Sprint running: a new energetic approach
1 Section of Physiology, Department of Biomedical Sciences and MATI
(Microgravity, Ageing, Training, Immobility) Centre of Excellence, University
of Udine, Udine 33100, Italy
2 School of Sport Sciences, University of Udine, Gemona (Udine) 33013,
Italy
3 Laboratory of Physiology, Unit PPEH (Physiology and Physiopathology of
Exercise and Handicap), University of Saint-Etienne, 42005 Saint-Etienne cedex
2, France
* Author for correspondence (e-mail: pprampero{at}makek.dstb.uniud.it)
Accepted 17 May 2005
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Summary |
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Key words: sprint, running, muscle energetics, human
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Introduction |
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In contrast to constant speed running, the number of studies devoted to
sprint running is rather scant. This is not surprising, since the very object
at stake precludes reaching a steady state, thus rendering any type of
energetic analysis rather problematic. Indeed, the only published works on
this matter deal with either some mechanical aspects of sprint running
(Cavagna et al., 1971; Fenn,
1930a
,b
;
Kersting, 1998
;
Mero et al., 1992
;
Murase et al., 1976
;
Plamondon and Roy, 1984
), or
with some indirect approaches to its energetics
(Arsac, 2002
;
Arsac and Locatelli, 2002
; van
Ingen Schenau et al., 1991
,
1994
;
di Prampero et al., 1993
;
Summers, 1997
;
Ward-Smith and Radford, 2000
).
The indirect estimates of the metabolic cost of acceleration reported in the
above-mentioned papers are based on several assumptions that are not always
convincing. In the present study we therefore propose a novel approach to
estimate the energy cost of sprint running, based on the equivalence of an
accelerating frame of reference (centred on the runner) with the Earth's
gravitational field. Specifically, in the present study, sprint running on
flat terrain will be viewed as the analogue of uphill running at constant
speed, the uphill slope being dictated by the forward acceleration
(di Prampero et al., 2002
).
Thus, if the forward acceleration is measured, and since the energy cost of
uphill running is fairly well known (e.g. see
Margaria, 1938
;
Margaria et al., 1963
; Minetti
et al., 1994
,
2002
), it is a rather
straightforward matter to translate the forward acceleration of sprint running
into the corresponding up-slope, and thence into the corresponding energy
cost. Knowledge of this last and of the instantaneous forward speed will then
allow us to calculate the corresponding metabolic power, which is presumably
among the highest values attainable for any given subject.
Theory
In the initial phase of sprint running, the overall acceleration acting on
the runner's body (g') is the vectorial sum of the forward
acceleration (af) and the Earth's acceleration of gravity
(g), both assumed to be applied to the subject's centre of mass (COM;
Fig. 1A):
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![]() | (2) |
![]() | (3) |
![]() | (4) |
![]() | (5) |
![]() | (6) |
![]() | (7) |
![]() | (8) |
|
Summarising, sprint running can be considered equivalent to constant speed
running on the Earth, up an equivalent slope ES, while carrying an additional
mass
M=Mb(g'/g1), so
that the overall equivalent mass EM becomes
EM=
M+Mb.
Both ES and EM are dictated by the forward acceleration (Eq. 4, 8); therefore they can be easily calculated once af is known. The values of ES and EM so obtained can then be used to infer the corresponding energy cost of sprint running, provided that the energy cost of uphill running at constant speed per unit body mass is also known.
It should be pointed out that the above analogy is based on the following
three simplifying assumptions, which will be discussed in the appropriate
sections. (i) Fig. 1 is an
idealised scheme wherein the overall mass of the runner is assumed to be
located at the centre of mass. In addition, (ii)
Fig. 1 refers to the whole
period during which one foot is on the ground, as such it denotes the
integrated average applying to the whole step (half stride). (iii) The
calculated ES and EM values are those in excess of the values applying during
constant speed running, in which case the subject's body is not vertical, but
leans slightly forward (Margaria,
1975).
Aims
The aim of the present study was that to estimate the energy cost and
metabolic power of the first 30 m of an all-out run from a stationary start,
from the measured forward speed and acceleration.
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Methods and calculations |
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The instantaneous speed of the initial 30 m of an all-out run from regular
starting blocks was continuously determined by means of a radar Stalker ATS
SystemTM (Radar Sales, Minneapolis, MN, US) at a sampling frequency of 35
Hz. Raw speed data were filtered (by a fourth order, zero lag, Butterworth
filter) using the ATS SystemTM acquisition software. The radar device was
placed on a tripod 10 m behind the start line at a height of 1 m,
corresponding approximately to the height of the subject's center of mass. To
check the reliability of the radar device, the 12 subjects performed an entire
100 m run. The times obtained on each 10 m section
(tradar) were compared to those obtained over the same
sections by means of a photocell system (tcells). The two
sets of data were essentially identical:
![]() | (9) |
The speedtime curves were then fitted by an exponential function
(Chelly and Denis, 2001;
Henry, 1954
;
Volkov and Lapin, 1979
):
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|
|
![]() | (11) |
![]() | (12) |
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The individual values of ES (Eq. 4) and EM (Eq. 8) were also obtained for
all subjects from the forward acceleration. This allowed us to calculate the
energy cost of sprint running with the aid of the data of literature. Indeed,
as reported by Minetti et al.
(2002) for slopes from
0.45 to +0.45, the energy cost of uphill running per unit of distance
along the running path C (J kg1
m1), is described by:
![]() | (13) |
![]() | (14) |
It is also immediately apparent that, when ES=0 and EM=1,
Csr reduces to that applying at constant speed running on
flat terrain, which amounted to about 3.6 J kg1
min1 (Minetti et al.,
2002), a value close to that reported by others (e.g. see
Margaria et al., 1963
; di
Prampero et al., 1986
,
1993
).
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Results |
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The energy cost of sprint running (Csr), as obtained from Eq. 13 on the basis of the above calculated ES and EM, is reported in Fig. 6 for a typical subject. This figure shows that the instantaneous Csr attains a peak of about 50 J kg1 m1 immediately after the start; thereafter it declines progressively to attain, after about 30 m, the value for constant speed running on flat terrain (i.e. about 3.8 J kg1 m1). This figure shows also that ES is responsible for the greater increase of Csr whereas EM plays only a marginal role. Finally, Fig. 6 also shows that the average Csr over the first 30 m of sprint running in this subject is about 11.4 J kg1 m1, i.e. about three times larger than that of constant speed running on flat terrain.
|
The product of Csr and the speed yields the instantaneous metabolic power output above resting; it is reported as a function of time for the same subject in Fig. 7, which shows that the peak power output, of about 100 W kg1, is attained after about 0.5 s and that the average power over the first 4 s is on the order of 65 W kg1.
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Discussion |
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The number of subjects of this study (12) may appear small. However the coefficients of variation of peak speeds and peak accelerations for this population (0.02 and 0.095) were rather limited, and the subjects were homogeneous in terms of performance (Tables 1, 2). Finally, the present approach is directed at obtaining a general description of sprint running, rather than at providing accurate statistical descriptions of specific groups of athletes.
The main assumptions on which the calculations reported in the preceding sections were based are reported and discussed below.
Metabolic power of sprint running
The peak metabolic power values reported in
Table 3 are about four times
larger than the maximal oxygen consumption
(VO2max) of elite sprinters which can be
expected to be on the order of 25 W kg1 (70 ml O2
kg1 min1 above resting). This is
consistent with the value estimated by Arsac and Locatelli
(2002) for sprint elite
runners, which amounted to about 100 W kg1, and with
previous findings showing that, on the average, the maximal anaerobic power
developed while running at top speed up a normal flight of stairs is about
four times larger than VO2max
(Margaria et al., 1966
).
|
The same set of calculations was also performed on one athlete (C. Lewis,
winner of the 100 m gold medal in the 1988 Olympic games in Seoul with the
time of 9.92 s) from speed data reported by Brüggemann and Glad
(1990). The corresponding peak
values of ES and EM amounted to 0.80 and 1.3, whereas the peak
Csr and metabolic power attained 55 J
kg1 m1 and 145 W kg1.
The overall amount of metabolic energy spent over 100 m by C. Lewis was also
calculated by this same approach. It amounted to 650 J kg1,
very close to that estimated for world record performances by Arsac
(2002
) and Arsac and Locatelli
(2002
). However, these same
authors, on the basis of a theoretical model originally developed by van Ingen
Schenau (1991
), calculated a
peak metabolic power of 90 W kg1 for male world records, to
be compared with the 145 W kg1 estimated in this study for
C. Lewis. The model proposed by van Ingen Schenau is based on several
assumptions, among which overall running efficiency plays a major role.
Indeed, the power values obtained by Arsac and Locatelli
(2002
) were calculated on the
bases of an efficiency (
) increasing with the speed, as described by
t=0.25+0.25. vt/vmax where
t and vt are efficiency and speed at time
t, respectively, and vmax is the maximal speed.
However, Arsac and Locatelli point out that, if a constant efficiency of 0.228
is assumed, then the estimated peak metabolic power reaches 135 W
kg1, not far from that obtained above for C. Lewis. Thus, in
view of the widely different approaches, we think it is the similarity between
the two sets of estimated data that should be emphasized, rather than their
difference.
Energy balance of sprint running
It is now tempting to break down the overall energy expenditure of 650 J
kg1 needed by C. Lewis to cover 100 m in 9.92 s, into its
aerobic and anaerobic components. To this end we will assume that the maximal
O2 consumption (VO2max) of an
élite athlete of the calibre of Lewis amounts to 25 W
kg1 (71.1 ml O2 kg1
min1) above resting. We will also assume that the overall
energy expenditure (Etot) is described by:
![]() | (15) |
The last term of this equation is the O2 debt incurred up to the
time te, because VO2max is
not reached instantaneously at work onset, but with a time constant ;
therefore, the overall amount of energy that can be obtained from aerobic
energy sources is smaller than the product
VO2maxte, by the quantity
represented by the third term of the equation. In the literature, the values
assigned to
range from 10 s (Wilkie,
1980
; di Prampero et al.,
1993
) to 23 s (Cautero et al.,
2002
). So, since in case of C. Lewis, Etot=650
J kg1 and VO2max=25 W
kg1; Ans (calculated by Eq. 15) ranged from about
560 J kg1 (for
=10 s) to about 600 J
kg1 (for
=23 s). Thus, for an élite athlete to
cover 100 m at world record speed the anaerobic energy stores must provide an
amount of energy on the order of 580 J kg1. Unfortunately we
cannot partition this amount of energy into that produced from lactate
accumulation and that derived from splitting phosphocreatine (PCr). However,
we can set an upper limit to the maximal amount of energy that can be obtained
from Ans as follows. Let us assume that the maximal blood
lactate concentration in an élite athlete can attain 20 mmol
l1. Thus, since the accumulation of 1 mmol
l1 lactate in blood is energetically equivalent to the
consumption of 3 ml O2 kg1 (see
di Prampero and Ferretti,
1999
), the maximal amount of energy that can obtained from lactate
is about:
![]() | (16) |
![]() | (17) |
![]() | (18) |
Of wind and down-slopes
In the preceding paragraphs, the effects of the air resistance on the
energy cost of sprint running were neglected; they will now be briefly
discussed. The energy spent against the air resistance per unit of distance
(Caer) increases with the square of the air velocity
(v): Caer=k'v2,
where the proportionality constant (k') amounts to about 0.40 J
s2 m3 per m2 of body surface area
(Pugh, 1971; di Prampero et
al., 1986
,
1993
). This allowed us to
calculate that Caer attained about 0.86 J
kg1 m1 at the highest speeds. Thus,
whereas in the initial phase of the sprint at slow speeds and high ES,
Caer is a negligible fraction of the overall energy cost,
this is not so at high speeds with ES tending to zero. Indeed, at the highest
average forward speed (vf) attained in this study (9.46 m
s1), Caer amounted to about 20% of the
total energy cost and required about 8 additional W kg1 in
terms of metabolic power. This is substantially equal to the data estimated by
Arsac (2002
) for sea level
conditions.
Finally, the analysis presented in Fig.
1 shows that, in the deceleration phase, sprint running can be
viewed as the analogue of downhill running at constant speed. According to
Minetti et al. (2002), Eq. 13
can also be utilised to describe the energetics of downhill running. So, the
negative values of ES, obtained when af is also negative,
can be inserted into Eq. 14 to estimate the corresponding
Csr values in the deceleration phase. Quantitatively,
however, the effects of deceleration on Csr are much
smaller than those described above for the acceleration phase, because
throughout the whole range of the downhill slopes (from 0 to 0.45), the
energy cost of running changes by a factor of 2, to a minimum of 1.75 J
kg1 m1 at a slope of 0.20, rising
again for steeper slopes, to attain a value about equal to that for level
running (3.8 J kg1 m1) at a slope of
0.45. This is to be compared with an increase of about fivefold from
level running to +0.45 (see Eq. 13 and
Minetti et al., 2002
).
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Conclusions |
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![]() | (19) |
![]() | (20) |
When, as is often the case, the sprint occurs in calm air and hence v=s, these two equations can be easily solved at any point in time, provided that the time course of the ground speed is known.
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List of symbols |
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Acknowledgments |
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References |
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