Vol. 92, Issue 5, 1781-1788, May 2002
Modeling the energetics of 100-m running by using speed
curves of world champions
Laurent M.
Arsac1 and
Elio
Locatelli2
1 Faculté des Sciences du Sport, Université
Victor Ségalen Bordeaux 2, Domaine Universitaire, 33607 Pessac
cedex; and 2 International Amateur Athletic Federation, 98007 Monaco cedex, France
 |
ABSTRACT |
The present study aims to
assess energy demand and supply in 100-m sprint running. A mathematical
model was used in which supply has two components, aerobic and
anaerobic, and demand has three components, energy required to move
forward (C), energy required to overcome air resistance (Caero), and
energy required to change kinetic energy (Ckin). Supply and demand were
equated by using assumed efficiency of converting metabolic to external work. The mathematical model uses instantaneous velocities registered by the 1997 International Association of Athletics Federations world
champions at 100 m in men and women. Supply and demand components obtained in the male champion were (in J/kg) aerobic 30 (5%), anaerobic 607 (95%), C 400 (63%), Caero 83 (13%), Ckin 154 (24%). Comparatively, a model that uses the average velocity of the male and
female 100-m champions overestimates Ckin by 37 and 44%, respectively, and underestimates Caero by 14%. We argued that such a model is not
appropriate because Ckin and Caero are nonlinear functions of velocity.
Neither height nor body mass seems to have any advantage in the
energetics of sprint running.
energy cost of running; acceleration; air resistance; anaerobic
energy; body size
| |
INTRODUCTION |
IT HAS BEEN PROPOSED
that the energetics of running might be appropriately described by
using a power-balanced model based on a supply-demand approach
(11, 21, 22, 25-27). In such a model, the supply side
has two components (aerobic and anaerobic) and the demand side has
three components [energy required to move forward (C), energy required
to overcome air resistance (Caero), and energy required to change
kinetic energy (Ckin)]
|
(1)
|
where Eaer and Eana (in J/kg) represent the amount of energy
released by aerobic and anaerobic processes, respectively, over the
time period t (in s); C, Caero, and Ckin are expressed in J · kg
1 · m1, and the
running velocity is V (in m/s). Most authors (10, 11,
21, 22, 25), but not all (26, 27), include in Caero
and Ckin the concept of efficiency (
) of converting external work to
its metabolic energy equivalent. C, however, has a metabolic dimension
in the literature (3, 10, 11, 16, 21, 24) so that no
assumption should be made about .
Concerning demand, the relative contribution of each component is
very different depending on the running distance. The longer the
running distance, the lower the contribution of Ckin and Caero (11). Thus, for short-distance running, such as a 100-m
race, both Ckin and Caero make significant contributions to demand.
The most developed application of Eq. 1 concerns middle- and
long-distance running in which the average running velocity can be
approximated by d/t, where d is the
known distance covered (in meters) and t the measured
running time (in s). In the model that uses the average velocity
(d/t), Caero = k · 1 · d2 · t2,
where k is the air friction constant (in
kg1 · m1) and = 0.5 (11, 21, 22), and Ckin = 0.5 · 1 · d · t2,
where = 0.25 (11, 21, 22).
In principle, this analytical model employed for the mathematical
analysis of a wide range of running performances (21) can
be applied to investigate the results of individual athletes. This has
been done successfully by di Prampero and colleagues (10),
who demonstrated good relationships between actual and predicted
performances in 36 individuals at marathon and half-marathon distances
(42 and 21 km) by using average velocity in the model. For such
long-distance races, demand is almost entirely described by C (92%)
because Caero is low in still air, ~0.3
J · kg1 · m1 or 8% of the
total demand, and Ckin is negligible.
Such reliability of results was also obtained (11) over
shorter distances (0.8-5 km) in 16 runners of intermediate level and 27 elite athletes tested by Lacour and colleagues. The model that
uses average velocity indicates that running 0.8 km in world record
time (101.11 s) would mean that Caero = 0.63 J · kg1 · m1, or 14% of
the total demand, and Ckin = 0.16 J · kg1 · m1, or 3% of the
total demand.
Also by using the average velocity, Peronnet and Thibault
(21) obtained a power-balanced Eq. 1 for a
100-m sprint covered in 9.95 s. Aerobic and anaerobic supply [42
J/kg (6%) and 650 J/kg (94%) above resting, respectively] were
balanced with C = 386 J/kg (56%), Caero = 104 J/kg (15%),
and Ckin = 202 J/kg (29%). However, it is worth noting that, in a
100-m race, the initial acceleration phase is so important that average
velocity is not appropriate when calculating Ckin. Considering Ckin as
0.5 · 1 · V2 · d1
would be strictly correct only if the final velocity attained during
the race is equal to the average velocity. This is far from being the
case in sprinting. There is also a problem with Caero for the same
reason: Ckin and Caero are nonlinear functions of running velocity. As
pointed out by Capelli et al. (5), when analyzing the
energetics of cycling over short distances, an improved energetic model
could be achieved when instantaneous velocities, rather than average
velocity, throughout the race is considered.
An alternative mathematical procedure to that of model
d/t can be identified in the literature
(25) in which supply and demand are equated by using
instantaneous velocities Vt. When using the
model Vt, Eq. 1 becomes
|
(2)
|
where Paert and
Panat (in W/kg) represent instantaneous aerobic
and anaerobic power, respectively; Caerot (in J · kg1 · m1) is the
instantaneous Caero; and 
Ekin (in J/kg) is obtained from changes in
kinetic energy:
0.5V(t+1)2 
0.5Vt2. For solving Eq. 2, V at any instant t+1 is calculated by
numerical integration and as a function of the precedent V
at instant t (25).
The model Vt was used with assumed supply and
calculated demand so that the speed curve and running performance
were predicted (25). It was also used inversely with
measured distance-time data of the 100-m sprint and predicted kinetics
of anaerobic metabolism (27).
For the first time in Athens, on the occasion of the 1997 International
Association of Athletics Federations (IAAF) World Championships in
Track and Field, laser apparatus were used to obtain the speed curves
of world-class sprint runners (4). For example, the speed
curves of both the male 100-m world champion (MWC) and female 100-m
world champion (FWC) were registered.
The aim of the present study was to assess energy supply and demand in
100-m world champions, considering Caero and Ckin. Because Caero and
Ckin are nonlinear functions of the running velocity, our hypothesis is
that a model, which uses instantaneous velocities rather than average
velocity, can provide more valid estimated results. For a complete list
of terms and their default values, refer to Table
1.
| |
METHODS |
Van Ingen Schenau et al. (25) first proposed the
theoretical model we used.
Supply in the model.
It was assumed that the kinetics of the aerobic pathway above resting
follow the characteristics of a first order system from the initiation
of a vigorous exercise (25) according to
Paert = MAP(1 et/
1), where Paer (in W/kg) represents the
aerobic power above resting, MAP is the subject's maximal aerobic
power above resting (in W/kg), and 
1 (in s) is the time
constant for reaching MAP at the onset of supramaximal efforts. A MAP
of 18.4 W/kg was obtained by van Ingen Schenau et al. (25)
in sprinters of intermediate level who had a 1 of
26 s, which was in close agreement with Ward-Smith and colleagues
(26, 27) and Péronnet and colleagues (21, 22).
In existing models of the energetics of sprinting, the anaerobic power
under conditions of all-out exercise is represented by
Panat = Pmax · et/2, where Pmax represents
the maximal anaerobic power (in W/kg) and 2 (in s) is
the parameter governing the rate of anaerobic energy release.
Therefore, in the present analysis, supply, which includes aerobic and
anaerobic components, is represented by
|
(3)
|
where MAP = 18.4 W/kg and 1 = 26 s
have fixed numerical values on the basis of a previous work
(25), whereas Pmax and 2 are unassigned and
are determined by using speed curves measured in world champions.
Demand in the model.
Demand includes parameters with numerical values fixed on the basis of
prior knowledge: C, k, and .
C, in Eqs. 1 and 2, has been measured in a wide
range of studies under submaximal conditions by using the steady-state
rate of oxygen uptake at a given running velocity. C was found to be essentially constant at any speed between 10 and 20 km/h (e.g., Ref.
11). Van Ingen Schenau et al. (25) used a value
around 4.25 J · kg1 · m1,
but, above resting, it should be 4 J · kg1 · m1 (11,
15). It is not yet known whether C remains the same at running
velocities >20 km/h.
Caero (J · kg1 · m1) is
k · V2, and, consequently, the power
lost to air friction during sprinting is
k · V3 (in W/kg), where k is
calculated from the values of air density (
; in kg/m3),
frontal area of the runner (Af; in m2), and Cd, according
to k = 0.5 · · Ap · Cd. The is
calculated by using barometric pressure (Pb; in Torr) and air
temperature (T°, in °C), according to = 0 · Pb · 7601 · 273 · (273 + T°)1, where 0 = 1.293 kg/m is the
at 760 Torr (101.3 kPa) and 273°K.
Af was obtained by using the runner's mass (in kg) and height
(in m) according to Af = (0.2025 · height0.725 · mass0.425) · 0.266.
The value of Cd (0.9) is the same as that of van Ingen Schenau et al.
(25).
For our calculation of k, both the mass and height of the male and
female runners (75 kg and 1.75 m and 64 kg and 1.78 m, respectively) were used. Also introduced in the calculation were the Pb
(760 Torr) and T° in Athens (25°C). The very limited effect of air
humidity on was not considered.
The men's 100-m final was run with a +0.2 m/s assisting wind (w),
whereas in the women's final, w = +0.4 m/s. Therefore, the power
lost because of air friction was calculated as k · (V
w)3, and Caero was calculated as
k · (V w)2, where V w
is the runner's relative velocity to the air.
Of converting metabolic to external work.
Van Ingen Schenau et al. (25) pointed out the necessity to
consider in power-balanced models. Di Prampero and colleagues (10, 11) and Peronnet and colleagues (21, 22)
made the same choice, although Ward-Smith and colleagues did not
(26, 27). In the present model, according to others
(10, 11, 21, 22, 25), it was considered that Caero and
Ckin should include a numerical value of . Caero in demand is
Caero = 1 · k · V2
and Ckin = 1 · [0.5V(t+1)2 0.5Vt2]. In the energetics
models, which use the average velocity (11, 21, 22), it is
usually considered that, during the acceleration phase of the sprint,
the for the transformation of metabolic energy into kinetic energy
is roughly = 0.25. Indeed, no recovery of elastic energy has
been considered during this early phase in which the running velocity
is low, and consequently the overall running must approach the of muscular contraction (11). Conversely, in association
with Caero, it is usually considered that, when speed increases, can reach 0.5 partly because of the storage and recoil of elastic
energy in exercising muscles (11).
With the above considerations in mind, the iterative procedure used in
the present study offers the opportunity to include in the calculation
of Caero and Ckin a value of that increases in a linear way
depending on instantaneous running velocity. The value of might
increase from 0.25 within the first movements of "pushing power" to
0.5 at maximal running velocity (Vmax; in m/s)
because "reactive" power increases progressively. Thus at any
instant t is obtained by 0.25 + (0.25 · Vmax1) · Vt,
where Vmax was 11.8 m/s for the MWC and 10.7 m/s
for the FWC.
Models.
The detailed calculation made with the model we used, model
Vt, is
|
(4)
|
where varies over the range from 0.25 to 0.5 as a function
of Vt as indicated above. Equation 4 is a nonlinear differential equation, which was solved
numerically and by using an iterative procedure; the numerical
integration was performed in steps of 0.01 s (25).
This mathematical model was compared with the model that uses model
d/t
|
(5)
|
where, in supply, Paert = MAP(1 et/1) and
Panat = Pmax · et/2 have been
integrated with respect to time between 0 and the duration of the race
(t in s), and where, in demand, C and k are defined above,
a = 0.50, b = 0.25, d is the running distance (d = 100 m),
and V = d/t.
Measurements.
The speed-time curves of the 100-m MWC and 100-m FWC were obtained from
laser measurements (4). In brief, laser apparatus (LAVEG
Sport, Jenoptik, Jena, Germany) were placed 15 m behind the start
line at a height of ~1.7 m. The laser beams were directed to the
lower part of the runner's back in the upright position. Consequently,
measurements were not possible during the first instants of the race
when the runners were crouched in their starting blocks. Speed values
were obtained from that instant when the athlete began to raise the
trunk until he/she had crossed the finish line (Figs.
1 and
2). Any error due to the difference in height of the system in relation to the height of the lower back is
considered insignificant.
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Fig. 1.
Measured and predicted speed curves of male 100-m world
champion (MWC). Squares are 10-m-interval video measurements.
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Fig. 2.
Measured and predicted speed curves of female 100-m world
champion (FWC). Squares are 10-m-interval video measurements.
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The system operated at 50 Hz and measured the distance covered by the
runner every 0.02 s. The system was scaled by using the exact
metric distance between laser apparatus and start line (15 m) and
finish line (115 m). Video cameras operating at 50 Hz were placed
perpendicular to the running direction on the upper stands at the 30-, 50-, and 60-m line, which allowed the distance-time results at regular
10-m intervals over 100 m to be measured (Figs. 1 and 2). Laser
and video measurements were compared, and there was a 0.10 ± 0.06-m (n = 10) average difference between video and laser measurements for MWC and 0.09 ± 0.06 m
(n = 10) for FWC.
Recorded speed curves of the MWC and FWC were fitted by using the
differential Eq. 4 and the least-square method. In Eq. 4, five parameters had values fixed on the basis of prior
knowledge as detailed in sections Supply in the model and
Demand in the model; they are MAP, 1,
C, k, and . Two parameters were allowed to float free, Pmax and
2, so that the solver in Microsoft Excel could calculate
the optimal values.
| |
RESULTS |
Running performances.
The 100-m sprint finals at the Sixth IAAF World Championships in Athens
1997 were won by Maurice Greene (MWC), who recorded 9.86 s (w + 0.2) including a 0.134-s reaction time, and Marion Jones (FWC), who
recorded 10.83 s (w + 0.4) including a 0.160-s reaction time.
Speed curve modeling.
Figures 1 and 2 show the predicted and calculated speed curves obtained
by laser and video measurements of the 100-m champions. The better fit
with model Vt (Eq. 4) was obtained
with Pmax = 90.7 W/kg and 2 = 12.1 s for
MWC and Pmax = 76.2 W/kg and 2 = 13.2 s
for FWC.
Energy cost of running.
Average velocity for MWC and FWC were, respectively, 100 m · (9.86 s 0.134 s)1 = 10.28 m/s
and 100 m · (10.83 s 0.160 s) = 9.37 m/s.
By using model d/t, the energy cost due
to acceleration (Table 2) was
obtained according to Ckin = b1 · 0.5 · V2 · d1,
where b = 0.25, d = 100 m, and
V = 10.28 m/s for MWC and V = 9.37 m/s for
FWC.
Aerodynamic cost (Table 2) was obtained according to Caero = a1 · k · (V w)2, where a = 0.50 and k = 0.0036 m1 · kg1 for MWC and k = 0.0040 m1 · kg1 for FWC;
V was 10.28 and 9.37 m/s for men and women, respectively, and w = 0.2 m/s for MWC and w = 0.4 m/s for FWC. The
contributions to demand of C, Caero, and Ckin are presented in Table 2.
By using model Vt, the instantaneous changes in
both Ckin and Caero were obtained (Figs.
3 and 4).
To compare Caero and Ckin with the values obtained with model
d/t, those instantaneous values were averaged
(Table 2).
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Fig. 3.
Time course of the demand components in MWC. Total
energy cost (Ctot) = Ckin + Caero + C, where Ckin is
energy required to change kinetic energy, Caero is the energy required
to overcome air resistance, and C is the energy required to move
forward.
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Ckin is the difference between the energy required to accelerate the
body in the early phase of the race and the energy recovered during the
final deceleration phase. The former amounted to 171 J/kg in MWC and
140 J/kg in FWC, and the latter to 17J /kg in MWC and 18 J/kg in FWC.
This means that 10-12% of the energy of acceleration is recovered
before the end of the race.
Ckin was overestimated with model d/t by 37% in
MWC and by 44% in FWC (Table 2). As a consequence, model
d/t predicted 1) Pmax 20 and 14%
higher than model Vt in MWC and FWC,
respectively; 2) a higher decrease in the rate of anaerobic
energy release; and 3) an 8% higher predicted contribution
of anaerobic metabolism.
Caero was underestimated by 14% in both champions with model
d/t.
| |
DISCUSSION |
The present analysis of supply and demand during sprint running
was based on the speed-time curves of MWC and FWC 100-m world champions
recorded by laser apparatus on the occasion of the 1997 IAAF World
Championships (4). A mathematical model, which uses the
recorded instantaneous velocities, model Vt, was
employed to describe the components of supply and demand. Results were compared with another model, which uses the average velocity
(21).
Model Vt: sensitive parameters.
The model we used includes seven parameters (Eq. 4). Five of
them, MAP, 1, C, k, and , have numerical values fixed
on the basis of prior knowledge, and only two, Pmax and
2, were allowed to float free. To assess the importance
of each parameter into the model, a sensitivity analysis was
undertaken. By using supply characteristics obtained for MWC and FWC,
the effects on predicted performance of a ±10% change to the initial
value of each parameter was tested.
First, even the largest ±10% variation in MAP and 1
resulted in only minor changes in predicted performance (0.02 s in MWC and 0.03 s in FWC). This is consistent with the small contribution (5%) of aerobic metabolism to energy supply obtained, according to
other studies (21, 22, 25-27).
Figures 5 and
6 show how the final time could be
affected by the other five parameters of Eq. 4. This
analysis clearly demonstrates that Pmax has the greatest influence on
the predicted running time, followed by C, , 2, and
to a lesser extent k. As a consequence, the supply-demand approach is
really informative only if it can be ensured that Pmax, C, , and
2 are reasonably assigned or predicted.
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Fig. 5.
Effect on the predicted performance of ±10% changes in
the initial values of five parameters in the velocity-time model
(Vt; Eq. 4) on MWC. Pmax, maximal
anaerobic power; , efficiency; k, air friction constant;
2, parameter governing rate of anaerobic activity; WR,
world record.
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Fig. 6.
Effect on the predicted performance of ±10% changes in
the initial values of five parameters in model
Vt (Eq. 4) on FWC.
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Parameters with assigned values.
The assigned values for C and have been plausibly derived from
previous literature (e.g., Ref. 11). However, the
values are partly unsecured. This is probably the weakest area of such mathematical models.
First, the numerical value for C was fixed on the basis of experimental
data obtained at submaximal running speeds, although much higher speeds
are concerned in our 100-m sprint model. Second, one should consider
the great variability of C among different subjects in submaximal
speeds. For example, in a group of middle-distance runners, Lacour et
al. (16) found a range of variation of 20% according to
previous results (4, 24) over the range 3.5-4.2 J · kg1 · m1. Assuming C
amounts to 
3.92 rather than 4 J · kg1 · m1 in our model,
it would be enough for MWC to set a new world record (Figs. 5 and 6).
The reason is that C is 63-67% of demand in 100-m sprint (Table
2).
Concerning , there is no evidence in the literature that might
be around 0.25 during the most propulsive phase of acceleration. Nevertheless, a recent study (6) supported the 0.25 value, noting a lack of correlation between leg stiffness and acceleration during sprinting. The authors argued that forward power rather than
reactive power is required during the acceleration phase. Conversely,
as leg stiffness correlates to maximal running velocity, this could be
a further argument for assuming an of ~0.5 at high speeds.
An of 0.228 was used in model Vt used by van
Ingen Schenau and colleagues (25). However, we observed
that the predicted speed curves in this work were far from those that
have been obtained with laser measurement. If the speed of MWC is
considered, assuming = 0.228, the predicted Pmax will be 135 W/kg and 2 at 9.6 s.
According to Ward-Smith and colleagues (26, 27), is
not usually assigned to Caero and Ckin. They argued that the entire dissipation of thermal power is taken into account in the magnitude of
C. Unfortunately, a standard value of C, e.g., 3.96 J · kg1 · m1
(26) was used in this model so that no additional thermal
energy concerning Caero and Ckin can be taken into account. This leads to the predicted Pmax being only twofold MAP, which is not realistic in
highly trained sprinters.
To conclude, there are many assumptions in the present model,
particularly with regard to .
Predicted parameters: anaerobic metabolism.
Pmax and 2 were the two parameters allowed to float free
in our model. This means that predicted values depend on other assumed parameters in the model. Pmax was predicted at around 90 and 75 W/kg in
MWC and FWC, respectively (Table 2); at an of 0.25, Pmax = 23 and 19 W/kg, respectively. This is very similar to the results of Pmax
obtained in male sprinters by Van Ingen Schenau and colleagues
(25) using cycling experimentation. Additionally, in
sprinters of national level clocking around 10.6 s for men and
11.6 s for women, cycling Pmax measured in free-accelerated conditions amounted to 20 and 17 W/kg, respectively (1).
These results are a first argument against using model
d/t for sprint analysis because this model
predicts a much higher Pmax (Table 2).
Again, Ward-Smith et al. (26) obtained values of
Pmax that do not compare with those presently obtained
because his mathematical framework did not include . In the
present study, Pmax (75-90 W/kg) was about four to five times
higher than MAP (18 W/kg), which is realistic for highly trained sprint runners.
Although there is a consensus in the literature about using
2 for ~30 s in models (21, 22, 25, 26),
lower time constants for anaerobic energy release were presently
predicted in world champions (Table 2). First, this rapid decrease in
anaerobic energy supply is a consequence of increasing rapidly to
0.5 so that the balanced external work in demand is moderate. Assuming is correct, there are many arguments for present values of
2 around 12-13 s as realistic for elite sprint
runners. For instance, it has been observed that the higher the initial
maximal power, the higher the decline in power in the following seconds
of exercise (18). This is mostly due to the great
participation of the glycolysis in the first few seconds of maximal
exercise (2, 12) and the inhibitory effect of proton on
phosphofructokinase. As MWC and FWC both had high predicted Pmax, it is
not surprising that the anaerobic rate decreased quickly.
By using a monoexponential model to describe anaerobic, energy release
is approximate. Anaerobic energy supply relies actually on different
components (stored phosphagens, stored oxygen, and glycolysis), each
within their own, different time constants (27). The
following may be reasonable estimates of time constants for each
component: phosphagens = 9 s, stored oxygen = 3 s,
and glycolysis = 35 s (e.g., Ref. 8). When most
of the measured rates of release are for longer periods, typically
30-210 s (19, 25), the overall time constant will be
dominated by the rate of release of glycolytic energy. Over shorter
periods, the more rapid components will dominate. So, fitted over
10 s, time constants are likely to be shorter than when applied to
longer periods of exercise. Additionally, by allowing for a faster rate
of release in specifically trained athletes, and particularly a faster
rate of release of energy from stored phosphagens, an overall time
constant of 12-13 s seems very likely.
Taking into account the predicted Pmax and 2 (Table 2),
we obtained an anaerobic contribution to energy supply amounting to 607 and 557 J/kg in MWC and FWC, respectively. On the basis of the direct
metabolic approach of anaerobic ATP turnover in 6 and 10 s of
maximal exercise (2, 12), these values might be
underestimated. By making space for ATP derived from oxygen stores
(i.e., attached to hemoglobin and myoglobin and available in the
lungs), which probably amounts to 6 ml/kg (120 J/kg) (19) and has a rapid half time in use, the strictly anaerobic ATP turnover might be 490 J/kg for MWC and 440 J/kg for FWC. However, direct examination of muscle metabolites (2) provided 130 mmol
ATP turnover (±5,200 J) per kilogram active muscle mass (5,200 J/kg) in 10 s. By assuming that a quarter of the body mass is highly active during sprinting, this leads to an ATP turnover of 1,300 J/kg, a
threefold higher value than that presently predicted in world-class
100-m runners.
Others have used postcompetition blood lactate concentrations as
indicators of anaerobic energy expenditure during 400- and 800-m races
(15). We are aware of post-100-m peak blood lactate concentrations ([Lac]b) noticeably different between
Caucasian and African runners. In a group of Caucasian sprint runners
with performance times of 10.54-10.69s, [Lac]b
reached 14.6-16 mM (17), whereas in Africans with an
average time of 10.70s, [Lac]b reached only 8.5 mM
(13). On the basis of calculations made by others (15, 19), the amount of energy yielded by the glycolysis
in Africans could be ±500 J/kg. Supply, obtained as the sum of oxygen stores (120 J/kg), glycolysis in Africans (±500 J/kg), and depletion in phosphagens (
400 J/kg), is higher than the supply predicted in our
model. Nevertheless, we can conclude that our understanding of whole
body anaerobic capacity is too limited. Perhaps modeling the running
performance is the most appropriate approach to study anaerobic energy
supply in brief maximal exercises as suggested by others
(27).
Energetics of sprint running.
The energetics of sprint and middle-distance running might differ for
several reasons. First, because of the comparative high speeds
sustained in sprint running, aerodynamic resistance is a nonnegligible
component of demand. Second, and more importantly, the cost of
acceleration (Ckin) is most likely to be high in world-class sprint
runners. This is because 1) the speed increases from 0 to 9 m/s in <1.8 s in men and from 0 to 8 m/s in <1.9 s in women and
2) the acceleration phase represents ~60% of the race
(4). Accordingly, the contribution of Ckin amounted to
20-25% of the total demand in our work (Table 2, Figs. 3 and 4).
This means that the model used to estimate Ckin has to be well defined,
as a small error in Ckin can lead to quite large discrepancies in both
predicted supply and demand. This confirms that using model d/t, where Ckin is not correctly defined,
discourages the modeling of the energetics of short running distances.
There is, as yet, no reason to reject model d/t
for distances 0.8 km on the basis of Ckin being 3% of demand.
Unfortunately, it might not be possible to create a model for 200- and
400-m races. As both are not maximal exercises, modeling the anaerobics
by using a simple first-order system is obviously not correct.
Furthermore, Ckin might be incorrectly approximate with model
d/t, taking into account its relative
contribution to the energy demand. Finally, Caero could be of
importance at such high speeds, but the effect of wind could be
difficult to assess as the runner changes direction during the race.
The model Vt we used makes it possible to obtain
instantaneous changes during the race in both Ckin and Caero (Figs. 3
and 4). Interestingly, after ~6 s of running, both MWC and FWC begin
to decelerate. This means that they are paying back kinetic energy so
that part of Caero requires no more supply. Demand is almost entirely
set by C, so that, in practical terms, the runner just has to replace
his or her limbs in the correct position before contact with the ground
and bounce on the track. Consequently; it is not surprising that muscle
stiffness, evaluated by using vertical rebounds, usually correlates
with running at maximal velocity (6, 17).
The estimated Caero amounted to 80 J/kg (Table 2). This is fairly
plausible on the basis of wind tunnel or other experiments (7,
14). Any changes in body size, Cd, or would affect Caero
through changes in k, as shown by k = 0.5 · · Af · Cd (see METHODS).
We show that a ±10% change in k leads to ~0.07 s advantage in
running time (Figs. 5 and 6). Especially in world-class women, we noted
some difference in height of comparable body mass. In the recent 2001 World Championship in Edmonton, Marion Jones (FWC in the present study;
weight = 64 kg, height = 1.78 m) lost her title to
Zhanna Pintussewich (weight = 64 kg, height = 1.64 m).
On the basis of their 6% difference in Af, the present model predicts
a 0.05-s advantage to Pintussewich in still air or moderate assisting
wind. However, with a head wind of 2 m/s, this advantage reaches
0.1 s. Height in sprint runners can be an advantage with regard to
stride length, but on the basis of its role in Caero, it can be a disadvantage.
Differences in body mass affect the energetics of sprint running in a
more complex manner. The supply-demand equation is balanced in J/kg
body mass in our work. Therefore, any increase in body mass, which is
less involved in power generation, would increase demand without
changing supply. Increased upper body mass would increase both Ckin and
Caero but in different proportions. We assessed that, in MWC, an
additional 5 kg upper body mass would increase Ckin by ±5% and Caero
by 0.4%, resulting in a performance time of 10.03 s (Fig.
7), which is obviously the lower limit
for a world-class running time. Inversely, supposing that upper body muscle mass has few other advantages, a 5-kg decrease resulted in a
running time of 9.69 s (new world record) mainly due to the advantage of a 5% reduced Ckin.
More than body mass itself, the repartition of that mass seems to
affect C. Previous investigations (20, 23) demonstrate that adding external masses to limb extremities widely increases the
energy cost of moving forward. In sprinting events in which extremities
are successively accelerated and decelerated at high rates, the lighter
the extremities are, the lower C is.
To conclude the effect of body size on sprint-running performance,
height presents no advantage in terms of energetics, but rather the
runner's mass should power muscles that are as proximal as possible.
It is interesting to note that runners increase in height and mass as
their running distance increases from 60 to 400 m. It may be that
Ckin is very important over short distances, as our analysis suggests,
but as distance increases, size also confers other advantages, such as
better reuse of elastic energy (6).
In conclusion, speed curves of world champions can be successfully used
to model the energetics of sprint running. Our model provides realistic
insights on components of both demand and supply, ensuring that Pmax,
the of converting metabolic into external work, and C can be
reasonably assumed or predicted. Unfortunately, and C are
unsecured, whereas Pmax receives supporting results in the literature.
A MWC who runs 100 m in 9.86 s might yield 640 J/kg,
including 95% anaerobic energy to balance an energy demand composed of 24% Ckin and 13% Caero. The remaining cost of C in
J · kg1 · m1 was supposed
to be the same as that required in running middle or long distances. A
high initial level of power output, amounting to at least 90 W/kg in
men and 75 W/kg in women, might be a prerequisite for top-level
results. Little is known about the rate of decrease in maximal power
during the race. A time constant for anaerobic energy release,
amounting to 12-13 s, has not been confirmed. Neither height nor
body mass seems to have any advantage in the energetics of sprint running.
| |
FOOTNOTES |
Address for reprint requests and other correspondence: L. M. Arsac, Faculté des Sciences du Sport, Université Victor
Ségalen Bordeaux 2, Domaine Universitaire, 12 Ave. Camille
Jullian, 33607 Pessac cedex, France (E-mail:
laurent.arsac{at}u-bordeaux2.fr).
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.
First published November 30, 2001;10.1152/japplphysiol.00754.2001
Received 23 July 2001; accepted in final form 6 November 2001.
| |
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