runners
of the remaining quartiles (b1: ﬁrst section; b2: second section; b3: third section).
A multiple regression analysis was conducted to predict mechanical vertical COM
power from the remaining variables. The analysis revealed that the variable mechanical
vertical COM power can be statistically signiﬁcantly predicted using net metabolic power
and vertical net metabolic cost of transport. This relationship held true across all sections
and slopes.
The resulting model can be expressed algebraically as follows (Equation (6)):
Mechanical Vertical COM power = αCmetab + βVCr + γ
(6)
Sensors 2023, 23, 9349
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where Cmetab represents net metabolic power (Equation (2)) and VCr stands for vertical
net metabolic cost of transport (Equation (5)).
The adjusted R2 of the multiple linear regression indicates that 94% of the variation in
mechanical vertical COM power is explained by the proposed model (R2adjusted = 0.942).
The scatter plot for this model is illustrated in Figure 4. The model reached a signiﬁcance
level of p < 0.001. All variables included in the model exhibited a signiﬁcance level below
0.001, suggesting their retention in the considered model. The Durbin–Watson test fell
within the critical interval (1 < D–W < 3), allowing the acceptance of residual linearity
and independence assumptions. However, Bland and Altman plots (Figure 5) revealed
randomly distributed residuals concerning the average net mechanical vertical COM power
predicted values. Only one value outside ±1.96 × SD was observed, and the residuals
exhibited normal distribution based on the Shapiro–Wilk test (SW = 0.941; p = 0.434).
All values presented a variance inﬂation factor (VIF) lower than 10 units. Therefore, the
multicollinearity assumption is satisﬁed.
Sensors 2023, 23, x FOR PEER REVIEW 
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The adjusted R2 of the multiple linear regression indicates that 94% of the variation 
in mechanical vertical COM power is explained by the proposed model (R2adjusted = 0.942). 
The scatter plot for this model is illustrated in Figure 4. The model reached a signiﬁcance 
level of p < 0.001. All variables included in the model exhibited a signiﬁcance level below 
0.001, suggesting their retention in the considered model. The Durbin–Watson test fell 
within the critical interval (1 < D–W < 3), allowing the acceptance of residual linearity and 
independence assumptions. However, Bland and Altman plots (Figure 5) revealed ran-
domly distributed residuals concerning the average net mechanical vertical COM power 
predicted values. Only one value outside ±1.96 × SD was observed, and the residuals ex-
hibited normal distribution based on the Shapiro–Wilk test (SW = 0.941; p = 0.434). All 
values presented a variance inﬂation factor (VIF) lower than 10 units. Therefore, the mul-
ticollinearity assumption is satisﬁed. 
 
Figure 4. Scatter plot of the multiple linear regression model. Each data point represents the value 
of a subject in the study. 
Figure 4. Scatter plot of the multiple linear regression model. Each data point represents the value of
a subject in the study.
Sensors 2023, 23, x FOR PEER REVIEW 
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Figure 5. Bland–Altman plot of the multiple linear regression model. Each data point represents 
the value of a subject in the study. 
The results of the Bland–Altman analysis indicate the absence of systematic biases 
and random errors in our regression model, attributed to the randomness of the scatter-
plot dispersion and the absence of outliers. 
Based on these results the following prediction equations are derived (Equations (7)
-0,15
-0,1
-0,05
0
0,05
0,1
0,15
U nstandarized residuals
A verage net m echanical vertical C O M  pow erpredicted values
1.96×SD=0.12
2
2.1
2.2
2.3
2.4
2.6
2.5
2.7
2.8
2.9
3
0.1
0.05
0
−0.05
−0.15
−0.1
0.15
Figure 5. Bland–Altman plot of the multiple linear regression model. Each data point represents the
value of a subject in the study.
Sensors 2023, 23, 9349
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The results of the Bland–Altman analysis indicate the absence of systematic biases
and random errors in our regression model, attributed to the randomness of the scatterplot
dispersion and the absence of outliers.
Based on these results, the following prediction equations are derived (Equations (7)
and (8)):
Mechanical Vertical COM power = 0.133 × Cmetab − 0.030 × VCr + 2.376
(7)
Net metabolic power =
V × g × sinθ − 2.376
0.133 − 0.030 × (V × g × sinθ)−1
(8)
Through mathematical calculation, the obtained algebraic expression allows us to
calculate the value of net metabolic power solely from the subject’s vertical velocity (parallel
velocity × sin θ (positive slope)).
4. Discussion
Metabolic efforts in trail running have recently become a signiﬁcant focus of research,
with studies conducted in both ultra-distance events and short trail running. In the ma-
jority of these studies, simulations of race slopes have been conducted using treadmill
tests [27–29]. However, the metabolic demand appears to differ when the test is conducted
outdoors, potentially making it a more suitable method [30]. To our knowledge, there are
no metabolic studies during a vertical kilometer ﬁeld test simulating a real race.
For these reasons, the primary objective of this study was to evaluate new concepts
such as mechanical vertical COM power, net metabolic power, net metabolic cost of trans-
port, vertical net metabolic cost of transport, and net mechanical efﬁciency during a real
outdoor vertical kilometer ﬁeld test, examining their changes with fatigue and the perfor-
mance level of the athletes. The secondary goal was to analyze their relationships with the
ﬁnal time of the test.
4.1. Vertical Kilometer Performance Analysis
The T-test results showed no signiﬁcant differences between genders, while revealing
distinctions based on the subjects’ performance level, as despicted in Table 3.
Concerning the mean value differences between the ﬁrst quartile and the remaining
quartiles, better mean values were observed in top-level runners across all sections and
inclines, achieving higher values in mechanical vertical COM power, net metabolic power,
velocity and vertical velocity. The results suggest that better runners can apply more force
and achieve greater vertical velocities as the slope increases. These disparities in power and
vertical velocity persist throughout the entire duration of the VK. These outcomes align
with expectations, as several researchers have observed that uphill running requires an
increase in net mechanical work to increase the potential energy of the body, with concurrent
increases in parallel propulsive force peaks and impulses with positive grades [31], since
the bouncing mechanism gradually disappears as speed and slope increase [22]. The hip
and knee joints are identiﬁed as the primary contributors to the augmented mechanical
power [14,32]. Additionally, in short trail running, it has been observed that local endurance
of knee extensors, assessed through repeated maximal concentric contractions, is a key
performance factor in uphill running sections [33].
Net metabolic power reﬂects the instantaneous energy requirement for running, and it
has been observed to increase linearly with speed in VK runners [34], attributable to the rise
in O2 consumption and CO2 production. The higher metabolic power values among ﬁrst
quartile athletes are primarily explained by their greater velocity, stemming from either
enhanced cardiorespiratory development or greater strength and power values. Moreover,
the same study suggest that running is more efﬁcient than walking above 0.8 m/s [34].
This reference value is crucial, as ﬁrst-quartile runners could maintain speeds greater
than 0.8 m/s with 20◦ positive grade in the section 3 of our VK test, while the remaining
Sensors 2023, 23, 9349
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quartiles’ runners could not. This decision to walk instead of running may partly account
for the observed difference in test performance.
Regarding the remaining variables, no signiﬁcant differences were found based on
performance level. Our results align with other studies where no differences were identiﬁed
in the cost of running [35], and only a 5–7% difference in efﬁciency values [15] was observed
among trail runners of different levels. The minimal variation in the net metabolic cost
of transport in a real VK race could indicate that, despite ﬁrst-quartile runners exhibiting
higher metabolic power, their ability to attain higher speeds resulted in comparable cost
of transport. This observation implies that net mechanical vertical COM power and net
metabolic power may serve as more informative indicators of trail running performance
compared to net metabolic cost of transport, as suggested by the existing literature [35].
These variables could prove more suitable for real-time tracking outdoors, utilizing po-
tentiometers [36] or mobile applications, or for analyzing average values in both men and
women to observe changes with training.
4.2. The Impact of Fatigue on the Vertical Kilometer
Analyzing the impact of fatigue throughout the progression of the VK (Table 4), we
observed a deterioration in mean values across all monitored variables, occurring with
all slopes, particularly notable between the ﬁrst section and subsequent sections, and to a
lesser extent between the second and third sections. The changes were more pronounced
with steeper inclines (20◦). There was a reduction in velocity and vertical velocity, possibly
associated with the diminished ability to apply force (indicated by lower mechanical
vertical COM power values). This reduction was more signiﬁcant between the ﬁrst and
third sections, especially with 15◦ and 20◦ inclines, which are the most demanding due to
lower use of elastic energy [21,37] and biomechanical changes during the transition from
running to walking [38].
This power loss could stem from central fatigue (decreased amplitude and frequency
of motor unit recruitment) or peripheral fatigue (alterations in potential transmission
along the sarcolemma, excitation–contraction coupling and actin–myosin myoﬁlament
interaction) [39]. Both types of fatigue might be implicated based on previous ﬁndings in
ultra-trail running [39–43].
Decreases in mechanical vertical COM power values could be attributed to fatigue
in both plantar ﬂexors and knee extensor muscles. Recent studies suggest that central
fatigue tends to affect knee extensors more, while peripheral fatigue affects the plantar
ﬂexors [39,41,44]. However, caution is warranted in applying these conclusions to the VK,
as these data were observed after an ultra-marathon.
A potential factor contributing to the onset of fatigue, particularly of central origin as
posited by the central command theory [45], is muscle damage and inﬂammation. However,
Pokora et al., (2014) [46] did not observe changes in creatine kinase (a marker of muscle
damage) after 1 h of uphill running (10◦) at 60%VO2max. Therefore, investigating muscle
damage as a cause of fatigue in uphill running requires further exploration [46].
Decreases in metabolic power values were also observed, possibly caused by impair-
ments in running biomechanics (such as increased step frequency, ankle joint changes and
duty-free alterations) [39], arising from neuromuscular fatigue and behavioral changes
in runners, especially with 15◦ and 20◦inclines, choosing gaits that minimize metabolic
cost [47].
Concerning net metabolic COT and vertical net metabolic COT, both continuously
increased across all sections with steeper uphill inclines due to greater loss of velocity
than metabolic power values as the test progressed. This suggests that neuromuscular,
rather than cardiorespiratory factors, may be the primary contributors to the decline in
performance in the VK. These increases align with observations in the literature after short-
distance running races [48,49], 1 h of treadmill running [50] and the vertical kilometer [34].
Multiple reasons have been proposed for this increase in COT. Firstly, the steep inclines
of the VK, coupled with a decrease in velocity, induce changes in running biomechanics,
Sensors 2023, 23, 9349
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such as decreased step length, increased non-optimal step frequency, mid- to fore-foot
strike patterns, and decreased leg stiffness, all associated with increased COT [9,51–53].
Prolonged running step contact times (“Groucho running” pattern concept) [54] could
impair spring-like bouncing and elevate the COT due to changes in potential-kinetic energy
savings [34,55]. These biomechanical changes may be induced by neuromuscular fatigue
(reﬂected in decreased mechanical power) [39,56] or serve as a protective mechanism to
reduce running impacts [57].
Regarding net mechanical efﬁciency changes, this variable decreased due to greater
losses in mechanical power than metabolic power. The substantial and continuous losses in
mechanical power could signify a decrease in workload due the loss of velocity, providing
a signiﬁcant limitation to performance due to the inability to utilize maximum metabolic
potential. This theory is supported by data from Ettema et al., (2009) [58], who stated that
power output is the main determinant of efﬁciency (more power leads to more efﬁciency
and vice versa), owing to a greater utilization of metabolic power in running. The imbalance
between mechanical power and metabolic power, resulting in a decrease in net mechanical
efﬁciency, could be attributed to decreased energy transduction (due to decreased speed
and stretch-shortening cycle) coupled with an increase in respiratory cost [24].
4.3. Examining Fatigue Effects Based on Runners’ Performance Levels
When examining the impact of fatigue based on the runners’ performance levels, we
observed differential changes in only two variables, namely mechanical vertical COM
power (Figure 2) and vertical velocity (Figure 3). Notably, elite runners demonstrated a
better ability to sustain power values across all slopes, particularly evident with 10◦ and
20◦ inclines, resulting in more pronounced differences in power values between slopes.
This phenomenon suggests their enhanced capability to exert force consistently across
all slopes throughout the entire race. Similarly, top-level runners exhibited a superior
ability to maintain vertical velocity values across all inclines, likely attributable to their
heightened application of force throughout the entire VK. These ﬁndings align with prior
research indicating a signiﬁcant correlation between performance in short trail running
races and neuromuscular capacity, as assessed by isometric knee extensor muscle torque,
maximal theoretical force and maximal power from the force–velocity curve [59]. This
underscores the importance of incorporating resistance training [60], uphill interval run-
ning training [61] and pulled running training [62] to enhance power and neuromuscular
function [39,62] in runners. Additionally, it emphasizes the signiﬁcance of monitoring
these two variables using apps that measure speed and incline or smartwatches, which are
increasingly employed in outdoor races and training sessions.
4.4. Metabolic Power Calculation
The outcomes of the multiple regression analysis revealed that 94% of the variance
in mechanical vertical COM power during the VK test could be accounted for by net
metabolic power and the vertical metabolic COT. This substantial explanation is primarily
attributed to the fact that these two variables elucidate the vertical velocity, a key component
of mechanical vertical COM power. From the derived equation (Equation (6)), three
coefﬁcients sensitive to the progression of the test and inclination were obtained (Table 6).
These coefﬁcients are likely subject to variations depending on the characteristics of the
uphill test, such as slope, section lengths and their interaction. This observation is consistent
with our study’s results, where net metabolic power levels exhibited changes due to slope
and fatigue. The ﬁndings of this regression analysis suggest that, once an ascent has
been characterized, net metabolic power can be estimated based on the runner’s vertical
velocity. Consequently, a reliable equation (Equation (8)) was established from the multiple
regression to calculate the runner’s metabolic power during a VK ﬁeld test. This equation
utilizes only the vertical velocity and the coefﬁcients found in the model, eliminating the
need for expensive portable gas analyzers. The ease of analysis with common devices
like phones, smartwatches and GPS is a notable advantage [63]. These results align with
Sensors 2023, 23, 9349
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the increasing interest among researchers to determine metabolic power during actual
competitions in various sports. This pursuit aims to enhance the understanding of the real
workload for athletes, thereby improving training methods and periodization [64–67].
Table 6. Multiple linear regression model for mechanical vertical COM power.
R
R2
adR2
SEE
p
Durbin–
Watson
B
SE
Beta
p
B
VIF
LL95%
UL95%
0.975
0.951
0.942
0.07
<0.001
1.911
α
0.133
0.009
1.243
<0.001
0.113
0.152
1.626
β
−0.030
0.003
−0.797
<0.001
−0.037
−0.023
1.626
γ
2.376
0.183
<0.001
1.973
2.779
R: correlation coefﬁcient, R2: determination coefﬁcient; adR2: adjusted determination coefﬁcient; SEE: standard
error of the estimation; p: signiﬁcance level; LL95%: lower limit for 95% conﬁdence interval; UL95%: upper
limit for 95% conﬁdence interval, B: multiple linear regression coefﬁcients of each variable; SE: B-standard error;
Beta: standardized coefﬁcients; VIF: variance inﬂation factor; α: net metabolic power coefﬁcient; β: vertical net
metabolic COT coefﬁcient; γ: independent coefﬁcient of the multiple regression.
Our formula, combined with the VO2 submax at 30◦ formula developed by Giovanelli
et al. [38], can serve as a valuable tool for characterizing VK runners based on easily
measured variables in a real ﬁeld test.
The study results offer novel insights into the signiﬁcance of utilizing mechanical
power, metabolic power and vertical velocity variables for performance analysis in vertical
kilometer runners, regardless of gender. Furthermore, it underscores their susceptibility to
impairment due to the inﬂuence of fatigue. These ﬁndings align with the increasing interest
in acquiring high-quality information on athletes’ internal load through the progressive
improvement of technology and data analysis methods [3]. Moreover, it opens up the
possibility of conducting further research to deeper analyze these variables across various
running modalities and both cyclic and acyclic sports.
A major strength of the present study lies in the simplicity with which these variables
can be implemented in any existing wearable sensor on the market that utilizes IMUs
and GNSS to calculate real-time velocity, accelerations, anthropometric data and terrain
characteristics. These data facilitate the calculation of key parameters, eliminating the need
for athletes and coaches to undergo time-consuming and fatiguing tests and allowing data
collection during training and competition [2].
Finally, possessing a comprehensive understanding of key variables within each
sporting context is crucial. This clarity is essential for precise data collection, enabling
researchers and companies to save a signiﬁcant amount of time developing software and
sensors [2].
As future lines of research, it would be interesting to validate the metabolic power
formula and continue studying runners through real ﬁeld tests.
5. Limitations
The main limitation of the study is the small sample size, with only 11 male and
4 female participants. This limitation arose from the technical complexity and time cost
associated with conducting the analyses in a true vertical kilometer ﬁeld test. Future
extensive analyses with a larger and more diverse sample should be conducted, particularly
for the reliability and validity assessment of the metabolic power formula identiﬁed in
this study.
Additionally, the absence of anthropometric analysis to determine the body fat per-
centage and the level of lower limb muscle mass among the runners represents another
limitation. This lack of information prevents readers from gaining insights into the sub-
jects’ ﬁtness levels, which would provide better context for the study’s ﬁndings. Notably,
individuals with lower body fat percentages and higher levels of leg muscle mass are often
observed to perform better in trail running tests. Consequently, future studies should
Sensors 2023, 23, 9349
16 of 19
incorporate analyses of these parameters. Lastly, another limitation is the absence of a
pre-vertical kilometer maximum treadmill test to assess the physiological condition of the
runners, as well as a strength test to gauge their neuromuscular level. These factors are also
crucial for race performance and should undergo thorough examination in future studies.
6. Conclusions
The study results revealed signiﬁcant differences in the mean values of variables such
as velocity, vertical velocity, mechanical vertical COM power and net metabolic power
when comparing top-level runners to low-level runners during a vertical kilometer ﬁeld
test. Additionally, all analyzed variables were affected by fatigue as the test progressed,
showing signiﬁcant differences in how fatigue altered mechanical vertical COM power and
vertical velocity when comparing top-level to low-level runners. A multiple regression
analysis demonstrated that 94% of the mechanical vertical COM power during the vertical
kilometer test could be explained by net metabolic power and vertical net metabolic cost
of transport. Subsequently, a reliable equation was derived from the multiple regression
to calculate each runner’s metabolic power during a vertical kilometer ﬁeld test, utilizing
only the vertical velocity and the coefﬁcients identiﬁed in the model. These ﬁndings
present an opportunity to explore new variables correlated with performance in short
trail running, particularly in vertical kilometer races. These new variables are sensitive to
performance disparities, exhibit changes with fatigue and are applicable to both male and
female athletes. Importantly, they can be easily measured through apps, smartwatches,
foot-pod potentiometers and GPS.
Author Contributions: Conceptualization, P.J.B., A.V.B.-C. and C.B.; methodology, H.G., J.R.-P. and
C.B.; formal analysis, P.J.B. and H.G.; investigation, A.V.B.-C., E.P. and J.R.-P.; data curation, P.J.B. and
H.G.; writing—original draft preparation, P.J.B. and H.G.; writing—review and editing, A.V.B.-C.,
C.B., E.P. and J.R.-P.; funding acquisition, C.B. All authors have read and agreed to the published
version of the manuscript.
Funding: This work was partially funded by Departamento de Ciencia, Universidad y Sociedad del
Conocimiento, from the Gobierno de Aragón (Spain) (Research Group ValorA, under grant S08_23R.
In addition, this research was partially supported by the Spanish Ministry of Universities (FPU grant
FPU19/00967).
Institutional Review Board Statement: This study was conducted in accordance with the Declaration
of Helsinki and approved by the Institutional Ethics Committee of the Universidad San Jorge, protocol
code Ref 005-19/20.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the
study. Written informed consent was obtained from the subjects to publish this paper.
Data Availability Statement: The raw data belong to the Universidad San Jorge and can be requested
from the corresponding author with the permission of Universidad San Jorge.
Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design
of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; or
in the decision to publish the results.
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Running Economy in the Vertical Kilometer.
Bascuas, Pablo Jesus,Gutiérrez, Héctor,Piedrafita, Eduardo,Rabal-Pelay, Juan,Berzosa, César,Bataller-Cervero, Ana Vanessa