J Appl Physiol 117: 507–517, 2014.
First published July 3, 2014; doi:10.1152/japplphysiol.00119.2014.
Effects of pole compliance and step frequency on the biomechanics and
economy of pole carrying during human walking
Eric R. Castillo,1 Graham M. Lieberman,2 Logan S. McCarty,3 and Daniel E. Lieberman1
1
Department of Human Evolutionary Biology, Harvard University, Cambridge, Massachusetts; 2Harvard University Medical
School, Boston, Massachusetts; and 3Department of Physics and Department of Chemistry and Chemical Biology, Harvard
University, Cambridge, Massachusetts
Submitted 10 February 2014; accepted in final form 19 June 2014
load carrying; gait; locomotion; energetics; mass-spring model; natural frequency; harmonic motion
HUMANS USE A VARIETY OF METHODS to carry loads, including
holding objects in the hands, suspending packs from the
shoulders, and balancing loads on the head. However, it remains unclear which methods are most economical and why.
Previous experiments suggest that carrying cost is predicted to
increase in proportion to the relative mass of the load, such that
a person carrying a load of 20% body mass uses ⬃20% more
energy than walking or running unloaded at the same speed
(30, 32, 34). Although some carrying methods (e.g., backpacks) tend to fit this prediction, others vary in relative energetic cost depending on various factors, such as where the load
is distributed on the body and how load distribution affects gait
(1, 18). For example, some African women who carry loads of
up to 20% body mass on their heads show no significant
increase in energy expenditure (25), although these findings are
disputed by some studies (23). Loads carried on the hip (37) or
Address for reprint requests and other correspondence: E. R. Castillo, 11
Divinity Ave, Cambridge, MA 02138 (e-mail: ercastil@fas.harvard.edu).
http://www.jappl.org
in the hands (35) are relatively more costly than predicted on
the basis of added mass.
One way to save energy when carrying loads is by using
devices whose material properties and design are able to
absorb, store, and return energy elastically (3). For instance,
Rome et al. (31) developed a backpack in which the load is
suspended from springs, designed to convert mechanical energy into electricity with each step. The measured volume of
oxygen consumed per second (V̇O2) by study participants
walking with the loaded device showed that metabolic power
input was reduced by roughly 60% compared with predicted
energy expenditure. Here we explore how flexible carrying
poles might take advantage of similar elastic energy storage
mechanisms to reduce metabolic costs.
Pole carrying has been documented worldwide, including
among Bushmen hunter-gatherers (21) and Venezuelan foragers (13, 14, 15), suggesting that it is an ancient method of
carrying. This technique is especially well known in East Asia
(17), where people commonly balance a bamboo pole over the
shoulder to transport loads suspended from either end. The
pole deforms with each step, acting like a spring during
locomotion. Despite the prevalence of pole-carrying behavior
around the world, only a handful of studies have collected data
on pole carrying in the field (13–15, 17) or in the lab (5, 19).
The most well known study to examine the biomechanics
and energetics of pole carrying was by Kram (19), who tested
whether flexible carrying poles reduce the work required to lift
a load repeatedly against gravity as the load’s center of mass
(CoM) fluctuates vertically. This study hypothesized that the
carrying pole acts as an out-of-phase oscillator to allow loads
to travel in a smooth horizontal trajectory with virtually no
vertical displacement. The hypothesis was tested by measuring
V̇O2 in four participants who ran on a treadmill at 3 m/s with
15-kg loads (19% average body mass) hung from 3.6-m-long
polyvinyl chloride poles. Two poles (one over each shoulder)
were used simultaneously to allow the arms to swing freely.
Results showed that although vertical displacement of the loads
was minimal (⬃1 cm), participants did not benefit from reduced energy expenditure compared with conventional carrying methods. However, the flexible pole was found to have
other advantages, including reducing absolute peak shoulder
forces by 40% and shoulder force fluctuation by 80%.
Although carrying poles may be useful for multiple reasons—such as reducing shoulder forces, increasing stability
during loading, or allowing people to carry a large volume of
goods effectively—we hypothesize that flexible poles can also
save energy. Here we test a new model for how carrying poles
might reduce metabolic costs by reducing the vertical CoM
displacement of the entire load-carrier system. Specifically,
8750-7587/14 Copyright © 2014 the American Physiological Society
507
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Castillo ER, Lieberman GM, McCarty LS, Lieberman DE. Effects of
pole compliance and step frequency on the biomechanics and economy of
pole carrying during human walking. J Appl Physiol 117: 507–517, 2014.
First published July 3, 2014; doi:10.1152/japplphysiol.00119.2014.—This
study investigates whether a flexible pole can be used as an energysaving method for humans carrying loads. We model the carrier and
pole system as a driven damped harmonic oscillator and predict that
the energy expended by the carrier is affected by the compliance of
the pole and the ratio between the pole’s natural frequency and the
carrier’s step frequency. We tested the model by measuring oxygen
consumption in 16 previously untrained male participants walking on
a treadmill at four step frequencies using two loaded poles: one made
of bamboo and one of steel. We found that when the bamboo pole was
carried at a step frequency 20% greater than its natural frequency, the
motions of the centers of mass of the load and carrier were approximately equal in amplitude and opposite in phase, which we predicted
would save energy for the carrier. Carrying the steel pole, however,
resulted in the carrier and loads oscillating in phase and with roughly
equal amplitude. Although participants were less economical using
poles than predicted costs using conventional fixed-load techniques
(such as backpacks), the bamboo pole was on average 5.0% less costly
than the steel pole. When allowed to select their cadence, participants
also preferred to carry the bamboo pole at step frequencies of ⬃2.0
Hz. This frequency, which is significantly higher than the preferred
unloaded step frequency, is most economical. These experiments
suggest that pole carriers can intuitively adjust their gaits, or choose
poles with appropriate compliance, to increase energetic savings.
508
Biomechanics and Economy of Pole Carrying
we test the hypothesis that energetic savings occur when the
natural frequency of the pole and the step frequency of the
carrier are at a ratio of ⬃1.2, producing a system where the
loads oscillate out of phase but with equal amplitude compared with oscillations of the center of mass of the carrier’s
body. We experimentally test this hypothesis by comparing
people walking with an average of 20% body mass using a
flexible bamboo pole and rigid steel pole at four step frequencies.
Glossary
g
k
l
mcarrier
mload
O2f
O2i
O2ss
Qf
relCOT
Tf
Ti
Tss
V̇O2
V
Xcarrier
Xload
␯
␸
␻carrier
␻load
amplitude of motion of the carrier
amplitude of motion of the load
center of mass
center of mass of the person carrying the load
center of mass of the load
center of mass of the entire system
cost of transport
driven damped harmonic oscillator
mean ventilation flow rate measured in the
mask at steady state
acceleration due to gravity
effective spring constant of the pole
leg length from the greater trochanter to the
ground
mass of the carrier
mass of the load
final O2% at the end of the trial
initial O2% measured before the trial
mean O2% measured at steady state
quality factor measuring the degree to which
the system is underdamped
relative cost of transport measured as the ratio
of loaded to unloaded COT
time when O2f was measured
time when O2i was measured
time when O2ss was measured
volume of oxygen consumed per second
velocity in m/s
vertical displacement of the CoM of the person carrying the load
vertical displacement of the CoM of the load
damping coefficient
relative phase between the carrier and the load
step frequency of the carrier
natural frequency of load oscillation
Castillo ER et al.
where Xload and Xcarrier are the vertical displacements of the
CoMs of the load and carrier, and mload and mcarrier are the
masses of the load and carrier, respectively. Because the
masses of the load and carrier do not typically change during
a carrying bout, the magnitude of oscillation of CoMsystem can
be reduced only by modifying the magnitude or direction of
Xload or Xcarrier. When carrying with a fixed-load system, such
as a backpack, Xload and Xcarrier are displaced equally with each
step, the motion of CoMsystem is unchanged, and only the load
mass is increased. This method of transport will increase the
total work performed compared with unloaded walking. In
contrast, a compliant pole system allows the motions of the
load and the carrier to oscillate independently. If the displacements Xload and Xcarrier are out of phase, then the total motion
of CoMsystem will be reduced, thereby reducing the total amount
of work an individual performs. For instance, if mload ⫽ mcarrier,
the motion of CoMsystem could be reduced to 0 using a carrying
pole if Xload and Xcarrier are equal in magnitude but opposite in
the direction of displacement (Xload ⫺ Xcarrier ⫽ 0). In our
experiments, where mload ⬇ 1/5 mcarrier, equal and opposite
displacements should reduce the magnitude of oscillation of
CoMsystem by 1/5, which we predict will reduce the metabolic
cost for the carrier compared with in-phase oscillation.
To predict the displacements of the centers of mass of the
load (CoMload) and carrier (CoMcarrier) during walking, we
model the pole-carrying system as a driven damped harmonic
oscillator (DDHO; Fig. 1). The carrier’s shoulder, the pole, and
the loads represent the driver, spring, and mass of the DDHO
system, respectively. The frequency and amplitude of load
displacement are dependent on the driver’s motion, which is
approximated using an inverted-pendulum model of walking
(33). In our model, we assume that cyclical oscillations of
CoMcarrier drive identical in-phase fluctuations of the shoulder
with each step, thus treating the attachment between CoMcarrier
and the shoulder as a rigid element. Given the fact that
oscillations of the shoulder are not exactly the same as those of
the body’s CoM during locomotion, we therefore compared the
phase and amplitude difference between the shoulder and a
marker near CoMcarrier to test whether these assumptions are
supported (see MATERIALS AND METHODS below).
The complete solution for a driven damped harmonic oscillator has a transient part, which dies away due to damping, and
a steady-state part that follows the motion of the driver (the
shoulder in this case). We are interested only in the steady-state
part of the solution, which will dominate the motion once
people reach a natural walking rhythm. We model the natural
vibrating frequency of the load as a function of the stiffness of
the pole and the mass of the load, defining
MODEL AND HYPOTHESES
Model. Assuming the energy an individual expends to carry
a load against gravity correlates with vertical CoM displacements during locomotion (19), our model predicts that energetic savings occur when the overall magnitude of CoM
displacement of the system as a whole (person plus carried
object) is reduced relative to unloaded walking. The vertical
CoM displacement of the system (CoMsystem) depends on the
individual displacements of the load and the carrier:
CoMsystem ⫽
1
mcarrier ⫹ mload
共Xcarriermcarrier ⫹ Xloadmload兲 (1)
␻load ⫽
冑
k
(2)
mload
where ␻load is the natural frequency of the load oscillation, and
k is the effective spring constant of the pole. The displacements
of the carrier and the load as a function of time t are given by
Xcarrier ⫽ Acarriercos共␻carriert兲
Xload ⫽ Aloadcos共␻loadt兲 (3)
where the amplitude of motion of the load Aload is given by
Aload ⫽
␻2loadAcarrier
兹共␻carrier ⫺ ␻load兲
2
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2
2
2
⫹ ␯2␻carrier
(4)
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Acarrier
Aload
CoM
CoMcarrier
CoMload
CoMsystem
COT
DDHO
FL
•
Biomechanics and Economy of Pole Carrying
•
Castillo ER et al.
509
and the relative phase ␸ between the carrier and the load is
␸ ⫽ tan ⫺1
冉
␯␻carrier
␻2load
2
⫺ ␻carrier
冊
(5)
In these expressions, Acarrier and ␻carrier are the amplitude
and step frequency of the carrier, and ␯ is the damping
coefficient. Derivations may be found in any introductory
physics textbook (e.g., Ref. 9).
All features of driven damped harmonic oscillation can be
summarized in three dimensionless ratios: the frequency ratio
(␻carrier/␻load), the amplitude ratio (Aload/Acarrier), and the phase
ratio (␸/␲). Plotting these ratios shows that the amplitude and
phase are determined by the frequency ratio and the degree of
damping in the system (Fig. 2). The amount of damping in the
system is measured by the quality factor (Qf ⫽ ␻load/␯), a
dimensionless variable representing the degree to which the
system is underdamped. The higher Qf, the less damped the
system, and the higher the proportion of energy stored vs.
energy dissipated during each oscillation cycle. As Fig. 2
demonstrates, a pole carrier can alter his or her step frequency,
or change the properties of the pole (according to Eq. 2), to
modify the amplitude and phase relationship of CoMload and
CoMcarrier.
In fixed-load carrying systems (e.g., backpacks), the attachment
between the carrier and the load is rigid (large k), and the pole’s
natural vibrating frequency is usually much greater than the step
frequency. This produces a state where ␻carrier ⬍⬍ ␻load, causing ␸ to approach 0 (in phase) and Aload/Acarrier ⬇ 1. However,
with a compliant pole, the relationship between load and
carrier is more variable. As ␻carrier approaches ␻load, Aload/
Acarrier increases dramatically and ␸ shifts from being in phase
to out of phase. When ␻carrier ⫽ ␻load, the system reaches a
Fig. 2. Relative amplitude and phase relationship based on the driven damped harmonic
oscillation model comparing frequency ratio
(␻carrier/␻load), amplitude ratio (Aload/Acarrier),
and phase ratio (␸/␲). Dotted and dashed lines
represent various Q factors (Qf). Mean values for the 2 poles and 4 step frequency trials
are shown. , Steel pole; Œ, bamboo pole.
Note that the 95% confidence intervals (CI)
are not plotted because they are too small to
be shown in this figure. [Modified with permission from Fitzpatrick (10)].
J Appl Physiol • doi:10.1152/japplphysiol.00119.2014 • www.jappl.org
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Fig. 1. Top: schematic of a person carrying
20% of body weight using the flexible bamboo pole at a step frequency of 2.00 Hz as
modeled in this study as a driven damped
harmonic oscillator (DDHO) system (see
Fig. 2). Weights were directly fixed to the
pole using nylon cordage and duct tape.
Series of images illustrates 3 moments during
the support phase of walking: heel strike (top
left), midstance (top center), and toe off (top
right). Carrying figure generated using
SketchUp. Bottom: when participants walked
at a frequency ratio of 1.2 relative to the
natural frequency of the pole, we found that
the compliant bamboo pole showed vertical
displacement of center of mass of the load
(CoMload) that was roughly equal in amplitude and opposite in direction compared
with center of mass of the person carrying
the load (CoMcarrier).
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Biomechanics and Economy of Pole Carrying
Castillo ER et al.
variation in leg length, body mass, and height (Table 1). Participants
were excluded due to any injury or medical condition that would
interfere with their ability to walk normally during experiments. They
were also excluded if they appeared unable to carry the poles safely,
or if (relative to other participants) a measured mass-specific cost of
transport (COT) value for any trial was considered abnormally high or
low according to a Grubbs’ test, a statistical method to identify
outliers among normally distributed univariate data. In the end, six
volunteers were excluded due to a pre-existing medical condition (n ⫽
1), inability or unwillingness to complete the experiment (n ⫽ 3), or
having outlier COT values (n ⫽ 2). Thus 16 participants completed
the experiment. Written informed consent was attained for all volunteers prior to testing, and research was approved by the Harvard
Committee on the Use of Human Subjects.
To replicate traditional carrying poles from East Asia, a pole was
sectioned from the wall of a single Phyllostachys edulis shoot into a
nearly flat bamboo slat measuring 1.85 m ⫻ 0.75 m ⫻ 1.5 cm. The
internodal discs were removed to create a smooth internal surface. The
steel pole was a galvanized steel pipe, 1.90-m long and 2.5 cm in
diameter. Plate weights were symmetrically attached directly to both
poles (not suspended) 1.40 m apart using nylon cordage and duct tape.
The total mass of each pole was set at 17.3 kg, ⬃20% of mean body
mass. Shoulder pads made of packing foam measuring 40 ⫻ 12 ⫻ 10
cm were centered between the weights of each pole and firmly
attached to the pole with duct tape to make carrying as comfortable as
possible.
The natural frequency and damping coefficient of each pole (with
shoulder pad) was measured while the poles were balanced on a rigid
post. The poles were tested several times before experiments and
modified until they achieved natural frequencies and frequency ratios
within the ranges predicted to show kinematic qualities described
above by P2 and P3. Reflective markers were placed on the front and
back loads. The ends of the poles were deflected and released,
allowing free vibration. Markers were tracked at 500 Hz using eight
infrared cameras (Oqus 1 Series, Gothenburg, Sweden) and Qualysis
Motion Tracking Software. The parameters ␻load and ␯ were determined by fitting the observed motion to a sinusoidal decay equation
using LoggerPro software. This equation took the following form:
Xload ⫽ Aloade␥tsin共␻loadt ⫹ ␸兲
where the time constant ␥ is related to the damping coefficient as ␥ ⫽
␯/2. To validate ␻load for each pole, we matched a metronome to the
observed frequency of the pole during free oscillation. Qf was calculated from the ratio ␻load/␯. Once the natural vibrating frequency of
the pole was found, Eq. 2 was used to calculate the effective spring
constant k.
Study volunteers performed 10 trials in the experiment. Each
participant carried both poles at 4 step frequencies: 1.83, 2.00, 2.17,
and 2.33 Hz. In addition, they performed two unloaded trials: one at
their preferred step frequency and one at 2.00 Hz, the step frequency
predicted to produce an energy-saving frequency ratio within the range
described by P3. Participants were not informed of the metronome
frequencies or hypotheses of the experiment. Walking speed was normalized to leg length using a Froude number of 0.2 calculated as
Froude ⫽
MATERIALS AND METHODS
Twenty-two male volunteers (age 18 –23), none with previous
experience carrying poles, were initially recruited to sample a range of
(6)
V2
(7)
gl
where V is velocity, g is gravitational acceleration, and l is leg length
from the greater trochanter to the ground (4). We chose a Froude
Table 1. Anthropometrics and Trial Speeds
Mean
SD
(Min., Max.)
Mass, kg
Leg Length, m
Height, m
Absolute Speed, m/s
86.16
21.33
(58.00, 136.60)
0.97
0.06
(0.83, 1.05)
1.86
0.10
(1.66, 2.00)
1.37
0.04
(1.27, 1.43)
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state of resonance, leading to instability as the loads vibrate
with high amplitude and quadrature phase relationship (␸ ⫽
␲/2). However, when ␻carrier ⬎⬎ ␻load, the system returns to a
more stable state, where ␸ approaches ␲ (out of phase) and
Aload approaches 0.
Hypotheses. We hypothesize that energy savings occur at a
frequency ratio that minimizes the magnitude of oscillation of
CoMsystem. To achieve out-of-phase motion between the load
and the carrier, the most economical frequency ratio should
have ␻carrier ⬎ ␻load. However, there is a trade-off between the
amplitude Aload and the phase ␸. If mload ⬍ mcarrier (as is
usually the case), one will want Aload/Acarrier ⬎ 1 to minimize
the motion of CoMsystem (Eq. 1). As Fig. 2 shows, achieving
high amplitude of the load requires motion near resonance—
yet that is the very regimen in which the phase ratio is in
transition, diminishing the effectiveness of the out-of-phase
motion in reducing the overall oscillation of CoMsystem. Conversely, to approach exactly out-of-phase motion, one must
have Aload/Acarrier approach 0, which would also negate the
effectiveness of the load in reducing the overall oscillation of
the CoMsystem. Given this model, we therefore expect that an
energy-saving step frequency will be somewhat above the
natural resonant frequency of the pole (to be out of phase),
while not being so high that the amplitude of oscillation of the
load is reduced to 0.
To test this model, we measured oxygen consumption in
participants carrying a tuned bamboo pole and a rigid steel
pole. We predict the following to support the hypothesis of
CoMsystem reduction described by our model.
(P1). When walking at a normal range of step frequencies,
participants will show a higher energetic cost when carrying
the rigid steel pole than when carrying the flexible bamboo
pole.
(P2). Carrying the loaded steel pole using a normal range of
walking step frequencies will show that the displacements of
CoMload and CoMcarrier are in phase (␸ ⬇ 0) and roughly equal
in amplitude (Aload/Acarrier ⬇ 1), similar to fixed-load carrying
systems.
(P3). Carrying the loaded bamboo pole using a normal range
of walking step frequencies will have ␻carrier ⬎ ␻load, which
should show overall out-of-phase motion (␸ ⬎ ␲/2) and an
amplitude consistent with the model. Within this range of
frequency ratios, there should be an energy-saving step frequency that minimizes the mass-specific cost of transport.
(P4). When ␻carrier is self-selected, we predict that participants will intuitively choose a step frequency when using the
compliant bamboo pole that minimizes the cost of transport,
but when using the rigid steel pole they will not make a
significantly different choice of step frequency compared with
their preferred unloaded step frequency.
•
Biomechanics and Economy of Pole Carrying
511
Castillo ER et al.
calculated in the statistical software R on every steady-state plateau
sampled to ensure that it was flat. Slopes ⱖ0.001% O2/s were
discarded and the trial was resampled.
V̇O2 was normalized for error due to system drift by taking a 30-s
sample of room air before and after each trial, and windows and doors
were kept closed during the experiment. Data were entered into a drift
removal formula following Perl et al. (27):
V̇O2 ⫽ FL
冋冉
O 2i ⫹
共O2f ⫺ O2i兲Tss
共Tf ⫺ Ti兲
冊
⫺ O2ss
册
(8)
where FL is the ventilation flow rate in the mask at steady state, O2i
is the initial O2% measured before the trial, O2f is the final O2% at the
end of the trial, O2ss is the mean O2% measured at steady state, Tss
is the time when O2ss was measured, Ti the time when O2i was
measured, and Tf the time when O2f was measured. Gross V̇O2 data
were subsequently converted to the mass-specific cost of transport
(COT, ml O2 kg⫺1 m⫺1) by dividing gross V̇O2 by total mass (load
and body mass) and treadmill walking speed. To measure the percentage increase in energy expenditure above baseline unloaded
walking, COT values were analyzed as the relative energetic cost of
transport (relCOT), commonly referred to as the metabolic ratio, by
dividing gross loaded COT by the participant-specific unloaded gross
walking COT measured during the preferred step frequency trial.
Although some authors advocate using net V̇O2 (gross V̇O2 ⫺ resting
V̇O2) for studies of locomotor economy (e.g., Ref. 38), we chose to
use a percentage calculation of cost to compare proportional increases
in energy expenditure to predicted costs based proportional increases
in load (loaded mass/unloaded mass), as is the convention in many
loading studies (e.g., Refs. 25, 34, 37).
To compare the economy of walking with the loaded poles,
energetic data were analyzed in the statistical software R. We used a
general linear mixed-effects model from the “nlme” package to
account for repeated measures (28). relCOT was the dependent
variable and pole type, step frequency (as a factor), and relative load
mass (mload/mcarrier) were treated as fixed effects; and participant
identification was the random effect. A post hoc Tukey test was used
for crosswise comparisons of step frequency and pole type with the
“multcomp” package in R (16). Additionally, the preferred step
frequencies chosen by each participant in each loading condition were
analyzed using a one-way, repeated-measures ANOVA. Mean preferred step frequency was the dependent variable, which was compared by the factor levels of loading condition (unloaded, steel pole,
and bamboo pole) with repeated measures controlling for participant
identification. Post hoc pairwise t-tests were used to compare step
frequencies between groups, with Bonferroni corrected P values to
account for multiple comparisons. An alpha level of 0.05 was set for
all statistical tests.
One of the assumptions of this model is that vertical motions of the
shoulder (the driver in the DDHO system) are similar in phase and
amplitude to the motion of the body’s CoM during loaded locomotion.
Therefore, we tested whether there was a significant kinematic difference between vertical oscillations of the shoulder and a proxy
marker at the L4 vertebral level representing CoMcarrier. One participant was chosen at random, and the motions of the shoulder marker
under load were compared with those of the lower back marker for 5
s of carrying. Although the body’s CoM changes continuously over
time during locomotion, a reasonable approximation of its dynamic
location is close to the L4 vertebral level, not far from its true
anatomical location (39). The mean amplitude and phase difference
were compared for each loading trial.
RESULTS
Measurements of each pole’s natural frequency, stiffness,
and damping coefficients are summarized in Table 2. The steel
pole was ⬃12.5 times stiffer than the bamboo pole, and ␻load
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number of 0.2 rather than the standard walking Froude number of 0.25
for 1 g of gravity on earth (8), because several studies have shown that
the optimum speed for carrying loads is sometimes slower than the
optimum speed predicted for the unloaded state, and one experiment
found that the minimum COT when carrying 16% body weight is
⬃80% the optimal unloaded walking speed (36). Therefore, we chose
a Froude number of 0.2 to optimize carrying speed. A slower walking
speed was also useful for ensuring the participants’ safety during the
loaded walking trials. Absolute walking speeds, height, weight, and
limb length are summarized in Table 1.
At the start of the experiment, carriers walked for at least 1 min on
a treadmill (Bertec, Columbus, OH) at a Froude number of 0.2 at the
two extreme step frequencies (1.83 Hz and 2.33 Hz) to become
accustomed to walking with the metronome. Participants were then
shown how to carry the poles by supporting the pole in a comfortable
position on the dominant shoulder with the dominant hand holding it
for stability while the other hung freely at their side (Fig. 1). Participants were fit with a nose clip and a V̇O2 respirometry mouthpiece
attached to a Hans-Rudolf, nonrebreathing T valve to collect all
expired gas. Participants stood at rest for 5 min to measure baseline
oxygen consumption and become comfortable with the V̇O2 system.
Then they performed 10 walking trials in random order. Trials lasted
4 – 6 min, enough time to gather steady-state V̇O2. Participants rested
for at least 2 min between trials. At the end of the metronome trials,
they were asked to walk on the treadmill with each pole for 2 min to
determine their preferred loaded step frequencies without the metronome. To avoid fatiguing participants during loading trials, the experiment was designed to last less than 90 min.
Infrared reflective markers were placed bilaterally on the acromion
processes, the right greater trochanter, bilateral calcaneal tuberosities,
the lower lumbar region (approximately L4), and the front and back
weights of each pole. Ten-second captures using the 8-camera system
were collected at 500 Hz during trials. Kinematic data were analyzed
using Qualysis Motion Tracking software. To calculate variables in
Eq. 3, positional data were analyzed in LoggerPro software using a
sinusoidal best-fit regression. The acromion marker on the shoulder
supporting the pole was used to calculate ␻carrier and Acarrier, whereas
the mean position of the front and back marker on the loads was used
to calculate ␻load and Aload.
The energetic cost of load carrying was measured using standard
open-flow N2 dilution methods for V̇O2 calibration and collection. For
details of these methods, see Fedak et al. (9). Before each experiment,
the metabolic system was calibrated using a measured flow of N2.
After calibration, we used a Sable Systems FlowKit-500H Mass Flow
Controller and Pump (Sable Systems International, Las Vegas, NV) to
generate a continuous flow of air pulled through the V̇O2 mouthpiece
and hose at 100 l/min (see Ref. 22 for discussion of pull-mode
respirometry). This high mass-flow rate is recommended by the
system manufacturer for open-flow V̇O2 studies of humans and other
medium-sized mammals to capture all expired air and is consistent
with pull-through flow rates used in other V̇O2 studies of walking
humans (29). A subsample of the expired air was then pulled at 100
ml/min by the gas subsampler (SS-4; Sable Systems International)
through a Drierite cobalt chloride desiccant column to remove water
vapor. Finally, the subsampled air was pushed at 100 ml/min into a
paramagnetic oxygen analyzer (PA-10 Oxygen Analyzer; Sable Systems International) to measure the fractional amount of O2 at 100 Hz.
The amount of O2 extracted from the air by the lungs was calculated
by subtracting the fraction of expired air that is oxygen from the
atmospheric concentration of oxygen (⬃20.93% O2). To calculate
V̇O2, this extracted O2% was corrected for system drift and multiplied
by the participant’s ventilation rate (the air moved in and out of the
lungs with each breath in l/min), measured by the incoming flow rate
sensor in the respirometry system (see Fig. 5 and Eq. 8 below).
Oxygen consumption data were sampled using LabChart over a 0.52-min period during which participants appeared to have reached a
flat, steady-state V̇O2 plateau (see Fig. 6). A linear regression was
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Table 2. Properties of the carrying poles
Natural Frequency, ␻load, Hz
Spring Constant, k, kN/m
Damping Coefficent, v, Hz
Q factor, Qf, ␻load/v
1.65
5.88
1.87
23.66
0.29
2.01
5.69
2.93
Bamboo pole
Steel pole
0.001), and relative load mass (P ⫽ 0.02) all had a significant
effect on relCOT. Results of the post hoc Tukey test used for
crosswise comparisons of step frequency and pole type are
shown in Table 5. These results suggest that mean relCOT at
the 1.83- and 2.17-Hz step frequency trials were not significantly different (P ⫽ 0.80), but differences between all other
combinations of carrying frequencies and pole conditions were
significant (P ⬍ 0.05). Because the relationship between relCOT and step frequency is U-shaped (P3), these data are
consistent with our finding of no significant difference in cost
between the 1.83-Hz and 2.17-Hz step frequencies.
The preferred step frequencies chosen by the participants are
shown in Fig. 4. Results of the repeated-measures ANOVA
indicate that the means of the loading conditions were statistically different (P ⫽ 0.03). Bonferroni-corrected pairwise
t-tests comparisons revealed that only the unloaded walking
and bamboo pole conditions were significantly different at an
alpha level of 0.05. As illustrated by the 95% confidence
intervals, the preferred step frequency when carrying the bamboo pole (1.94 ⫾ 0.07 Hz) encompassed the energy-saving
frequency of 2.00 Hz. However, the mean preferred frequency
for the steel pole (1.89 ⫾ 0.05 Hz) was within the confidence
limits of the mean unloaded preferred frequency (1.84 Hz).
Although step frequencies were generally elevated when
using the steel pole relative to unloaded walking, it appears
participants increased step frequencies even more when
using the bamboo pole. We interpret this to suggest that
participants intuitively chose step frequencies that were
most economical (P4).
Participant 7 was chosen at random to test the phase and
amplitude differences between the motions of the center of
mass of the body (approximated using the lower lumbar
marker) and the shoulder. Results of this comparison are
shown in Table 6. Over the 5 s analyzed, 8 –11 complete cycles
of oscillation of the shoulder and lower spine were used for
comparison in each trial. The difference between the amplitude
Table 3. Energetic data
Gross V̇O2, ml O2·kg⫺1·min⫺1
Condition
Bamboo pole
1.83 Hz
2.00 Hz
2.17 Hz
2.33 Hz
Steel pole
1.83 Hz
2.00 Hz
2.17 Hz
2.33 Hz
Unloaded
2.00 Hz
Preferred
Resting
Standing (unloaded)
COT, ml O2·kg⫺1·m⫺1
relCOT, loaded COT/unloaded COT
Mean
SD
Mean
SD
Mean
SD
12.8
12.3
13.1
13.8
1.71
1.56
1.70
1.72
0.159
0.152
0.161
0.171
0.027
0.024
0.023
0.024
1.36
1.30
1.37
1.45
0.14
0.14
0.16
0.14
13.6
12.9
13.4
14.6
2.48
1.83
1.54
1.47
0.165
0.159
0.166
0.177
0.033
0.026
0.025
0.02
1.41
1.36
1.41
1.51
0.20
0.20
0.14
0.12
10.1
9.9
1.04
0.86
0.124
0.117
0.015
0.012
1.05
—
0.08
—
1.26
—
—
—
—
3.81
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was found to be 1.65 Hz for the bamboo pole and 5.88 Hz for
the steel pole. Qf was measured as 5.69 for the bamboo pole
and 2.93 for the steel pole. The four trial step frequencies
produced ␻carrier/␻load ratios during steady-state carrying of
1.11, 1.21, 1.31, and 1.41 for the bamboo pole and 0.31, 0.34,
0.37, and 0.40 for the steel pole.
The average positional data for the load and shoulder during
carrying trials suggest that the behavior of the carried poles is
consistent with a DDHO system during steady-state carrying
(Fig. 2). The motions of the steel pole fit the prediction that the
load and the carrier moved in phase and with approximately
equal amplitude (P2). In contrast, the bamboo pole displayed
overall out-of-phase motion with varying amplitude, as predicted by P3.
A summary of the mean and standard deviations of the gross
V̇O2, COT, and relCOT values are reported in Table 3, and
example ventilation patterns and V̇O2 profiles are shown in
Figs. 5 and 6, respectively. On average, carrying the steel and
bamboo poles was less economical than the 20% increase in
energetic cost (relCOT ⫽ 1.20) predicted by conventional
fixed-load carrying methods (30, 32, 34). Participants had an
average relCOT of 1.35 (range of 1.04 –1.68) for the bamboo
condition compared with 1.41 (range of 1.14 –1.92) for the
steel condition. However, we found support for our prediction
that using the bamboo pole was overall more economical than
the steel pole (P1). Mean gross COT for all trials (regardless of
step frequency) show that carrying the steel pole was on
average 5.0% more energetically costly than the bamboo pole
(P ⬍ 0.001). Plotting mean relCOT by ␻carrier demonstrates a
U-shaped relationship for both pole types (Fig. 3). The observation of an energetic minimum within the range of step
frequencies tested supports our third prediction (P3). At the
2.00 Hz step frequency, the mean gross COT for the steel pole
was 4.6% greater than the bamboo pole (P ⫽ 0.03).
Results of the general linear mixed-effects model are shown
in Table 4. Step frequency (P ⬍ 0.0001), pole type (P ⬍
Biomechanics and Economy of Pole Carrying
Relative Cost of Transport
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Castillo ER et al.
Table 5. Tukey pairwise comparisons from the mixed-effects
model
Steel
Bamboo
1.55
1.50
1.45
1.40
1.35
Hypothesis
Adj. P Value
2.00-1.83 Hz ⫽ 0
2.17-1.83 Hz ⫽ 0
2.33-1.83 Hz ⫽ 0
2.17-2.00 Hz ⫽ 0
2.33-2.00 Hz ⫽ 0
2.33-2.17 Hz ⫽ 0
Steel–bamboo ⫽ 0
⬍0.05
0.80
⬍0.0001
⬍0.05
⬍0.0001
⬍0.0001
⬍0.0001
Holm-Bonferroni adjusted P values
1.30
1.25
1.83
2.00
2.17
2.33
Step Frequency(Hz)
of the shoulder and the L4 marker motion was typically within
an average of 0.15 cm (range of 0.04 – 0.41 cm). Comparisons
of amplitude were not statistically different given an alpha
level of 0.05, although it is important to note that the bamboo
1.83-Hz and steel 2.33-Hz trials were approaching significance
with P ⫽ 0.09 and P ⫽ 0.12, respectively. However, the
oscillation of the shoulder and the lower lumbar region were
shown to be almost completely in phase for all trials, with
overall ␸/␲ ratios between 3 and 8% out of phase for the
bamboo pole and less than 1% out of phase for the steel
carrying trials. As expected, the phase difference between
shoulder and lower back was greater for the bamboo pole, a
finding explained by the time lag during deformation of the
flexible bamboo pole.
To summarize, the goal of this study was to test whether
people can save energy when using flexible poles to carry
loads. We used a driven damped harmonic oscillation model to
predict the relative amplitude, phase, and oscillation frequency
of the CoM of the pole carrier and the carried load (Fig. 2). Our
main hypothesis, derived from principles of harmonic motion
(11), was that energetic savings would occur when the ratio
Table 4. Results of the linear mixed-effects model
Fixed Effects
F Ratio
P Value
Step frequency
Pole type
Relative load mass
Parameter
16.97
14.75
7.53
Coeff.
⬍0.0001
0.0002
0.02
SE
T Value
P Value
(Intercept)
2.00 Hz
2.17 Hz
2.33 Hz
Steel Pole
Relative load mass
0.975
⫺0.055
0.006
0.105
0.062
1.726
0.136
0.023
0.023
0.023
0.016
0.629
7.156
⫺2.409
0.260
4.596
3.841
2.745
⬍0.0001
0.02
0.80
0.0001
0.0002
0.02
Preferred Step Frequency (Hz)
DISCUSSION
2.05
2.00
1.95
1.90
1.85
1.80
Unloaded
Steel
Bamboo
Fig. 4. Results of the self-selected mean preferred step frequencies used by
participants during the loading trials. Error bars represent 95% CI. Solid
horizontal line is the mean step frequency for all participants during unloaded
walking without a metronome. Dashed horizontal line represents the energysaving step frequency for the bamboo pole that was shown to minimize
carrying cost during experimental trials that manipulated step frequency.
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Fig. 3. Relative cost of transport (relCOT ⫽ loaded COT/unloaded COT)
measured during the 4 step frequency trials in this study. Error bars represent
1 standard error. When load mass and repeated measures were accounted for
in the linear mixed model (Table 4), steel and bamboo pole trials are all
significantly different (P ⬍ 0.05), with the exception of the 1.83-Hz and
2.17-Hz step frequencies (Table 5).
between the carrier’s step frequency and the pole’s natural
vibrating frequency was greater than 1, but not so high that the
load oscillation amplitude approached 0. We found empirical
support for this hypothesis, measuring a minimum cost of
transport at ␻carrier/␻load ⬇ 1.2 for both the steel and bamboo
poles (Table 3). For the steel pole, this frequency ratio produced a system where CoMload and CoMcarrier oscillated in
phase and with approximately equal amplitude, supporting our
second prediction (P2). For the bamboo pole, a frequency ratio
of 1.2 produced a system where CoMload and CoMcarrier oscillated out of phase and with approximately equal amplitude
(Figs. 1 and 2). As predicted by P3, for the bamboo pole this
state reduced displacement of CoMsystem and the energy required to repeatedly lift the loads against gravity.
In general, these results supported our model’s hypothesis
that the pole system behaves like a DDHO (Fig. 2), although
some of our energy expenditure results only partially supported
predictions. Our first prediction (P1) was supported by our
energetic results in that people on average used less energy
when carrying a compliant bamboo pole compared with the
rigid steel pole (Fig. 3; Table 3). However, bamboo pole
carrying overall was more costly than expected based on
previous studies of fixed-load systems (30, 32, 34). Nonetheless, when participants were able to self-select their step
514
Biomechanics and Economy of Pole Carrying
Castillo ER et al.
•
Table 6. Kinematic comparison between shoulder motion and body’s center of mass for participant 7
Condition
N
Pole Type, Step Freq.
No. of steps
Mean amplitude (cm)
SD (cm)
Mean amplitude (cm)
10
10
11
11
2.39
2.24
2.21
2.13
0.58
0.53
0.32
0.52
9
10
11
8
3.82
2.94
2.52
2.04
0.41
0.45
0.51
0.38
Bamboo pole
1.83 Hz
2.00 Hz
2.17 Hz
2.33 Hz
Steel pole
1.83 Hz
2.00 Hz
2.17 Hz
2.33 Hz
Right Shoulder
Lower Back
Effect Size
Phase
SD (cm)
P value
Cohen’s d
␸/␲
2.80
2.39
2.25
2.21
0.44
0.31
0.17
0.37
0.09
0.59
0.72
0.69
0.84
0.36
0.16
0.19
0.079
0.052
0.023
0.031
3.70
2.90
2.46
2.31
0.22
0.19
0.28
0.26
0.45
0.80
0.74
0.12
0.39
0.12
0.15
0.89
0.005
0.006
0.004
0.003
the CoM of the system as a whole, we account for work done
by the carrier on the loaded pole, as well as work done by the
loaded pole on the carrier. Nonetheless, it is important to note
that the seemingly ideal situation, in which the load oscillates
exactly out of phase with sufficient amplitude to reduce the
motion of the CoMsystem to 0, cannot be attained with the
materials and loads used in this study. According to Eq. 1, we
speculate that carrying 1/5 body weight would require the loads
to oscillate with 5 times the amplitude of the carrier to achieve
zero motion of CoMsystem. Figure 2 shows that the Aload/Acarrier
ratio of that magnitude would require the system to be almost
exactly at resonance, which would destroy the desired phase
relationship.
Although the CoM reduction hypothesis has some utility, the
model tested here does not fully explain the findings. Carrying
studies often show high variability in economy based on how
the load is carried. Some variables that affect the energetic cost
of carrying include where the load is distributed on the body (1,
18, 23, 25, 35, 37), the optimal speed of load carrying (1, 36),
and the presence of elastic elements involved in load suspension (5, 19, 31). However, in general the energetic cost is
predicted to scale proportionately with the relative mass of the
load (30, 32, 34). In our study, this prediction is not met.
According to Eq. 1, when carrying 1/5 body weight such that
Xload ⫺ Xcarrier ⫽ 0, the displacement of the CoMsystem is
theoretically reduced by ⬃1/5 in the bamboo trials relative to
CoMcarrier. One might expect the bamboo pole would therefore
increase metabolic cost by less than 20% compared with
unloaded walking. Because of time constraints, we did not
measure energy expenditure using fixed-load systems, like
backpacks or weighted vests (which would be the ideal comparison). To keep participants from becoming too fatigued and
to avoid the possible unwanted effects of a V̇O2 slow component (6; see below), we kept the experiment under 90 min.
Nonetheless, according to predictions from the literature, our
data show that both poles were more costly than expected on
the basis of added mass.
One possible reason we did not find the bamboo pole to be
more economical than conventional fixed-load carrying methods, like backpacks, was that our participants were inexperienced with this carrying method, which requires practice to do
effectively. It is difficult to quantify the effect of experience,
but we attempted to control for practice during the experiment
by randomizing trial order. A post hoc analysis of trial order
and relCOT showed no significant effect of practice time on
economy during the experiment. As previous work demon-
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frequencies, they chose an energy-saving cadence (2.00 Hz)
significantly above that of their preferred unloaded frequencies
(Fig. 4). This supported the fourth prediction (P4), suggesting
that the inexperienced pole carriers studied here have some
intuition for how to modify their gaits to carry oscillating load
systems in the most economical way. These results suggest that
people are able to take advantage of the energy-saving properties of the DDHO system.
Although this is not the first study to investigate the biomechanics of pole carrying (5, 13, 14, 15, 17, 19), our study
differs significantly from previous work in several ways. Compared with Kram (19), who also tested a CoM hypothesis for
energetic savings, the poles tested in our study were ⬃50%
shorter, and they were carried unilaterally over one shoulder
during walking (not running) to simulate behaviors observed in
East Asia. Furthermore, we tested a biomechanical model
focused on the ratio between step frequency and the natural
frequency of the pole, which has not been directly tested by
previous pole-carrying studies. This was important because
studies of head carrying, for instance, have suggested that
loading does not affect step frequency compared with unloaded
walking (25). Participants in Kram’s study (19), however, were
observed to increase their step frequency by an average of 10%
compared with unloaded running. This would have resulted in
a mean carrier step frequency of 2.98 Hz, roughly three times
the measured natural frequency of the pole (␻carrier/␻load ⬇ 3).
According to our model, such a state would have caused ␻carrier
to be maximally increased relative to ␻load, driving Aload/
Acarrier to approach 0 to minimize CoMload (see Fig. 2). Our
study confirms Kram’s findings that reducing CoMload in this
manner does not lead to lower energy expenditure for the
carrier, because the 2.33-Hz bamboo pole trial in our study
(i.e., the highest ␻carrier/␻load ratio) was actually the most
energetically costly for the flexible pole condition (Fig. 3).
As noted previously, reducing displacements of CoMload
does not result in energetic savings because, although reducing
CoMload creates a system in which no work is done on the loads
to resist gravity, the carrier must still perform work to bend the
pole with each step (19). Other studies that have used a model
based on the hypothesis of reducing the CoM of the load to
explain energetic savings have also had mixed findings (23, 25).
What distinguishes our model from these studies is our proposal
that pole carriers save energy, not by reducing CoMload displacement relative to a fixed frame of reference (i.e., the ground) but
rather by reducing total CoM displacement of the reference
frame containing both the carrier and the load. By considering
t-Test
Biomechanics and Economy of Pole Carrying
•
Castillo ER et al.
Ventilation Flow Rate (L min-1)
175
125
100
106
104
50
102
100
25
Time (min)
strated, untrained participants carrying a load unilaterally over
one shoulder with a “yoke” experience postural changes as the
line of gravity is shifted laterally, leading to vertebral-pelvic
asymmetry, altered gait patterns, and contralateral spinal muscle activation to maintain stability (5). Participants recruited
for this experiment also reported that balancing the pole was
difficult and uncomfortable. Yet pole carriers in South America
(13–15) and East Asia (17) often balance poles over one
shoulder, so we speculate that training probably attenuates
some of these effects. We predict that the energetic savings of
using a compliant pole would be more prevalent among habitual pole carriers in East Asia, and perhaps even more economical than fixed-load carrying methods.
In addition to our participants having little experience with pole
carrying, differences in participant body size and shape likely
contributed to variation in carrying performance (see Table 1), as
previous studies have found (18, 35). We chose participants to
sample a range of body sizes because we anticipated that the
frequency ratio would be the greatest determinant of the
behavior of the DDHO system, regardless of anthropomorphic
differences between participants. Thus, participants ranged in
body mass from 58 to 136 kg and 1.66 to 2.00 m in height. We
controlled for leg length in relative speed and V̇O2 via Froude
number (Eq. 7) and COT calculations, respectively. Because
all participants used the same poles, this caused variability
in the relative mass and size of the poles. For example, pole
mass ranged from ⬃13 to 30% of participant body mass,
leading to varying degrees of carrying difficulty during the
experiments. The relative mass of the load was statistically
accounted for in the energetic analysis using the mixedeffects model (Table 4), but to estimate its impact on
between-participant variation, an ordinary least-squares regression between relCOT and relative load mass showed
that pole mass explains 20% of the variation in relCOT.
Also, one might predict that a variably sized load oscillating
on the participant’s shoulder might affect breathing patterns
during load carrying. However, ventilation patterns were
apparently normal (see Fig. 5), so we are confident that the
bouncing of the poles did not influence the participants’ breathing energetics to a significant degree.
2.00
steel, 2.33 Hz
bamboo, 2.00 Hz
Oxygen uptake (L min-1)
unloaded walking
1.50
1.00
0.50
0.00
0
1
2
3
4
5
6
7
8
9
Fig. 6. Three representative V̇O2 profiles from 1
individual in the experiment. Signals were filtered
via decimation to reduce sampling rate by half
(from 100 to 50 Hz) but are otherwise shown as
raw (unsmoothed) curves. Trial loading conditions
were undertaken in a random order. Solid bold
curve is the unloaded (preferred) walking trial (84
min from the start of the experiment), the dashed
curve is walking with the bamboo pole at the 2.00
Hz (at 22 min), and the dotted curve represents
steel pole trial at a step frequency of 2.33 Hz (at
64 min), which was the most challenging and most
costly condition. Solid flat horizontal lines through
each curve are drawn at the mean values over which
steady-state V̇O2 was measured. Linear regressions
were fit to every sample to ensure that the slope of
the curve was not statistically different from the flat
lines shown (P ⬍ 0.05). These V̇O2 profiles demonstrate that there was no additional rise in V̇O2 that
would indicate a slow component due to exercise
intensity above the lactate threshold.
Time (min)
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Fig. 5. Representative example of the flow rate of
the gas pulled through the V̇O2 mouthpiece and
hose (FL), measured by the incoming flow rate
sensor of the respirometry system. Variation in
flow rate represents the breath-by-breath ventilation pattern of the subject. After initially putting
on the V̇O2 mask, the flow rate drops as the
resistance of the flow changes and the pullthrough flow generator increases to bring the system back to the set sampling rate of 100 l/min. A
1-min subsample between 4 and 5 min is expanded and shown in the box at the bottom.
Subsample illustrates steady, normal ventilation
pattern for the 98-kg man in terms of breaths per
minute and volume of air each breath. This suggests that ventilation was unaffected by the bouncing of the pole on the participant in a way that
would significantly influence energetic measurements. Sample corresponds to a challenging carrying trial (walking with the bamboo pole at a step
frequency of 1.83 Hz) from the same individual
whose V̇O2 profiles are depicted in Fig. 6.
150
75
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Castillo ER et al.
Despite these limitations, we believe that this study has
utility for understanding both evolutionary and engineering
questions. The ability to carry objects must have been an
important selective force during human evolution, and many
scholars hypothesize that hominins relied on various carrying
behaviors to transport resources (such as food or stone tools),
as well as to hold infants during foraging (12, 20, 36, 37). The
evolutionary role of pole carrying has not been well studied in
part because little is known of the antiquity and geographical
range of pole-carrying behavior because of the paucity of
archaeological and ethnographic information. Because bamboo
and wood rarely fossilize, one can only conjecture whether this
simple technology of a flexible carrying pole may have been an
energy-saving technique used by hominins. In addition, the
current study builds on recent work that highlights the utility of
load suspension systems for moving loads without wheels, not
only in humans but also in polypedal machines that must
transport loads economically (2, 31).
ACKNOWLEDGMENTS
We thank Rodger Kram and three anonymous reviewers for advice on the
manuscript, Ayse Baybars, Adam Daoud, Anna Warrener, and Daniel Perl for
assistance with the experiments. We also thank Bob Ganong and Larry Flynn
for help manufacturing the poles. For statistical advice, we thank Erik OtárolaCastillo and the IQSS Research Consulting at Harvard University.
GRANTS
This study was supported by the Hintze Charitable Foundation, the American School of Prehistoric Research (D.E.L.), the Harvard College Research
Program (G.M.L.), and the National Science Foundation Graduate Research
Fellowship Program (E.R.C.).
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the author(s).
AUTHOR CONTRIBUTIONS
Author contributions: E.R.C., G.M.L., and D.E.L. conception and design of
research; E.R.C. and G.M.L. analyzed data; E.R.C., G.M.L., L.S.M., and D.E.L.
interpreted results of experiments; E.R.C. prepared figures; E.R.C. and D.E.L.
drafted manuscript; E.R.C., G.M.L., L.S.M., and D.E.L. edited and revised
manuscript; E.R.C., L.S.M., and D.E.L. approved final version of manuscript;
G.M.L. performed experiments.
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The choice to use the same poles, and therefore a fixed rather
than variable weight based on participant body mass, was
deliberate because our study was designed to experimentally
manipulate the ratio between step frequency and the natural
pole frequency. Thus we needed to precisely control both step
frequency (using a metronome) and the natural frequency of
the pole, which is a function of the pole’s stiffness and mass
(Eq. 2). For this reason, all participants carried the same two
poles with identical loads at set step frequencies. Note that if
we had varied pole loads to make them exactly the same
percentage of each participant’s body mass, we would have
altered the pole’s natural frequency, which would have then
necessitated different step frequencies to produce the desired
frequency ratios. These different step frequencies potentially
could have been much higher or lower than those typical of the
given walking Froude number of 0.2.
Although a comprehensive V̇O2 kinetics analysis was not
undertaken in this study, we are confident that there was no
significant V̇O2 slow component affecting the oxygen consumption data. A V̇O2 slow component is characterized by a
delayed and increased uptake of O2 (typically after more than
2 min at a heavy work rate) as a result of sustained lactic
acidosis, which occurs when an individual continuously exercises at intensities above their anaerobic threshold (6). However, given our relatively low mean V̇O2 values, moderate load
magnitude carried (⬃20% body mass), and rigorous testing of
the V̇O2 sample to ensure a flat steady-state V̇O2 plateau (see
Materials and Methods), we believe that the effects of a slow
component were absent or minimal. To support this inference,
Fig. 6 illustrates three V̇O2 profiles for unloaded walking, the
most economical loading trial, and least economical loading
trial, none of which have an apparent slow component. Also,
although we did not measure V̇O2 max, we can make a conservative estimate that our participants (who were moderately fit,
young adult men) had an average V̇O2 max of 45 ml O2·kg⫺1·
min⫺1 (26). The highest mean V̇O2 for any trial measured in
our study was less than 15 ml O2·kg⫺1·min⫺1 (steel pole 2.33
Hz trial; Table 3). Given our estimate of V̇O2 max, the participants in our study were likely performing at ⬃33% V̇O2 max,
which is well below estimates of a typical anaerobic threshold
at 45–55% V̇O2 max (7). For these reasons, we believe the study
participants were exercising in the moderate domain of intensity, which should not be affected by a V̇O2 slow component.
We acknowledge that another limitation of this study is that
we did not measure CoM directly, but instead inferred its
position via a proxy marker on L4. Oscillations of the lower
lumbar marker were found to be similar to the shoulder in
amplitude and phase but not exactly the same (Table 6). For the
purposes of our model, however, they appear to be good
proxies of CoM motion. Future studies conducted on pole
carrying should use a marker placement and methodology
capable of constructing a full body motion analysis of the
body’s center of mass. An additional limitation was that
weights were directly attached to the pole rather than suspended (Fig. 1). Pole carriers in East Asia often suspend loads
from poles using bamboo strips or fibrous twine, which may
act as secondary springs and/or dampers. The explanation for
this choice is that initial pilot experiments using loads suspended from the pole resulted in considerable pendular motions, making it dangerous for participants to walk safely on
the treadmill.
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