# Wexp: W' expended. In trackeR: Infrastructure for Running, Cycling and Swimming Data from GPS-Enabled Tracking Devices

## Description

Calculate W' expended, i.e., the work capacity above critical power/speed which has been depleted and not yet been replenished.

## Usage

 ```1 2``` ```Wexp(object, w0, cp, version = c("2015", "2012"), meanRecoveryPower = FALSE) ```

## Arguments

 `object` Univariate `zoo` object containing the time stamped power output or speed values. (Power should be in Watts, speed in meters per second.) `w0` Inital capacity of W', as calculated based on the critical power model by Monod and Scherrer (1965). `cp` Critical power/speed, i.e., the power/speed which can be maintained for longer period of time. `version` 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. `meanRecoveryPower` Should the mean of all power outputs below critical power be used as recovery power? See Details.

## 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/τ with τ 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.

## References

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.

trackeR documentation built on May 15, 2019, 5:04 p.m.