Calculate W' expended, i.e., the work capacity above critical power/speed which has been depleted and not yet been replenished.
Wexp(object, w0, cp, version = c("2015", "2012"),
meanRecoveryPower = FALSE)
Univariate zoo
object containing
the time stamped power output or speed values. (Power should be
in Watts, speed in meters per second.)
Inital capacity of W', as calculated based on the critical power model by Monod and Scherrer (1965).
Critical power/speed, i.e., the power/speed which can be maintained for longer period of time.
How should W' be replenished? Options include
'2015'
and '2012'
for the versions presented in
Skiba et al. (2015) and Skiba et al. (2012), respectively. See
Details.
Should the mean of all power outputs below critical power be used as recovery power? See Details.
Skiba et al. (2015) and Skiba et al. (2012) both describe an exponential decay of \(W'\) expended over an interval \([t_{i-1}, t_i)\) if the power output during this interval is below critical power:
$$W_exp (t_i) = W_exp(t_{i-1}) * exp(nu * (t_i - t_{i-1}))$$
However, the factor nu differs: Skiba et al. (2012) describe it as \(1/\tau\) with \(\tau\) estimated as
$$tau = 546 * exp(-0.01 * (CP - P_i)) + 316$$
Skiba et al. (2015) use \((P_i - CP) / W'_0\). Skiba et
al. (2012) and Skiba et al. (2015) employ a constant recovery power
(calculated as the mean over all power outputs below critical
power). This rationale can be applied by setting the argument
meanRecoveryPower
to TRUE
. Note that this uses
information from all observations with a power output below
critical power, not just those prior to the current time point.
Monod H, Scherrer J (1965). 'The Work Capacity of a Synergic Muscular Group.' Ergonomics, 8(3), 329--338.
Skiba PF, Chidnok W, Vanhatalo A, Jones AM (2012). 'Modeling the Expenditure and Reconstitution of Work Capacity above Critical Power.' Medicine & Science in Sports & Exercise, 44(8), 1526--1532.
Skiba PF, Fulford J, Clarke DC, Vanhatalo A, Jones AM (2015). 'Intramuscular Determinants of the Abilility to Recover Work Capacity above Critical Power.' European Journal of Applied Physiology, 115(4), 703--713.