# Wprime

##### W': work capacity above critical power/speed.

W': work capacity above critical power/speed.

##### Usage

```
Wprime(object, session = NULL, quantity = c("expended", "balance"), w0,
cp, version = c("2015", "2012"), meanRecoveryPower = FALSE,
parallel = FALSE, ...)
```

##### Arguments

- object
A

`trackeRdata`

object.- session
A numeric vector of the sessions to be used, defaults to all sessions.

- quantity
Should W'

`'expended'`

or W'`'balance'`

be returned?- 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.

- parallel
Logical. Should computation be carried out in parallel? If

`TRUE`

computation is performed in parallel using the backend provided to`foreach`

. Default is`FALSE`

.- ...
Currently not used.

##### 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.

##### Value

An object of class `trackeRWprime`

.

##### 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.

##### Examples

```
# NOT RUN {
data('runs', package = 'trackeR')
wexp <- Wprime(runs, session = c(11,13), cp = 4, version = '2012')
plot(wexp)
# }
```

*Documentation reproduced from package trackeR, version 1.5.2, License: GPL-3*