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Critical Power: Implications for Determination of V˙O2max and Exercise Tolerance


Abstract and Figures

For high-intensity muscular exercise, the time-to-exhaustion (t) increases as a predictable and hyperbolic function of decreasing power (P) or velocity (V ). This relationship is highly conserved across diverse species and different modes of exercise and is well described by two parameters: the "critical power" (CP or CV), which is the asymptote for power or velocity, and the curvature constant (W') of the relationship such that t = W'/(P - CP). CP represents the highest rate of energy transduction (oxidative ATP production, V˙O2) that can be sustained without continuously drawing on the energy store W' (composed in part of anaerobic energy sources and expressed in kilojoules). The limit of tolerance (time t) occurs when W' is depleted. The CP concept constitutes a practical framework in which to explore mechanisms of fatigue and help resolve crucial questions regarding the plasticity of exercise performance and muscular systems physiology. This brief review presents the practical and theoretical foundations for the CP concept, explores rigorous alternative mathematical approaches, and highlights exciting new evidence regarding its mechanistic bases and its broad applicability to human athletic performance.
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Critical Power: Implications for Determination
of V
and Exercise Tolerance
School of Sport and Health Sciences, St. Luke’s Campus, University of Exeter, Exeter, Devon, England,
Department of Sport and Exercise Sciences, Aberystwyth University, Aberystwyth, Ceredigion,
Institute of Food Nutrition and Human Health, Massey University, Palmerston North,
Departments of Kinesiology, Anatomy and Physiology, Kansas State University, Manhattan, KS
JONES, A. M., A. VANHATALO, M. BURNLEY, R. H. MORTON, and D. C. POOLE. Critical Power: Implications for Deter-
mination of V
and Exercise Tolerance. Med. Sci. Sports Exerc., Vol. 42, No. 10, pp. 00–00, 2010. For high-intensity muscular
exercise, the time-to-exhaustion (t) increases as a predictable and hyperbolic function of decreasing power (P) or velocity (V). This
relationship is highly conserved across diverse species and different modes of exercise and is well described by two parameters: the
‘critical power’’ (CP or CV), which is the asymptote for power or velocity, and the curvature constant (W) of the relationship such that
t=W/(PjCP). CP represents the highest rate of energy transduction (oxidative ATP production, V
) that can be sustained without
continuously drawing on the energy store W(composed in part of anaerobic energy sources and expressed in kilojoules). The limit of
tolerance (time t) occurs when Wis depleted. The CP concept constitutes a practical framework in which to explore mechanisms of
fatigue and help resolve crucial questions regarding the plasticity of exercise performance and muscular systems physiology. This
brief review presents the practical and theoretical foundations for the CP concept, explores rigorous alternative mathematical approaches,
and highlights exciting new evidence regarding its mechanistic bases and its broad applicability to human athletic performance.
It is a common experience that running, cycling, or
swimming at a relatively fast yet comfortable pace can
be continued for a considerable period without undue
fatigue. However, even slightly increasing the pace sub-
stantially increases the perceived effort and dramatically
reduces the tolerable duration of exercise. It is perhaps less
well appreciated that these experiences have solid mathe-
matical and physiological bases, which are enshrined in the
critical power (CP) concept. The CP thus represents an im-
portant parameter of aerobic function (in addition to gas
exchange threshold (GET), maximal O
uptake (V
and exercise efficiency) and one that provides an invaluable
framework in which to study and understand more fully the
mechanisms of fatigue and exercise intolerance. It is only
relatively recently that some of the key features of the con-
cept have come to light, although the concept has been
studied, in one form or another, since the scientific investi-
gation of exercise began.
This review builds on the historical foundations of the
CP concept (Historical bases for the critical power concept
section) to provide essential perspectives for the reader to
appreciate the importance of contemporary discoveries and
relevance to human (and animal) muscular performance.
Two key problems that have hampered a broader imple-
mentation and interpretation of the CP concept have been
overcome in very recent investigations and are the focus
of the sections on Mechanistic bases of the critical power
concept and Application of the critical power concept to
all-out exercise. Specifically, lack of knowledge regarding
specific intramyocyte fatigue mechanisms operant during
high-intensity (severe) exercise above the CP (Mechanistic
bases of the critical power concept section) and the cum-
bersome nature of the multiple fatiguing tests thought to
be requisite for defining the power–time-to-exhaustion
(i.e., Pt) relation and extracting the parameters CP and W
(Application of the critical power concept to all-out exercise
section). The Mathematical features of the critical power
concept section places the two-parameter Ptmodel in its
mathematical perspective and addresses whether a more
complex three-parameter model is justifiable theoretically
and practically. Crucially, this section investigates optimal
race strategies from a mathematical orientation, which leads
Address for correspondence: Andrew M. Jones, Ph.D., School of Sport and
Health Sciences, University of Exeter, Heavitree Road, Exeter, EX1 2LU,
United Kingdom; E-mail:
Submitted for publication November 2009.
Accepted for publication February 2010.
Copyright Ó2010 by the American College of Sports Medicine
DOI: 10.1249/MSS.0b013e3181d9cf7f
Copyeditor: Jamaica Polintan
Copyright @ 2010 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
appropriately into the final section where practical applica-
tions of the CP concept are explored more fully (Practical
applications of the critical power concept section).
It can be no overstatement that the history of human
physical endeavor has been shaped and constrained by the
Ptrelationship (Fig.
F1 1). Across millennia, the performance
of soldiers, laborers, and elite athletes locomoting over land,
in water, and, more recently, in flight has been bounded by
the CP and Wparameters. For example, the Roman military
genius Vegetius, writing more than two millennia ago,
presents evidence that legionaries were required to march for
several hours at the military step (2.85 mph, 4.6 kmIh
carrying 43.25 lb (19.6 kg) (51,81). Whipp et al. (80,81)
have estimated that this required sustaining a metabolic rate
somewhere between 1.4 and 1.7 L of O
. As the
penalty for failure to reach this objective was death, the
military step had to be set below the CP (or CV) of most
legionaries to avoid crippling the ranks and eroding morale.
That the Roman military was arguably the finest mobile
fighting force in the world for several centuries implies that
the military step was not positioned too far below CP (CV).
In more contemporary times, the English physiologist
A. V. Hill conflated his observations in contracting isolated
frog muscles with those of exercising humans in an attempt
to understand the physiological determinants of extraordi-
nary physical performance and muscle fatigue. This led to
his construction of velocity–time curves, similar to that
schematized in Figure 1, from world records for runners,
swimmers, rowers, and cyclists (29) (see also Hill [30]). It is
pertinent that current (2009) world records also fit velocity–
time curves similar to those of Hill (29). Central to Hill
(and Otto Meyerhoff ), winning the 1922 Nobel prize was
his demonstration that both aerobic and anaerobic energy
sources were recruited to power high-intensity muscle con-
tractions (see Bassett [3] for review). It is fitting, therefore,
that our present understanding of the Ptrelationship is
founded on the compartmentalization and coordinated func-
tion of these two energy sources.
In 1965, Monod and Scherrer (54) defined the CP of a
muscle (or muscular group) as ‘‘the maximum rate (of work)
that it can keep up for a very long time without fatigue.’
They considered both dynamic work and isometric exercise
and extracted the two parameters, CP and a finite amount of
work performable above CP (‘‘energy store’’ component,
later termed W), by plotting total work done (abscissa)
against time-to-exhaustion (ordinate) for multiple fatiguing
exercise bouts. Linear regression for the points yielded an
intercept that corresponded to W, and CP was given by
the slope of the parallel line displaced downward to project
from the origin. By studying continuous and intermittent
isometric contractions and noting the improved performance
on the latter, Monod and Scherrer (54) considered CP to be
dependent, in part, on muscle blood flow and hence O
livery. Subsequent experiments (see below) have demon-
strated unequivocally that CP is determined by oxidative
function and that Wcan be manipulated independently, for
example, by altering muscle phosphocreatine (PCr) stores,
consistent with its dependence on finite anaerobic energy
sources (52,53,65,74).
Because of the functional significance of CP, its position
relative to other signatory parameters of aerobic function—
the so-called ‘‘anaerobic threshold’’ (now more appropriately
termed the GET or lactate threshold (LT) and V
of great importance. In the early 1980s, two contrasting
viewpoints held that CP was placed at apparently widely
divergent locations. Specifically, the brilliant physiologist
Douglas R. Wilkie (83), whose interests included the feasi-
bility of man-powered flight (eventually realized by Bryan
L. Allen’s epic crossing of the English Channel in the
Gossamer Albatross in 1979), formulated an equation that
situated CP at a power output somewhere above V
In marked contrast, Moritani et al. (55) placed CP at a
much lower V
not different from that at the ‘‘anaerobic
threshold’’ (considered by those authors to be synonymous
with LT or GET). Obviously, these two notions are mutu-
ally exclusive, and resolution of this crucial issue rests on
a combination of theoretical modeling and experimental
FIGURE 1—Top panel: Schematic showing the power–time (Pt) rela-
tionship for high-intensity exercise. Notice that although it has become
customary to illustrate the nonlinear model using reversed axes,
tremains the dependent variable. Bottom panel: Determination of
parameters CP and Wfrom the linear Pj1/ttransform.
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physiological approaches that characterized gas exchange
and metabolic behaviors near CP as detailed below.
Wilkie’s formulation was a valiant attempt to bring to-
gether mechanical and physiological determinants of high-
intensity exercise tolerance:
where Pis a constant-power output that designates CP, Eis
the power at V
,Ais work available from anaerobic
energy sources (notionally synonymous with W), tis
elapsed time, and Tis a V
time constant of 10 s (13,83).
Despite ostensibly providing a close fit to some data sets,
this equation errs dramatically: it places CP at a power out-
put above V
and presumes the same very rapid Tfor
all work rates and individuals. The disparity between the T
of 10 s selected by Wilkie and the 25–40 s measured in
young healthy subjects was attributed to time delays in-
curred between V
in the muscle and its (then) site of
measurement via pulmonary gas exchange (83). It is now
known that TV
approaches 10 s only in a select few
cases; certain elite athletes such as Paula Radcliffe, the
women’s marathon world record holder (44), some cyclists
(47), and horses (49). However, in most individuals, it is
far slower and, when the transit time between muscle and
mouth is accounted for (È10–20 s), Tat the mouth faith-
fully represents that at the exercising muscle, is far longer
than 10 s, and is quite variable among individuals (26,48).
Moreover, it has been well established that constant-power
outputs that engender V
are sustainable only for a
relatively short period (35,64).
At the other end of the spectrum, the conclusion of
Moritani et al. (55) that the CP is located at a V
is correlated with, and not different from, the V
at the
‘anaerobic threshold,’’ LT, or GET must be challenged on
the basis of more recent evidence. Specifically, although
CP is correlated with the LT or GET, it is clear that the CP
occurs at a substantially higher metabolic rate (and thus,
power output) at least in non–highly trained individuals
(64,65). However, it is pertinent that the metabolic rate
(i.e., V
) difference between GET/LT and CP becomes
compressed in very fit individuals (44) such that, in these
individuals, GET/LT and CP lie in closer proximity, but with
CP always at the higher V
. In summary, refinements in
data collection and modeling have demonstrated beyond
any reasonable doubt that the CP is a distinct and meaningful
parameter, not simply an alternative to maximal oxygen up-
take or the GET/LT. Its determination, however, remains a
challenge to the experimental physiologist (see Application
of the critical power concept to all-out exercise section).
In 1982, Whipp et al. (78) used a simple two-parameter
hyperbolic fit to the power–time relation:
which may be transformed into its linear formulation
P¼ðW=tÞþCP ½1:3
The power–time (Pt) curves were constructed using data
obtained from four or more independent high-intensity
constant-power exercise bouts for which the tolerable dura-
tion was 2–15 min (64). Higher-power outputs that were
predicted to induce exhaustion in G2 min were expressly
avoided because of concerns that constraints related to me-
chanical power generation might become apparent. Simi-
larly, far lower power outputs, where the subject would not
fatigue until 915–20 min and which would likely entail a
greater motivational component, were not used to determine
CP and W.
Poole et al. (64) used this hyperbolic analysis to charac-
terize empirically the physiological response to exercise
performed near CP in a cohort of healthy, physically active,
but not highly trained, young men. The CP was found to
occur at È80% V
, approximately midway between
GET and V
(Fig. F22). Accepting a margin of determi-
nation imprecision, this represented the highest power out-
put (or, more correctly, metabolic rate) (2) at which V
and blood [lactate] could be stabilized. Specifically, at
CP, the profile of V
demonstrated a pronounced slow-
component rise that was superimposed on the rapid initial
‘fundamental’’ increase (Fig. F33). However, after several
minutes or more at CP, the V
leveled off as did blood
[lactate] that increased from resting values (È1 mM) to
stabilize at 5–6 mM on average. In marked contrast, exer-
cise at a power output just 5% above CP induced a com-
pletely different metabolic response: V
rose inexorably
to V
and blood [lactate] increased systematically
until the subject was unable to continue the exercise task
(Fig. 3). F4Figure 4 demonstrates that, for just an increment-
ally small increase in power output above CP, V
increase (via the V
slow component) by a liter or more
(22,64). The CP therefore presents the upper boundary of
the heavy exercise intensity domain and the lower boundary
of the severe-intensity exercise domain in which all power
outputs lead to V
, and the tolerable duration of work
FIGURE 2—Schematic of the power–time (Pt) relationship for high-
intensity exercise illustrating the location of the LT (synonymous with
the GET) relative to CP for healthy, physically active young men.
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is highly predictable from the Ptrelationship (Figs. 1 and 2).
In deference to Wilkie, note from Figure 4 that, whereas CP
cannot be above the power output corresponding to V
when the slow-component increase in V
is allowed to run
its course and elevate V
to V
, work rates only in-
crementally above CP result in the achievement of V
To date, the essential characteristics of the Ptrelation-
ship (and its parameters CP and W) describe exercise toler-
ance for locomotory activity across many species including
salamander (20), mouse (5), and horse (50), as well as for
different muscle contraction protocols (e.g., isometric [54]
and isotonic [42]) and exercise modes (running [19,37], cy-
AQ2 [28,31,32,63–66,68,70,82], swimming [77], and rowing
[33]) in humans. Thus, as will be demonstrated more fully
below, the highly conserved hyperbolic Ptrelationship, its
mechanistic underpinnings, and tight coherence with systemic
responses (V
and blood [lactate]) and muscle metabolism
support its key role in defining muscular performance in its
broadest context.
As developed above, the Ptrelationship is defined by
two constants: the power-asymptote known as the CP and
the curvature constant W. The W(J) indicates the maxi-
mum amount of work that can be performed 9CP so that
the magnitude of this work capacity remains the same re-
gardless of the chosen work rate 9CP (Fig. 1, top panel).
The CP has been defined as the highest sustainable rate
of aerobic metabolism (31,54,55) that occurs at a similar
work rate to the so-called maximal lactate steady state (66).
According to the classic interpretation, the W(sometimes
inaccurately called the ‘‘anaerobic work capacity’’) com-
prises the energy derived through substrate-level phos-
phorylation using PCr and glycogen, with an additional
small aerobic contribution from myoglobin- and (venous)
hemoglobin-bound O
stores (15,52–55). However, the
precise physiological underpinnings of the Ptrelationship
are challenging to address experimentally and have been
the subject of some controversy.
FIGURE 3—Group mean oxygen uptake (V
)(top panel) and blood
[lactate] (bottom panel) responses (n= 8) to constant-power exercise at
CP (solid symbols) and 5% above CP (open symbols). Arrows denote
point of fatigue for CP + 5% bout; note achievement of V
. For
exercise at CP, V
and blood lactate both stabilized, and the bout was
stopped at 24 min without fatigue. SE bars were omitted for clarity. See
text for more details. Used with permission from Poole et al. (64).
FIGURE 4—Top panel: Oxygen uptake (V
)/work rate relationship
for incremental exercise (solid symbols), where work rate is increased
by 25 WImin
to fatigue and V
was achieved during constant-
power exercise (open symbols) for one healthy subject. The leftmost
open symbol is at critical power (CP), which denotes the highest power
output at which V
can be stabilized (see Fig. 3). All other five open
symbols denote that V
is achieved in response to constant-power
exercise even when the power output is far below the maximum achieved
on the incremental test (i.e., CP + 5%). Bottom panel:Schematicillus-
trating the extraordinary size of the V
slow component necessary to
achieve V
at a power output just above CP (i.e., at the lower end
of the severe-intensity exercise domain). On the basis of data from
Poole et al. (64).
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It is pertinent to note that the Ptparameters differ
from any physiological index of fitness in that they are
based on the measurement of performance as t(i.e., time-
to-exhaustion) and on the externally measured mechanical
work done (per unit time) rather than the behavior of any
single physiological variable, such as blood lactate concen-
tration or pulmonary V
. In other words, given the mul-
tifaceted nature of fatigue during high-intensity exercise
(1,18), any one solitary physiological index is unlikely to
entirely account for the Wor the CP. The complex mecha-
nistic bases of the Ptrelationship have been elucidated by
various interventions used to manipulate individually the
CP and W. Specifically, it has been established that the
CP increases after short-term continuous endurance training
(38) and after high-intensity interval training (23,65,72)
and may be reduced when exercise is performed in hyp-
oxia (55). The Wis reduced after previous high-intensity
(9CP) exercise (17,28,74) and by glycogen depletion (53)
and can be increased by short-term sprint-interval training
(39). In addition, there is some evidence that the Wmay
be enhanced by dietary creatine loading (52,69) (see also
Eckerson et al. [16] and Vanhatalo and Jones [75]) and by
previous heavy-intensity exercise (41). Walso tends to de-
crease after training interventions that increase the CP
(38,72). Interpretation of these results is challenging because
of the complex and interrelated physiological nature of CP
and W; thus, an intervention aimed specifically at manipu-
lating the CP might also affect the Wand vice versa.Con-
sidering that some of the metabolites associated with
‘anaerobic’’ energy transfer (which have been thought to be
related to the W) act as signaling mechanisms to stimulate
mitochondrial respiration (which defines the CP), it is clear
that the classic interpretation of CP and Was distinct aerobic
and anaerobic parameters, respectively, is overly simplistic.
The severe-intensity exercise domain, which defines the
applicable range of the Ptrelationship, is characterized by
two unique predictable features: at exhaustion, the V
equal V
and the amount of external work done in ex-
cess of CP will equal W(35,64,82). The characterization of
Was a fixed anaerobic energy reserve (54,55), which is
primarily determined by the available intramuscular PCr and
glycogen stores (e.g., Ferguson et al. [17] and Jones et al.
[42]), is now gradually becoming redefined. It is acknowl-
edged that the magnitude of the Wmight also be attributed
to the accumulation of fatigue-related metabolites, such as
and P
and extracellular K
(18), which occurs in concert
with the depletion of intramuscular PCr and glycogen. It
has been postulated further that the Wis intrinsically related
to the development of the V
slow component, which is
truncated ultimately at V
(10,17,41). That the intra-
muscular [PCr] follows similar kinetics to pulmonary O
during exercise (67), thereby exhibiting an intensity domain–
specific behavior (42), suggests that the Ptrelationship may
be intrinsically linked to muscle metabolic and respiratory
control processes within the severe-intensity exercise domain.
Below, we discuss two recent studies that were the first to
investigate the muscle metabolic underpinnings of the Pt
The Historical bases for the critical power concept section
described the landmark study by Poole et al. (64), which
established the CP as the demarcation between the heavy-
and severe-intensity exercise domains, with distinct pulmo-
nary gas exchange and blood acid–base profiles above and
below CP (Fig. 3). Whether a metabolic steady state is at-
tained or not has important implications for the development
of muscular fatigue and exercise intolerance. However, the
mechanistic bases of the CP boundary at the level of the
contracting muscle were only recently addressed systemati-
cally. The contention that the Ptrelation was defined by
muscle energetics seemed reasonable given that the two-
parameter CP model had originally been established for
small muscle group exercise (54). Jones et al. (42) examined
this contention using
P magnetic resonance spectroscopy
P MRS). The hypothesis that the intramuscular [PCr] and
associated phosphate-linked regulators of oxidative metab-
olism would exhibit the same intensity domain-specific be-
havior near the CP as the established systemic responses was
tested (64). During separate knee extension exercise trials
performed 10% below (20 min in duration) and 10% above
(to exhaustion) CP, the intramuscular [PCr], [P
], and pH
were monitored using
P MRS. All subjects completed
20 min of heavy exercise at 10% below CP without undue
exertion, and steady-state responses in [PCr] (È68% of
baseline), pH (È7.01), and [P
](È314% of baseline) were
attained within 1–3 min at levels, indicating only moderate
metabolic perturbation (Fig. F55). In contrast, when exercise
was performed 10% above CP, within the severe-intensity
exercise domain, the limit of tolerance was reached after
14.7 T7.1 min. The [PCr] and pH fell progressively with
time reaching È26% of resting values and È6.87, respec-
tively, at exhaustion, and the [P
] increased to È564% above
baseline (Fig. 5). These findings established the CP as a
boundary above which intramuscular [PCr], [P
], and pH
cannot be stabilized. The distinct responses recorded above
and below CP within a very narrow range of work rates
(CP T2 W) demonstrate the existence of a critical threshold
at CP for muscle metabolic control beyond (i.e., above)
which a physiological steady state is unattainable.
The study by Jones et al. (42) demonstrated that the in-
tramuscular [PCr] and pH continued to decrease until the
limit of tolerance when exercise was performed at a work
rate slightly above CP. It had been speculated that the pre-
dictable exercise tolerance above CP may reflect the rate of
decrease in some intramuscular fatigue–inducing factor or
factors toward some ‘‘low, limiting value’’ and that these
factors may include [PCr] and/or pH (64). However, Jones
et al. (42) did not resolve whether these variables would reach
the same low values at exhaustion at different work rates
within the severe-intensity exercise domain. Such behavior,
if present, would resemble the consistent attainment of pul-
monary V
at fatigue in the severe-intensity exercise
domain irrespective of the work rate (35,64). Inspiration of
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hyperoxic gas during exercise is associated with a reduced
[PCr] slow component and improved high-intensity exercise
tolerance (27). Surprisingly, only one study has addressed the
consequences of manipulating the inspired O
fraction on the
Ptrelationship: in a limited sample of two subjects, hyp-
oxia was shown to reduce the CP with no consistent effect on
the W(55). In a recent study, Vanhatalo et al. (73) therefore
tested the hypotheses that hyperoxia would increase the
‘aerobic’’ CP parameter without changing the Wand that
intramuscular [PCr] and pH would reach the same low, pos-
sibly limiting, values at exhaustion during exercise at differ-
ent work rates within the severe-intensity exercise domain.
Using exhaustive single-leg knee extension bouts at four
different exercise intensities above CP, the Ptrelation
was determined in normoxia (i.e., 0.21 O
AQ3 ) and hyperoxia
(0.70 O
, balance N
) (73). Using
P MRS, [PCr] (È5%–
10% of resting baseline) and pH (È6.65) values measured
at the limit of tolerance were not significantly different ei-
ther among the different work rates or with different in-
spired O
fractions. Rather, consistent with CP being a
parameter of oxidative function, hyperoxia increased CP
(normoxia = 16.1 T2.6, hyperoxia = 18.0 T2.3 W, PG0.05),
thereby extending the time-to-exhaustion (in trials lasting
longer than È4 min) and reducing the rate at which [PCr] and
pH decreased with time. Surprisingly, however, hyperoxia
served to reduce W(1.92 T0.70 vs 1.48 T0.31 kJ, PG0.05)
such that there was an inverse correlation between changes
in CP and W(r=j0.88)—a finding that contradicts the
classic definition of the Wparameter as a fixed anaerobic
energy reserve (73). Exercise training is also associated with
a similar mutual interdependency between CP and W(72),
which may be attributed to the relative changes induced by
a given intervention on the CP (the lower boundary of the
severe-intensity exercise domain) and the V
in a change in the range of work rates that encompass the
severe-intensity exercise domain (10). These recent findings
indicate that the Wmay not represent a fixed ‘‘anaerobic’
substrate store, per se, but rather a mechanical work capacity
that can be used while [PCr] and pH project toward a nadir
value, which occurs near V
and ultimately exhaustion
(35,64). It is important to note that the limit of tolerance in
severe exercise might occur when a particular intramuscular
environment is achieved (36), of which the [PCr] and pH
measured in this study should be regarded as only two of
many possible indicators.
Collectively, these recent MRS investigations have ex-
tended our knowledge of the mechanistic bases of the Pt
relationship. Specifically, it is now known that CP repre-
sents a critical threshold for intramuscular metabolic control,
above which exhaustive exercise results in the attainment of
consistently low end-exercise pH and [PCr] values irre-
spective of the chosen work rate within the severe-intensity
exercise domain. This Ptrelationship therefore encom-
passes a specific range of high-intensity work rates where
exercise induces a predictable and inexorable progression of
increasing intramuscular metabolic perturbation, which ul-
timately limits exercise tolerance. The Ptrelationship may
therefore be regarded as an inherent characteristic of muscle
Despite the physiological significance of the CP concept
and its broad applicability across exercise modes and species
(see Historical bases for the critical power concept section
for references), estimation of its parameters is not routine
during either physiological research or diagnostic exercise
testing. We believe that the primary reason for this is that
the cumbersome nature of the repeated fatiguing exercise
bouts required for CP and Wresolution has limited its
wider application. In contrast, the incremental exercise test
that permits extraction of several key aerobic parameters
FIGURE 5—Muscle [PCr] (A), pH (B), and [P
] (C) responses to GCP
(solid circle) and 9CP (open circle) knee extension exercise in a repre-
sentative subject. [PCr] and [P
] data are expressed as percentage
change from resting baseline. Redrawn from Jones et al. (42).
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(i.e., GET/LT, V
, efficiency) in a single procedure has
become almost ubiquitous in exercise testing facilities. To
address this problem, recent investigations have explored
the potential of using prolonged all-out exercise to deter-
mine CP and Win a single test.
All-out cycle exercise bouts of 30 s (Wingate test) and up
to 90 s (12,25) have been used to measure maximal power
output and to estimate the so-called ‘‘anaerobic capacity’
and accumulated O
deficit. During these all-out tests, power
output typically falls to less than 50% of its initial/peak
value, which is well below the power output at V
measured during fast-ramp incremental exercise protocols
(12,14). Although these tests were too short to determine
CP (7), a potential link between all-out exercise and CP
was suggested (7,14). However, these investigations begged
two crucial questions: 1) If all-out exercise continued be-
yond 90 s, would power output eventually stabilize? 2) As
the theoretical precepts of the CP concept mandate, once
Wis expended, would this stable power output be CP?
Our pilot experiments established that the stabilization of
power output required approximately 3 min of all-out cy-
cling against a fixed resistance using a Lode Excalibur Sport
ergometer (11). Crucial aspects of this test protocol include
fully familiarized with the test protocol before data collection.
2) During the test, pacing is prevented by absence of any
time-based feedback, and the subject is strongly encouraged
to maximize cadence, and therefore power output, at all
times. 3) A valid test is characterized by a V
response that
depicts no decremental trend at any point during the test and
attains 995% of ramp test–determined V
. In our ex-
perience, having carried out eight experimental studies in
two laboratories using the 3-min test, healthy untrained sub-
jects are capable of reaching V
within the first 60 s
and sustaining this for the remainder of the test.
When these conditions are met, a distinct plateau in power
output is present within 3 min. The end-test power output, as
calculated from the mean power output during the final 30 s
of the test, occurs at a power output significantly above the
GET but significantly below the power output recorded at
the end of a ramp test (i.e., at approximately one-third of
peak power; Fig.
F6 6A) (11). One remarkable feature of this
response is that V
is not only achieved extremely rap-
idly but also sustained, confirming that all-out exercise can
provide a maximal challenge to the aerobic system (24,84)
despite the relatively modest end-test power output.
Practically, these experiments demonstrated that end-
test power in the 3-min all-out test was near CP. This is in
agreement with CP theory, in that once the Whas been used,
the highest power output that can be attained is CP because
(as defined in equation 1.3) P=(W/t) + CP, and therefore,
when W= 0, this equation reduces to P=CP(11,70).
Moreover, the work performed in the 3-min test above CP
(termed ‘‘WEP’’) should equal W. This logic led us to test
the hypothesis that the CP and Wparameters could be
established using a single 3-min all-out test. To demonstrate
FIGURE 6—(A) Power profile during a 3-min all-out test in a well-
trained cyclist. Dashed lines represent the power output achieved at the
end of a 30 WImin
ramp test (upper) and the power output associated
with the GET (lower). Note the similarity of the end-test power (316 W)
with the independently determined critical power (317 W, dotted line).
(B) Correlation between the critical power and the end-test power dur-
ing the 3-min all-out test from the study of Vanhatalo et al. (70). Dashed
line, line of identity; solid line, best-fit least-squares linear regression.
(C) Knee extensor torque during 60 intermittent MVC performed in a
5-min period in a single subject (data reproduced from Burnley [9]).
Dashed line represents the independently determined critical torque.
As with the responses to cycle exercise, the ‘‘end-test torque’’ (74.3 NIm)
coincides closely with the critical torque (74.2 NIm).
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that the CP and the end-test power were synonymous, it
was necessary to measure CP independently, in the same
subjects, using established methods (i.e., five tests to fatigue
performed on separate days). When this was done, the end-
test power in the 3-min all-out test closely matched CP
(Fig. 6B) (70). Indeed, in 8 of 10 cases, the end-test power
was within 5 W of CP. Moreover, the WEP was not different
from W, although the results were considerably more vari-
able for this parameter (70).
An important feature of the CP concept is that it conflates
mechanical (i.e., power) and metabolic (V
and lactate)
response profiles according to the established behavior
characteristic of the heavy- and severe-intensity exercise
domains (Historical bases for the critical power concept and
Mechanistic bases of the critical power concept sections)
(11,64). Thus, when constant-load exercise was performed
15 W below the end-test power, 9 of 11 subjects completed
30 min of exercise and 7 did so, achieving our criteria for
the attainment of a steady state (G1 mM increase in blood
[lactate] from 10 to 30 min). In contrast, none of the subjects
completed 30 min of exercise above the end-test power,
with exhaustion occurring within 13 min, on average. Dur-
ing exercise above the end-test power, V
rose to reach
at exhaustion, and blood [lactate] continued to in-
crease. These data provide further support that the 3-min
end-test power occurs near the heavy/severe–intensity ex-
ercise domain boundary (i.e., CP) and also the maximal
steady state for V
and [lactate].
The correspondence between the parameters of the 3-min
all-out test (end-test power and WEP) and those of the Pt
relationship (CP and W) was further investigated using in-
terval training (72) and previous exercise (74). Specifically,
4 wk of high-intensity interval training increased the con-
ventionally established CP and the 3-min test end-test power
by È25 W, with no difference between CP estimates derived
from different protocols either before or after training (72).
Previous high-intensity or sprint exercise, followed by limited
or no recovery time to restore intramuscular W-associated
energy stores (19,54,58,64), has been shown to reduce the
W(17,28). Similarly, a 30-s all-out sprint performed 2 min
(but not 15 min) before a 3-min all-out test reduced WEP
but not the end-test power (74). These investigations have
demonstrated that the end-test power and WEP are sensitive
to interventions expected to influence CP and/or W.Other
interventions that have been used to manipulate the 3-min all-
out test performance include protocol manipulation (71) and
dietary supplementation (75,76). Both the end-test power and
the WEP were shown to be unaffected by short-term dietary
creatine loading (75), short-term bicarbonate ingestion (76),
and pacing during the first 30 s of the all-out test (71).
Collectively, the evidence summarized above supports
that 3-min end-test power and WEP represent faithful esti-
mates of CP and W, respectively. However, the possibility
that the agreement between parameters is coincidental rather
than mechanistic must be considered: perhaps because of the
arbitrary selection of a fixed resistance on the one hand (71)
and of the limits placed on power output consequent to the
attainment of V
on the other (11,72). In contrast, if
the power profile of all-out cycle exercise has a fundamental
physiological basis, then the performance of a completely
different exercise mode should produce similar agreement
between end-test muscle performance and the exercise mode
equivalent to CP. To test this supposition, Burnley (9) in-
vestigated the agreement between the ‘‘end-test torque’
measured during a series of intermittent isometric maximal
voluntary contractions (MVC) of the quadriceps and the
‘critical torque’’ estimated from five separate tests involving
submaximal intermittent contractions of the quadriceps con-
tinued until task failure (at È35%–60% MVC). A 5-min pe-
riod of maximal contractions (3-s contraction and 2-s rest)
was required to achieve a plateau in torque at È29% MVC,
and this plateau corresponded to the critical torque (Fig. 6C).
In other words, the results of these experiments were strictly
analogous to the cycling experiments detailed above and
supported the contention that all-out exercise results in the
eventual attainment of CP (or torque) irrespective of the mode
of exercise.
The two-parameter CP model. The CP concept de-
fines a two-component bioenergetic supply-and-demand
system, which lends itself ideally to mathematical modeling.
Both supply components are endogenous, but demand is de-
termined exogenously. As originally defined, the assumptions
1) There is an ‘‘aerobic’’ energy supply component that is
rate- but not capacity-limited. This rate limit is denoted as
the CP.
2) There is an ‘‘anaerobic’’ energy supply component that is
capacity- but not rate-limited. This capacity limit is
denoted as W.
3) Exercise can continue at any power output as long as
supply is adequate to meet demand.
Thus, we can deduce that if an individual exercises con-
tinuously at a constant power Pless than or equal to CP,
exercise duration is ‘‘infinite’’ because the entire demand
can be met aerobically, and the limit of tolerance cannot be
predicted using the power–duration relationship. On the
other hand, if P9CP, then the aerobic supply alone is in-
sufficient, and the excess power requirement above CP must
be met by using the Wcomponent. The length of time until
exhaustion, t, that this excess requirement can be sustained
can be deduced by dividing the available capacity, W,by
the rate at which it is required (PjCP), yielding:
Because this equation defines a rectangular hyperbola, asymp-
totic to the horizontal axis at t= 0 and to the vertical axis at
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P= CP, it is usually called the hyperbolic form of the CP
model. Because the total amount of work, W, accomplished
during the interval 0 to t, is given by W=Pt (Fig. 1), five
other algebraically equivalent equations can be deduced:
=tþCP ½4:1b
W¼W0þCPt ½4:1c
t¼ðWW0Þ=CP ½4:1d
Equations 4.1c and 4.1d are linear forms, the former well
known and due originally to Monod and Scherrer (54). All
the other equations are hyperbolae, although equation 4.1b
is usually linearized by substituting x=1/t. It is important
to realize that, although mathematically equivalent, these
equations are not statistically equivalent when it comes
to estimating the parameters from collected data (21,34).
Equation 4.1a with tas dependent variable and Pas inde-
pendent is the most natural to use, although equations 4.1c
and 4.1d are almost as natural, and 4.1b using x=1/tis often
used. Given the capabilities of modern computing equip-
ment, there is no reason to prefer a linear to a hyperbolic
equation. Application of the model is unlimited by exercise
modality as long as any two of the three variables t,P,orW
(or their analogs, velocity and distance, in other exercise
modalities) can be measured.
The two-parameter CP model has been adapted for ramp
exercise (56), where the ramp rate (or slope) variable, s,is
used in place of P. In this instance, assuming that P=0at
t= 0, whence W= 1/2st
, there are similarly six algebraically
equivalent equations. As sis the only logical independent
variable, the most natural and mathematically simplest equa-
tion is as follows:
could be used if work is to be measured as the dependent
variable. Early evidence (61) suggests that parameter esti-
mates obtained for the same subjects from ramp and constant-
power protocols are equivalent.
The two-parameter CP model has also been adopted for
intermittent exercise (60). In this application, nis the num-
ber of completed work and rest cycles; t
and t
are the
durations, and P
and P
are the power outputs of the
corresponding work and rest periods, respectively. nis ob-
served as exercise proceeds, but t
, and P
are set
before exercise commences. Subject to certain constraints on
feasible combinations of these last four variables, total en-
durance time is given by the following equation:
t¼nðtwþtrÞþ½W0nPwCPÞtwðCP PrÞtrg=ðPwCPÞ½4:3a
No other equivalent forms of this equation have been pub-
lished, although they could theoretically be derived. Instead
of equation 4.3a, equation 4.1c has been used (4,45) to es-
timate CP and Wby cumulating both Wand tover all the
repeated work and rest cycles, whether complete or not.
Although unpublished, this can be shown algebraically and
numerically to provide the same estimates of CP and Was
equation 4.3a, and experimental observations have con-
firmed their equivalence (8).
The three assumptions above are sufficient to derive all
the mathematical equations presented so far, but it is im-
portant to realize that, in theory, implicitly embedded in
these assumptions are several others, specifically:
4) Aerobic power is available at its limiting rate CP the
moment exercise begins, remaining so until exercise
ceases at exhaustion.
5) The power domain over which the model applies is all
6) The time domain over which the model applies is all of
7) CP and Ware constants, independent of Pand/or t.
8) The efficiency of transformation of metabolic energy to
mechanical energy is constant across the whole power
(and time) domain(s).
All of these assumptions have been questioned previ-
ously (58), and it should be noted that when prediction trials
are limited to the severe-intensity exercise domain, where
2 min GtG15 min (Historical bases for the critical power
concept section) (64), data conform well to the original two-
parameter model. The fine-tuning of the mathematical
model, as discussed below, may allow the extension of this
applicable range at the extremes of the power (and time)
continuum or improved fit when using different exercise
To deal with assumption 4), Wilkie (83) introduced a
correction factor for oxygen uptake kinetics on the basis of
a single exponential with time constant Tand without delay.
Replacing the Edesignating power at V
in Wilkie’s
original suggestion with CP (equation 1.1), equation 4.1c
now becomes:
If Tis known and times to exhaustion no less than about 3T
are used in the estimation of Wand CP, then the exponential
term may be regarded as negligible, and a revised and larger
estimate of Wcan be obtained by adding CPTto the original
Westimate. However, if Tis unknown, it may be estimable
trial data are collected. No correction factor has been pub-
lished or derived for any of the other forms of equations 4.1,
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4.2, or 4.3, although the unnecessarily complex mathematics
could be done if required.
The three-parameter CP model. The three-parameter
CP model (57) has been developed to deal with assumptions
5), 6), and 7) simultaneously, although assumptions 4) and 8)
remain in force. The key difference between the two- and
three-parameter models from a mathematical standpoint is
simply that the horizontal asymptote of the rectangular hy-
perbola (where Pis plotted as the independent and tis plot-
ted as the dependent variable) is no longer constrained to
t= 0 but rather regarded as a real third parameter that can be
estimated from the data at t=k,wherekis the temporal
asymptote. Equation 4.1a is therefore reformulated with the
third parameter as:
From a physiological standpoint, the three-parameter model
conjectures a dynamic feedback that limits maximal available
power output between a finite amount (P
cording to the existing anaerobic energy supply at any instant,
where P
can be interpreted as a maximum ‘‘instantaneous
power.’ Graphically, it is because kG0, P
is the finite
point where the hyperbola crosses the horizontal axis at t=0.
In practical terms what this means is that when a subject is
fully rested, P
could be developed as a maximal effort, but
when the anaerobic store is fully depleted, only CP could be
developed. Between these extremes, maximal power declines
proportionally. This manifests, for example, by observing
that a maximal finishing sprint at the end of, say, a 1500-m
race is not as fast it would be if the athlete was fully rested.
As previously, there are six algebraically equivalent equa-
tions. Equation 4.4a is the most natural, but:
WþCPkW0Þ24CPkW g=2CP
could both be contemplated. The temporal asymptote kG0
is unhelpful from a physiological standpoint because neg-
ative endurance times are meaningless. More relevant physi-
ologically is P
,sokcan be replaced if preferred by the
reparameterization W/(P
jCP). Equation 4.4c is an up-
ward-sloping concave curved line, starting at 0 and tending
toward the straight line (equation 4.1c) from below for large t.
Indeed, data ‘‘dropping below’’ the straight line in this way
(see Bishop et al. [6], their Fig. 2, p.127) (54) are frequently
observed phenomena when tdurations span a wider range.
Note that letting k= 0 in any of equations 4.4 reduces them
to the corresponding versions of equations 4.1. If kis repa-
rameterized, letting P
YVachieves the same result. Note
also that like the two-parameter model, the three-parameter
model is unlimited by exercise modality, as long as any two
of the three variables t,P,orW(or their analogs, velocity and
distance, in other forms of exercise) can be measured.
There are no published equations or applications, as yet,
of the three-parameter model to ramp exercise. The mathe-
matics can easily be done, yielding as the most natural
and it will be again noted that, when k= 0 (or letting
YVin the reparameterization), this equation reverts
to the two-parameter equation 4.2a. Further mathemati-
cally equivalent equations could be algebraically derived if
desired. No three-parameter equations for intermittent ex-
ercise have yet been developed, although it may be spec-
ulated that using the cumulative procedure described above
ought to work with equation 4.4c.
The feedback system of the three-parameter model per-
mits the investigation of another exercise modality, all-out
effort, not possible with the two-parameter model where Pis
unbounded. Morton (59) has shown that the time course of
power output during all-out effort declines exponentially
from P
at t= 0, asymptotically to CP as tYVaccording
to the following equation:
P¼CP þðPmax CPÞet=k½4:6b
In practice, there is usually a short-lived period of buildup
of Pobserved, due, for example, to inertial or acceleration
considerations (11,59), rather than observing a genuine P
start at t= 0 (Fig. 6A). By integrating equation 4.6b assum-
ing a zero start, work performed, W, follows an exponential
rise toward linearity with time according to the equation:
In some applications, W(or more usually, its analog distance)
may be given, and tis the dependent variable. Reversing the
variables in equation 4.6e is not possible because equation
4.6e is a transcendental equation in t, and an iterative solu-
tion to equation 4.6e is the only feasible expedient. In respect
to assumption 4), Wilkie’s correction applied to the three-
parameter model has not been published for any of the three-
parameter equations given, although again the mathematics
could be done if required.
Mathematically optimal strategies. Given the rele-
vance in today’s world of competitive sports performance,
and the reward accruing to winners, it is natural to ask
whether performance time (or the amount of work accom-
plished) can be mathematically optimized. The early work of
Keller (46) gives a hint of the complexities. Nevertheless,
Fukuba and Whipp (19) have investigated the problem for
the two-parameter CP model. They demonstrate that there
is no unique optimal strategy, in that any one of an infinite
number of strategies, involving stagewise steps of periods
of constant power, produces an identical endurance time,
provided that Pnever drops below CP. In fact, any smooth
and continuous trace of P, never dropping below CP, will
also yield exactly the same endurance time because the in-
tegral of Pabove CP equals W. That this is so is a direct
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consequence of the lack of any feedback system in the two-
parameter model.
The situation in the three-parameter model is quite dif-
ferent. It has been mathematically proven that there is a
unique optimal solution, although it may be as unacceptable
to as many sport scientists as is the above solution for
the two-parameter model, albeit for different reasons. That
unique strategy turns out to be maximal all-out effort for
the entire duration of the exercise (59), and equations
AQ5 4.6b
and 4.6e apply. As an optimal strategy, all-out effort for a
short-duration exercise is universally accepted, but for a
longer-duration exercise, it quite definitely runs counterin-
tuitively to what is generally believed and what is normally
practiced. Nevertheless, it fits well to at least 3 min of all-out
data (59), and it can quite easily be numerically demonstrated
to be optimal. Despite some empirical evidence of the supe-
riority of faster starting (e.g., Jones et al. [43]), this raises a
question mark concerning the three-parameter model.
The CP and Wparameters that can be educed from the
Ptrelationship for severe-intensity exercise domain have
a variety of applications in sport and exercise science and
medicine, although these have not been as widely appre-
ciated to date as, perhaps, they should be. These appli-
cations include the assessment of physical fitness, the
prescription of exercise training, and the prediction of per-
formance during high-intensity exercise. Although this sec-
tion will focus on competitive athletes, it should be noted
that many of these same concepts could be equally applied
to other populations including patients, physical laborers, and
those involved in recreational physical activities. However,
in athletes, an understanding of the CP concept is addition-
ally important in the design of optimal warm-up programs
and in informing pacing strategy and the tactics used during
As has been highlighted earlier in this review, there is
evidence that the CP represents the highest power output
that can be sustained without a progressive loss of homeo-
stasis as indicated by 1) a continuous decline in muscle
[PCr] and pH and in blood pH and [bicarbonate] and 2) a
continuous increase in blood [lactate], pulmonary V
, and
ventilation (42,64). These data, along with evidence that the
CP occurs at a similar exercise intensity to the so-called
‘maximal (lactate) steady state’’ (66), have led to the sug-
gestion that the CP represents the highest rate of oxidative
metabolism that can be sustained without a progressively
increasing contribution to energy turnover from substrate-
level phosphorylation (i.e., PCr hydrolysis and ‘‘anaerobic’’
glycolysis). In contrast, the Wrepresents a fixed amount of
work (kJ) that can be completed during exercise above the
CP, which is derived principally from anaerobic processes.
Although it is becoming clear that Wis a mechanical work
capacity that is related, at least in part, to the ‘‘distance’
between the CP and the V
rather than to an ‘‘anaerobic
capacity,’per se, it is notable that the CP increases because
of continuous or interval endurance training (23,38,65,72)
and that the Wincreases because of power or sprint train-
ing (39), although the effects are not mutually exclusive.
The measurement of changes in the Ptrelationship after
a training intervention is likely to be functionally more
valuable than the measurements of discrete physiological
constructs such as, for example, V
, GET/LT, or ‘‘an-
aerobic power.’’ However, the requirement for subjects to
complete a series of constant work rates to exhaustion both
before and after the training period has possibly precluded
widespread assessment of training-induced changes in the
Ptrelationship in practice. In this regard, the advent of a
single all-out test for the estimation of CP and W(Appli-
cation of the critical power concept to all-out exercise sec-
tion) (11,70), which is sensitive at least to endurance
training (72), might facilitate more routine assessment of
changes in the Ptrelationship after training.
Given that the time-to-exhaustion (t) at a specific constant
severe-intensity power output can be accurately estimated
using equation 4.1a, it is clear that knowledge of an indi-
vidual athlete’s CP and Wparameters should enable exer-
cise performance capacity (i.e., the time required to cover a
given distance) to be accurately predicted. For example, if
a distance runner wishes to complete a continuous severe-
intensity training run (often termed ‘‘tempo’’ running), then
the maximum sustainable time for a given velocity will be
given by:
Also, the shortest time that the runner could complete a
given distance (D) is given by:
t¼ðDD0Þ=CV ½5:2
If the runner’s CV is 6.0 mIs
and his/her Dis 150 m,
then the endurance time at a velocity of 6.2 mIs
would be
750 s (12.5 min), and the endurance time at a velocity of
6.1 mIs
would be 1500 s (25 min). This information could
be used by a coach to prescribe a training session that is
challenging but manageable, resulting in physiological ad-
aptation but with the avoidance of overreaching. The CP
concept can also be applied in the design of interval training
sessions (60). With the assumption that the power output
during the work interval (P
) is greater than CP (but not so
great that exhaustion occurs within the first bout of work)
and that the power output during the recovery interval (P
is less than the CP, it can be calculated that the Wduring
exercise will be consumed by a function of:
and that the Wduring recovery will be restored as a func-
tion of:
ðCP PrÞtr:½5:4
If the mean power output over the work/recovery cycle is
greater than the CP, then Wwill fall predictably at the end
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of each work interval, and the endurance time for any
combination of work interval power output, recovery inter-
val power output, work interval duration, and recovery in-
terval duration (i.e., the number of complete work intervals
and one partial work interval that can be accomplished be-
fore Wis expended) can be calculated (equation 4.3a). This
assumes that the CP and Ware essentially the same during
intermittent exercise as during continuous exercise and that
the processes that consume and restore Ware linear, as-
sumptions that are yet to be verified (60).
Knowledge of CP and Wwill also enable an athlete and
his or her coach to make informed decisions on appropri-
ate pacing and tactical strategies to maximize competitive
performance. One important consideration, which is often
overlooked, is that the time to cover a given competitive
distance depends not only on the metabolic capability of the
athlete but also on the athlete covering the minimum possi-
ble distance for the event. For example, if we consider the
5000-m track event, an athlete will only cover 5000 m if he
or she runs close to the curb for the entire distance, some-
thing that is rare in practice. If the athlete runs wide on the
bends, the actual distance covered can be significantly in-
creased. Taking an extreme example, an athlete who ran in
the second lane for the entire 5000-m event would actually
cover approximately 5100 m (equivalent to giving a more
conservative opponent a head start of 100 m).
It can be shown that an athlete’s maximal mean velocity
for a given distance (and hence, the shortest time possible
for that distance) is dictated by the crossing point of his or
her individual velocity–time curve and the distance–time
curve (Fig.
F7 7). Where the athlete covers a distance that is
greater than the theoretical race distance, the point of inter-
section will move downward and to the right, thus reducing
the maximal mean velocity and increasing the time taken to
complete the distance (Fig. 7). These considerations are not
just theoretical. Jones and Whipp (40) have reported that
the athletes who ran at the highest mean velocity in both the
800- and 5000-m events at the Olympic Games in 2000 were
not the winners of those races; rather, the winners were able
to husband their metabolic resources to better effect by run-
ning closer to the actual race distance. Thus, athletes in these
and other events and sports that are performed in the severe-
intensity exercise domain should be conscious of minimizing
the distance covered in any competition because the race
outcome is not simply a function of the energetic potential of
the athlete at the outset of the competition.
Knowledge of the ratio D/CV (or W/CP) might also
prove useful to the athlete and coach in terms of the selection
of competition tactics that play to the metabolic strengths of
the athlete and/or act to expunge the metabolic advantages
of a competitor. Fukuba and Whipp (19) have demonstrated
mathematically that for severe-intensity exercise (which
spans the 800-, 1500-, 3000-m steeplechase and 5000- and
possibly 10,000-m races in track athletics), the theoretical
best time for a given distance can never be attained if any
portion of the race distance is covered at a velocity below
CV (i.e., it is not possible to ‘‘make up for lost time’’ with a
sprint finish). Moreover, the ‘‘endurance parameter ratio’
(D/CV) dictates the flexibility of the race pace that can be
selected while still enabling an athlete to attain their best
mean velocity for the distance. Therefore, the best tactics for
an athlete with a high CV and a low Drelative to the rivals
might be to operate at the highest possible mean velocity for
the distance (as dictated by their individual velocity–time
relationship). In contrast, an athlete with the opposite meta-
bolic characteristics would do better to attempt to slow the
race pace down below their main rival’s CV for some portion
of the race and to use their superior Din a sprint finish.
It is, of course, possible that the performance impact of
the D/CV ratio is intuitively known by athletes and that this
‘subconsciously’’ dictates their pacing strategy. However,
information on the D, CV, and D/CV ratio might still prove
invaluable in precompetition comparison of the metabolic
‘strengths’’ and ‘‘weaknesses’’ of individual athletes and
the creation of tactical plans designed to optimize perfor-
mance. With regard to the latter, there is increasing evidence
that a fast start (43) or even an all-out pacing strategy (59)
might optimize performance at least during exercise at the
upper end of the extreme domain (i.e., 2–3 min in duration).
A fast-start strategy results in a faster rise of V
the maximum, thus resulting in a greater overall O
sumption during the exercise bout (10,43). Given the same
energy yield through the complete depletion of W, this
would be expected to enhance exercise tolerance or per-
formance. The completion of a ‘‘priming’’ bout of exercise
has the potential to enhance performance during subse-
quent high-intensity exercise at least in part through a sim-
ilar mechanism (10,17,41). Further research is required to
FIGURE 7—Schematic illustration of the effect of race distance on the
time to complete the race. Curves a and care the distance curves to 800
and 5000 m, respectively; curves b and dare examples of distance
curves that may pertain if the athlete did not run the shortest possible
distance (e.g., by running wide on the bends in track races). Note that
because of the shape of the individual Vtcurve, a small reduction in
average velocity results in a relatively large increase in race time as race
distance increases. See text for detailed explanation. Redrawn from
Jones and Whipp (40).
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ascertain the effects of different pacing strategies and pre-
vious exercise protocols on the CP and Wand their rela-
tionships to changes in V
The relative importance of the CV and Dto success in
different events can be illustrated about two hypothetical
elite female endurance athletes and the use of equation 5.2.
Assume that athlete A has a CV of 5.85 mIs
and a Dof
75 m, whereas athlete B has a marginally inferior CV of
5.82 mIs
but a superior Dof 95 m. In a head-to-head race
of 800 or 1500 m, it can be calculated that athlete B would
be the clear winner (by around 3 and 2 s, respectively).
However, at 3000 m, the predicted difference between the
athletes becomes negligible, and at 5000 m and beyond, it
can be calculated that athlete A would have an increasingly
significant advantage. Theoretically, this concept could be
used by handicappers in selecting the race distance at which
the metabolic capabilities of two athletes (e.g., a 1500-m
specialist and a 5000-m specialist) are precisely matched,
thus guaranteeing the closest of finishes for the benefit of
This section has provided some of the practical applica-
tions of the CP concept to human athletic endeavor. How-
ever, it is reiterated that the concept also has important
implications for understanding exercise intolerance, de-
scribing exercise performance potential, and investigating
the efficacy of potentially ergogenic interventions in dis-
eased as well as healthy populations (62) and in the elderly
as well as the young (63). Indeed, in almost all situations, it
might be considered that the CP (and W) is more relevant,
from a functional perspective, than are the more commonly
measured aerobic performance parameters of LT/GET and
. Along with others (79), we therefore urge that,
wherever possible, this is taken into account in the design
of studies that are interested in defining or enhancing ex-
ercise tolerance.
The hyperbolic two-parameter (i.e., CP, W) power–time
(Pt) relation defines exercise tolerance within the severe-
intensity exercise domain for t(time-to-exhaustion) values
between approximately 2 and 15 min. Thus, all metabolic
rates above CP (or CV, the asymptote for power or velocity)
yield an inexorable increase in both V
(to V
) and
blood [lactate], as Wis progressively depleted to fatigue.
Whereas the time-to-exhaustion can be manipulated by al-
tering work rate and/or O
supply, for example, the within-
subject fatigue process is characterized by depletion of W
and corresponding perturbations of intramuscular [PCr]
(close to 100% depletion), [P
] and [H
]. In marked contrast,
work rates at or below CP (i.e., in the heavy domain) facil-
itate achievement of an apparent steady state for V
blood [lactate] as well as for intramuscular [PCr], [P
], and
]. Knowledge of an athlete’s CP (or CV) and W(or D)
can be used to refine and monitor training protocols and to
optimize competition pacing strategies. Hopefully, the re-
cent development of a single test to define an individual’s
CP and W, combined with the development of Ptmodels
that encompass exercise durations outside the 2- to 15-min
window and intermittent exercise, will help the CP concept
fulfill its considerable potential utility in exercise science
and medicine.
This work has not been supported by any funding agency.
The results presented in this review do not constitute endorse-
ment by the American College of Sports Medicine.
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AQ4 0Please check if equation numbering is correct.
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... Endurance athletes are exposed to a fast pace, but even a slight increase in pace may lead to a reduction in the tolerable duration of exercise. This is what CP can predict [2]. From the mathematical viewpoint, CP is defined as the power-asymptote of the hyperbolic relationship between power output (PO) and time-to-exhaustion [3]. ...
... We believe that this a simple overview that could help with the selection of the tests, according to the information in Figure 3, which is a more theoretical guideline for each test. 1 Time efficiency means the time needed to complete one testing procedure (i.e., one laboratory visit or testing in the field on one occasion). If the number of testing procedures is greater than one and requires additional measurements before testing CP (e.g., preliminary test to obtain VO 2max , measuring of body weight, anthropometry diagnostic using dual-energy X-ray absorptiometry), it is marked YES, otherwise NO. 2 Professional competence implies that an educated person (e.g., sports physician or cardiologist or sports scientist or fitness specialist) is necessary to complete the test. If such a person is needed, it is marked YES, otherwise NO. 3 Technical requirements reflect any demands for additional equipment (e.g., wattmeter, bicycle ergometer, or other devices that are not commonly available). ...
Critical power represents an important parameter of aerobic function and is the highest average effort that can be sustained for a period of time without fatigue. Critical power is determined mainly in the laboratory. Many different approaches have been applied in testing methods, and it is a difficult task to determine which testing protocol it the most suitable. This review aims to evaluate all possible tests on bicycle ergometers or bicycles used to estimate critical power and to compare them. A literature search was conducted in four databases (PubMed, Scopus, SPORTDiscus, and Web of Science) published from 2012 to 2022 and followed the PRISMA guidelines to process the review. Twenty-one articles met the eligibility criteria: records with trained or experienced endurance athletes (adults > 18), bicycle ergometer, a description of the testing protocol, and comparison of the tests. We found that the most widely used tests were the 3-min all-out tests set in a linear mode and the traditional protocol time to exhaustion. Some other alternatives could have been used but were not as regular. To summarize, the testing methods offered two main approaches in the laboratory (time to exhaustion test andthe 3-min all-out test with different protocols) and approach in the field, which is not yet completely standardized.
... Therefore, fatigue resistance depends on the ability to maintain critical oxygenation (CO) over time with lower SmO 2 values [19]. OC is the ability of the muscle to maintain adequate oxygen supply to match oxygen demand as the basis for steady-state exercise theory [34,36] In our study, athletes > 65VO 2 max achieved greater desaturation levels than less highly trained athletes; this is supported by Fontana et al. [37], who found that the oxygen used after passing the RCP is lower and depends on the capacity for ATP production that comes from non-oxidative metabolic pathway. To explain the physiological mechanisms of the progressive decrease in SmO 2 and increase in VO 2 from a systemic perspective, it is the result of a linear increase in cardiac output (i.e., systemic blood flow) and a hyperbolic increase in the arterio-venous O 2 difference (that is, systemic O 2 extraction) until depletion [38]. ...
Full-text available
Purpose Near-infrared spectroscopy (NIRS) sensors measure muscle oxygen saturation (SmO2) as a performance factor in endurance athletes. The objective of this study is to delimit metabolic thresholds relative to maximal metabolic steady state (MMSS) using SmO2 in cyclists. Methods Forty-eight cyclists performed a graded incremental test (GTX) (100 W-warm-up followed by 30 W min) until exhaustion. SmO2 was measured with a portable NIRS placed on the vastus lateralis. Subjects were classified by VO2max levels with a scale from 2 to 5: L2 = 45–54.9, L3 = 55–64.9, L4 = 65–71, L5 = > 71, which represent recreationally trained, trained, well-trained, and professional, respectively. Then, metabolic thresholds were determined: Fatmax zone, functional threshold power (FTP), respiratory compensation point (RCP), and maximal aerobic power (MAP). In addition, power output%, heart rate%, VO2%, carbohydrate and fat consumption to cutoff SmO2 point relative to MMSS were obtained. Results A greater SmO2 decrease was found in cyclists with > 55 VO2max (L3, L4 and L5) vs. cyclists (L2) in the MMSS. Likewise, after passing FTP and RCP, performance is dependent on better muscle oxygen extraction. Furthermore, the MMSS was defined at 27% SmO2, where a non-steady state begins during exercise in trained cyclists. Conclusion A new indicator has been provided for trained cyclists, < 27% SmO2 as a cut-off to define the MMSS Zone. This is the intensity for which the athlete can sustain 1 h of exercise under quasi-steady state conditions without fatiguing.
Full-text available
To the Editor. As previously demonstrated by Iannetta et al. (1), a model considering intensity domains for exercise prescription and for describing physiological characteristics of individuals should be recommended. Recently, Podlogar et al. (5) suggested that the critical power (CP)/critical speed (CS), the power/speed at the boundary of the heavy and severe intensity domains, should be considered as the parameter that is capable of best predict performance across a wide range of intensities. However, CP/CS is not the only and exclusive parameter separating two intensity domains. Other parameters such as oxygen uptake kinetics, lactate and ventilatory thresholds, and maximum lactate steady-state can be used. In fact, high and very high correlations were obtained between CS and ventilatory threshold, respiratory compensation point, and maximal oxygen uptake (3). Moreover, although CP/CS concept is of interest, a significant effect of the mathematical models (3) and fitting procedures (4) used to estimate CS was observed. Therefore, coaches/researchers should i) choose a statistically appropriate fitting procedure to their specific dataset to define CS and corresponding intensity domains, and maintain it over the season (4); ii) physiologically verify the CS estimation during the season; and iii) use training prescription around CS (±10%) to take into account the confidence interval of its estimation and the day-to-day variability (3). On the other hand, using CP in running could be useful to prescribe training intensity when running speed is no longer a relevant metric to rely upon (e.g., when running on a variable terrain or in a very windy condition) (2).
Full-text available
TO THE EDITOR: Podlogar et al. (1) have nicely discussed current methods for classifying athletes in applied physiology studies attending to their training or performance level. We agree with them that relying on a single physiological marker such as maximum oxygen uptake is not without limitations and endorse the use of more performance-based indicators. However, before proposing critical power/speed (CP/ CS) as the primary indicator of an athlete's training status, the robustness of these variables and the best method for their determination remains to be confirmed. Differences in mathematical models or test durations can indeed have a remarkable impact on an individual's CP/CS (e.g., up to $1 km/ h for CS in top-level runners) (2). More research is needed to provide reference or "norma-tive" values of CP/CS allowing classification of athletes into different performance/fitness categories. An alternative, at least in cycling, might be classifying athletes attending to the highest power output that they can achieve for a given duration the so-called "mean maximum power" (MMP) (3). This approach does not require the use of mathematical calculations or additional laboratory testing and is sensitive enough to allow discerning actual performance even between the two highest category levels-Union Cycliste Internationale [UCI] ProTeam versus UCI WorldTour-in professional cyclists (4). We have recently reported normative MMP values for male (n = 144) (4) and female professional cyclists (n = 44) (5). If a similar approach was used in cyclists of a lower training/com-petition level, scientists and coaches could accurately classify participants in cycling physiology studies. DISCLOSURES No conflicts of interest, financial or otherwise, are declared by the authors. REFERENCES 1. Podlogar T, Leo P, Spragg J. Using V _ o 2max as a marker of training status in athletes-can we do better? J Appl Physiol (1985). TO THE EDITOR: We read with interest the Viewpoint by Podlogar et al. (1) proposing that critical power (CP, defined as power at the boundary of the heavy/severe-exercise intensity domains) rather than maximal oxygen uptake (V _ O 2max) should be used as the primary descriptor of participants' training status, and we offer the following comments: 1. Correct classification of athletes should be based only on performance criteria and not on any physiological factors that, either isolated or combined, can never encompass the complexity of the multiple components of endurance performance. 2. V _ O 2max remains a gold-standard criterion and there is no doubt that values above 85 mL/kg/min characterize world-class endurance athletes. However, limiting the classification of aerobic level of athletes to V _ O 2max is restrictive and the analysis of submaximal intensity factors should complement but not replace it. 3. We disagree with the statement that CP is the best (or least bad) of these submaximal factors. Important 148 8750-7587/22
TO THE EDITOR: Podlogar et al. (1) have nicely discussed cur- rent methods for classifying athletes in applied physiology studies attending to their training or performance level. We agree with them that relying on a single physiological marker such as maximum oxygen uptake is not without limi- tations and endorse the use of more performance-based indi- cators. However, before proposing critical power/speed (CP/ CS) as the primary indicator of an athlete’s training status, the robustness of these variables and the best method for their determination remains to be con!rmed. Differences in mathematical models or test durations can indeed have a re- markable impact on an individual’s CP/CS (e.g., up to $1 km/ h for CS in top-level runners) (2). More research is needed to provide reference or “norma- tive” values of CP/CS allowing classi!cation of athletes into different performance/!tness categories. An alternative, at least in cycling, might be classifying athletes attending to the highest power output that they can achieve for a given dura- tion—the so-called “mean maximum power” (MMP) (3). This approach does not require the use of mathematical calcula- tions or additional laboratory testing and is sensitive enough to allow discerning actual performance even between the two highest category levels—Union Cycliste Internationale [UCI] ProTeam versus UCI WorldTour—in professional cyclists (4). We have recently reported normative MMP values for male (n = 144) (4) and female professional cyclists (n = 44) (5). If a similar approach was used in cyclists of a lower training/com- petition level, scientists and coaches could accurately classify participants in cycling physiology studies.
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TO THE EDITOR: We appreciate the physiologically informed discussion presented in the Viewpoint by Podlogar et al. (1). However, it is well known that the determinants of endurance performance are the maximal oxygen uptake (V_ o2max), exercise economy (RE), and lactate threshold (LT) (2). The inclusion of the critical power/speed as proposed by the authors is a good alternative, although we consider that there is not enough data in the literature to compare between subjects. V_ O2max is strongly correlated with endurance performance in heterogeneous groups; however, this relationship is lower in homogeneous groups of endurance athletes. Thus, other factors such as fractional utilization of V_ O2max and exercise economy/efficiency (3) might help to explain the differences between athletes. We propose to establish a classificationaccording to the three main determinant factors mentioned above relative to the upper limit for each sport found in the literature or relative to V_ O2max/peak. For example, relative V_ O2max values 80 and 85mL·kg 1·min 1 for female and male distance runners, respectively, have been reported previously in the literature (4). Regarding the RE, the Ethiopian runner Zersenay Tadese has showed values of 150 mL O2·kg· 1·km 1 at 19 km·h 1 or the British female distance runner Paula Radcliffe has showed values of 44 mL·kg 1·min 1 at 19 km·h 1. Finally, high values of LT ( 83% of V_ O2peak) or lactate turn-point ( 92% of V_ O2peak) have been found in elite distance runners and critical speed (CS) occurring at 90% of V_ O2peak (5). Therefore, a male runner with 70 mL·kg 1·min 1 of V_ O2max, 200 mL O2·kg· 1 ·km 1 at 19 km·h–1, and lactate turn-point of 80% of V_ O2peak would represent an average 82% relative to the best distance runners.
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The prediction of running performance at different competitive distances is a challenge, since it can be influenced by several physiological, morphological and biomechanical factors. In experienced male runners heterogeneous for maximal oxygen uptake (VO2max), endurance running performance can be well predicted by several key parameters of aerobic fitness such as VO2max and its respective velocity (vVO2max), running economy, blood lactate response to exercise, oxygen uptake kinetics and critical velocity. However, for a homogeneous group of well-trained endurance runners, the relationship between aerobic fitness parameters and endurance running performance seems to be influenced by the duration of the race (i.e., middle vs. long). Although middle-distance and ultramarathon runners present high aerobic fitness levels, there is no accumulating evidence showing that the aerobic key parameters influence both 800-m and ultramarathon performance in homogeneous group of well-trained runners. The vVO2max seems to be the best predictor of performance for 1500 m. For 3000 m, both vVO2max and blood lactate response to exercise are the main predictors of performance. Finally, for long distance events (5000 m, 10,000 m, marathon and ultramarathon), blood lactate response seems to be main predictor of performance. The different limiting/determinants factors and/or training-induced changes in aerobic parameters can help to explain this time- or distance-dependent pattern.
p>More and more data have been generated in city planning in the past few years. Clear visualizations of these data are helpful to support information comprehension and retention for urban practitioners and policy-makers. Much research has been carried out on modeling and integrating data, and different tools have been developed for their visualization. However, such tools are generally application dependant and cannot be easily tailored to other problems. This work introduces GENOR, a generic platform for indicator assessment in city planning. It consists of a client-server application able to store and process any indicator and provide 2D and 3D map-based views for visualization. A game engine (Unity<sup>1</sup>) was used to create the client application, and the server consists of a REST API and a Database Management System (DBMS). Two cases studies were conducted to show the use of the platform: walkability and bus service availability assessment, both in the city of Ålesund, Norway. Obtained results demonstrate that the platform is flexible as it can be tailored to different applications seamlessly.</p
p>Urban planning is a complex task often involving many stakeholders of varying levels of knowledge and expertise over periods stretching years. Many urban planning tools currently exist, especially for mobility planning. However, the use of such tools often relies on ad-hoc modelling of “expensive“domain experts, which hampers to incorporate new knowledge and insights into the planning process over time. Another issue refers to the lack of interactivity, i.e., stakeholders can not easily change configurations of simulations and visualize the impact of those changes. This paper presents and discusses the benefits of using a graphical digital twin to overcome such shortcomings. We demonstrate how a digital-twin-based approach improves the current planning practices from two perspectives. The first refers to automating the configuration and data integration in models, making the tool flexible and scalable to large-scale planning involving multiple cities on a national level and supporting automatic updates of employed models when input data is updated. The second refers to supporting interaction with the model through a user interface that allows stakeholders to perform actions, leading to insightful what-if scenarios and therefore better-informed decisions. We demonstrate the effectiveness of using graphical digital twins in a compelling real usage case study concerning urban mobility planning in Ålesund, Norway. Finally, this paper also outlines recommendations and further research opportunities in the area.</p
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The relationship between exhaustion time (tlim) and distance Dlim for running exercises at constant velocity until exhaustion can be described by a linear relationship (Dlim = a + b tlim) whose slope corresponds to a critical velocity. Seven runners participated to the study which compared the critical velocity of continuous versus intermittent running exercises. The critical velocity for continuous running (Vcritc) was calculated from the results (tlimc and Dlimc) of running exercises performed at 95 and 105 % of the final velocity of the Montreal Track Test (vMTT). The intermittent running consisted of repetitions of running exercises performed at 95 and 105 % vMTT during a time equal to half the value of the corresponding tlimc, The subjects recovered during a time equal to running time while jogging at a slow pace. The critical velocity for intermittent running (Vcriti) was calculated from the cumulated running distance (Dlimi) and cumulated running time (tlimi) corresponding to 95 and 105 % vMTT. Vcriti was equal to Vcritc (4.56 0.444 m.s–1 vs 4.60 0.416 m.s–1). Nevertheless, in some subjects, the repetition numbers were very different for the intermittent running exercises at 95 and 105 % vMTT. This paradoxical result could be explained by the fact that the value of Vcrit should be theoretically little sensitive to a large error in the value of tlim corresponding to a velocity slightly higher than critical velocity, for intermittent exercises as well as continuous exercises.
The basis of the critical power concept is that there is a hyperbolic relationship between power output and the time that the power output can be sustained. The relationship can be described based on the results of a series of 3 to 7 or more timed all-out predicting trials. Theoretically, the power asymptote of the relationship, CP (critical power), can be sustained without fatigue; in fact, exhaustion occurs after about 30 to 60 minutes of exercise at CP. Nevertheless, CP is related to the fatigue threshold, the ventilatory and lactate thresholds, and maximum oxygen uptake (V̇O2max), and it provides a measure of aerobic fitness. The second parameter of the relationship, AWC (anaerobic work capacity), is related to work performed in a 30-second Wingate test, work in intermittent high-intensity exercise, and oxygen deficit, and it provides a measure of anaerobic capacity. The accuracy of the parameter estimates may be enhanced by careful selection of the power outputs for the predicting trials and by performing a greater number of trials. These parameters provide fitness measures which are mode-specific, combine energy production and mechanical efficiency in 1 variable, and do not require the use of expensive equipment or invasive procedures. However, the attractiveness of the critical power concept diminishes if too many predicting trials are required for generation of parameter estimates with a reasonable degree of accuracy.
We tested the hypotheses that creatine loading would result in no alteration in critical power (CP) or the total work done > CP (W� ) as estimated from a novel 3-minute all-out cycling protocol. Seven habitually active male subjects completed 3-minute all-out tests against fixed resistance on an electrically-braked cycle ergometer after a 5-day dietary supplementation with 20 g·d−1 of a glucose placebo (PL) and the same dose of creatine monohydrate (CR). The CP was estimated from the mean power output over the final 30 seconds of the test and the Wwas estimated as the power-time integral above the end-test power output. Creatine supplemen- tation resulted in a significant increase in body mass (from 80.4 ± 9.2 kg to 81.5 ± 9.5 kg; p < 0.05), whereas the body mass was not different after placebo supplementation (80.3 ± 9.3 kg; p > 0.05). There were no dif- ferences in the power outputs measured during the 3-minute all-out tests following PL and CR supplementa- tion (CP—PL: 252 ± 30 W vs. CR: 255 ± 28 W, p > 0.05; W� —PL: 19.4 ± 3.5 kJ vs. CR: 19.2 ± 3.4 kJ, p > 0.05; total work done—PL: 64.8 ± 4.9 kJ vs. CR: 65.0 ± 4.9 kJ, p > 0.05). Creatine loading had no ergogenic effect on the CP measured using the novel all-out protocol. In contrast to earlier studies which established the power- duration relationship using the conventional protocol, the finite work capacity > CP (W� ) for all-out exercise was not enhanced by creatine loading. ( J Exerc Sci Fit  Vol 7  No 1  9-17  2009)
World records for running provide data of physiological significance. In this article, I shall provide a theory of running that is simple enough to be analyzed and yet allows one to determine certain physiological parameters from the records. The theory, which is based on Newton&apos;s second law and the calculus of variations, also provides an optimum strategy for running a race. Using simple dynamics one can correlate the physiological attributes of runners with world track records and determine the optimal race strategy.
The tolerable duration of high-intensity exercise can be described by a simple hyperbolic function of power or velocity, with an asymptote referred to as the 'critical power/velocity' and a curvature constant referred to as the 'anaerobic work/distance capacity'. More recently, this hyperbola has been generalized by permitting a non-zero temporal asymptote. Using this three-parameter model, we consider the consequences of running the initial part of a race at a speed different from the constant rate proscribed by the hyperbola. We show that for any distance split, an improved time is achievable and that the least time occurs when both parts of the race are run at speeds determined by applying the hyperbola to each part. Further improvement is possible by an appropriate selection of initial distance, with the first part being run at a higher speed than the second. Still further improvement is possible if the athlete follows an all-out running strategy, and we prove that for this model an all-out strategy is uniquely optimal. Significant performance gains appear possible for events of less than 10-min duration. Thus, under this model, an athlete, who at any time during a race drops below their all-out pace, can never make up for lost time. This result is contrary to conventional wisdom. Accordingly, we examine some recent empirical evidence which confirms the predicted nature of all-out power development over short time periods and suggests that pace variation, at least to some degree, may not be as suboptimal as previously assumed.
A new conception of dynamic or static muscular work tests is presented. The authors define the critical power of a muscular work from the notions of maximum work and maximum time of work. The work capacity is then considered in the case of dynamic work, and of continuous or intermittent static work. From the data presented it is possible to define the maximum amount of work that can be performed in a given time as well as the conditions of work performed without fatigue. (French & German summaries) (22 ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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