Physiological Reports. 2021;9:e15076. 
 
  | 1 of 15
https://doi.org/10.14814/phy2.15076
wileyonlinelibrary.com/journal/phy2
RUNNING ECONOMY (RE) at a specific submaximal 
running velocity is defined as oxygen consumption (VO2) 
per minute per kg body mass. RE can also be normalized 
with respect to distance as VO2 kg−1 km−1. Normalization 
to body mass allows for comparisons between individu-
als. RE is a complex measure, which reflects the combined 
functioning of biomechanical, anatomical, metabolic and 
cardio- respiratory factors (Tawa & Louw, 2018). Even 
among well- trained runners, RE can be seen to differ 
up to approximately 30% between individuals (Barnes 
et al., 2014; Larsen, 2003; Saunders et al., 2004a; Scholz 
et al., 2008). This makes RE a most decisive performance 
Received: 3 September 2021 | Accepted: 15 September 2021
DOI: 10.14814/phy2.15076  
O R I G I N A L  A R T I C L E
Factors correlated with running economy among elite 
middle-  and long- distance runners
Cecilie E. Hansen1 |   Martin Stensvig1 |   Jacob Wienecke2 |   Chiara Villa3 |   
Jakob Lorentzen1 |   John Rasmussen4 |   Erik B. Simonsen1
This is an open access article under the terms of the Creat ive Commo ns Attri bution License, which permits use, distribution and reproduction in any medium, provided 
the original work is properly cited.
© 2021 The Authors. Physiological Reports published by Wiley Periodicals LLC on behalf of The Physiological Society and the American Physiological Society
1Department of Neuroscience, 
University of Copenhagen, Copenhagen 
N, Denmark
2Department of Sport and Nutrition, 
University of Copenhagen, Copenhagen 
N, Denmark
3Department of Forensic Medicine, 
University of Copenhagen, Copenhagen 
Ø, Denmark
4Department of Materials and 
Production, Aalborg University, 
Aalborg Ø, Denmark
Correspondence
Erik B. Simonsen, Department 
of Neuroscience, University of 
Copenhagen, Blegdamsvej 3, 2200 
Copenhagen N, Denmark.
Email: eksn@sund.ku.dk
Funding information
No funding information provided.
Abstract
Running economy (RE) at a given submaximal running velocity is defined as oxy-
gen consumption per minute per kg body mass. We investigated RE in a group of 
12 male elite runners of national class. In addition to RE at 14 and 18 km h−1 we 
measured the maximal oxygen consumption (VO2max) and anthropometric meas-
ures including the moment arm of the Achilles tendon (LAch), shank and foot 
volumes, and muscular fascicle lengths. A 3- D biomechanical movement analysis 
of treadmill running was also conducted. RE was on average 47.8 and 62.3 ml 
O2 min−1 kg−1 at 14 and 18 km h−1. Maximal difference between the individual 
athletes was 21% at 18 km h−1. Mechanical work rate was significantly correlated 
with VO2 measured in L min−1 at both running velocities. However, RE and rela-
tive work rate were not significantly correlated. LAch was significantly correlated 
with RE at 18 km h−1 implying that a short moment arm is advantageous regard-
ing RE. Neither foot volume nor shank volume were significantly correlated to 
RE. Relative muscle fascicle length of m. soleus was significantly correlated with 
RE at 18 km h−1. Whole body stiffness and leg stiffness were significantly corre-
lated with LAch indicating that a short moment arm coincided with high stiffness. 
It is concluded that a short LAch is correlated with RE. Probably, a short LAch al-
lows for storage of a larger amount of elastic energy in the tendon and influences 
the force– velocity relation toward a lower contraction velocity.
K E Y W O R D S
Achilles tendon moment arm, biomechanics, fascicle length, running economy, stiffness
2 of 15 |   
HANSEN et al.
factor in competitive middle- and long- distance running 
together with VO2max and “Utilization of VO2max,” which 
often refers to the relative load corresponding to “onset of 
blood lactate.” (Larsen & Sheel, 2015).
A few anatomical measures have been shown to re-
late to RE. One is the moment arm of the Achilles ten-
don (LAch) about the ankle joint, another is the ratio 
between the length of the forefoot and LAch (Scholz 
et al., 2008; Spurrs et al., 2003). The size of the LAch is 
highly determined by the size of the calcaneus bone and 
is regarded as a highly specialized feature of the human 
species for the evolution of Endurance Running and 
Persistence Hunting (PH) in the genus Homo (Raichlen 
et al., 2011). It is speculated that hominids during PH 
ran at speeds that forced animals to enter hyperthermia 
(Pontzer et al., 2009).
Despite the remarkable differences in RE between run-
ners, it is largely unknown, which factors are decisive for 
a high RE (low VO2 kg−1 at a specific velocity). Since 1968, 
African and especially Kenyan runners have dominated 
the international scene in middle- and long- distance races 
to a degree that has been termed the greatest geographical 
concentration of sports excellence in the annals of sports 
(Larsen & Sheel, 2015). Accordingly, the Kenyan runners 
have been subjected to research projects regarding their 
anatomy, physiological capabilities, and biomechani-
cal characteristics. Saltin et al. (Saltin, 2003) concluded 
that no differences between Kenyan and European run-
ners could be observed regarding VO2max, muscle fiber 
type distribution, number of capillaries or metabolic en-
zymes (Saltin, Kim et al., 1995; Saltin, Larsen et al., 1995). 
Biomechanically, only contact time has been reported 
shorter in Kenyan runners (Santos- Concejero et al., 2017). 
Regarding anatomical differences, it has been reported that 
elite Kenyans had longer shanks and longer Achilles ten-
dons than Japanese elite runners (Kunimasa et al., 2014; 
Sano et al., 2015). However, the Achilles tendon moment 
arm (LAch) was found to be longer in Kenyan than Japanese 
elite runners (Kunimasa et al., 2014), which is contradic-
tory to studies reporting significant correlations between 
LAch and RE (Barnes et al., 2014; Scholz et al., 2008) show-
ing a positive effect of a short LAch. Due to these discrepan-
cies, it was decided to measure the LAch of the athletes in 
the present study and reinvestigate any possible correlation 
with RE.
It seems obvious that RE somehow should relate to 
“running technique,” but no studies have been able to 
show a relation between the movement pattern of mid-
dle- and long- distance running and RE. Within Track and 
Field Athletics it is well known that changing the move-
ment pattern of a distance runner is “dangerous” and will 
often result in impaired performance. Most often run-
ners successfully choose their step frequency and stride 
length from subjective criteria, which was shown already 
by Högberg (1952). Accordingly, one purpose of the pres-
ent study was to relate biomechanical calculations of me-
chanical energy during running to RE in elite middle- and 
long- distance runners.
Lower leg thickness has been found to correlate signifi-
cantly to RE and especially for Kenyan runners, who were 
claimed to have more slender legs than European runners 
(Saltin, 2003). Based on this finding it was suggested that 
it would be less energy demanding to move a lower leg 
mass back and forward during the swing phase of running 
(Larsen et al., 2004; Saltin, 2003). It was therefore decided 
to measure foot and lower leg volume of the athletes in the 
present study to see if this anatomical parameter would be 
significantly correlated with RE.
Muscular fascicle length has been shown to correlate 
significantly with maximal sprint running speed and it 
was suggested that longer muscle fibers would infer a 
more beneficial force– velocity relationship of the leg mus-
cles (Abe et al., 2001). As this mechanism also could cause 
the muscles to produce the same muscle force at a lower 
contraction velocity and thereby the use of fewer muscle 
fibers at a given running velocity, it was decided to mea-
sure muscular fascicle length by use of ultrasonography 
and relate this parameter to RE.
1 | METHODS
1.1 | Subjects
Twelve elite, male, middle- and long- distance runners 
(Table 1) gave their voluntary consent to participate in 
the study. The athletes competed at national or inter-
national level in events ranging from 800 m to 10 km. 
Characteristics of the subjects are presented in Tables 
1 and 2. The protocol was approved by the Research 
Ethics Committee for Science and Health, University of 
Copenhagen, Denmark.
1.2 | Experimental protocol
The subjects visited the laboratory on 3 consecutive 
days. On day 1, a treadmill test was completed to de-
termine running economy (RE) and VO2max. On day 
TABLE 1 Subject data
Height 
(m)
Weight 
(kg)
BMI
Age 
(y)
VO2max
Mean
1.82
68.5
20.54
22.4
67.0
SD
0.06
7.66
1.21
3.1
4.2
   | 3 of 15
HANSEN et al.
2, anthropometric and muscular variables were deter-
mined. On day 3, biomechanical variables related to run-
ning were determined.
1.3 | Running economy and VO2max
Running Economy was determined as the rate of oxygen 
consumption (VO2) per kg body mass while running at 
two different submaximal velocities on a motorized tread-
mill (Woodway Desmo Pro Treadmill, Woodway Inc). 
The speed of 14 km h−1 was chosen as a “safe” velocity 
with regard to the expected aerobic capacity of the ath-
letes. The speed of 18 km h−1 was chosen to represent a 
velocity close to the conditions during competition. After 
a standardized warm up on the treadmill, the subjects ran 
at two submaximal running speeds 14 and 18 km h−1, 0% 
grade, for 4 min separated by 1– 2 min rest. During the 4- 
min stages, in and expired gases were measured continu-
ously by a gas analyzer (MasterScreen CPX, CareFusion). 
Breath- by- breath data were processed by the software sys-
tem JLab (CareFusion). Running economy (RE) was de-
termined as the mean VO2 (ml kg−1 min−1) during the last 
minute of each 4- min bout.
A few minutes after the last submaximal run, an in-
cremental test to exhaustion was completed to determine 
VO2max. The test started at 16 km h−1 and the speed was 
increased by 1 km h−1 each minute until 20 km h−1. After 
a minute at this velocity, the treadmill gradient was in-
creased by 1% each minute until exhaustion. VO2max was 
determined as the highest mean VO2 over a 30 s period. 
Values of VO2expressing resting values were obtained 
from the difference between VO2at 14 and 18 km h−1 di-
vided by 4 km h−1. These values were subtracted from all 
the measured values of VO2.
1.4 | Anthropometric measurements
The subjects’ Achilles tendon moment arm (LAch) was 
measured by the method presented by Scholz et al. (2008). 
Briefly, the most prominent part of the lateral and medial 
malleolus of the subjects’ right foot was marked. The sub-
jects were seated in a chair with their foot on a reference 
block. First, foot and leg were positioned so that the lateral 
edge of the foot was aligned with the reference block and 
the anterior border of the tibia was vertical. From this po-
sition the lateral side of the foot and leg was photographed 
(Figure 1). The same procedure was used for the medial 
side. The medial edge of the foot was aligned with the ref-
erence block, the anterior border of the tibia was vertical, 
and the medial side was photographed (Figure 1). The 
horizontal distance from the marked spot on the malle-
olus to the posterior aspect of the Achilles tendon was 
measured on the pictures. This was performed for both 
the lateral and medial sides, and the LAch was determined 
as the mean of two values.
From the picture of the lateral side, the length of the 
forefoot was also determined by measuring the horizontal 
distance from the marked spot on the lateral malleolus to 
the head of the fifth metatarsal (marked by a spot). The 
TABLE 2 Personal best results of the athletes
Athlete
800 m
1500 m
5000 m
10.000 m
1
1.53.99 min
3.41.17 min
2
1.51.11 min
3.53.35 min
3
31.03.00 min
4
30.45.00 min
5
1.58.17 min
3.57.92 min
6
1.57.73 min
3.57.69 min
7
1.54.00 min
3.53.37 min
8
1.49.44 min
3.49.59 min
9
4.06.26 min
14.51.25 min
10
4.04.13 min
11
1.55.55 min
3.49.44 min
12
1.49.50 min
FIGURE 1 The lateral Achilles tendon moment arm (a) (top) 
and (bottom) the medial Achilles tendon moment arm (c). The 
resulting Achilles tendon moment arm (LAch) was calculated as the 
mean of a and c. The length of the forefoot is shown as distance b
4 of 15 |   
HANSEN et al.
length of the forefoot was determined as the mean of two 
consecutive measurements.
Lower leg and foot volume were determined by scan-
ning the lower leg and foot with a hand- held 3- D surface 
scanner (Artec Eva, Artec 3D, Luxembourg) (Tierney et al., 
1996). Proximally, the lower leg was marked by two mark-
ers, one on caput fibula and one on tibia at about equal 
heights. Distally, the lower leg was marked by two addi-
tional markers, one on the lateral malleolus (of tibia) and 
one on the medial side at about equal heights (approxi-
mately 1 cm below the medial malleolus). This procedure 
was used on both the right leg and the left leg. The distal 
markers on the lower legs were used to mark the feet as 
well.
During the scanning of the lower legs, the subjects 
were instructed to stand in a relaxed upright position with 
enough space between the feet for the scanner to be able 
to scan the medial side of the lower legs. Tape was used 
to mark the subject's foot position to guarantee accuracy 
during and between the measurements. A minimum of 
three scans were applied to the lower legs.
During the scanning of the feet, the subjects sat in a 
chair with their right lower leg resting on another chair, 
so that the foot was free from the chair. The subjects were 
instructed to relax their foot during all scans and the lower 
leg was fastened with sports tape, so that movement of the 
lower leg and foot was minimized. This was repeated for 
the left leg, and a minimum of three scans were performed 
on each foot.
A 3- D model was constructed and further processed 
using Artec Studio (Artec 3D, Luxembourg). The lower 
legs were isolated from the 3- D model by cutting off ev-
erything proximally and distally to the two marker pairs, 
respectively. The feet were isolated by cuts proximal to 
the distal markers. The volumes of the 3- D models of 
the isolated lower legs and feet were calculated using the 
Artec Studio software. The volumes of two successful 
scans of each lower leg were calculated, and the volume 
of the lower leg was determined as the mean of these. 
The same procedure was applied to calculate the volume 
of the foot.
Body mass and height were measured using standard 
procedures and, in addition, the following anthropo-
metric variables on the subjects’ right side were deter-
mined: total leg length (from the ground to spina iliaca 
anterior superior), thigh length (from trochanter major 
to the lateral condyle of the femur), shank length (from 
caput fibulae to the lateral malleolus of the tibia), foot 
length (from the back of the heel to the tip of the lon-
gest toe), forefoot length from the lateral malleolus to 
the fifth metatarsal joint (Figure 1), and toe length (from 
the head of the first metatarsal to the tip of the first pha-
lanx distalis).
1.5 | Fascicle length
Fascicle length (Lf) was estimated using a B- mode ultra-
sound scanner (LS128, CEXT- 1Z, Telemed Ltd.) and trans-
ducer (LV8- 5L60N- 2 veterinary, Telemed Ltd.). The vastus 
lateralis (VL), gastrocnemius medialis (GM), and soleus 
(SOL) muscle of the subject's right leg were scanned. For 
VL, the transducer was placed at a point midway between 
trochanter major and the lateral condyle of the femur. For 
GM and SOL, the transducer was placed at a point approxi-
mately 30% proximally between the medial condyle and 
the medial malleolus of the tibia and midway between the 
medial and lateral borders of the GM (Abe, 2002). During 
the scans, the subjects stood in an upright relaxed position 
and the transducer was placed parallel to the muscle fibers 
and adjusted if necessary to get the optimal picture. The 
ultrasound images of the muscles were recorded by Echo 
Wave II software (3.4.0, Telemed Ltd.). The fascicle pen-
nation angle (α) was determined as the angle between the 
deep aponeurosis and the fascicles of the specific muscle 
(Abe et al., 2000; Cronin & Lichtwark, 2013; Kawakami 
et al., 2002). The isolated muscle thickness (Tm) was de-
termined by measuring the distance between the deep and 
superficial aponeurosis of the specific muscle (Aggeloussis 
et al., 2010). This was performed for both the proximal 
and distal ends of the muscle visualized in the ultrasound 
image, and a mean of these two distances was used as Tm. 
The Lf was estimated using the following equation:
The Lf of each muscle was determined as a mean of 
three estimated Lf of the specific muscle and expressed 
both in absolute values (cm) and relative to the related 
segment length (cm cm−1).
1.6 | 3- D biomechanical 
movement analysis
Due to injuries (not related to this study), only 10 of the 
12 subjects managed to complete a 3- D biomechanical anal-
ysis of treadmill running to determine stride frequency (fs), 
stride length (Ls), contact time (tc), swing time (ts), vertical 
oscillations, and mechanical work. Thirty- five spherical re-
flective markers were placed on selected anatomical land-
marks (Figure 2). After a standardized warm up, the subject 
ran at the two submaximal velocities from the RE protocol 
(14 and 18 km h−1, 0% grade) while recorded by a Qualisys 
system for movement analysis (Qualisys AB). Eleven high- 
speed infrared cameras (300 Hz) recorded a minimum of 
15 steps at each velocity. Three- dimensional coordinates of 
Lf =
Tm
sin(훼)
   | 5 of 15
HANSEN et al.
the markers were exported to the software system AnyBody 
(AnyBody version 7.1, AnyBody Technology A/S), which 
was used to analyze the recordings. Simultaneously, the 
athletes were recorded on video (120 frames s−1) and these 
recordings were later used to obtain contact time, stride 
frequency, swing time, and stride length. Stride length was 
calculated as velocity divided by stride frequency.
AnyBody is a multibody dynamics system, which dis-
cretizes the body into links representing the bones as 
rigid segments articulating at the anatomical joints. To 
each bone was assigned the mass of the other tissues sur-
rounding the bone, such that the sum of segment masses 
equaled the total body mass and the distribution of masses 
followed Dempster (Dempster, 1955).
The potential energy of the system was computed as 
the sum of potential energies of the segments. Similarly, 
the kinetic energy was computed as the sum of segment 
kinetic energies, where each segment's kinetic energy con-
tained translational and rotational contributions (Winter, 
1979). The mechanical energy of each segment and of the 
entire system, Emech, was calculated as the sum of poten-
tial and kinetic energy (Winter, 1979).
During motion, energy is converted between kinetic and 
potential contributions, existing energy is exchanged between 
segments via joint reaction forces and muscle connections, 
and energy is produced or dissipated by positive and negative 
muscle work in a complex interplay. The internal exchange 
of energy between segments is complicated, but disregard-
ing friction, air resistance, and other dissipative effects, the 
net change in mechanical energy of the entire system is at-
tributed to muscle work (Winter, 1979). We therefore defined 
the mechanical muscle power of the whole system as follows:
Ppos and Pneg were defined as the sum of the positive 
and negative increments in Pmech, respectively.
Pmech = d Emech
dt
FIGURE 2 Reflective spherical markers were placed at anatomical landmarks. Reproduced with permission of Qualisys AB
6 of 15 |   
HANSEN et al.
Subsequently, we computed the metabolic power as
that is, different metabolic efficiencies for concentric and 
eccentric muscle work (Aura & Komi, 1986; Laursen et al., 
2000). When expressing the mechanical work intensity as 
liter O2 min−1, an energetic value of 20 kJ per liter oxygen 
was used. A measure of gross efficiency was obtained by di-
viding Pmech by Pmetab.
1.7 | Stiffness
Stiffness of the whole body was measured during running as 
previously described (Cavagna et al., 1977; Ferris et al., 1998; 
McMahon & Cheng, 1990; Morin et al., 2005). The vertical 
ground reaction force was calculated in the AnyBody sys-
tem by the methods described by Fluit et al. (2014) and by 
Skals et al. (2017). The vertical trajectory of the body center 
of mass (BCM) was also computed by the AnyBody system 
using anthropometrics from Dempster (1955). Thus, the ver-
tical stiffness kvert in kN m−1 was calculated by the formula:
where Δy is the vertical displacement of BCM from touch 
down (heel strike) till Fmax, which is the peak value of the 
vertical ground reaction force.
Leg stiffness of the support leg during running was cal-
culated by the formula:
where:
where L is leg length and Δy is the vertical displacement of 
the body center of mass at its lowest point during the contact 
phase. It has been shown that BCM is at its lowest point at the 
time of Fmax (Morin et al., 2005). At each running velocity, stiff-
ness was measured in three consecutive steps and averaged.
1.8 | Statistics
Spearman's rank correlation analysis was used to deter-
mine the relationship between RE and the anthropometric, 
biomechanical, and muscular variables of the subjects 
(Matlab R2018a, The MathWorks Inc). The level of signifi-
cance was set to p < 0.05.
2 | RESULTS
Personal data and VO2max of the athletes are listed in 
Tables 1 and 2. The group mean value of VO2max was 
67.0  ml O2  kg−1 (range: 61.7– 78.2), which confirmed 
that the athletes were all well- trained elite runners 
(Table 3).
Resting values calculated from the difference be-
tween VO2 at the two running velocities were on 
average 3.66 ml O2 kg−1 min−1 (±0.60). Running econ-
omy (RE) corrected for resting values was (averaged 
across subjects) 44.1 and 58.7 ml O2 kg−1 min−1 at 14 
and 18 km h−1, respectively (Table 3). This implied at 
14 km h−1 a difference of 22% and at 18 km h−1 a dif-
ference of 21% between the best athlete and the poor-
est athlete. RE at 14 and 18  km  h−1 was significantly 
correlated (Rho = 0.79, p = 0.0021) indicating a linear 
relationship between RE and running velocity as shown 
before (Saltin, Kim, et al., 1995; Saltin, Larsen, et al., 
1995; Saunders et al., 2004a, 2004b).
Without correction for resting metabolism, RE was 
on average 47.8 (±2.8) ml O2 kg−1 min−1 and 62.4 (±3.6) 
ml O2  kg−1  min−1 at 14 and 18  km  h−1, respectively. 
Uncorrected VO2max was 70.8 (±4.7) O2 kg−1 min−1.
The relative load of the athletes at 14 and 18 km h−1 
was on average 66.1% (±5.0) and 87.9% (±4.8) with respect 
to VO2max (Table 3).
Biomechanical and temporal parameters related to the 
step cycle (step rate, step length, contact time, swing phase, 
and BCM oscillations) were not correlated with RE (Table 4).
The mechanical work intensity (Pmech) was 3.41 (0.28) and 
3.79 (0.54) W kg−1 for 14 and 18 km h−1, respectively (Figure 
3). None of the parameters expressing mechanical work 
intensity were significantly correlated with RE. However, 
body mass was significantly correlated with VO2 (L min−1) 
at 14 km h−1 (Rho = 0.89, p = 0.0014) and at 18 km h−1 
(Rho = 0.93, p = 0.0001). Body mass was also significantly 
correlated with Pmech at 18 km h−1 (Rho = 0.71, p = 0.0275).
When the mechanical work intensity was expressed 
as liter O2  min−1, significant correlations were found 
between mechanical work intensity and the measured 
VO2 in L min−1 (Figure 4). At 14 km h−1, Rho was 0.66 
(p = 0.044) and at 18 km h−1 Rho was 0.84 (p = 0.0045) 
(Figure 4). Respiratory quotient ratio (RER) values were 
0.85 (range: 0.68– 0.93) and 0.935 (range: 0.76– 1.04) for 14 
and 18 km h−1, respectively.
Gross efficiency calculated on mechanical data only 
was 41.4% and 41.9% at 14 and 18 km h−1, respectively.
Pmetab =
{
Pmech∕0.25
if Pmech ≥0
Pmech∕−1.20
if Pmech <0
kvert = Fmax
Δy
kleg = Fmax
ΔL
ΔL = L −
√
L2 −
(v⋅tc
2
)2
+ Δy
   | 7 of 15
HANSEN et al.
Pmech at 14 and 18  km  h−1 was significantly cor-
related (Rho = 0.68, p = 0.055) as was Pneg (Rho = 0.66, 
p = 0.044).
The Achilles tendon moment arm (LAch) was on aver-
age 3.91 cm and was significantly correlated with RE at 
18 km h−1 (Rho = 0.73; p = 0.007) (Figure 5) (Table 5). 
This implied that a short moment arm is an advantage 
regarding RE at 18 km h−1 while not at 14 km h−1. The 
LAch varied from 3.46 to 4.21 cm corresponding to a differ-
ence of 17.8% between the extremes of the group (Table 5; 
Figure 5).
Fascicle length of m. soleus (SO) was 4.1 cm on aver-
age and varied from 3.2 to 4.9 cm corresponding to a 36% 
difference between the subject with the shortest and the 
subject with the longest fascicles. Similar differences were 
observed for the gastrocnemius (GM) (mean 5.6 cm; range: 
4.5– 6.8) and the vastus lateralis (VL) (mean 6.6 cm; range: 
5.6– 7.9). Individual range for the GM corresponded to 34% 
and for the VL 29%. No significant correlations were found 
between absolute fascicle length and RE, neither at 14 nor 
at 18 km h−1. However, when normalized to leg (shank) 
length the soleus fascicles showed a significant correlation 
with RE at 18 km h−1 (Rho = −0.62; p = 0.03) (Figure 6).
Total leg length, shank length, foot length, and toe 
length were not significantly correlated with RE (Table 5). 
TABLE 3 Running economy at 14 and 18 km h−1, respectively
Athlete
VO2 
ml kg−1 min−1
14 km h−1
VO2 
ml kg−1 km−1
14 km h−1
VO2 ml kg−1 min−1
18 km h−1
VO2 ml kg−1 km−1
18 km h−1
VO2max 
ml kg−1 min−1
% VO2max
14 km h−1
% VO2max
18 km h−1
1
45.3
194
58.2
194
65.4
69.3
89.1
2
47.9
205
62.2
207
68.6
69.7
90.6
3
39.8
170
54.5
182
68.0
58.5
80.2
4
44.2
189
57.5
192
66.3
66.7
86.7
5
45.7
196
65.7
219
78.2
58.5
84.1
6
47.3
202
61.1
204
67.4
70.1
90.6
7
42.9
184
59.8
199
66.0
65.0
90.7
8
40.9
175
57.0
190
61.7
66.2
92.3
9
41.4
177
54.4
181
69.1
59.9
78.7
10
48.6
208
60.2
201
64.7
75.1
93.1
11
43.1
185
56.3
188
65.7
65.6
85.8
12
42.4
182
57.7
192
62.4
67.9
92.4
Mean
44.1
189
58.7
196
67.0
66.1
87.9
SD
2.9
12.3
3.3
10.9
4.2
5.0
4.8
TABLE 4 Running step parameters. “BCM oscillations” are body center of mass vertical oscillations. No significant correlations between 
these parameters and running economy were observed
Step rate
Step length
Contact time
Swing phase
BCM oscillation
14 km h−1
2.82 (Hz)
(0.12)
1.38 (m)
(0.06)
171 (ms)
(9.22)
541 (ms)
(31.7)
8.8 (cm)
(1.2)
18 km h−1
2.96 (Hz)
(0.09)
1.70 (m)
(0.05)
138 (ms)
(10.4)
542 (ms)
(31.7)
8.3 (cm)
(1.0)
FIGURE 3 Mechanical work intensity Pmech. The positive 
(Ppos), negative (Pneg), and the metabolic calculated work (Pmetab) 
are corrected by 25% efficiency for positive work and −120% for 
negative work. Error bars are one standard deviation
8 of 15 |   
HANSEN et al.
The same was the case for shank and foot volumes (Table 5). 
However, the foot ratio between the forefoot and the 
Achilles tendon moment arm was significantly correlated 
with RE at 18 km h−1 (Rho = −0.64; p = 0.030) (Table 
5) (Figure 5), that is, a greater ratio seems an advantage 
regarding RE.
Whole body stiffness normalized to body mass was 
930 (±227) N  m−1  kg−1 at 14  km  h−1 and 1240 (±240) 
N m−1 kg−1 at 18 km h−1. Leg stiffness (kleg) was 900 (±220) 
and 1200 (±230) N  m−1  kg−1. None of these stiffnesses 
were significantly correlated with RE (Rho  =  −0.18, 
p = 0.63 and Rho = −0.58, p = 0.088, respectively). Whole 
body stiffness at 14  km  h−1 (Rho  =  −0.69; p  =  0.035) 
and at 18 km h−1 (Rho = −0.75; p = 0.018) was signifi-
cantly correlated with the Achilles tendon moment arm 
(LAch) (Figure 7) indicating that a short moment arm co-
incided with high stiffness. Also leg stiffness was signifi-
cantly correlated with the Achilles tendon moment arm 
at 14 km h−1 (Rho = −0.7; p = 0.025) and at 18 km h−1 
(Rho = −0.83; p = 0.006). The ratio between whole body 
FIGURE 4 
Left: Relation 
between mechanical work expressed 
as ml O2 min−1 kg−1 and measured 
VO2 min−1 kg−1 at 18 km h−1. Right: 
Relation between mechanical work 
expressed as liter O2 min−1 and actually 
measured VO2 at 18 km h−1
FIGURE 5 
Relation (top) between 
Achilles tendon moment arm (LAch) and 
RE and (bottom) relation between foot 
ratio and RE. Foot ratio is forefoot LAch
−1
   | 9 of 15
HANSEN et al.
stiffness and LAch was significantly correlated with RE at 
18 km h−1 (Rho = −0.72, p = 0.024) (Figure 7). Absolute 
whole body stiffness (N m−1) was significantly correlated 
with body mass (Rho = 0.68, p = 0.035) and to absolute 
VO2 (L min−1) (Rho = 0.71, p = 0.028).
3 | DISCUSSION
3.1 | Mechanical power
By use of 2- D biomechanical movement analysis, it has 
earlier been attempted to quantify mechanical power ex-
erted by the muscles during human running. However, 
different approaches have been used as the mechani-
cal work may be defined and/or divided into external 
work on the surroundings and internal work due to the 
movements of segments like arms, legs, and trunk. The 
external work has been measured by force platforms 
(Cavagna et al., 1976), accelerometers (Cavagna et al., 
1964), or by movements of the center of mass of the whole 
body (Luhtanen & Komi, 1978). The internal work is cal-
culated by summation of potential and kinetic energy of 
all body segments (Laursen et al., 2000; Winter, 1979). By 
use of these different approaches power values of 556 W 
(Cavagna & Kaneko, 1977), 172 W (Norman et al., 1976), 
931 W (Luhtanen & Komi, 1978), and 396 W (Williams 
& Cavanagh, 1983) have been reported. These studies 
were based on 2- D cinematography except the study of 
Williams and Cavanagh (Williams & Cavanagh, 1983), 
which was three dimensional with running velocities var-
ying between 3.6 and 3.9 m s−1 (13– 14 km h−1). Williams 
and Cavanagh subdivided their subjects into three groups 
based on RE at 3.57  m  s−1 (approximately 13  km  h−1) 
and observed a trend between relative positive power 
and three “Physiological Efficiency Groups” (Williams & 
Athlete
Achilles tendon
moment arm (cm)
Shank volume 
(liters)
Foot volume 
(liters)
1
3.74
3.59
1.24
2
3.96
3.01
1.00
3
3.46
2.78
0.81
4
3.69
2.93
0.89
5
4.21
2.78
0.92
6
4.03
2.28
0.77
7
4.14
2.71
0.97
8
4.50
2.65
0.90
9
3.60
2.39
0.83
10
4.05
2.64
0.88
11
3.60
2.01
0.76
12
3.91
2.49
0.85
Mean
3.91*
2.69
0.90
SD
0.30
0.40
0.13
TABLE 5 Soleus moment arm, leg 
(shank) and foot volumes. * denotes a 
significant correlation to running velocity 
at 18 km h−1 (Rho = −0.66; p = 0.02)
FIGURE 6 
Relation between RE and 
relative soleus fascicle length at 14 and 
18 km h−1. The correlation at 18 km h−1 
was statistically significant (Rho = −0.62; 
p = 0.03)
10 of 15 |   
HANSEN et al.
Cavanagh, 1983) but, to the best of our knowledge, no-
body has found a significant correlation between biome-
chanical calculations of power and measured VO2 during 
running.
In the present study, a 3- D modeling approach was ap-
plied to velocities of 14 and 18 km h−1 and the mechanical 
power was found to be 237 (30.3) and 264 (53.9) Watt cor-
responding to 3.41 (0.28) and 3.79 (0.54) W kg−1, respec-
tively (Figure 3). When mechanical power was expressed 
as metabolic cost corresponding to liter O2 min−1 a signifi-
cant correlation was found between the mechanical calcu-
lations and the measured VO2 (Figure 4), indicating that 
there is a mechanical explanation behind RE. However, 
since body mass was also highly correlated with VO2 mea-
sured in absolute values, it is possible that the correlation 
only reflects the fact that heavy subjects consume more 
oxygen and produce more mechanical energy.
It was remarkable that VO2 calculated from mechan-
ical power was almost twice as high as the actually mea-
sured VO2. A fixed value of 20 kJ per liter O2 was used to 
“convert” power to VO2 but using the actually measured 
respiratory quotient ratios would only have changed the 
calculated VO2 a negligible degree. The most likely expla-
nation for the high calculated values is that summation 
of segment energies cannot account for storage and reuse 
of elastic energy in the tendons. This energy should be 
subtracted, but there is no way we can calculate or esti-
mate the size of it.
When mechanical power was normalized to body 
mass, no significant correlations were found regarding 
RE, which could be due to oxygen consumption not being 
linearly related to body mass in terms of physiology. This 
is a well- known phenomenon and it has been suggested 
to use body mass0.75 (Bergh et al., 1991). However, even 
body mass0.66 did not improve the correlations of the 
present study. It is not straight forward to explain the 
missing correlation between RE and relative mechan-
ical work rate, but it may be an inherent problem that 
most biomechanical methods use anthropometric tables, 
like Dempster (Dempster, 1955), to calculate segmental 
masses and moments of inertia. This is also the case for 
the method presented by Winter (1979), which was used 
in the present study. When these body parameters only 
vary with body mass and segment lengths, it is obvious 
that this causes individual subjects to become more iden-
tical and thereby more difficult to separate mechanically 
regarding RE. A future approach to relate biomechanical 
movement analysis to RE should deal with individual 
differences between the real body segments of the sub-
jects as we found an extreme difference of 56% between 
the highest and the lowest shank volume in the present 
study (Table 5).
FIGURE 7 
On top: relation between 
whole body stiffness and Achilles tendon 
moment arm. Bottom: relation between 
RE and the ratio between stiffness and 
Achilles tendon moment arm
   | 11 of 15
HANSEN et al.
The method used by the present study and by Williams 
& Cavanagh (1983) was introduced by Winter (1979, 2009). 
It accounts for exchange of energy both between and within 
segments, but it cannot deal with storage and reuse of elas-
tic energy in the muscle– tendon unit. The method allows 
for calculating the positive and the negative mechanical 
work separately and by assuming a mechanical efficiency 
for eccentric and concentric work it is possible to estimate 
a net efficiency for running only based on biomechanical 
movement analysis. In the present study, net efficiency was 
41.6 (0.26) % and 41.9 (1.09) % for 14 and 18 km h−1, respec-
tively. This corroborated the net efficiency of 44% reported 
by Williams & Cavanagh (1983) and it indicates that the 
mechanical efficiency of running is significantly higher as 
the approximately 25% efficiency of pure concentric mus-
cle work (Asmussen, 1953; Asmussen & Bonde- Petersen, 
1974; Aura & Komi, 1986).
More simple biomechanical parameters like contact 
time, stride rate, and stride length have been investigated 
on numerous occasions and have rarely been found to have 
any influence on RE (Barnes et al., 2014). One study found 
a shorter contact time in Kenyan runners and argued that 
this would influence stiffness and the ability to store and 
reuse elastic energy (Santos- Concejero et al., 2017). In the 
present study, no significant correlations between these 
parameters and RE were seen (Table 4).
3.2 | Achilles tendon moment 
arm and RE
In the study of Scholz et al. (2008) a significant correlation 
(r = 0.75) was reported between running economy (RE) 
at 16 km h−1 and the Achilles tendon moment arm (LAch). 
In the present study, a significant correlation (Rho = 0.66) 
was found between LAch and RE at 18 km h−1.
In an extensive study of RE, 63 runners (24 females, 
39 males) of collegiate or national level were examined 
regarding RE and Achilles tendon moment arm (LAch) 
(Barnes et al., 2014). For all subjects, LAch showed a very 
high and significant correlation (r  =  0.90) with RE at 
14 km h−1 implying that a short moment arm is advanta-
geous regarding RE. The LAch was on average 4.4 cm for 
males and 3.5 cm for females with r- values of 0.82 and 
0.81 between RE and LAch. Accordingly, males and fe-
males had the same RE despite differences in LAch (Barnes 
et al., 2014).
In a study of Kenyan and Japanese long- distance 
runners by Kunimasa et al. (2014) it was found that the 
Kenyan runners had significantly longer LAch (4.46 cm) 
than the Japanese runners (4,07  cm). LAch of the 
Kenyans ranged from approximately 3.6– 5.1 cm (Figure 3  
in Kunimasa et al., (2014)) and, when both Kenyan and 
Japanese runners were pooled, a significant correlation 
(r  =  0.55) was found between LAch and a performance 
index (International Athletics Amateur Federation). This 
indicated a long moment arm to be an advantage, but 
notably, RE was not measured directly (Kunimasa et al., 
2014; Spiriev, 2011).
Considering the results of the present study with an 
r- value of 0.66, and the previous results from the litera-
ture with even higher r- values (Barnes et al., 2014; Scholz 
et al., 2008), it appears safe to conclude that LAch is highly 
correlated with RE despite the results of (Kunimasa et al. 
(2014).
3.3 | Running economy
RE at 16 km h−1 was 48 ml O2 kg−1 min−1 in Scholz et al. 
(2008) corresponding to 182 ml O2 kg−1 km−1 while in the 
present study RE was 44 ml O2 kg−1 min−1 at 14 km h−1 cor-
responding to 189 ml O2 kg−1 km−1. This remarkable differ-
ence is difficult to explain. The maximal oxygen uptake was 
67 ml O2 min−1 kg−1 in the present study but only 55 ml 
O2 min−1 kg−1 in Scholz et al. (2008), so it cannot be excluded 
that a systematic difference existed between the appara-
tus used for gas analysis during running, especially as the 
Dutch athletes were described as “highly trained” (Scholz 
et al., 2008). When RE is expressed as ml O2 kg−1 km−1, it 
is possible to compare RE at different running velocities. 
Accordingly, RE ranges from 170 to approximately 250 ml 
O2 kg−1 km−1 in the literature. The athletes of the present 
study ranged from 170 to 219 ml O2 kg−1 km−1 (Table 3) 
and the Olympic Champion Frank Shorter (USA, Olympic 
marathon winner, 1972) has been reported to have had a 
RE of 172 ml O2 kg−1 km−1 while Joseph Ngugi (Kenyan 
Olympic gold medalist on 5000 m, 1988) has been reported 
to have had a RE of 170 ml O2 kg−1 km−1 (Saltin, Larsen, 
et al., 1995). Besides the study of Scholz et al. (2008), one 
other study has reported very low values of VO2 during sub-
maximal running (147– 157 ml O2 kg−1 km−1) (Spurrs et al., 
2003) and correspondingly low values of VO2max (< 60 ml 
O2 min−1 kg−1). In fact, the runners in Spurrs et al. (2003) 
appeared to have a RE better than the best Kenyan and 
African runners ever measured (Larsen, 2003; Larsen & 
Sheel, 2015; Saltin, 2003; Saltin, Larsen, et al., 1995; Weston 
et al., 2000), which is highly unlikely.
3.4 | Foot lever ratio
Kunimasa et al. found a significant correlation between IAAF 
score (Spiriev, 2011) and a ratio between the forefoot and the 
LAch (Kunimasa et al., 2014). It turned out that the Kenyans 
had a shorter forefoot and longer LAch than the Japanese 
12 of 15 |   
HANSEN et al.
runners. A contradictory and significant correlation was 
found between the same foot ratio and RE at 18 km h−1 in 
the present study (Figure 5). A possible explanation for this 
could be that RE was not measured in the study of Kunimasa 
et al. (2014) as an IAAF score was used instead. The foot lever 
ratio is an interesting property as it has been suggested that 
a certain gear ratio between the active muscles and the mo-
ment arm of the external ground reaction force may affect 
the energy cost of locomotion (Biewener et al., 2004; Carrier 
et al., 1994; Karamanidis & Arampatzis, 2007).
3.5 | Leg volume
A strong relation has been reported between RE and lower 
leg circumference, which further indicated a trend toward 
Kenyan elite runners having a lower (smaller) leg thick-
ness than European runners (Saltin, 2003), and it has been 
suggested that lighter shanks could partly explain the 
superior RE observed in Kenyan runners (Larsen, 2003; 
Larsen et al., 2004; Saltin, 2003; Saltin, Kim, et al., 1995; 
Saltin, Larsen, et al., 1995). Supposedly, it should require 
less energy to accelerate a lighter lower leg back and for-
ward due to a lower segment moment of inertia. Scholz 
et al. (2008) measured foot length, lower leg length, lower 
leg volume, and lower leg moment of inertia in 15 Dutch 
well- trained runners and found significant correlations 
between lower leg volume and RE and between lower leg 
moment of inertia and RE. However, after analysis for 
covariation with the Achilles tendon moment arm, they 
rejected the influence of these parameters (Scholz et al., 
2008). In the present study, shank and foot volumes were 
measured by surface scanning, but no significant correla-
tions were found between shank or foot volume and RE 
(Tables 5 and 6), although there were 56% difference be-
tween the smallest and the largest shank volume. Running 
experiments have shown that shod running is less expen-
sive compared to barefooted but adding an extra weight 
of 100 g per shoe increased VO2 by 1% (Franz et al., 2012).
Different animal species exhibit often very different 
anatomy of the legs. Taylor et al. (1974) calculated that 
cheetahs, gazelles, and goats had equal energy cost mov-
ing their limbs during running despite large anatomical 
differences regarding limb mass, length, and distance to 
limb center of mass. It was therefore suggested that most 
of the energy expended in running at constant speed is not 
used to accelerate and decelerate limbs.
3.6 | Fascicle length
In the present study, the fascicles of the soleus muscle 
showed a significant correlation to RE at 18 km h−1 when 
fascicle length was normalized to shank length (Figure 
6). This indicated that longer muscle fibers have a posi-
tive influence on RE. However, this is not supported by 
the literature. On the contrary, Japanese runners were 
found to have longer GM fascicles than Kenyan runners 
(Sano et al., 2015). In the present study the medial gas-
trocnemius (GM) fascicles were 5.62 (0.72) cm on average 
(range: 4.50– 6.84 cm), which corresponds very well the 
5.36 (0.72) cm reported by Abe et al. (2000) for the GM in 
distance runners while 6.64 (1.32) cm for sprint runners. It 
was suggested that long muscle fibers would be beneficial 
for sprint runners due to a more optimal force– velocity 
relation (Abe et al., 2000; Lee & Piazza, 2009). Longer fas-
cicles than in controls have also been reported for sumo 
wrestlers, and it was suggested that fascicle length may 
increase with strength training (Kearns et al., 2000).
Long fascicles imply long muscle fibers and more sar-
comeres in series. As longer muscle fibers can contract 
at a higher shortening velocity than shorter fibers this 
would indicate a more beneficial force– velocity relation-
ship of the muscles in question (Abe et al., 2001). At sub-
maximal muscle activation, this means that the muscle 
can generate more force at the same shortening velocity. 
However, it is an important question whether the mus-
cle fibers of, for example, the GM actually lengthen and 
shorten during running or the ankle joint movements 
are accomplished only by elastic length changes of the 
Achilles tendon. Giannakou et al. have shown that the 
TABLE 6 Correlations (Spearman's Rho) between 
anthropometry and RE. * indicates a statistically significant 
correlation (Achilles tendon moment arm and RE at 18 km h−1). 
Foot ratio is Forefoot∙LAch
−1
14 km∙h−1
18 km∙h−1
Leg length
Rho = 0.06
p = 0.85
Rho = 0.34
p = 0.28
Thigh length
Rho = 0.09
p = 0.77
Rho = 0.45
p = 0.14
Shank length
Rho = 0.18
p = 0.59
Rho = 0.46
p = 0.164
Foot length
Rho = 0.22
p = 0.49
Rho = 0.47
p = 0.12
Toe length
Rho = 0.08
p = 0.80
Rho = 0.37
p = 0.24
LAch
Rho = 0.33
p = 0.30
Rho = 0.66
p = 0.02*
Shank vol.
Rho = 0.19
p = 0.56
Rho = 0.33
p = 0.30
Foot vol.
Rho = 0.27
p = 0.39
Rho = 0.49
p = 0.11
Foot ratio
Rho = −0.41
p = 0.18
Rho = −0.60
p = 0.043*
   | 13 of 15
HANSEN et al.
GM fascicles stretch and shorten approximately 2.5 cm 
during running (11 km h−1) in 12 long- distance runners 
(Giannakou et al., 2011) and Lai et al. found that the so-
leus fascicles covered 20% of the lengthening/shortening 
of the muscle– tendon unit during running at various 
speed (Lai et al., 2015). Since muscle strength is not re-
lated to the length of the muscle fibers, it is certain that 
longer muscle fibers with more sarcomeres in series con-
sume more energy than shorter fibers when producing 
the same force (Walmsley & Proske, 1981). The force– 
length relationship of the muscle fibers is, on the other 
hand, highly influenced by fiber length, as longer fibers 
exhibit a wider range of length for optimal force produc-
tion (Walmsley & Proske, 1981).
Finally, the most important feature of longer muscle 
fibers may be an altering of the force– velocity relation so 
that the muscle can produce more force at the same short-
ening velocity (Abe et al., 2000; Lee & Piazza, 2009). Only 
the relative length of the soleus fascicles correlated signifi-
cantly to RE at 18 km h−1 in the present study (Figure 4), 
so additional research is required to establish whether long 
muscle fibers are an advantage regarding RE. This is espe-
cially interesting as reports exist showing that the number 
of sarcomeres in series can be increased in rats after down-
hill running (Lynn & Morgan, 1994; Lynn et al., 1998).
3.7 | Stiffness and storage of 
elastic energy
A significant correlation between muscle– tendon stiffness 
and RE was found by Barnes et al. (2014). It was, however, 
poorly described how, exactly, stiffness was measured, 
but it was a maximal stiffness measured during vertical 
jumping. Barnes et al. also found a significant correlation 
between LAch and stiffness (Barnes et al., 2014), which was 
also found in the present study (Figure 7) where stiffness 
was measured during running. In both cases it seems that 
a short moment arm and a high stiffness follow each other 
and are somehow beneficial for RE. In Scholz et al. it was 
argued that a short moment arm of the Achilles tendon 
would imply a higher muscle force when producing a cer-
tain moment about the ankle joint as compared to a longer 
moment arm (Scholz et al., 2008). The higher muscle force 
would cause an increased stretch of the Achilles tendon 
during the eccentric contraction and thereby store more 
elastic energy in the tendon to be reused during the im-
mediately following concentric contraction. This may cer-
tainly be true, but it requires the length and the stiffness of 
the tendon to match the muscle force exactly, so that the 
required range of joint motion is achieved.
Sano et al. found longer Achilles tendons in Kenyan than 
Japanese runners but also longer shanks. The cross- sectional 
area of the Achilles tendon was also significantly larger 
than that of the Japanese (Kunimasa et al., 2014; Sano et al., 
2015). Interestingly, given an upper limit on allowable tis-
sue stress, a longer tendon would allow for storage of more 
elastic energy as would a stiffer tendon, which is the impli-
cation of a larger cross- sectional area.
Another effect of a short Achilles tendon moment arm 
may be a positive influence on the force– velocity relation 
of skeletal muscles. At a given angular motion in the ankle 
joint during plantar flexion, a shorter LAch will cause a lower 
shortening velocity than a longer LAch, simply due to geom-
etry. In this way the required muscle force may be produced 
by fewer motor units and thereby fewer muscle fibers.
4 | CONCLUSIONS
As the first study, we were able to show a significant cor-
relation between biomechanical calculations of mechani-
cal power and absolute oxygen consumption. However, 
this correlation did not exist when data were normalized 
to body mass. This is probably partly due to differences in 
anthropometry not accounted for in biomechanical move-
ment analysis.
The Achilles tendon moment arm is considered highly 
important for RE as a short moment arm theoretically can 
be beneficial for both storage of elastic energy and for the 
force– velocity relation of skeletal muscles. The ratio be-
tween forefoot and Achilles tendon moment arm is also 
significantly correlated with RE due to a beneficial gearing 
of the foot with respect to the external forces. Stiffness of 
the whole body and the stance leg is indirectly important 
for RE as stiffness and Achilles tendon moment arm are 
significantly correlated. High stiffness of the leg muscles 
is very likely to favor storage and reuse of elastic energy 
during running.
CONFLICT OF INTEREST
The authors declare no conflict of interest.
AUTHOR CONTRIBUTION
C. E. Hansen planned and conducted the experiments, 
participated in the calculations, discussion of results, and 
in writing the manuscript. E. B. Simonsen planned and 
conducted the experiments, participated in the calcula-
tions, discussion of results, and in writing the manuscript. 
M. Stensvig participated in the biomechanical data col-
lection and in writing the manuscript. J. Rasmussen par-
ticipated in the biomechanical calculations, discussion 
of results, and in writing the manuscript. J. Wienecke 
participated in data collection and in writing the manu-
script. J. Lorentzen participated in collection of data from 
ultrasonography, data interpretation, and in writing the 
14 of 15 |   
HANSEN et al.
manuscript. C. Villa participated in collection and inter-
pretation of surface scans and in writing the manuscript.
ORCID
Erik B. Simonsen 
 https://orcid.
org/0000-0002-6378-6595 
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How to cite this article: Hansen, C. E., Stensvig, 
M., Wienecke, J., Villa, C., Lorentzen, J., 
Rasmussen, J., & Simonsen, E. B. (2021). Factors 
correlated to running economy among elite 
middle-  and long- distance runners. Physiological 
Reports, 9, e15076. https://doi.org/10.14814/ 
phy2.15076

Factors correlated with running economy among elite middle- and long-distance runners.
Hansen, Cecilie E,Stensvig, Martin,Wienecke, Jacob,Villa, Chiara,Lorentzen, Jakob,Rasmussen, John,Simonsen, Erik B