J Appl Physiol 99: 2099 –2107, 2005.
First published July 28, 2005; doi:10.1152/japplphysiol.00103.2005.
Minimizing center of mass vertical movement increases metabolic
cost in walking
Justus D. Ortega and Claire T. Farley
Locomotion Laboratory, Department of Integrative Physiology, University of Colorado, Boulder, Colorado
Submitted 28 January 2005; accepted in final form 22 July 2005
“The Major Determinants of Normal
and Pathological Gait,” Saunders et al. (41) suggest that minimizing the body’s vertical movements during walking minimizes mechanical work and metabolic cost. Although most
researchers agree that the dynamics of walking affect metabolic cost, an alternative view suggests that the vertical movements of the center of mass allow pendulum-like exchange of
mechanical energy that decreases the net external work to
move the center of mass and metabolic cost of walking (2, 11).
Our goal was to examine whether minimizing the vertical
movements of the center of mass reduces the net external work
and metabolic cost of walking.
According to Saunders et al. (41), walking with a flat center
of mass trajectory reduces the muscular work required to lift
the body and, consequently, reduces the metabolic cost of
locomotion. Saunders et al. (41) identify six “determinants of
gait” that smooth and flatten the center of mass trajectory
during walking and thereby reduce the muscular work required
during walking. These determinants of gait include pelvic
rotation, pelvic tilt, stance phase knee flexion, foot and knee
mechanics, and lateral displacement of the pelvis. Although
Saunders et al.’s (41) determinants of gait view of walking has
been widely accepted, particularly in clinical biomechanics
(18, 30, 37, 48), it has not been rigorously tested until recently.
Although no studies have examined whether using a flat
trajectory minimizes the metabolic cost of walking, several
studies have provided insight into this issue. Two determinants
of gait, pelvic rotation and heel lift, do indeed reduce the
vertical movements of the center of mass (13, 28, 29). In
contrast, stance phase knee flexion and pelvic tilt do not
appreciably affect center of mass vertical displacement in
normal walking (21, 22). Furthermore, individuals who naturally prefer to walk with exaggerated stance phase knee flexion
perform more external work to move the center of mass (50).
Although a recent simulation of walking suggests the energetic
cost of raising the body’s center of mass is significant (39), no
study has tested the central hypothesis of Saunders et al. (41)
that decreasing an individual’s center of mass vertical movement minimizes mechanical work to move the center of mass
and metabolic cost. Moreover, an alternative and contradictory
view has emerged.
According to the alternative view, the vertical movements of
the center of mass allow the exchange of mechanical energy
and thereby reduce mechanical work required to move the
center of mass and the metabolic cost of walking (2, 10, 11).
This energy exchange and the center of mass trajectory during
walking have been modeled using an inverted pendulum with
the stance leg represented as a rigid strut that supports a point
mass equal to body mass (2, 10, 11). Like an inverted pendulum, a human walker’s center of mass rises and slows in the
first half of the stance phase and then falls and accelerates
during the second half of the stance phase (6, 34, 35, 38, 42).
Consequently, in the first half of the stance phase, kinetic
energy is converted into gravitational potential energy (11). In
the second half of the stance phase, the opposite conversion
occurs. Because the gravitational potential energy and kinetic
energy fluctuations are nearly equal in magnitude and ⬃180°
out of phase in walking, humans can exchange substantial
mechanical energy. To achieve this exchange, muscles must
generate force to maintain a stiff stance limb and prevent the
center of mass from collapsing, and thus energy exchange is
not a purely passive process in walking humans. Nonetheless,
this model accurately represents the mechanical energy fluc-
Address for reprint requests and other correspondence: J. D. Ortega, Locomotion Laboratory, Dept. of Integrative Physiology, 354 UCB, Boulder, CO
80309-0354 (e-mail: [email protected]).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
biomechanics; determinants of gait; inverted pendulum; locomotion;
mechanical work
IN A CLASSIC PAPER TITLED
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Ortega, Justus D., and Claire T. Farley. Minimizing center of
mass vertical movement increases metabolic cost in walking. J Appl
Physiol 99: 2099 –2107, 2005. First published July 28, 2005;
doi:10.1152/japplphysiol.00103.2005.—A human walker vaults up
and over each stance limb like an inverted pendulum. This similarity
suggests that the vertical motion of a walker’s center of mass reduces
metabolic cost by providing a mechanism for pendulum-like mechanical energy exchange. Alternatively, some researchers have hypothesized that minimizing vertical movements of the center of mass during
walking minimizes the metabolic cost, and this view remains prevalent in clinical gait analysis. We examined the relationship between
vertical movement and metabolic cost by having human subjects walk
normally and with minimal center of mass vertical movement (“flattrajectory walking”). In flat-trajectory walking, subjects reduced center of mass vertical displacement by an average of 69% (P ⫽ 0.0001)
but consumed approximately twice as much metabolic energy over a
range of speeds (0.7–1.8 m/s) (P ⫽ 0.0001). In flat-trajectory walking,
passive pendulum-like mechanical energy exchange provided only a
small portion of the energy required to accelerate the center of mass
because gravitational potential energy fluctuated minimally. Thus,
despite the smaller vertical movements in flat-trajectory walking, the
net external mechanical work needed to move the center of mass was
similar in both types of walking (P ⫽ 0.73). Subjects walked with
more flexed stance limbs in flat-trajectory walking (P ⬍ 0.001), and
the resultant increase in stance limb force generation likely helped
cause the doubling in metabolic cost compared with normal walking.
Regardless of the cause, these findings clearly demonstrate that human
walkers consume substantially more metabolic energy when they
minimize vertical motion.
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METABOLIC COST OF FLAT WALKING
MATERIALS AND METHODS
Experimental design. Kinetic and metabolic data were collected for
eight healthy adult humans (5 women, 3 men) without any known
orthopedic, neurological, or cardiovascular disease. The subjects had
an average age of 26.6 yr (SD 2.6), mass of 66.1 kg (SD 10.7), and
height of 1.73 m (SD 0.07). Before the experiment, all subjects gave
their written, informed consent. This protocol was approved by the
University of Colorado committee for the protection of human subjects.
Each subject participated in three sessions including a practice
session and two testing sessions. In all sessions, subjects walked on a
custom-built motorized treadmill mounted on a force platform (31).
During the practice session, subjects walked for at least 20 min with
a normal center of mass trajectory and 20 min with a flattened center
of mass trajectory (i.e., flat-trajectory walking) at two speeds (1.3 and
1.8 m/s) to habituate subjects to the two types of walking. This session
exceeded the minimum treadmill habituation time of 10 min recommended by Wall and Charteris (45). During the testing sessions,
subjects walked normally and with a flattened center of mass trajectory at five speeds (0.7, 1.0, 1.3, 1.5, and 1.8 m/s) that were randomly
assigned to the first testing session (3 speeds) or the second testing
session (2 speeds). During the last 3 min of each 7-min trial, we
J Appl Physiol • VOL
collected stride frequency, rate of O2 consumption and CO2 production, and ground reaction force data. Three minutes of rest were given
after each flat-trajectory walking trial. At the beginning and end of the
practice session and each testing session, we collected metabolic and
mechanical data at 1.3 m/s to quantify whether any habituation effect
occurred.
During the flat-trajectory walking trials, subjects were provided
with real-time visual feedback to help them minimize the vertical
displacement of the center of mass. A reflective marker over the fourth
lumbar vertebra was videotaped from a posterior view at a rate of 60
Hz and projected onto a monitor with horizontal grid lines in view of
the subject. The camera was zoomed so that 1-cm displacement of the
marker appeared as 4 cm on the monitor. The only instruction given
to each subject was to minimize the vertical movement of the marker,
and thus we did not know what strategy the subjects would use before
the study. At the beginning of the practice sessions, subjects tended to
experiment with a variety of techniques to achieve this goal. However,
by the end of the practice session, they all converged on the strategy
of increasing flexion of stance limb joints.
Metabolic cost. We measured the rates of O2 consumption and
carbon dioxide production using open-circuit indirect calorimetry
(Physio-Dyne Instruments, Quogue, NY). During each trial, we gave
subjects 4 min to reach metabolic steady state before collecting
metabolic data for the last 3 min. Using the average O2 consumption
(ml O2/min) and carbon dioxide production (ml CO2/min) for the last
3 min, we calculated average metabolic rate per kilogram body weight
(W/kg) (5). For 7 min at the beginning of each session, we measured
the standing metabolic rate. We subtracted standing metabolic rate
from gross metabolic rate and divided by speed to calculate net
metabolic cost of transport (J 䡠 kg⫺1 䡠 m⫺1).
Ground reaction force and mechanical work. A force-sensing
treadmill was used to measure the vertical, horizontal, and lateral
ground reaction force components for two 10-s periods (about 20
strides total) within the last 2 min of each trial. The force treadmill
consisted of a custom-built motorized treadmill mounted on a force
platform (AMTI, model ZBP-7124-6-4000) and has been described in
detail by Kram et al. (31). We collected force data at 1,000 Hz and
low-pass filtered the data using a fourth-order zero-lag Butterworth
filter with a cutoff frequency of 20 Hz. We used the ground reaction
force data to calculate the acceleration of the center of mass in each
direction. We then double integrated the acceleration data with respect
to time for an integral number of strides to determine the instantaneous center of mass velocity and displacement in each direction
(4, 7).
We determined the kinetic energy, gravitational potential energy,
and total energy of the center of mass from its velocity and displacement and subsequently determined the external work performed on
the center of mass. We calculated total kinetic energy (Ek,t) from body
mass (m) and the resultant center of mass velocity (V) determined
from its vertical, horizontal, and lateral components:
E k,t ⫽ 1/2 mV2
(1)
Gravitational potential energy (Ep,g) was calculated from mass (m),
the acceleration due to gravity (g), and the vertical displacement of the
center of mass relative to heelstrike (⌬h):
E p,g ⫽ mg ⌬h
(2)
By taking the instantaneous sum of gravitational potential energy and
kinetic energy, we calculated the total energy of the center of mass
(Etot):
E tot ⫽ Ep,g ⫹ Ek,t
(3)
We determined the net external work required to lift and accelerate the
center of mass by summing the positive increments in its total energy
over each step (7). “Net external” work represents the net work
performed by the overall muscular system to lift and accelerate the
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tuations and the pendulum-like energy exchange in an amazing
variety of animals, including those in Refs. 11, 19, 20, 24,
26, 36.
According to the inverted pendulum model, the out-of-phase
fluctuations in gravitational potential energy and kinetic energy
represent a continuous exchange of mechanical energy. This
exchange reduces the net mechanical work performed by the
overall muscular system to lift and accelerate the center of
mass (“net external work”) by up to 65% and consequently
reduces the metabolic cost in walking (9). In fact, both net
external work and metabolic cost of transport are minimized at
about the same intermediate walking speed where pendulum
energy exchange is maximized (10). Minetti et al. (38) showed
that metabolic cost and net external work are minimized at the
same freely chosen stride frequencies and that recovery decreases at stride frequencies above the freely chosen stride
frequency. This link between energy exchange, net external
work, and metabolic cost in a number of situations (8, 10 –12,
38) suggests center of mass vertical movement is advantageous
because it allows pendulum-like energy exchange, reduces net
external work, and reduces metabolic cost in walking.
The two divergent views regarding the relationship between
center of mass vertical motion and metabolic cost have not yet
been reconciled. The aim of this study is to determine how
minimizing center of mass vertical motion affects inverted
pendulum exchange, net external work, and metabolic cost in
walking. We hypothesized that walking with a flattened center
of mass trajectory does not reduce net external work performed
on the center of mass because it reduces inverted pendulum
energy exchange. Moreover, contrary to Saunders et al. (41),
we hypothesized that metabolic cost would not decrease when
humans walk with a flattened center of mass trajectory. To test
our hypotheses, we examined metabolic cost, mechanical energy exchange, and net external work for humans walking with
small vertical movements of the center of mass compared with
walking with normal center of mass movements. In addition to
testing the hypothesis of Saunders et al. (41), this study will
provide insight into the fundamental mechanical determinants
of metabolic cost in walking.
METABOLIC COST OF FLAT WALKING
Phase angle ⫽ 共⌬t/T兲 䡠 360⬚ ⫹ 180⬚
(4)
where ⌬t represents the time interval between minimum ⌬Ek,t and
maximum ⌬Ep,g and T represents the time interval between consecutive heelstrikes. Thus, when the minimum ⌬Ek,t and the maximum in
⌬Ep,g occurred simultaneously, phase angle was 180°.
Finally, we evaluated how much inverted pendulum energy exchange reduced the net external work required to lift and accelerate
the center of mass by calculating the mechanical energy recovery
(11):
Recovery共%兲 ⫽ 共Wp,g ⫹ Wk,t ⫺ Wext兲/共Wp,g ⫹ Wk,t兲 䡠 100
(5)
where Wp,g was calculated as the sum of the positive increments in
gravitational potential energy over a step and was the work required
to lift the center of mass and Wext is net external work. We calculated
the work required to accelerate the center of mass (Wk,t) as the sum of
the positive increments in the kinetic energy over a step. All mechanical work values are expressed per kilogram body mass and per meter
traveled.
Kinematics. We measured sagittal plane kinematics of the right
lower limb using high-speed video (200 fields/s, JC Labs, Mountain
View, CA) and reflective markers on the iliac crest, greater trochanter,
lateral femoral condyle, lateral malleolus, and lateral border of the
fifth metatarsal head. We digitized the video (Peak Performance
Technologies, Englewood, CO) and filtered the position data using a
fourth-order zero-lag Butterworth filter with a cutoff frequency of 6
Hz (49). From the position data, we calculated the hip, knee, and ankle
angles during the stance phase of walking. Each joint angle was
defined as the acute angle between adjacent segments. We determined
the average angle and minimum angle for each joint during the stance
phase. We focused on the stance phase because stance limb action is
the primary determinant of the motion of the center of mass.
Statistical analyses. The effects of walking condition on metabolic
cost and walking mechanics were tested using a two-way mixed
repeated-measures ANOVA and Student-Newman-Keuls post hoc
tests where appropriate. For the habituation data, we tested the effects
of habituation on vertical displacement, stride frequency, and metabolic cost using one-way repeated-measures ANOVA. We tested the
effects of habituation between trials within each session as well as
across all sessions. All statistical analyses were performed using SPSS
11.5 (SPSS) software and an ␣ level of 0.05.
J Appl Physiol • VOL
RESULTS
The metabolic cost and kinematics of normal and flattrajectory walking remained constant within and among testing
sessions, suggesting that subjects were fully habituated to both
types of walking at the end of the practice session. Metabolic
cost remained constant across the practice and testing sessions
for normal and flat-trajectory walking (P ⫽ 0.63 and P ⫽ 0.76,
respectively), and stride frequency also did not change (P ⫽
0.97 for both types of walking). Moreover, in normal walking,
subjects maintained a nearly constant vertical displacement of
3.0 cm (SD 0.4) for all practice and testing sessions (P ⫽ 0.99).
In flat-trajectory walking, subjects reduced the vertical displacement from 1.5 cm (SD 0.3) to 1.0 cm (SD 0.2) between
the beginning and end of the practice session (P ⫽ 0.002) but
then maintained a constant vertical displacement over the
testing sessions (P ⫽ 0.92). Although most subjects experimented with a variety of techniques for flat-trajectory walking
at the beginning of the practice session, all subjects appeared to
consistently use one technique by the end of the practice
session.
In flat-trajectory walking, the center of mass moved vertically by 69% (SD 4) less than in normal walking (P ⬍ 0.0001),
whereas other aspects of the center of mass dynamics remained
similar (Fig. 1). The average vertical displacement of the center
of mass in flat-trajectory walking was 0.9 cm (SD 0.1) for all
speeds and was independent of speed (P ⫽ 0.32; Fig. 1A). In
contrast, in normal walking, the vertical displacement increased from 1.8 cm (SD 0.1) to 4.2 cm (SD 0.2) across the
range of speeds (P ⫽ 0.0001). Thus, in flat-trajectory walking,
the center of mass moved vertically by 54 –78% less than in
normal walking at the slowest and fastest speeds, respectively.
Despite reducing the vertical displacement of the center of
mass to ⬍1 cm during flat-trajectory walking, subjects did not
substantially change lateral displacement (P ⫽ 0.26) or stride
frequency (P ⫽ 0.17). Specifically, in flat-trajectory walking,
subjects maintained center of mass lateral displacement within
0.4 cm (Fig. 1B) and stride frequency within 0.04 Hz (Fig. 1C)
of the values in normal walking.
Subjects used substantially more flexed stance limbs during
flat-trajectory walking than during normal walking. Average
joint angle for the stance phase decreased by 10° (SD 4) at the
hip (P ⬍ 0.001), 18° (SD 5) at the knee (P ⬍ 0.001), and 7°
(SD 2) at the ankle (P ⬍ 0.001) between flat-trajectory walking
and normal walking. Average stance phase joint angles did not
change with walking speed (P ⫽ 0.409, 0.179, and 0.848,
respectively) (Figs. 2 and 3).
Despite the minimal vertical movements of the center of
mass during flat-trajectory walking, subjects consumed, on
average, twice as much metabolic energy to travel a meter than
during normal walking (P ⬍ 0.0001) (Fig. 4). During flattrajectory walking, subjects consumed the least metabolic energy to travel a meter at the intermediate speed of 1.0 m/s (3.74
J 䡠kg⫺1 䡠m⫺1, SD 0.45) and consumed 4 and 8% more at the
slowest and fastest speeds, respectively (P ⫽ 0.01). During
normal walking, subjects consumed the least metabolic energy
at the intermediate speed of 1.3 m/s (1.8 J䡠kg⫺1 䡠m⫺1, SD 0.1)
and consumed 17 and 27% more at the slowest and fastest
speeds, respectively (P ⫽ 0.01). Even at those extreme speeds,
the cost of transport was on average 1.8-fold greater in flattrajectory walking than in normal walking.
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center of mass and is quantitatively identical to external work as
defined by Cavagna (7). Because the two limbs and antagonist
muscles can work against each other and internal work is performed
to move the limbs relative to the center of mass, net external work is
less than the total muscle work performed during walking (1, 43, 44,
51). Net external work was calculated using the net ground reaction
force that was the instantaneous sum of ground reaction forces under
both limbs. Thus this calculation involved the mathematical cancellation of simultaneous positive and negative work performed by the
individual limbs during the double support phase (17). We used the
term net external work to emphasize that it represents the minimum
work performed to move the center of mass and does not account for
the “extra” muscle work needed to move the center of mass due to
opposing forces of individual limbs or of antagonist muscles.
To evaluate the potential for inverted pendulum energy exchange,
we examined the relative magnitudes and timing of the kinetic energy
and gravitational potential energy fluctuations. Gravitational potential
energy and kinetic energy each fluctuated once per step, and ⌬Ep,g and
⌬Ek,t corresponded to the magnitudes of these fluctuations normalized
to body mass and speed (J 䡠 kg⫺1 䡠 m⫺1) to compare to net external
work values. We compared the magnitudes of ⌬Ep,g and ⌬Ek,t by
taking their ratio, and we quantified their relative timing by calculating phase angle (9):
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METABOLIC COST OF FLAT WALKING
At all speeds of flat-trajectory walking, gravitational potential energy fluctuated much less than kinetic energy, and this
mismatch led to reduced energy exchange by the inverted
pendulum mechanism than in normal walking. In flat-trajectory
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Fig. 1. Center of mass vertical displacement (A), center of mass lateral
displacement (B), and stride frequency (C) vs. speed during normal walking
(F) and flat-trajectory walking (‚). Values are means ⫾ SD. In flat-trajectory
walking, vertical displacement of the center of mass was smaller than in
normal walking, and lateral displacement of the center of mass was similar in
both types of walking. Stride frequency was similar in both types of walking.
Lines are least squares regressions. *Significant differences (P ⬍ 0.05)
between flat-trajectory walking and normal walking.
J Appl Physiol • VOL
Fig. 2. Representative joint angles at the hip (A), knee (B), and ankle (C)
during the stance phase of normal walking (solid lines) and flat-trajectory
walking (broken lines) vs. time for a single stance phase at 1.3 m/s. Time is
expressed as a percent of the stance phase duration. Throughout the stance
phase of flat-trajectory walking, subjects had greater flexion at the hip, knee,
and ankle (P ⬍ 0.001).
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METABOLIC COST OF FLAT WALKING
2103
Fig. 3. Average stance phase joint angles for the hip (A), knee (B), and ankle
(C) vs. speed during normal walking (F) and flat-trajectory walking (E). Values
are means ⫾ SD. In flat-trajectory walking, the hip, knee, and ankle were more
flexed during stance than in normal walking. Lines are least squares regressions. *Significant differences (P ⬍ 0.05) between flat-trajectory walking and
normal walking.
J Appl Physiol • VOL
walking, gravitational potential energy fluctuated an average of
63% (SD 16) less than kinetic energy fluctuated over the range
of speeds (Figs. 5B and Fig. 6C). This mismatch occurred
because gravitational potential energy fluctuated minimally
(0.13 J䡠kg⫺1 䡠m⫺1, SD 0.01) (Fig. 6A), whereas kinetic energy
fluctuated only slightly less than in normal walking (0.39
J䡠kg⫺1 䡠m⫺1, SD 0.10) (Fig. 6B). Moreover, the relative timing
of these energy fluctuations (i.e., phase angle) tended to deviate
more from the ideal value for pendulum-like energy exchange
(180°) in flat-trajectory walking (256°, SD 22) than in normal
walking (P ⫽ 0.0004) (Fig. 7A). In contrast, in normal walking, gravitational potential and kinetic energy fluctuated nearly
out of phase (199°, SD 9) and approximately equally at all
speeds (0.42 J䡠kg⫺1 䡠m⫺1, SD 0.06, and 0.44 J䡠kg⫺1 䡠m⫺1, SD
0.14, for ⌬Ep,g and ⌬Ek,t, respectively) (Figs. 5A and 6, A–C).
Thus the energy fluctuation magnitudes and timing were close
to ideal for energy exchange in normal walking but not in
flat-trajectory walking.
In flat-trajectory walking at moderate speeds, subjects recovered only about one-half as much mechanical energy by the
inverted pendulum mechanism as in normal walking (P ⬍
0.0001) (Fig. 7B). In flat-trajectory walking, mechanical energy recovery by the inverted pendulum mechanism decreased
from 41% (SD 3) to 21% (SD 4) as subjects walked faster (P ⫽
0.04), whereas in normal walking, recovery remained 63% (SD
2) over the range of speeds (P ⫽ 0.24). Recovery was low in
flat-trajectory walking primarily because the decrease in gravitational potential energy was less than the increase in kinetic
energy in the second half of stance (Fig. 5B). Consequently, the
conversion of gravitational potential energy to kinetic energy
was lower in flat-trajectory walking than in normal walking.
Although recovery was low in flat-trajectory walking, a
similar amount of net external work was needed to move the
center of mass as in normal walking (P ⫽ 0.31) (Fig. 7C). In
flat-trajectory walking, the gravitational potential energy fluctuations were on average 69% smaller than in normal walking
(P ⬍ 0.0001), and, consequently, substantially less net work
was needed to lift the center of mass in the first half of stance.
However, substantially more net work was needed to acceler-
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Fig. 4. Net metabolic cost of transport vs. speed for normal walking (F) and
flat-trajectory walking (‚). Values are means ⫾ SD. In flat-trajectory walking,
subjects consumed about twice as much metabolic energy per kilogram of
body weight to travel a given distance than in normal walking. Lines are least
squares regressions. *Significant differences (P ⬍ 0.05) between flat-trajectory
walking and normal walking.
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METABOLIC COST OF FLAT WALKING
Fig. 5. Representative data for total energy
(Etot), kinetic energy (Ek,t), and gravitational
potential energy (Ep,g) of center of mass vs.
time at 1.3 m/s for normal walking (A) and
flat-trajectory walking (B). A single step from
heel strike of one foot to heel strike of opposite foot is shown. All energy values are normalized to body mass. In flat-trajectory walking, Ep,g fluctuated much less than in normal
walking. Total energy fluctuations were not
smaller in flat-trajectory walking than in normal walking due to lack of energy exchange.
DISCUSSION
Contrary to the view of Saunders et al. (41) and in agreement
with our hypothesis, minimizing the vertical motion of the
center of mass during walking does not reduce the mechanical
work required to move the center of mass and approximately
doubles the metabolic cost. Although some evidence suggests
that the metabolic cost of lifting the center of mass is substantial (39), the results of this study emphasize that vertical
motion allows inverted pendulum energy exchange and therefore reduces the mechanical work required to accelerate the
center of mass in normal walking. In accordance with the
determinants of gait view, the mechanical work required to lift
the center of mass decreases in flat-trajectory walking. However, because little gravitational potential energy is available to
be converted to kinetic energy, the work required to accelerate
the center of mass increases in flat-trajectory walking. Due to
these offsetting effects, minimizing vertical motion does not
change the net external work required to move the center of
mass. Therefore, other factors probably contribute to the high
metabolic cost of flat-trajectory walking, including greater
muscle force generation to support body weight and greater
positive muscle work performed to compensate for co-contraction.
The high metabolic cost of flat-trajectory walking may be
explained by greater muscle force generation to support body
weight due to increased stance leg flexion (25, 32). Because
our subjects uniformly chose to flatten the center of mass
trajectory by increasing stance leg flexion, it is likely that the
ground reaction force had longer moment arms about the joints
and the effective mechanical advantage of the stance limb
extensor muscles decreased (3). Consequently, subjects likely
had to generate greater muscle force to support body weight in
flat-trajectory walking than in normal walking. Several studies
on human walking demonstrate that exaggerated hip and knee
J Appl Physiol • VOL
flexion leads to greater muscle activation, muscle force, and
metabolic cost (14, 23, 25, 46, 47). However, in the extreme
case of human walkers maintaining a knee angle of ⬍135°
during the stance phase, metabolic cost increases by only 38%
(47). Given that metabolic cost doubled in our study, it is likely
that other factors contribute to doubling metabolic cost in
flat-trajectory walking.
Although unlikely to be a major contributor, another factor
that could underlie the high metabolic cost of flat-trajectory
walking is the opposing actions of the individual limbs during
double support (17, 33). In the double-support phase of walking, the two limbs work against each other as the body
transitions from one inverted pendulum arc to the next. The
leading limb performs negative work to change the direction of
the center of mass while the trailing limb simultaneously
performs positive work to accelerate the center of mass upward
and forward. This simultaneous limb work is not fully reflected
in net external work because the opposing components of the
forces under the two limbs mathematically cancel each other.
In flat-trajectory walking, the center of mass changes direction
during double support less dramatically than in normal walking
because it follows a flatter arc in each single-support phase.
Because the negative work by the leading limb primarily acts
to change the direction of the center of mass during double
support, the leading limb likely performs less negative work in
flat-trajectory walking. As a result, the simultaneous positive
work performed by the trailing limb that compensates for the
negative work by the leading limb should also be less than in
normal walking. Therefore, the total individual limb work
performed by the leading and trailing limbs during double
support is likely not greater and may even be less than in
normal walking.
Increased co-contraction of antagonist stance limb muscles
may also contribute to the high metabolic cost of flat-trajectory
walking. When antagonistic extensors and flexors of the stance
limb are simultaneously active, the flexors absorb some of the
positive work performed by the extensors, and thus the net
work performed by the combined active muscles is less than
the positive work performed by the extensors. Consequently, if
there is co-contraction of antagonists in the stance limb, the net
external work will differ from the total work performed by
individual muscles. Co-contraction of antagonist muscles may
increase in flat-trajectory walking because it is an unfamiliar
task. Grasso et al. (23) found that walking with exaggerated
knee flexion increases co-contraction of stance limb muscles.
However, co-contraction might have been especially high in
that study (23) because it did not familiarize subjects to
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ate the center of mass in the second half of stance than in
normal walking. Specifically, gravitational potential energy
decreased so little in flat-trajectory walking that inverted pendulum energy exchange supplied only a small portion of the
energy needed for the simultaneous increase in kinetic energy.
In contrast, energy exchange provided the majority of the
energy needed to accelerate the center of mass in normal
walking (Figs. 5A and 6C). Because minimizing vertical displacement increased the net work required for reacceleration,
net external work was not lower in flat-trajectory walking (0.35
J䡠kg⫺1 䡠m⫺1, SD 0.09) compared with normal walking (0.32
J䡠kg⫺1 䡠m⫺1, SD 0.07) (P ⫽ 0.31) (Fig. 7C).
METABOLIC COST OF FLAT WALKING
2105
bent-posture walking before the experimental trials. Our study
included a practice session, and the constant metabolic cost
over the practice and experimental sessions suggests that subjects had become familiar with flat-trajectory walking. Nonetheless, it would be useful for a future study to measure
electromyogram of the stance limb muscles during flat-trajec-
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 14, 2017
Fig. 6. Magnitude of Ep,g (⌬Ep,g; A), magnitude of Ek,t (⌬Ek,t; B), and ratio of
Ep,g fluctuation to Ek,t (⌬Ep,g/⌬Ek,t; C) vs. speed (means ⫾ SD) in normal
walking (F) and flat-trajectory walking (‚). In flat-trajectory walking, ⌬Ep,g/
⌬Ek,t was smaller than in normal walking primarily because Ep,g fluctuated less
than in normal walking. Lines are least squares regressions, and energy
fluctuation values are normalized to body mass and expressed per meter to
facilitate comparisons to net external work. *Significant differences (P ⬍ 0.05)
between flat-trajectory walking and normal walking.
J Appl Physiol • VOL
Fig. 7. Phase angle between Ep,g maximum and Ek,t minimum (A), inverted
pendulum recovery of mechanical energy (B), and net external work (C) vs.
speed (means ⫾ SD) for normal walking (F) and flat-trajectory walking (‚). To
maximize inverted pendulum energy exchange, Ep,g and Ek,t should be out of
phase (i.e., phase angle of 180°). In flat-trajectory walking, phase angle
deviated more from 180° and varied more than in normal walking. Recovery
was much greater in normal walking than in flat-trajectory walking, but net
external work per kilogram body mass was similar. Lines are least squares
regressions. *Significant differences (P ⬍ 0.05) between flat-trajectory walking and normal walking.
99 • DECEMBER 2005 •
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2106
METABOLIC COST OF FLAT WALKING
ACKNOWLEDGMENTS
The authors thank the members of the Locomotion Laboratory for help with
this study.
GRANTS
This study was supported by National Institute on Aging Grant AG-00279.
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