Vol. 85, Issue 4, 1376-1383, October 1998
Scaling of submaximal oxygen uptake with body mass and
combined mass during uphill treadmill bicycling
Daniel P.
Heil
Department of Exercise Science, University of Massachusetts,
Amherst, Massachusetts 01003
 |
ABSTRACT |
This study examined the scaling relationships of
net O2 uptake
[
O2(net) = O2 
resting
O2] to body mass
(MB) and
combined mass (MC = MB + bicycle)
during uphill treadmill bicycling. It was hypothesized that
O2(net)
(l/min) would scale proportionally with
MC [i.e.,
O2(net) 
M1.0C] and less than proportionally with
MB [i.e.,
O2(net) MB].
Twenty-five competitive cyclists [73.9 ± 8.8 and 85.0 ± 9.0 (SD) kg for
MB and
MC,
respectively] rode their bicycles on a treadmill at 3.46 m/s and
grades of 1.7, 3.5, 5.2, and 7.0% while
O2 was measured. Multiple
log-linear regression procedures were applied to the pooled
O2(net)
data to determine the exponents for
MC and
MB after
statistically controlling for differences in treadmill grade and
dynamic friction. The regression models were highly significant (R2 = 0.95, P < 0.001). Exponents for
MC (0.99, 95%
confidence interval = 0.80-1.18) and
MB (0.89, 95%
confidence interval = 0.72-1.07) did not differ significantly from
each other or 1.0. It was concluded that the 0.99 MC exponent was
due to gravitational resistance, whereas the
MB exponent was
<1.0 because the bicycles were relatively lighter for heavier
cyclists.
allometry; regression
| |
INTRODUCTION |
THE NET EXTERNAL power demand
(
D, W) of
endurance sport performance can be modeled as the product of the net
resistance (Rnet, N) to forward motion and the
average maximal rate, or ground speed
(·max, m/s), at which
Rnet is resisted (6)
|
(1)
|
To
maintain a given ·max
during an endurance performance, however, an athlete's maximal
steadystate metabolic power supply [S(max)]
must be capable of at least matching
D [i.e.,
S(max) D].
Substituting
S(max) for
D in
Eq. 1 gives
|
(2)
|
where
k is a constant. When the performance
is not maximal, however, Eq. 2 reduces
to
|
(3)
|
where
S is the
submaximal steady-state metabolic power [i.e., submaximal
O2 uptake
(O2)] and
· is the steady-state traveling speed. Thus the
submaximal O2 required to
maintain a given · should be directly proportional to the
net external resistance to forward motion (i.e.,
S O2 Rnet).
During outdoor bicycling the external forces impeding forward motion
include aerodynamic drag (RD, N),
gravitational resistance (RG, N),
and the rolling friction (RR, N)
between the tires and road surface (7). During bicycling at a level
grade, RD is the dominant
resistive force (7). In contrast, during bicycling up steep hills or on
an inclined treadmill, RG is the
dominant resistive force and RD
can be considered negligible (7). Thus, for steep uphill or inclined
treadmill bicycling, it follows that Rnet = RG + RR and
S for a given
· is provided by (from Eq. 3)
|
(4)
|
where
(7)
|
(5)
|
and
(16)
|
(6)
|
where
MC is the
combined mass of the cyclist with bike and gear (kg),
g is the constant of gravitational
acceleration (9.81 m/s2), 
is
the inclination of the road surface (degrees),
v is the air velocity relative to the
bicycle and rider (m/s; v = · on a treadmill), and
µS and
µD are the coefficients of
static and dynamic friction (both dimensionless), respectively. If it
is further assumed that the magnitude of
RR is negligible, by substituting Eq. 5 into Eq. 4 the metabolic power required to overcome
gravitational resistance is given as
![<A><AC>W</AC><AC>˙</AC></A><SUB>S</SUB> = <IT>k</IT> [<IT>M</IT><SUB>C</SUB> × <IT>g</IT> × (sin &thgr;)] × <A><AC>s</AC><AC>˙</AC></A>](/content/vol85/issue4/fulltext/1376/img007.gif)
|
(7)
|
Thus,
for a given and ·, the submaximal steady-state
metabolic power required for steep uphill or inclined treadmill
bicycling should be directly proportional to
MC (i.e.,
S MC = M1.0C).
Interestingly, research involving the energetic demands of uphill
bicycling have mostly been limited to issues of pedal cadence and body
position (26, 27). Thus the relationship between submaximal
O2 and
MC during uphill
bicycling has never been addressed experimentally.
The related issue of O2
demand during uphill bicycling as a function of body mass
(MB) was
evaluated by Swain (25) using allometric scaling procedures. Swain
concluded that the O2 cost of
uphill bicycling was proportional to
MB raised to the
0.79 power (i.e., O2 M0.79B). Because the 0.79 exponent was <1.0, heavier cyclists tended to expend less energy than
smaller cyclists relative to
MB when uphill
treadmill bicycling at the same and ·. Swain further
speculated that the differential expense of energy for graded treadmill
bicycling and the 0.79 MB exponent was
the result of the cyclists' bicycles being relatively lighter for the
heavier cyclists (i.e., as a percentage of
MB). The
potential influence of RR on the
derived MB
exponent, however, was never addressed. Although the plausibility of
Swain's hypothesis seems reasonable, it has never been verified
experimentally.
The above review outlines a theoretical framework for predicting the
scaling relationship between submaximal
O2 and
MC and MB during uphill
bicycling. The theoretical dependence of
O2 on
MC
(O2 M1.00C), however, has never been verified experimentally, whereas Swain's (25) 0.79 exponent for
MB has never been
explained theoretically or experimentally. Thus the present study was
designed to evaluate both of these issues by measuring submaximal
O2 for trained cyclists
during uphill treadmill bicycling. These data were then evaluated using log-linear multiple regression techniques (19, 20) to define the
appropriate scaling relationships.
| |
METHODS |
Subjects.
Volunteer competitive cyclists from the local area read and signed an
informed consent document, as well as a cycling history questionnaire,
before any testing in the Human Performance Laboratory at the
University of Massachusetts (Amherst, MA). Subjects refrained from
strenuous activity on the day before each visit and abstained from
caffeine ingestion for 
3 h before arriving at the laboratory.
Testing of peak O2.
On the first laboratory visit, each subject completed a continuous,
incremental cycle ergometry test to exhaustion (model 829E cycle
ergometer, Monark Bodyguard Fitness, Varberg, Sweden). Before each
test, the ergometer was calibrated according to procedures outlined by
the manufacturer. In addition, seat height and handlebar position were
set according to each subject's preference. Resting O2 was measured first with
subjects sitting quietly on the ergometer (no pedaling) over a 5-min
period. This was followed by a standardized warmup of 3 min at 80 W
while pedaling 80 rpm, 3 min at 150 W and 80 rpm, and finally 3 min at
180 W and 90 rpm. The peak
O2 (O2 peak) test began
immediately thereafter by increasing power output by 30 W at 1-min
intervals during pedaling 90 rpm until volitional exhaustion. Each
subject's O2 peak
was defined as an average of the highest two or three values within 2.0 ml · kg
1 · min1
of each other. The
O2 peak values were
considered valid if at least two of the three following criteria were
satisfied: 1) a leveling of
O2, despite an increase in
power output, 2) a maximal heart
rate >10 beats below each subject's age-predicted maximal heart rate
(220 age in years), and 3) a
respiratory exchange ratio 1.1.
Graded treadmill bicycling.
On the second laboratory visit, body height (m), as well as separate
mass measures for the body, the bike, and the cyclists' extra gear for
riding (i.e., helmet and cycling cleats), was obtained. Mass was
determined using a standard beam scale to the nearest 0.1 kg. Bicycles
were stripped of extraneous equipment such as tire pumps, spare tubes,
and water bottles before mass measurements.
On the basis of observations during pilot testing and reports by other
researchers (26), a separate laboratory visit for practice riding on
the treadmill was not necessary. Thus subjects practiced and warmed up
before testing by riding their own bicycles on the laboratory treadmill
(Trackmaster TM500-E, JAS Fitness Systems). The treadmill's surface
measured 2.3 m long × 1.8 m wide, with speed and incline ranges
of 1-11 m/s and 0-12.7°, respectively. The practice
session also served to acquaint each subject with the specific
treadmill speed and grades to be tested. Practice and testing on the
treadmill were limited to the left side of the treadmill, where a
handrail was installed down the entire length of the treadmill. The
amount of practice time on the treadmill, which varied between 10 and
25 min, depended on how quickly each subject became comfortable with
the task of treadmill bicycling. As an added safety measure, two
mattresses were placed directly behind the treadmill to cushion the
subject in the event of a fall.
Before treadmill practice and testing, all bicycle tires were inflated
to the manufacturers' suggested pressure (i.e., 69-83 N/cm2). The four treadmill
bicycling conditions corresponded to treadmill grades of 1.7%
(1°), 3.5% (2°), 5.2% (3°), and 7.0% (4°), all at a
treadmill speed of 3.46 m/s. Pilot testing indicated that these
combinations of speed and grade would elicit a wide range of
steady-state energetic demands in moderately trained cyclists. Subjects
began their test session with a 2- to 3-min warmup on the treadmill at
a speed of 3.46 m/s and grade of 1.7%, which was followed immediately
with an adjustment of the grade to match the first condition being
tested. The four grades were tested successively, with 6 min of riding
at each grade, the order of which was counterbalanced across subjects.
Subjects received verbal feedback during all treadmill bicycling and
were encouraged to maintain a steady position on the treadmill that was
centered lengthwise but within reach of the handrail. Subjects were
also required to maintain the same gripping position (i.e., hands on the brake hoods of handlebars) on their handlebars during all four
conditions to minimize changes in body position relative to the
bicycle.
Because the subjects' bicycles were equipped with various gear
combinations, it was not feasible for all subjects to use the same
gearing without major equipment modifications to many of the bicycles.
Alternatively, the subjects used the gearing available on their own
bicycles to achieve similar gear ratios and thus similar pedal
cadences. The gear ratios actually used were 1.75 (42/24 = TF/TR,
where TF is the number of teeth on
the front chain ring and TR is the
number of teeth on the rear cog), 1.62 (42/26), 1.70 (39/23), and 1.63 (39/24).
Pedal cadence and treadmill speed were measured twice near the end of
each condition; grade was measured at the beginning of each condition.
Cadence was determined by timing 10 pedal revolutions; a digital hand
tachometer (Biddle Instruments, Blue Bell, PA) was used to measure
treadmill speed. Treadmill grade was measured within ±0.5°
using an inclinometer on a flat surface adjacent to the treadmill belt.
Estimating µD.
The µD was determined for each
subject at each grade for use as a covariate in the regression
analyses. The Rnet to treadmill bicycling was computed as the sum of
RG and
RR (7, 16)
![× (&mgr;<SUB>S</SUB> + &mgr;<SUB>D</SUB> × <IT>v</IT>) × (cos &thgr;)]](/content/vol85/issue4/fulltext/1376/img009.gif)
|
(8)
|
The value of µS can be
assumed constant at ~0.0025 (16). Rearranging Eq. 8 to solve for
µD gives
![× [<IT>g</IT> × <IT>M</IT><SUB>C</SUB> × (cos &thgr;) × <IT>v</IT>]<SUP>−1</SUP>](/content/vol85/issue4/fulltext/1376/img011.gif)
|
(9)
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where Rnet is the only
unknown, since
MC, , and
v were measured
(v = · for treadmill
bicycling), and g and
µS are constants.
Values for Rnet were measured
directly as the towing force required to maintain a stationary position
on the treadmill. After the metabolic testing described above, the head
tube of each subject's bicycle was attached via a lightweight cable to
a hand-held digital dynamometer (model DFIS 100, range 0.5-500 N,
Chatillon, Greensboro, NC) that was zeroed before each measurement.
Subjects maintained a balanced position on the moving belt of the
treadmill for 5-10 s while the researcher held and visually read
the digital display on the dynamometer. The most stable dynamometer
reading was recorded within 0.5 N.
Anthropometry.
Percent body fat and lower limb mass
(MLL) were also
determined for use as potential covariates in the statistical analyses. Percent body fat was estimated from hydrostatic measures of body density (8) and the formula derived by Brozek et al. (4). Lower limb
volume for each subject was also estimated using a geometric modeling
technique validated by Sady et al. (23) and Freedson et al. (10). All
lower limb anthropometric measures were taken on the right side of the
body by the same investigator using standard anthropometers (lengths
and breadths) and cloth tape measures (circumferences) according to the
procedures outlined by Lohman et al. (18). Total
MLL (kg) was
computed as follows: MLL = 2(
TVT + LVL + FVF),
where the subscripts T, L, and F refer to estimated segment densities
(, g/cm3) and segment volumes
(V, liters) for the thigh, leg, and foot, respectively. Segment
densities were estimated as 1.06, 1.08, and 1.10 g/cm3 for the thigh, leg, and
foot, respectively (30).
O2 instrumentation.
Standard indirect calorimetry procedures were used to determine
submaximal O2 and
O2 peak. Expired
gases were continuously sampled (250 Hz) from a 3-liter mixing chamber
and analyzed for O2 and
CO2 concentrations via a
computer-based system (286 Leading Edge computer using VO2Plus Software
from Exeter Research, Brentwood, NH) interfaced with Ametek
O2 (model S-3AI) and
CO2 (model CD-3A) analyzers. The
gas analyzers and Rayfield Equipment dry gas meter (for measuring
inspired gas volumes) were interfaced to the computer via an
analog-to-digital board. The computer system compiled
O2 information at 60- and 30-s
intervals for the submaximal
O2 and
O2 peak protocols,
respectively. The metabolic system analyzers were calibrated using
standardized gases of verified O2
and CO2 concentrations before each
test. Heart rate was monitored continuously during the
O2 peak test with a
Vantage heart rate monitor (Polar CIC).
Statistical analyses.
All submaximal O2 values
were converted to
O2(net)
values by subtracting subjects' sitting resting
O2 from their respective submaximal O2 values from
the four conditions. Computed
O2(net) > 0 l/min were then assumed to represent the energetic needs of the
bicycling task above those required for sitting at rest. The internal
consistency of reliability of replicate
O2(net)
measures across minutes 3-5 for
resting
O2(net)
and across minutes 4-6 for each
test grade was assessed using a two-factor repeated-measures intraclass
correlation
(Rxx) model,
as described by Baumgartner (3). Mean
O2(net)
values were determined by averaging across the last 3 min of
measurement. Measured values for treadmill speed, pedal cadence, and
mean
O2(net)
were analyzed for differences across treadmill grades using
single-factor repeated-measures ANOVA procedures. The above
significance tests were performed at the 0.05 alpha level.
Standard log-linear regression analysis techniques (19, 20) were used
to determine the dependence of
O2(net)
on MC and MB. The
log-linear model for
O2(net)
takes the following form
|
(10)
|
where log(k) is the
y-intercept,
b1 is a
dummy-coded slope term for a nominal scale variable
(G),
b2 is a slope
term for any continuous scale covariate
(C),
b3 is the slope
term for mass (M, kg), and 
is an
additive error term. Transformed out of the logarithmic scale,
Eq. 10 becomes
|
(11)
|
where
a is a constant that varies with the
value of the nominal scale variable,
aCb2
is the mass coefficient with units
l · min1 · kgb3,
is a multiplicative error term, and
b3 is the mass
exponent that describes the scaling relationship between
O2(net)
and mass [i.e.,
O2(net) Mb3]. Treadmill grade was modeled as a set of nominal scale variables (C1,
C2, and
C3 with values of
0 or 1). The repeated measurements on individual subjects were also
treated as a cluster of nominal scale variables, as outlined by Lee et
al. (17). Possible continuous scale covariates in the regression
analysis included years of endurance training experience, computed
values for µD and
MLL, and percent
body fat. If b3 = 1, then changes in
O2(net)
were directly proportional to mass. If 0 < b3 < 1, however, then the O2(net)
associated with performing a specific uphill treadmill cycling task
decreased with an increase in mass. The significance of all
coefficients and possible interactions between covariates were verified
with partial F tests (14) at the 0.15 alpha level, whereas the overall model significance was evaluated at
the 0.05 alpha level. Normality of the log-linear model residuals was
evaluated with the Shapiro-Wilk W test
for normality (24).
| |
RESULTS |
The 25 subjects (23 men and 2 women) averaged 24.7 ± 5.7 (range 19-40) yr old, 1.80 ± 0.09 (range 1.57-1.96) m
body height, 11.7 ± 4.5% (range 6-22%) body fat, 4.61 ± 0.79 (range 2.5-5.98) l/min
O2 peak, and 6.2 ± 3.4 (range 0.5-13) yr of endurance activity experience and were
riding 262 ± 126 (range 100-523) km/wk at the time of testing.
Mass measurements averaged 73.9 ± 8.8 (range 56.48-97.39) kg
for MB,
10.1 ± 0.66 (range 8.86-11.00) kg for bike mass,
1.13 ± 0.19 (range 0.80-1.48) kg for all additional mass
(helmet and cleats), and 85.0 ± 9.0 (range 66.93-108.86) kg
for MC. Measures
of treadmill speed (P = 0.95) and
pedal cadence (P = 0.88) did not
differ across the four test grades. Pedal cadence averaged 59.9 ± 1.6 rpm, while individual pedal cadences ranged from 57 to 63 rpm (this
was a result of the slightly different gear ratios available on each
subject's bicycle).
Data for three subjects on the steepest grade (7.0%) were dropped from
all analyses, because the subjects could not maintain a steady-state
O2(net).
With use of the remaining data (n = 97), all intraclass correlations for
O2(net)
during uphill bicycling were high
(Rxx = 0.96-0.99) with no significant differences between mean minute
values over the 3 min of measurement
(P > 0.255). Therefore, mean
O2(net)
values were computed over the last 3 min of measurement for use in all
ensuing analyses.
Mean
O2(net)
values for treadmill grades of 1.7% [1.10 ± 0.17 (SD)
l/min], 3.5% (1.67 ± 0.22 l/min), 5.2% (2.26 ± 0.25 l/min), and 7.0% (2.88 ± 0.32 l/min) differed significantly from
each other (P < 0.001). Slopes for
the regression of
log[O2(net)] on log(MB)
(Fig. 1) and
log(MC) (Fig.
2) did not differ significantly across the
four test grades (P > 0.344) (13).
This indicated that the
log[O2(net)]
data for all four test grades could be pooled for the final regression
analyses.
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Fig. 1.
Log-log plot of net O2 uptake
[O2(net)]
as a function of differences in body mass
(MB) and 4 treadmill grades of 1.7% ( ), 3.5% ( ), 5.2% ( ), and 7.0%
( ); n = 97.
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Fig. 2.
Log-log plot of
O2(net)
as a function of differences in combined mass
(MC) and 4 treadmill grades of 1.7, 3.5, 5.2, and 7.0%;
n = 97. See Fig. 1 legend for
explanation of symbols.
|
|
The resulting coefficients from the pooled regression of
O2(net)
on MB are
provided in Table 1. The only consistently
significant covariate across all regression analyses was
µD, an increase of which was
associated with a positive increase in
O2(net).
The results in Table 1 suggest that, after controlling for
differences in treadmill grade and
µD,
O2(net)
increased positively with an increase in
MB raised to the
0.89 power (95% confidence interval = 0.72-1.07;
R2 = 0.95, P < 0.001). The nominal scaled
subject variables were not significant and thus were dropped from the
final regression model (P > 0.08).
The same analysis was performed for the regression of
O2(net)
on MC (Table
2), which found that
O2(net)
increased in proportion to
MC raised to the
0.99 power (95% confidence interval = 0.80-1.18;
R2 = 0.95, P < 0.001). Neither the exponent for
MB (0.89) nor
that for MC
(0.99) differed statistically from 1.0. Finally, neither regression
model's residuals demonstrated a lack of normality (P > 0.20) (24).
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Table 1.
Final log-linear regression model relating
O2(net) to differences in
MB for uphill treadmill bicycling in trained cyclists
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Table 2.
Final log-linear regression model relating
O2(net) to differences in
MC for uphill treadmill bicycling in trained cyclists
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DISCUSSION |
The energetic demands of uphill bicycling have been modeled by a number
of researchers (7, 16, 21), each utilizing some form of
Eq. 1. The exact scaling relationship
between
O2(net) demand and MB or
MC for uphill
bicycling, however, has never been verified or explained
experimentally. Thus the purpose of this study was to evaluate these
issues using logarithmically based multiple regression analysis and
allometric scaling procedures as analytic tools.
It was hypothesized that, for a given grade and speed, the energetic
cost of overcoming gravitational resistance would be directly
proportional to
MC (i.e.,
O2 M1.00C). Indeed, results from
the present study indicate that
O2(net) scaled with MC
raised to the 0.99 power. Thus the results of this study support the
premise by others (7, 21) that the
O2(net) demand for overcoming gravitational resistance during uphill bicycling is directly proportional to the combined mass of the cyclist, the
bicycle, and all other equipment being transported uphill. The effects
of small changes in
MC on submaximal
energy demand during uphill cycling and the theoretical relationships
between MC and
MB on uphill
time-trial cycling performance are discussed in the
APPENDIX.
The present study also found that
O2(net)
scaled with MB to
the 0.89 power. This value is higher, although not significantly, than
the 0.79 MB
exponent reported by Swain (25) for
O2 during uphill treadmill
bicycling at a 10% grade. These differences may be the result of
different approaches to the statistical analysis. In the present study,
for example, it was necessary to use computed values of
µD as a covariate in the
analysis, whereas Swain did not report the use of any covariates for
deriving the 0.79 exponent. Values for
µD in the present study averaged
2.06E-03 ± 9.13E-04 (SD), which is much higher than 3.4E-05
reported for high-pressure sew-up racing tires on a smooth surface
(16). These high µD values are
attributed to the treadmill surface, which was specifically designed
with a high rolling friction so that in-line skating at steep grades
was possible. When the regression model in Table 1 for
O2(net)
was recomputed without µD as
a covariate, the MB exponent
decreased from 0.89 to 0.75, which is similar to Swain's reported
value of 0.79. Therefore, Swain's 0.79 MB exponent may be due, in part, to a lack of statistical control over high
µD values as a covariate.
Initially, there was some doubt concerning the physiological
significance of the 0.89 MB exponent,
since it did not actually differ statistically from 1.0. This issue was
addressed by using various energetic equations of locomotion from the
literature (1, 7, 12) to verify the experimental derivation of the 0.89 exponent. For example, an equation for the metabolic cost of walking
with various-size loads carried on the back is given by
(12)
![+ G [0.2 + 0.07 (<IT>v</IT> − 2.5]}](/content/vol85/issue4/fulltext/1376/img016.gif)
|
(12)
|
where E is the metabolic
cost (kcal/h),
MEM is the
external mass carried (kg), v is
walking speed (km/h), and G is treadmill grade (%). Values of
E were then computed for
MB between 50 and 100 kg for various combinations of speed and grade and assuming no
external load
(MEM = 0). With
use of the log-linear regression procedures described earlier, the
computed MB
exponent for log(E) vs.
log(MB) for
every combination of speed and grade was exactly 1.0 (in this instance,
MB = MC because
MEM = 0). These
results mirror the present study findings precisely for the combined
mass of the cyclists and their equipment. To simulate the energy cost of locomotion with an external load, values of
E were then recomputed for
MEM of 10 kg
(which is similar to the nearly constant 10.1 kg of cyclists'
equipment). This time the
MB exponent
decreased from 1.0 to 0.88 while the exponent for
MC (where
MC = MB + 10 kg)
remained at 1.0 for every combination of speed and grade. Again, these
results appear to simulate the experimentally derived 0.89 and 1.0 exponents for MB
and MC,
respectively, determined for uphill bicycling in the present study.
Furthermore, the simulations described above can be replicated exactly
(with and without external loads) using generalized equations
predicting the metabolic cost of level and graded walking (1), level
and graded running (1), and graded bicycling (7). Thus the scaling
relationships described by the present study findings appear to be
independent of speed and grade, the nature of the added mass (e.g.,
increased fat mass, bicycle equipment mass, backpack mass), and the
mode of locomotion (bicycling, walking, running), so long as gravity is
the primary external resistance. One should also note that the above
equations were derived on adults similar in body size (e.g., adults
were not evaluated together with children). Briefly, the consistency of
the above simulations with the present experimental findings suggests
that the MC and
MB exponents
reported in Tables 1 and 2 reflect predictable physiological
consequences to the steady-state resistance of gravity and are not
merely statistical artifacts.
Although the simulations described above support the present study
findings, the simulations appear to contradict reports in the
literature (22, 28). Rogers et al. (22), for example, determined that
an MB exponent of
0.75 was more appropriate than 1.0 for comparing the submaximal
energetic cost of treadmill running between prepubertal children,
circumpubertal children, and adults. The authors noted that the 0.75 exponent was probably a function (in part) of the children having a
greater stride frequency than the adults. Similar observations were
reported by Taylor et al. (28) for an interspecies comparison of
submaximal energetic data on 62 avian and mammalian species. Taylor et
al., however, followed up their observations with a computation of the
energy required per stride per unit mass at the relative speed where a
quadruped changes gaits from a trot to a gallop. This analysis revealed
that the quadrupeds, with a fourfold range in
MB (0.01-100 kg), consumed a nearly constant 5 J · stride1 · kg1
when compared at a physiologically similar running speed (i.e., speed
corresponding to gait transition). Thus, when compared by relative
rates of limb movement, the submaximal energetic cost of running at any
given speed was directly proportional to
MB (e.g.,
O2(net) MB, where
MB = M1.0C for animals not
transporting a load). Clearly, this conclusion is similar to those from
the present study, where the rate of limb movement (i.e., pedal
cadence) was held constant and was not allowed to vary according to
body size. The inconsistency of the findings by Rogers et al. with the
present study, as well as the conclusions by Taylor et al. and the
simulated exponents derived earlier (i.e., exponents for loaded and
unloaded steady-state walking, running, and cycling), suggest that the
comparison of adults and children during running is not an appropriate
analogy to the results of the present study.
Swain (25) suggested that the relatively lighter bicycle mass, as a
percentage of MB,
for heavier cyclists should decrease the
MB exponent below
1.0 for combined mass. To investigate this issue in the present study,
the extra mass
(MEM) of the
bicycle, cleats, and helmet worn by each cyclist was calculated as
follows: MEM = MC MB. With use of
the same statistical procedures described earlier and
MEM as the
dependent variable (no covariates),
MEM in the
present group of cyclists scaled to the 0.11 power of
MB (MEM M0.11B;
R2 = 0.22). Because MC
is composed entirely of
MB and
MEM and
O2(net) M1.0C, the derived
MC exponent
(Table 2) should be equivalent to the sum of the exponents for
MEM (0.11) and
MB (0.89). For
example, using the
MB exponent
of 0.89 for O2(net)
in Table 1, one can compute
M0.89B × M0.11B M1.00C, which is close to the
MC exponent of
0.99 for
O2(net)
(Table 2). Thus the
MB exponent was
lower than the respective
MC exponent because of the exclusion of the
MEM component of
mass as a contributor to the energy demand for the
MB regression
model. This verifies that Swain's suggestion regarding the influence
of bike mass (i.e., MEM) on
lowering the MB
exponent was indeed correct.
Interestingly, the estimated
MLL did not enter
either regression model (Tables 1 and 2) as a significant covariate.
Initially, this was unexpected, because segmental energy analyses (29) and physiological evaluations of pedaling efficiency (9, 11) have
demonstrated how influential movement of the lower limb segments during
pedaling can be on the total energy demand of a cycling task. A closer
evaluation of the
MLL data suggests
two reasons for its exclusion from the regression models. First, the
MB and MC regression
models already had 95% of the total variance explained with the
inclusion of MB,
µD, and treadmill grade as
dependent variables (Tables 1 and 2). Second, even if
MLL could have
entered the models as a significant covariate, it would not have
changed the MB or
MC mass
coefficients. By use of the same log-linear regression statistical
procedures described earlier, it can be shown that
MLL for the group
of cyclists studied scaled with
MB raised to the
1.01 power (i.e.,
MLL M1.01B; R2 = 0.80). Thus
MLL increased
proportionally with
MB and,
therefore, represented a constant fraction of
MB, which is
consistent with the literature (9). This means that
individual differences in
MLL values were
already being accounted for by the presence of
MB in the
MB and
MC terms.
In summary, the results of this study support the premise by others (7,
21) that the submaximal energetic demand of uphill bicycling increases
proportionally with
MC [i.e.,
O2(net) net M1.0C].
Furthermore, this scaling relationship will remain independent of road
speed, road grade, and the type of mass being transported (biologic
mass vs. equipment mass) so long as gravity is the dominant resistive
force and the cyclists are at a steady state. In contrast, the same
energetic demands scale with
MB less than
proportionally [i.e.,
O2(net) M0.89B], because
the extra mass associated with bicycling equipment (bicycle, cleats,
and helmet) is relatively lighter for heavier cyclists than for lighter
cyclists (i.e., MEM M0.11B). These findings could
be useful to researchers in constructing allometric models of endurance bicycling performance as a function of differences in
MB or
MC.
| |
APPENDIX |
The results of this study can be used to predict the influence of mass
on the submaximal energetics and performance of uphill time-trial
cycling.
Submaximal energetics.
From Table 2 it is given that
O2(net) MC for
a constant grade and velocity on steep uphill climbs (influence of
RR assumed constant,
RD assumed negligible). It
follows, therefore, that a decrease in
MC should cause a
proportional decrease in
O2(net) for any given grade and velocity. By use of the coefficients from Table
2 and insertion of the mean value for
µD (0.00206), a generalized description of the contribution of
MC to
O2(net)
at a 7% grade is given by
|
(A1)
|
where
0.036 is a constant {[antilog(1.514 + 0.412) + 0.002060.127] from Table
2} for 3.46 m/s and 7% grade. For example, two cyclists with
MC of 50 kg
(MB = 42 kg,
MEM = 8.0 kg) and
100 kg (MB = 91 kg, MEM = 9.0 kg)
will have
O2(net)
of 1.80 and 3.60 l/min, respectively (Eq. A1). Thus
O2(net)
for a cyclist with
MC of 100 kg will
be exactly twice that of a cyclist with
MC of 50 kg to
overcome gravity at the same steady-state speed. When scaled by
MC, these
O2(net)
values are 36.00 ml · kg1 · min1,
indicating that neither cyclist appears to have an energetic advantage.
However, 91% of the heavier cyclist's
O2(net)
goes toward moving
MB, whereas only
9% of
O2(net)
is used to move MEM uphill. In
contrast, 84% of the lighter cyclist's
O2(net) is utilized to move
MB and 16% is
used to move MEM
uphill. Thus, given a constant steep uphill speed and incline, the
lighter cyclist will expend ~7% (84% 91%) less energy
(relative to total energy) to move his own
MB but 7% (16% 9%) more energy to move his cycling equipment up steep
inclines than the heavier cyclist.
Interestingly, if
MC is decreased
by an absolute amount through a decrease in equipment mass or percent
body fat (the source of mass is not important so long as the cyclist is
in an energetic steady state), the smaller cyclist will actually gain
an advantage (Table 3). By use of
Eq. A1, the percent decrease in
O2(net) expected with absolute decreases in
MC between 0.5 and 3.0 kg are provided for
MC values between
50 and 100 kg (Table 3). For example, a 50-kg cyclist can decrease
O2(net)
by 3.0% by decreasing MC by 1.5 kg, but
a 100-kg cyclist must decrease
MC by 3.0 kg to
realize the same decrease in
O2(net).
The percentages provided in Table 3 should apply so long as the
cyclists are at the same speed and grade and at an energetic steady
state (Eq. 7) and should not be
dependent on gender.
View this table:
[in this window]
[in a new window]
|
Table 3.
Predicted percent decrease in
O2(net) to overcome
gravitational resistance when MC of cyclist, bicycle, and
cycling gear are decreased by 0.5-3.0 kg
|
|
Uphill time-trial cycling performance.
The influence of mass on uphill time-trial cycling performance can also
be evaluated theoretically by determining the mass exponent for the
ratio of metabolic power
[S(max)]
to RG. Rearranging Eq. 2 to solve for
·max and substituting
RG for
Rnet gives
|
(A2)
|
where
·max is the average
speed maintained during an uphill time-trial race. If it is assumed
that O2 peak and
other measures of aerobic power (2, 13, 25) scale with
MB to the
power [i.e.,
S(max) M0.67B] and that
RG MB (assuming
MB = MC,
Eq. 5), it follows that
Thus
·max M0.333B, which means
that ·max should tend
to decrease with an increase in
MB to the
power. For uphill cycling, however, the present study
indicates that RG M0.89B and not
M1.00B. Recalculating the
·max performance exponent with M0.89B
which
still indicates that the smaller cyclist will tend to have a
performance advantage when time-trial cycling on steep uphill courses.
The difference between the theoretical exponent and
the predicted 0.233 exponent is due to the need for cyclists of
all sizes to carry a nearly constant mass of 10 kg uphill along with
their own bodies. One might predict, therefore, that the
exponent would more closely describe uphill running
performance where the contribution of equipment mass to the total mass
being transported is minimal. Again, the scaling relationships
described above should be independent of gender.
Predicted and theoretical performance exponents for steep uphill
cycling are consistent with anecdotal observations that lighter cyclists tend to win uphill time trials and stage races that end with a
long steep climb. The 0.223 depends completely, however, on the
present experimental finding that
RG M0.89B and thus may vary
somewhat between subject samples because of the ever-changing
preferences for and availability of bicycle equipment.
| |
ACKNOWLEDGEMENTS |
The author acknowledges the assistance of Edward Debold and Bill
Stekle, as well as the enthusiastic participation of the University of
Massachusetts Cycling Team members, in the successful completion of
this study.
| |
FOOTNOTES |
Address for reprint requests: D. P. Heil, Dept. of Health and Human
Development, 103 Romney, Montana State University, Bozeman, MT
59717-3540.
Received 24 February 1997; accepted in final form 15 June 1998.
| |
REFERENCES |
1.
American College of Sports Medicine.
ACSM's Guidelines for Exercise Testing and Prescription (5th ed.). Philadelphia, PA: Williams & Wilkins, 1995, p. 275-279.
2.
Åstrand, P.-O.,
and
K. Rodahl.
Textbook of Work Physiology (3rd ed.). New York: McGraw-Hill, 1986, p. 399-400.
3.
Baumgartner, T. A.
Norm-referenced measurement: reliability.
In: Measurement Concepts in Physical Education and Exercise Science, edited by M. J. Safrit,
and T. M. Wood. Champaign, IL: Human Kinetics, 1989, p. 45-72.
4.
Brozek, J.,
F. Grande,
J. T. Anderson,
and
A. Keys.
Densitometric analysis of body composition: revision of some quantitative assumptions.
Ann. NY Acad. Sci.
101:
113-140,
1963.
5.
Craig, N. P.,
K. I. Norton,
P. C. Bourdon,
S. M. Woolford,
T. Stanef,
B. Squires,
T. S. Olds,
R. A. J. Conyers,
and
C. B. V. Walsh.
Aerobic and anaerobic indices contributing to track endurance cycling performance.
Eur. J. Appl. Physiol.
67:
150-158,
1993.
6.
Di Prampero, P. E.
The energy cost of human locomotion on land and in water.
Int. J. Sports Med.
7:
55-72,
1986[Medline].
7.
Di Prampero, P. E.,
G. Cortilli,
P. Mognoni,
and
F. Saibene.
Equation of motion of a cyclist.
J. Appl. Physiol.
47:
201-206,
1979[Abstract/Free Full Text].
8.
Fox, E. L.,
R. W. Bowers,
and
M. L. Foss.
The Physiological Basis for Exercise and Sport (5th ed.). Madison, WI: Brown & Benchmark, 1993, p. 545-547.
9.
Francescato, M. P.,
M. Girardis,
and
P. E. Di Prampero.
Oxygen cost of internal work during cycling.
Eur. J. Appl. Physiol.
72:
51-57,
1995.
10.
Freedson, P.,
S. Sady,
V. Katch,
H. Reynolds,
and
B. Campaigne.
Total body volume in females: validation of a theoretical model.
Hum. Biol.
51:
499-505,
1979[Medline].
11.
Gaesser, G. A.,
and
G. A. Brooks.
Muscular efficiency during steady-rate exercise: effects of speed and work rate.
J. Appl. Physiol.
38:
1132-1139,
1975[Abstract/Free Full Text].
12.
Givoni, B.,
and
R. F. Goldman.
Predicting metabolic energy cost.
J. Appl. Physiol.
30:
429-433,
1971[Free Full Text].
13.
Heil, D. P.
Body mass scaling of oxygen uptake and power output at peak and ventilatory threshold in competitive cyclists (Abstract).
Res. Q. Exerc. Sport
68:
A-22,
1997.
14.
Kleinbaum, D. G.,
L. L. Kupper,
and
K. E. Muller.
Applied Regression Analysis and Other Multivariable Methods (2nd ed.). Belmont, MA: Duxbury, 1988, p. 126-131, 262-266.
15.
Kyle, C. R.
Mechanics and aerodynamics of cycling.
In: Medical and Scientific Aspects of Cycling, edited by E. R. Burke,
and M. M. Newsom. Champaign, IL: Human Kinetics, 1988, p. 235-251.
16.
Kyle, C. R.
The aerodynamics of handlebars and helmets.
Cycling Sci.
1:
22-25,
1989.
17.
Lee, J.,
K. S. Chia,
and
H. P. Lee.
Regression analysis of biomedical research data based on a repeated measure or cluster sample.
Ann. Acad. Med. Singapore
25:
129-133,
1996[Medline].
18.
Lohman, T. G.,
A. F. Roche,
and
R. Martorell
(Editors).
Anthropometric Standardization Reference Manual. Champaign, IL: Human Kinetics, 1988.
19.
Nevill, A. M.,
and
R. L. Holder.
Scaling, normalizing, and per ratio standards: an allometric modeling approach.
J. Appl. Physiol.
79:
1027-1031,
1995[Abstract/Free Full Text].
20.
Nevill, A. M.,
R. Ramsbottom,
and
C. Williams.
Scaling physiological measurements for individuals of different body size.
Eur. J. Appl. Physiol.
65:
110-117,
1992.
21.
Olds, T. S.,
K. I. Norton,
E. L. A. Lowe,
S. Olive,
F. Reay,
and
S. Ly.
Modeling road-cycling performance.
J. Appl. Physiol.
78:
1596-1611,
1995[Abstract/Free Full Text].
22.
Rogers, D. M.,
B. L. Olson,
and
J. H. Wilmore.
Scaling for the O2-to-body size relationship among children and adults.
J. Appl. Physiol.
79:
958-967,
1995[Abstract/Free Full Text].
23.
Sady, S.,
P. Freedson,
V. L. Katch,
and
H. M. Reynolds.
Anthropometric model of total body volume for males of different sizes.
Hum. Biol.
50:
529-540,
1978[Medline].
24.
Shapiro, S. S.,
and
M. B. Wilk.
An analysis of variance test for normality (complete samples).
Biometrika
52:
591-611,
1965[Free Full Text].
25.
Swain, D. P.
The influence of body mass in endurance bicycling.
Med. Sci. Sports Exerc.
26:
58-63,
1994[Medline].
26.
Swain, D. P.,
and
J. P. Wilcox.
Effect of cadence on the economy of uphill cycling.
Med. Sci. Sports Exerc.
24:
1123-1127,
1992[Medline].
27.
Tanaka, H.,
D. R. Bassett,
S. K. Best,
and
K. R. Baker.
Seated versus standing cycling in competitive road cyclists: uphill climbing and maximal oxygen uptake.
Can. J. Appl. Physiol.
21:
149-154,
1996[Medline].
28.
Taylor, C. R.,
N. C. Heglund,
and
G. M. O. Maloiy.
Energetics and mechanics of terrestrial locomotion. I. Metabolic energy consumption as a function of speed and body size in birds and mammals.
J. Exp. Biol.
97:
1-21,
1982[Abstract/Free Full Text].
29.
Wells, R.,
M. Morrissey,
and
R. Hughson.
Internal work and physiological responses during concentric and eccentric cycle ergometry.
Eur. J. Appl. Physiol.
55:
295-301,
1986.
30.
Winter, D. A.
Biomechanics and Motor Control of Human Movement (2nd ed.). New York: Wiley, 1990, p. 115-116.
J APPL PHYSIOL 85(4):1376-1383
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Top
Abstract
Introduction
![&mgr;<SUB>D</SUB> = [R<SUB>net</SUB> − <IT>g</IT> × <IT>M</IT><SUB>C</SUB> × (sin &thgr;) − <IT>g</IT> × <IT>M</IT><SUB>C</SUB> × (cos &thgr;) × &mgr;<SUB>S</SUB>]](/content/vol85/issue4/fulltext/1376/img010.gif)
![log [<A><AC>V</AC><AC>˙</AC></A><SC>o</SC><SUB>2(net)</SUB>] = log (<IT>k</IT> )](/content/vol85/issue4/fulltext/1376/img012.gif)
![<IT>E</IT> = (<IT>M</IT><SUB> B</SUB> + <IT>M</IT><SUB> EM</SUB>) × {[2.3 + 0.32 (<IT>v</IT> − 2.5)<SUP>1.65</SUP>]](/content/vol85/issue4/fulltext/1376/img015.gif)
