REVIEW ARTICLE
Factors limiting maximal performance in humans
Accepted: 4 July 2003 / Published online: 9 August 2003

Springer-Verlag 2003
Abstract Theoretical best performance times (t
theor
)in
track running are calculated as follows. Maximal met-
abolic power (E
_
max
) is a known function of maximal
oxygen uptake (V
_
O
2max
), of maximal anaerobic capacity
(AnS) and of effort duration to exhaustion (t
e
): E
_
max
=f
(t
e
). Metabolic power requirement (E
_
r
) to cover the
distance (d) in the performance time t
p
is the product of
the energy cost of locomotion per unit distance (C) and
the speed: E
_
r
=C·d/t
p
. The time values for which E
_
max
(t
e
)=E
_
r
(t
p
), assumed to yield t
theor
, can be obtained for
any given subject and distance provided that V
_
O
2max
,
AnS and C are known, and compared with actual best
performances (t
act
). For 15 min‡t
e
‡100 s, the overall
ratio t
act
/t
theor
was rather close to 1.0. To estimate the
relative role of the different factors limiting V
_
O
2max
,
several resistances to O
2
transport are identified, in-
versely proportional to: alveolar ventilation (R
V
*), O
2
transport by the circulation (R
Q
), O
2
diffusion from
capillary blood to mitochondria (R
t
), mitochondrial
capacity (R
m
). Observed changes of V
_
O
2max
are
accompanied by measured changes of several resis-
tances. The ratio of each resistance to the overall resis-
tance can therefore be calculated by means of the O
2
conductance equation. In exercise with large muscle
groups (two legs), R
Q
is the major (75%) limiting factor
downstream of the lung, its role being reduced to 50%
during exercise with small muscle groups (one leg).
R
t
and R
m
account for the remaining fractions. In
normoxia R
V
* is negligible; at high altitude it increases
progressively, together with R
t
and R
m
, at the expense
of R
Q
.
Keywords Maximal anaerobic capacity Æ Maximal
metabolic power Æ Maximal performances Æ
Running Æ V
_
O
2max
limits
Introduction
The present article is devoted to a brief review of the
factors setting maximal performances in track running.
The problem will be addressed considering the energy
requirement for covering a given distance, on the one
hand, and the maximal rate of metabolic energy output
from aerobic and anaerobic sources on the other. In-
deed, the best performance time over a given distance is
equal to the minimum time allowing the subject to ob-
tain (from the energy-yielding mechanisms) the amount
of energy necessary and sufficient for covering the dis-
tance at stake. The analysis will be applied to track
running over distances (and times) such that the rate of
O
2
consumption can be maintained at its maximal level
(V
_
O
2max
) throughout the effort duration. However, the
model can be applied to any other forms of locomotion,
such as cycling or swimming, the energy cost of which is
known as a function of the speed and/or for distances
such that the rate of O
2
consumption maintained
throughout the effort is <100% V
_
O
2max
.
The first section of this article will be devoted to show
that the best performance times, for any given distance
and subject, can be predicted rather accurately, once his/
her energy cost of running, together with his/her V
_
O
2max
and maximal anaerobic capacity are known. This section
will also show that V
_
O
2max
plays a central role among
the energy-yielding mechanisms. Therefore, the second
part of the study will be devoted to an analysis of the
factors limiting V
_
O
2max
. In this section it will be shown
that the commonly held view that V
_
O
2max
is set essen-
tially by the O
2
transport system (maximal cardiac
output and O
2
carrying capacity) is fundamentally cor-
rect for exercises with large muscle groups at sea level.
However, at high altitude or for exercises with small
Eur J Appl Physiol (2003) 90: 420–429
DOI 10.1007/s00421-003-0926-z
Pietro Enrico di Prampero
P. E. di Prampero
Department of Biomedical Sciences and Technology MATI
(Microgravity Ageing Training Immobility) Centre,
University of Udine, P. le M. Kolbe 4, 33100 Udine, Italy
E-mail: pprampero@makek.dstb.uniud.it
Tel.: +39-0432-494330
Fax: +39-0432-494301

muscle groups, other factors, such as ventilation or the
mitochondrial capacity, assume a substantial role in
setting V
_
O
2max
.
In concluding this Introduction, it seems crucial to
point out that the factors considered in this study must
be viewed as the ‘‘energetic bottleneck’’ setting actual
performances. It seems a platitude to state that this
bottleneck cannot be surpassed. Whether or not it is
indeed reached by a given subject in a given instance
depends on a set of other factors that I do not dare to
discuss. They are reviewed in this same issue by Bengt
Kayser.
Of best performance times
The overall amount of energy (E
r
) required to cover the
distance d is the product of the energy cost of transport,
per unit of distance (C) and the distance itself:
E
r
¼ C
d ð1Þ
where C is the integrated average over the distance d.
For an exercise intensity greater than V
_
O
2max
and for an
exercise duration sufficient for complete exploitation of
the anaerobic energy stores (AnS), but within the range
for which V
_
O
2max
can be maintained at 100%, the
metabolic energy output (E
m
) is given by
E
m
¼ AnSþMAP t
e
ð2Þ
where MAP is the maximal aerobic metabolic power, as
obtained expressing V
_
O
2max
in the appropriate units,
and t
e
is the exhaustion time. Thus, setting Eq. 1 equal
to Eq. 2, and solving for t
e
:
t
e
¼t
p
¼ C
d AnSðÞ=MAP ð3Þ
the calculation of the best performance time, assumed to
be equal to the exhaustion time (t
p
) for any given subject
and distance may appear to be a straightforward task,
provided that C is known. It is a melancholy fact,
however, that Eq. 3 cannot be solved analytically, be-
cause of the following reasons.
1. The energy cost of transport is an increasing function
of the speed, so that C and t in Eq. 3 are not inde-
pendent. It should also be pointed out that, from this
viewpoint, track running is relatively privileged, since
C increases only slightly with the speed.
2. Since the majority of the actual competitions begin
from a stationary start, C must take into account the
energy necessary to accelerate the body in the initial
phase of the run. Thus, again, this fraction of C is
dependent on both t
e
and d.
3. In addition, the time range to which Eq. 3 can be
meaningfully applied is rather restricted (from about
50 s to about 10 min), because this equation is based
on the assumption that: (1) the anaerobic energy
sources are fully exploited and (2) V
_
O
2max
(MAP) is
maintained at 100% throughout the duration of the
run.
4. Finally, as written, Eq. 3 implies that V
_
O
2max
(MAP)
is attained at the very onset of exercise. Therefore,
once more, the actual performance time must be gi-
ven due consideration in assigning numerical values
to AnS and MAP in Eq. 3.
In spite of these drawbacks, Eq. 3 has the advantage
of making explicit the role of the energy cost (C), of the
capacity of the anaerobic stores (AnS) and of the max-
imal aerobic power (MAP) in setting maximal perfor-
mances in human locomotion.
For endurance running, under which conditions the
role of AnS is negligible and C is essentially independent
of the speed, Eq. 3 reduces to:
t
p
¼C
d= F
MAPðÞ ð4Þ
where F is the maximal fraction of V
_
O
2max
that can be
maintained throughout the run. Indeed, for marathon or
semi-marathon (21 km) t
p
, as calculated from Eq. 4, is
not significantly different from the actual running time
(di Prampero et al. 1986; Brueckner et al. 1991).
To extend the analysis to shorter times and distances,
wherein the simplification represented by Eq. 4 does not
apply, a somewhat more tortuous route will be followed.
For a given distance and subject, both the power
requirement to cover the distance at stake (E
_
r
) and the
maximal metabolic power that the subject in question is
able to sustain until exhaustion (E
_
max
) will be repre-
sented on the same time axis. The time value for which
the dependent variables of the two functions [E
_
r
=f(t);
E
_
max
=f(t)] become equal will be calculated graphically,
or by iterative procedures, and will be taken to represent
the best performance time, the additional underlying
assumption being that best performance and exhaustion
time coincide (Keller 1973). It will be shown that the so
calculated best performance times are remarkably close
to the actual best individual performances.
This approach was originally proposed by di
Prampero (1984, 1989) and further developed by several
other authors for running (Pe´ ronnet and Thibault 1989;
di Prampero et al. 1993; Alvarez-Ramirez 2002; Arsac
2002; Arsac and Locatelli 2002) and cycling (Olds et al.
1993, 1995; Capelli et al. 1998). For a comprehensive
analysis of this approach, the reader is referred to these
studies as well as to van Ingen Schenau (1991) and
Capelli (1999).
Of maximal metabolic power
When the energy requirement of the exercise is greater
than can be aerobically provided by the subject’s
V
_
O
2max
, the exercising muscles must rely on anaerobic
energy sources. These are: (1) net splitting of phospho-
creatine (PCr) with a concomitant fall of its concentra-
tion in the working muscles and (2) net production of
lactate, leading to an increase in its concentration in the
body fluids. So, since the ATP concentration in the
working muscle is essentially unchanged, the maximal
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