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Department of Physiology, St. George's Hospital Medical School, University of London, London SW17 0RE, United Kingdom
It has been repeatedly demonstrated that the
tolerable duration (t) of
high-intensity cycling is well characterized as a hyperbolic function
of power (P) with an asymptote that
has been termed the "fatigue threshold" and with a curvature
constant. This hyperbolic P-t
relationship has also been confirmed in running and swimming, when
speed (V) is used instead of
P; that is,
(V 
VF) · t = D', where
VF is the
V at the fatigue threshold, and
D' is the curvature constant.
Therefore, we theoretically analyzed herein the consequences of an
athlete performing the initial part of an endurance event at a
V different from the constant rate
that would allow the performance time to be determined by the
hyperbolic
V-t
relationship. We considered not only the
V-t
constraints that limit the athlete's ability to make up the time lost
by too slow an early pace but also the consequences of a more rapid
early pace. Our analysis demonstrates that both the
VF and
D' parameters of the athlete's
V-t
curve play an important role in the pace allocation strategy of the athlete. That is, 1) when the
running V during any part of the whole
running distance is below
VF, the athlete
can never attain the goal of achieving the time equivalent to that of
running the entire race at constant maximal
V (i.e., that determined by one's own
best
V-t
curve); and 2) the "endurance
parameter ratio"
D'/VF is
especially important in determining the flexibility of the race pace
that the athlete was able to choose intentionally.
power-duration hyperbolic curve; speed-duration hyperbolic curve; endurance athlete performance; race-pace strategy; theoretical analysis
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