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Adding carbon fiber to shoe 
soles may not improve running 
economy: a muscle‑level 
explanation
Owen N. Beck1,2*, Pawel R. Golyski1,3 & Gregory S. Sawicki1,2,3
In an attempt to improve their distance‑running performance, many athletes race with carbon fiber 
plates embedded in their shoe soles. Accordingly, we sought to establish whether, and if so how, 
adding carbon fiber plates to shoes soles reduces athlete aerobic energy expenditure during running 
(improves running economy). We tested 15 athletes as they ran at 3.5 m/s in four footwear conditions 
that varied in shoe sole bending stiffness, modified by carbon fiber plates. For each condition, we 
quantified athlete aerobic energy expenditure and performed biomechanical analyses, which included 
the use of ultrasonography to examine soleus muscle dynamics in vivo. Overall, increased footwear 
bending stiffness lengthened ground contact time (p = 0.048), but did not affect ankle (p ≥ 0.060), 
knee (p ≥ 0.128), or hip (p ≥ 0.076) joint angles or moments. Additionally, increased footwear bending 
stiffness did not affect muscle activity (all seven measured leg muscles (p ≥ 0.146)), soleus active 
muscle volume (p = 0.538; d = 0.241), or aerobic power (p = 0.458; d = 0.04) during running. Hence, 
footwear bending stiffness does not appear to alter the volume of aerobic energy consuming muscle in 
the soleus, or any other leg muscle, during running. Therefore, adding carbon fiber plates to shoe soles 
slightly alters whole‑body and calf muscle biomechanics but may not improve running economy.
In competitive athletics, marginal differences distinguish champions from their competitors. For instance, if 
any of the top-five 2016 Olympic women’s marathon finishers ran 0.51% faster, they would have been crowned 
Olympic champion. Such miniscule differences highlight the importance for athletes to optimize all factors that 
influence race performance. One way to optimize athletic performance is to don the best footwear. Using footwear 
that reduces athlete aerobic energy expenditure at a given running speed (improves athlete running economy) can 
augment distance-running performance by decreasing user relative aerobic  intensity1–3. An established method 
of improving footwear to augment athlete distance-running performance is to reduce its  mass1,2,4,5. Based on 
literature values, if an aforementioned Olympic marathoner re-raced in shoes that were 100 g less than their 
original footwear, they would have expended aerobic energy at an ~ 0.8% slower  rate5, run the marathon ~ 0.56% 
 faster6, and taken the gold medal back to their country.
A longstanding footwear technology that has polarized the running community is the incorporation of car-
bon fiber plates in shoe  soles7. Despite the rampant use of carbon fiber plates in  athletics8–10, policy makers are 
regulating the use of these plates in distance-running footwear based on the notion that they provide wearers an 
‘unfair advantage’ over competitors without such  technology11. These views persist even though it is inconclusive 
whether adding carbon fiber to shoe soles improves running  economy12–16 or distance-running performance. 
To date, two studies have reported that adding optimally stiff carbon fiber plates to shoe soles improves running 
economy by 0.812 and 1.1%13, while data from four other studies suggest that adding carbon fiber plates to shoe 
soles does not affect running  economy14–17.
Moreover, neither study that improved athlete running economy by adding carbon fiber plates to their 
shoes measured a physiologically-relevant link between the footwear-altered biomechanics and aerobic energy 
 expenditure12,13. Namely, the first study did not identify a biomechanical  mechanism12 while the second study 
suggested that adding carbon fiber plates to shoe soles improves running economy by altering a parameter that 
likely does not affect  metabolism13. Specifically, the second study reported that adding carbon fiber plates to 
OPEN
1George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 
USA. 2School of Biological Sciences, Georgia Institute of Technology, Atlanta, GA, USA. 3Parker H. Petit Institute 
for Bioengineering and Biosciences, Georgia Institute of Technology, Atlanta, GA, USA. *email: obeck3@
gatech.edu
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shoe soles improves running economy by decreasing the leg-joint’s summed angular impulse (integral of torque 
with respect to time) during push-off13. However, decreasing angular impulse via greater peak torque and much 
shorter durations worsen running  economy18–20. Consequently, it remains uncertain whether adding carbon fiber 
plates to shoe soles improves running economy, and if so how—we need a muscle-level explanation.
Muscle contractions drive whole-body aerobic energy expenditure during  locomotion21. To date, no study 
has assessed muscle fascicle dynamics from athletes running with shoes that have carbon fiber soles. Based on 
leg-joint analyses, which do not necessarily reflect the underlying fascicle  dynamics22,23, metatarsophalangeal- 
and ankle-joint dynamics are more affected during running with the addition of carbon fiber plates to shoe 
soles than knee- and hip-joint  dynamics13,14,24–26. Since intrinsic foot muscles do not directly affect running 
 economy27, altered plantar flexor fascicle dynamics may help explain changes in running economy with versus 
without carbon fiber plates added to shoe soles.
How does adding carbon fiber plates to shoe soles affect athlete plantar flexor dynamics during running? 
Adding carbon fiber plates to shoe soles increases the footwear’s 3-point bending  stiffness12,13,15,17,24,25,28 and 
typically shifts the athlete’s center of pressure more anterior along the foot during ground  contact24,25,28,29. These 
altered biomechanics generally yield a longer moment arm between the ground reaction force (FGRF) and the 
ankle-joint center ( RGRF)13,24. Longer moment arms lead to greater GRF-induced ankle-joint  moments12,13,24,29. 
To prevent the ankle-joint from collapsing, plantar flexor muscle-tendons (MTs) need to generate a greater force 
( FMTs ) and apply an equal and opposite moment about the joint throughout ground contact.
The moment arm between the plantar flexor MTs and ankle-joint center is indicated by rMT30. Increased MT 
force is driven by greater plantar flexor muscle fascicle force ( FM ), which increases metabolic energy  expenditure31 
and can be calculated using the following (Eq. (2)): plantar flexor MT force ( FMT) , its physiological cross-sec-
tional area relative to respective agonist muscles 

PCSA m
tot

30, and pennation angle ( θM).
Adding carbon fiber plates to footwear may also cause plantar flexors to operate at relatively shorter lengths; 
incurring less economical muscle force  production32–35. That is because running in footwear that have carbon 
fiber plates elicits similar leg-joint  angles12,13 and MT lengths ( LMT)36 versus running in footwear absent of 
carbon fiber plates. Hence, reasoning that muscle pennation changes are relatively small, increased MT force 
may further stretch spring-like tendons (tendon length: LT ) and yield shorter in-series muscles lengths ( LM).
Lastly, adding carbon fiber plates to shoe soles may decrease plantar flexor muscle fascicle shortening velocity 
during ground  contact14,29, and elicit more economical force  production33,34. Absent of meaningful changes in 
ankle-joint mechanical power ( Pank ) and plantar flexor MT moment arms ( rMTs ), increasing plantar flexor MTs 
force ( FMTs ) decreases ankle-joint angular velocity ( ωank)14.
In turn, decreased ankle-joint angular velocity may translate to slower MT and muscle fascicle shortening 
velocities.
Perhaps adding carbon fiber to shoe soles can optimize the trade-off between active muscle force (Fact ), 
force–length ( FL ) and force–velocity ( FV ) potential to minimize the active plantar flexor muscle volume ( Vact
)37 (Eq. (5)) and whole-body aerobic energy expenditure during  running12,13. σ is muscle stress and lm is optimal 
fascicle length.
Conceptually, active muscle volume is the quantity of muscle that has adenosine triphosphate (ATP) splitting 
actin-myosin cross-bridges37. Hence, active muscle volume is proportional to metabolic energy expenditure.
The purpose of this study was to reveal if and how adding carbon fiber plates to shoe soles alters running 
biomechanics and economy. In particular, we sought to investigate how footwear 3-point bending stiffness affects 
soleus fascicle dynamics and running economy. Based on the reported interactions between adding carbon 
fiber plates to shoe soles, footwear 3-point bending  stiffness12–15,17,24,25,28,29, and ankle-joint  dynamics13,14,24,29, 
we hypothesized that running with shoes that have stiffer carbon fiber plates would increase soleus fascicle 
force generation while decreasing its operating length and shortening velocity during the ground contact. We 
also hypothesized that an optimal footwear bending stiffness would minimize soleus active muscle volume and 
aerobic energy expenditure. To test our hypotheses, we quantified ground reaction forces, stride kinematics, 
limb-joint biomechanics, soleus dynamics, muscle activation patterns, and aerobic energy expenditure from 15 
athletes running at 3.5 m/s using four separate footwear conditions that spanned a 6.4-fold difference in bend-
ing stiffness (Table 1).
(1)
rMTs · FMTs = RGRF · FGRF
(2)
FM =
FMTPCSA m
tot
cos (θM)
(3)
LM = (LMT − LT)
cos(θM)
(4)
ωank =
Pank
rMTs · FMTs
(5)
Vact =
Fact · lm
σ · FL · FV
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Results
Footwear conditions. 
Each athlete ran in the Adidas Adizero Adios BOOST 2 running shoes (Adidas) 
without carbon fiber plates, as well as in the Adidas with 0.8, 1.6, and 3.2 mm thick carbon fiber plates. The 
Adidas’ average ± SD 3-point bending stiffness was 13.0 ± 1.0 kN/m, and adding 0.8, 1.6, and 3.2 mm thick car-
bon fiber plates to the shoes soles increased the average ± SD footwear 3-point bending stiffness to 31.0 ± 1.5, 
43.1 ± 1.6, and 84.1 ± 1.1 kN/m, respectively. Further, the slope of each footwear-condition’s 3-point bending 
force–displacement profile was well-characterized by a linear function (average ± SD; Adidas  R2: 0.97 ± 0.02; 
Adidas plus in-soles:  R2: 0.99 ± 0.01).
Limb‑joint dynamics. 
Footwear bending stiffness did not affect hip, knee, or ankle angles or moments 
(Fig. 1). Specifically, footwear bending stiffness was not associated with average, minimum, or maximum ankle 
(all p ≥ 0.121) (Fig. 1e and Fig. 2g,h), knee (all p ≥ 0.128) (Fig. 1c), or hip (all p ≥ 0.076) angle (Fig. 1a). Simi-
larly, footwear bending stiffness did not affect average or maximum ankle (both p ≥ 0.060) (Fig. 1f), knee (both 
p ≥ 0.239) (Fig. 1d), or hip (both p ≥ 0.112) (Fig. 1b) moment.
Stride kinematics and ground reaction forces. 
Increased footwear bending stiffness was associated 
with longer ground contact time (p = 0.048), but not step time (p = 0.956). Regarding GRFs, neither stance aver-
age vertical (p = 0.209) (Fig. 2a,b), braking (p = 0.441) (Fig. 2c,d), nor propulsive (p = 0.133) (Fig. 2c,d) GRF 
differed across footwear bending stiffness conditions. Additionally, footwear bending stiffness did not affect the 
fraction of vertical (p = 0.881) or horizontal (p = 0.816) GRF exhibited during the first half of ground contact.
Muscle–tendon dynamics. 
Footwear bending stiffness did not affect soleus muscle–tendon (MT) dynam-
ics (Fig. 3). Neither average soleus MT force (p = 0.080) (Fig. 3a,b), length (p = 0.150) (Fig. 3c,d), nor velocity 
(p = 0.719) (Fig. 3e,f) during ground contact changed with altered footwear bending stiffness. Additionally, the 
ratio of the GRF versus soleus MT moment arms to the ankle-joint center (gear ratio, also known as 1/effec-
tive mechanical advantage) was not affected by footwear bending stiffness (average and maximum gear ratio 
p = 0.371 and p = 0.752, respectively) (Fig. 2e,f).
Soleus dynamics. 
Footwear bending stiffness did not influence average or maximum soleus fascicle pen-
nation angle (both p ≥ 0.476) (Fig. 4a,b), force (both p ≥ 0.115) (Figs. 4c,d, 5b), length (p ≥ 0.286) (Fig. 4e,f and 
Fig. 5a), or velocity (both p ≥ 0.224) (Fig. 4g,h and Fig. 5c). As such, footwear bending stiffness did not affect 
stride-average soleus active muscle volume (p = 0.538; d = 0.241) (Figs. 5d, 6b).
Muscle activation. 
Footwear bending stiffness did not affect stance- or stride-averaged activation of any 
measured muscle: soleus (both p ≥ 0.315) (Fig. 7a), medial gastrocnemius (both p ≥ 0.538) (Fig. 7b), tibialis ante-
rior (both p ≥ 0.445) (Fig. 7c), biceps femoris (both p ≥ 0.190) (Fig. 7d), vastus medialis (both p ≥ 0.146) (Fig. 7e), 
gluteus maximus (both p ≥ 0.603) (Fig. 7f), or rectus femoris (both p ≥ 0.406) (Fig. 7g) (Table 2).
Running economy. 
Footwear bending stiffness did not affect gross aerobic power (p = 0.458; d = 0.04) 
(Fig. 6a). Only the 84.1 ± 1.1 kN/m footwear bending stiffness condition elicited a mean gross aerobic power 
Table 1.  Participant characteristics. Four and eleven participants initiated ground contact with a mid/forefoot 
strike (M/FFS) and heel strike (HS), respectively. All participants maintained the same foot strike pattern 
across footwear conditions.
Participant
Age (yrs)
Height (m)
Mass (kg)
Leg length (m)
US men’s shoe size
Initial foot strike
Standing aerobic 
power (W/kg)
1
20
1.65
57.0
0.89
9
HS
1.37
2
27
1.73
65.6
0.91
10
M/FFS
1.21
3
19
1.77
60.0
0.91
9
HS
1.98
4
27
1.88
66.4
0.97
12
M/FFS
1.44
5
27
1.70
58.9
0.83
10
HS
1.42
6
23
1.80
72.8
0.97
10
HS
1.70
7
19
1.76
71.5
0.91
10
HS
1.67
8
24
1.78
71.3
0.93
10
HS
1.58
9
20
1.80
66.5
0.95
10
HS
1.72
10
28
1.80
73.2
0.98
9
M/FFS
1.76
11
28
1.74
74.5
0.83
10
HS
1.32
12
28
1.89
75.4
0.95
12
M/FFS
1.21
13
42
1.74
73.6
0.90
11
HS
1.04
14
26
1.79
62.2
0.90
10
HS
1.38
15
23
1.78
65.2
0.89
9
HS
1.28
Average ± SD
25.4 ± 5.7
1.77 ± 0.06
67.6 ± 6.1
0.91 ± 0.05
10.1 ± 1.0
4 M/FFS 11 HS
1.47 ± 0.26
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value that was numerically less (non-significantly) than the footwear condition without a carbon fiber plate 
(13.0 ± 1.0 kN/m). Compared to the 13.0 ± 1.0 kN/m footwear condition, the 84.1 ± 1.1 kN/m footwear bending 
stiffness condition yielded 0.3 ± 2.2% lower gross aerobic power (paired t-test p = 0.663). To achieve a strong 
statistical power regarding the gross aerobic power elicited from the 84.1 ± 1.1 kN/m versus 13.0 ± 1.0 kN/m 
footwear bending stiffness condition (statistical power = 0.8), post-hoc analyses suggest that we would need to 
test 9104 participants.
Individually, the footwear condition that minimized running economy was 13.0 ± 1.0 kN/m for 1 participant, 
31.0 ± 1.5 kN/m for 4 participants, 43.1 ± 1.6 kN/m for 4 participants, and 84.1 ± 1.1 kN/m for 6 participants. Also, 
the footwear bending condition that elicited the worst running economy was 13.0 ± 1.0 kN/m for 5 participants, 
31.0 ± 1.5 kN/m for 3 participants, 43.1 ± 1.6 kN/m for 3 participants, and 84.1 ± 1.1 kN/m for 4 participants 
(Supplementary Fig. S1a–o).
Discussion
Across a 6.4-fold increase in footwear bending stiffness, our participants ran with nearly identical body, limb-
joint, and calf muscle mechanics, as well as elicited non-different running economy values. Footwear bending 
stiffness did not affect participant GRFs, limb-joint kinematics, or kinetics. Similarly, soleus MT and fascicle 
dynamics were unaltered across conditions. Regarding our hypotheses, running in stiffer footwear did not affect 
soleus fascicle force, length, or velocity; leading us to reject our initial hypothesis. While no previous study 
has quantified muscle fascicle dynamics from athletes running in shoes that varied in bending stiffness, our 
participant’s unaltered ankle-joint dynamics contrasts some previous  reports12,13,24. Yet, the only biomechanical 
difference between our study and the classic investigation that reported that adding carbon fiber plates to shoe 
soles improve running  economy12 is that the classic investigation found an increased maximum ankle moment 
with the use of stiffer footwear, whereas we did not. Further, while there are likely covariates, one previous 
study reported that athletes running in commercial shoes with curved carbon fiber plates embedded in their 
soles exhibited shorter GRF-ankle joint moment arms during ground contact compared to without carbon fiber 
 plates38. Therefore, footwear with increased bending stiffness may not universally increase ankle-joint gear ratio.
Despite controlling for shoe mass, adding carbon fiber plates to footwear did not affect running economy nor 
soleus active muscle volume. Thus, we rejected our second hypothesis. Because footwear bending stiffness did 
not affect the stride-average activation for any of the measured muscles (Table 2, Fig. 7), none of the respective 
active muscle volumes changed across footwear conditions (active muscle volume = total muscle volume × relative 
activation)37. This is now the fourth study that failed to replicate Roy and Stefanyshyn’s classic  investigation12, 
Figure 1.  Average (a,b) hip, (c,d) knee, and (e,f) ankle angle and net moment versus time during running with 
footwear of varied 3-point bending stiffness: 13.0 (black), 31.0 (blue), 43.1 (green), and 84.1 kN/m (orange). 
Vertical lines indicate the average end of ground contact for the respective footwear condition. Flexion (Flx) and 
Extension (Ext).
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which stated that adding carbon fiber plates to shoe soles improves running  economy14–17. Since the classic 
investigation, only Oh and  Park13 reported that adding carbon fiber plates to running shoes elicited a relative 
footwear stiffness that improves running economy at 2.4 m/s. Moreover, the classic  investigation12 reported that 
participant body mass was inversely correlated with the change in oxygen uptake at their intermediate footwear 
stiffness condition (38 kN/m) relative to footwear condition that did not have a carbon fiber plate (18 kN/m). 
Hence, compared to their smaller participants, the running economy of their larger participants improved more 
by adding carbon fiber plates to their shoe soles. In the present study, post-hoc analyses revealed that participant 
body mass was independent to the change in aerobic power during the most compliant footwear condition ver-
sus any of the stiffer footwear conditions (all p ≥ 0.502). Moreover, due to the implications of muscle dynamics 
on aerobic  power37, we performed post-hoc linear regressions which revealed that the change in aerobic power 
from the footwear condition that did not contain a carbon fiber insole (13.0 ± 1.0 kN/m) was not correlated 
to the corresponding change in contact time (p = 0.135), soleus force generation (p = 0.614), or soleus velocity 
(p = 0.324). Further, there were two a potentially spurious weak correlations: (1) soleus active muscle volume 
versus gross aerobic power (r = -0.329; p = 0.039) and (2) change in soleus length versus change in gross aerobic 
power (r = 0.311, p = 0.040). Thus, we did not uncover any reasonable muscle-level parameters that correlated 
with the aerobic power when athletes ran in footwear conditions using carbon fiber plates versus without carbon 
fiber plates.
Figure 2.  (Left) Average (a,b) vertical and (c,d) horizontal ground reaction force (GRF), (e,f) soleus muscle 
tendon (MT) gear ratio, and (g,h) net ankle moment versus time and (right) footwear 3-point bending stiffness 
(right): 13.0 (black), 31.0 (blue), 43.1 (green), and 84.1 kN/m (orange). Vertical lines indicate the average end of 
ground contact for the respective condition and error bars indicate SE when visible.
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If footwear bending stiffness does not affect running economy, why does wearing Nike prototype footwear 
with carbon fiber plates embedded in their midsole (Nike) improve running economy compared to wearing 
Adidas footwear?39 Perhaps Nike’s carbon fiber plate provide the structure necessary for the midsole foam to 
function. Despite a 264% increased bending stiffness, when athletes run in Nike they elicit slightly shorter 
GRF to ankle-joint moment arms compared to running in Adidas  footwear38. This increased footwear bending 
stiffness and shortened ankle-joint moment arm may be related to Nike’s curved carbon-fiber midsole  plates39. 
Additionally, compared to the Adidas footwear, the respective Nike soles are ~ 8 mm taller (35–62% taller depend-
ing on midsole location), the midsole foam is roughly half as stiff (in-series linear stiffness, not bending), and 
its hysteresis is 11.1% less during vertical loading and  unloading39. Altogether, because both decreased linear 
 stiffness40–42 and relative mechanical energy  dissipation43 in-series to the stance-limb are associated with more 
economical running, Nike footwear may elicit superior running economy values than Adidas footwear due to 
their relatively compliant and resilient midsole foam—not increased bending stiffness.
This study has potential limitations. First, our carbon fiber plates were located between the athlete’s sock and 
the Adidas midsole foam. The lack of cushioning on top of the stiffer carbon fiber plates may have elicited less 
comfortable footwear compared to the more compliant footwear conditions. Second, prior to the experimental 
trials, each participant performed a five-minute treadmill running habituation trial in the Adidas footwear 
without a carbon-fiber in-sole. Thus, differences in the habituation time between the footwear bending stiffness 
conditions may have affected our results. Even though humans adapt their biomechanics in just one step when 
landing onto terrain with different  compliance44–46, running with carbon fiber insoles may require a more exten-
sive habituation period, like that of more complicated lower-limb devices (e.g. exoskeletons)47–49. Additionally, 
we quantified soleus dynamics and not gastrocnemius dynamics because the soleus is the largest ankle plantar 
 flexor50, it is the primary muscle that lifts and accelerates the participant’s center of mass during  locomotion51,52, 
it likely generates the greatest muscle force of any plantar  flexor30, and it is often estimated to consume the most 
metabolic energy of any plantar flexor during  running30,53,54. Consistent with previous running studies that related 
longitudinal bending stiffness to metabolic energy  expenditure12,13, we used a controlled laboratory environment 
and adequate sample size to relate metabolic energy expenditure collected in one session to biomechanical data 
Figure 3.  (Left) Average (a,b) soleus muscle–tendon (MT) force, (c,d) length, and (e,f) velocity versus time 
and (right) footwear 3-point bending stiffness (right): 13.0 (black), 31.0 (blue), 43.1 (green), and 84.1 kN/m 
(orange). Vertical lines indicate the average end of ground contact for the respective footwear condition and 
error bars indicate SE when visible.
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collected from a separate  session55. Moreover, regardless of how little footwear technology improves metabolic 
energy expenditure, even small improvements help separate champions from their peers in competitive athletics.
Conclusion
Changing footwear bending stiffness hardly changes athlete biomechanics and may not improve running econ-
omy. Therefore, if competitive distance runners went back in time, added carbon fiber plates to their footwear, 
and re-raced, their performance would likely not change.
Methods
Participants. 
Fifteen males participated (Table 1). All participants were apparently free of cardiovascular, 
orthopedic, and metabolic disorders, and could run 5 km in < 25 min. Prior to the study, each participant gave 
informed written consent in accordance with the Georgia Institute of Technology Central Institutional Review 
Board. During the study. We followed the Georgia Institute of Technology Central Institutional Review Board’s 
approved protocol and carried out the study in accordance with these approved guidelines and regulations.
Figure 4.  (Left) Average (a,b) soleus (Sol) fascicle angle, (c,d) force, (e,f) length, and (g,h) velocity versus time 
and (right) footwear 3-point bending stiffness (right): 13.0 (black), 31.0 (blue), 43.1 (green), and 84.1 kN/m 
(orange). Vertical lines indicate the average end of ground contact for the respective footwear condition and 
error bars indicate SE.
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Figure 5.  Estimated (a) Soleus (Sol) force–length and (c) force–velocity relationships during ground contact. 
The marker indicates soleus initial ground contact and the horizontal line indicates soleus operating range 
during ground contact. (b) Sol force and (d) volume (Vol) throughout ground contact and vertical lines indicate 
the average end of ground contact.
Figure 6.  Average (± SE) (a) gross aerobic power and (b) activated soleus (Sol) volume (Vol) per stride. Right 
axis: Percent difference in the respective variables from the Adidas condition without a carbon fiber plate versus 
shoe bending stiffness.
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Footwear. 
We acquired the Adidas Adizero Adios BOOST 2 (Adidas) running shoes in US men’s size 9, 10, 
11, and 12. The Adidas are the same shoe model that Dennis Kimetto wore to set a previous marathon (42.2 km) 
world record (2:02:57 h:min:s). Next, we fabricated sets of custom carbon fiber in-soles that were 0.8, 1.6, and 
3.2 mm thick to fit the Adidas shoes.
We characterized the 3-point bending stiffness of each shoe and in-sole condition following previously 
described  methods12,25,29. Briefly, we performed 3-point bending tests by placing each footwear condition in a 
frame with two supporting bars 80 mm apart. We applied a vertical force to the top of each footwear condition 
Figure 7.  Average (a) soleus (Sol), (b) medial gastrocnemius (MG), (c) tibialis anterior (TA), (d) biceps femoris 
(BF), (e) vastus medialis (VM), (f) gluteus maximus (GM), and (g) rectus femoris (RF) versus time (left) across 
footwear 3-point bending stiffness: 13.0 (black), 31.0 (blue), 43.1 (green), and 84.1 kN/m (orange). Vertical lines 
indicate the average end of ground contact and stride for the respective footwear condition.
Table 2.  Stride averaged normalized muscle activation ± SD normalized to the respective muscle’s average 
maximum value during running with the Adidas (13.0 kN/m) footwear condition.
Footwear bending 
stiffness (kN/m)
Tibialis anterior (%)
Soleus (%)
Medial gastroc-
nemius (%)
Vastus medialis (%)
Rectus femoris (%)
Biceps femoris (%)
Gluteus maximus 
(%)
13.0 ± 1.0
37 ± 7
24 ± 16
24 ± 5
19 ± 2
27 ± 10
40 ± 14
31 ± 15
31.0 ± 1.5
37 ± 9
21 ± 5
26 ± 3
20 ± 3
22 ± 12
39 ± 14
28 ± 9
43.1 ± 1.6
39 ± 9
21 ± 3
28 ± 4
19 ± 4
26 ± 12
38 ± 10
23 ± 6
84.1 ± 1.1
38 ± 9
20 ± 3
25 ± 3
20 ± 3
27 ± 13
40 ± 10
26 ± 7
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midway between the two supporting bars, approximately where the foot’s metatarsophalangeal joint would be 
located using a materials testing machine (Instron, Norwood, MA, USA). We applied force three consecutive 
times to displace each shoe 10 mm following a 2 N preload (loading rate: 8 mm/s). We calculated footwear 
3-point bending stiffness during loading using the average linear slope of the force–displacement data (100 Hz) 
from the following displacement range: 5 to 9 mm. We also set each athlete’s footwear mass equal to their largest 
footwear condition, which was the Adidas plus thickest carbon fiber in-sole. For example, the size 9 Adidas shoe 
is 199 g and its stiffest in-sole was 60 g. Accordingly, we set all size 9 footwear conditions to 259 g by securing 
mass to the tongue of each shoe.
Protocol. 
Each participant completed two experimental sessions. During the first session (aerobic session), 
participants performed a 5-min standing trial followed by five 5-min treadmill (Bertec Corporation, Columbus, 
OH, USA) running trials at 3.5 m/s. Prior to each trial, participants rested for at least 5 min. The first running 
trial served as habituation to treadmill running in the Adidas footwear (no carbon fiber in-sole). During each 
subsequent trial, participants ran using a different footwear condition: Adidas as well as Adidas with 0.8, 1.6, 
and 3.2 mm thick carbon fiber in-soles. We randomized footwear trial order. Each participant’s second session 
(biomechanics session) occurred at the same time of day and < 10 days following their first session. During the 
second session, participants performed four 2-min treadmill running trials at 3.5 m/s using the same footwear 
conditions as the first session in a re-randomized order. We performed separate aerobic and biomechanics ses-
sions to mitigate the potential for technical difficulties to arise by measuring biomechanics over a briefer session 
than needed for accurate metabolic measurements.
Aerobic energy expenditure. 
We asked participants to arrive to their aerobic session 3-h post-prandial. 
Throughout each of the aerobic session’s trials, we used open-circuit expired gas analysis (TrueOne 2400, Parvo-
Medic, Sandy, UT, USA) to record the participant’s rates of oxygen uptake (V̇o2) and carbon dioxide production 
(V̇co2). We monitored each participant’s respiratory exchange ratio (RER) throughout each trial to ensure that 
everyone primarily relied on aerobic metabolism during running; indicated by an RER ≤ 1.031. Next, we averaged 
V̇o2 and V̇co2 over the last 2-min of each trial and used a standard  equation56 to calculate aerobic power (W). 
Subsequently, we subtracted the corresponding session’s standing aerobic power (Table 1) from each running 
trial and divided by participant mass to yield mass-normalized aerobic power (W/kg).
Biomechanics. 
Prior to the biomechanics session’s running trials, we placed reflective markers on the left 
and right side of each athlete’s lower body following a modified Helen Hayes marker set: superficial to the head of 
the 1st and 5th metatarsal, posterior calcaneus, medial and lateral malleoli, lateral mid-shank, medial and lateral 
knee-joint center, lateral mid-thigh, greater trochanter, anterior superior iliac crest, posterior superior iliac crest, 
and superior iliac crest. During the ensuing trials, we recorded vertical and anterior–posterior GRFs (1000 Hz) 
as well as motion capture (200 Hz) data during the last 30 s of each trial. We performed a fast fourier transform 
on the raw GRF data from six random participants and then filtered the raw GRFs and center-of-pressure data 
appropriately: using a fourth-order low-pass critically damped filter (14 Hz)54,57,58. We filtered motion capture 
using a fourth-order low-pass Butterworth filter (7 Hz)57,59–62. Using the filtered GRFs, we calculated whole-body 
stride kinematics (stance and stride time) and GRF parameters (stance average vertical and resultant GRF, as 
well as mean braking and propulsive horizontal  GRFs63) with a custom MATLAB script (Mathworks, Natick, 
MA) that detected periods of ground contact using a 30 N vertical GRF threshold. We categorized each partici-
pant as a heel striker or mid/forefoot striker based on visual inspection and whether their vertical GRF trace had 
an impact peak or not (Table 1). If the participant visually appeared to contact the ground with their heel and 
displayed a vertical GRF impact peak they were deemed a heel  striker64. Participants that did not satisfy these 
criteria were deemed a mid/forefoot strikers.
We performed inverse dynamics and determined limb joint kinematics (limb joint angles and GRF-to-joint-
center moment arms) and kinetics (limb joint moments) (C-motion Inc., Germantown, MD; Mathworks Inc., 
Natick, MA, USA). Subsequently, we computed each participant’s instantaneous soleus muscle–tendon (MT) 
moment arm, length, velocity, and force. We used participant anthropometric data and limb-joint angles to cal-
culate the respective soleus MT  length36, velocity, and moment  arm36,65. Next, we used each soleus MT moment 
arm (r) and net ankle-joint moment (M) to calculated soleus MT force (F) by deeming that the soleus generates 
54% of total plantar flexor force based on its relative physiological cross sectional  area66.
Prior to the biomechanics session’s trials, we secured a linear-array B-mode ultrasound probe (Telemed, 
Vilnius, Lituania) to the skin superficial of each athlete’s right soleus. Using ultrasonography, we recorded mid-
soleus fascicle images (100 Hz) during at least five consecutive strides per trial. We processed the images using 
a semi-automated tracking  software67 to determine instantaneous soleus pennation angle and fascicle length. 
For semi-automated images that did not accurately track the respective soleus fascicle angle and/or length, we 
manually redefined the respective fascicle’s parameters. We used soleus MT force and fascicle angle to calculate 
soleus fascicle force, length, and velocity in congruence with previous  studies37,57. We filtered soleus fascicle 
angle and length using a fourth-order low-pass Butterworth filter (10 Hz) and took the derivative of fascicle 
length with respect to time to determine fascicle velocity. Subsequently, we determined relative soleus fascicle 
length and velocity by deeming that soleus fascicles are at 97% of their optimal length at initial ground contact 
in the Adidas  condition32 and that their maximum velocity is 6.77  L0/s53, respectively. We deemed average ± SD 
maximum soleus velocity to equal 297.1 ± 16.5 mm/s. Due to technical difficulties, we were unable to compute 
accurate active soleus volume during 18 of 60 trials; spanning 5 participants.
We recorded surface EMG signals from the biomechanics session’s running trials using the standard proce-
dures of the International Society for Electrophysiology and  Kinesiology68. Prior to the first trial, we shaved and 
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lightly abraded the skin superficial to the medial gastrocnemius, soleus, tibialis anterior, vastus medialis, rectus 
femoris, biceps femoris, and gluteus maximus of each participant’s left leg with electrode preparation gel (NuPrep, 
Weaver and Co., Aurora, CO). Next, we placed a bipolar surface electrode (Delsys Inc., Natick, MA) over the 
skin superficial to each respective muscle belly and in the same orientation as the respective muscle fascicle. 
We recorded EMG signals at 1000 Hz and verified electrode positions and signal quality by visually inspecting 
the EMG signals while participants contracted the respective muscle. Based on visual inspection and technical 
difficulties, we removed 97 of 420 potential muscle activation signals due to their poor signal quality; spanning 
4 participants. To analyze EMG signals from the running trials, we band-pass filtered the raw EMG signals to 
retain frequencies between 20 and 450 Hz, full-wave rectified the filtered EMG signals, and then calculated the 
root mean square of the rectified EMG signals with a 40 ms moving  window69,70. Lastly, we normalized each 
muscle activation to the average maximum activation of the respective muscle during running in the Adidas 
condition sans carbon fiber  plates70.
Statistics. 
An a priori analysis on Roy and Stefanyshyn’s  data12, suggested that fifteen participants would 
achieve a strong statistical power (0.895) between footwear bending stiffness and metabolic power. We per-
formed a linear regression on the footwear’s force–displacement profile, which was measured from a materials 
testing device. We performed independent repeated measures ANOVAs to determine whether footwear bend-
ing stiffness (independent variable) affected athlete running biomechanics (hip, knee, and ankle stance average, 
minimum, and maximum angle; hip, knee, and ankle stance average and maximum moment; ground contact 
time; step time; stance average vertical, braking, and propulsive GRF; fraction of vertical and horizontal GRF 
during the first half of stance; stance average muscle–tendon force, length, velocity, and gear ratio; stance aver-
age and maximum soleus fascicle pennation angle, force, length, velocity; stance average, stride average soleus 
active muscle volume; stance average and stride average soleus, medial gastrocgnemius, tibialis anterior, biceps 
femoris, vastus medialis, gluteus maximus, and rectus femoris; and gross aerobic power (dependent variables). 
We presented cohen’s d effect size for gross metabolic power and stride average soleus active muscle volume. We 
performed all statistical tests using R-studio (R-Studio Inc., Boston, USA) and G*Power software.
Received: 23 October 2019; Accepted: 21 September 2020
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Acknowledgements
We thank Dr. Frank Hammond and Lucas Tiziani for the use of the materials testing machine, in addition to Dr. 
Young-Hui Chang for the use of his analysis software. We thank PoWeR and EPIC Lab members, namely Lindsey 
Trejo for assisting data collection and Krishan Bhakta for assisting data analysis. This study was supported by 
O.N.B.’s National Institute of Health’s, Institute of Aging Fellowship: F32AG063460; P.R.G.’s National Science 
Foundation Graduate Research Fellowship: DGE-1650044; G.S.S’s National Institute of Health’s, Institute of Aging 
Award: R0106052017; and G.S.S.’s support from the George W. Woodruff School of Mechanical Engineering.
Author contributions
O.N.B. and G.S.S. came up with the study design. O.N.B. and P.R.G. acquired and analyzed the study’s data. 
O.N.B. and G.S.S. interpreted the data. O.N.B. drafted the manuscript, P.R.G. and G.S.S. edited the manuscript. 
All authors approved the manuscript, agree to be accountable for their contributions, and will ensure that ques-
tions related to the accuracy or integrity of any part of the study are appropriately investigated, resolved, and the 
resolution documented in the literature.
Competing interests 
The authors declare no competing interests.
Additional information
Supplementary information is available for this paper at https ://doi.org/10.1038/s4159 8-020-74097 -7.
Correspondence and requests for materials should be addressed to O.N.B.
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© The Author(s) 2020

Adding carbon fiber to shoe soles may not improve running economy: a muscle-level explanation.
Beck, Owen N,Golyski, Pawel R,Sawicki, Gregory S