Wbalance: Calculate W' balance
In jmackie4/elpatron: Bicycling Data Analysis with R

Description Usage Arguments Details Value References Examples

This function provides an efficient implementation of Dr. Skiba's W' balance algorithm (Skiba et al., 2012).

1 2	Wbalance(time.s, power.W, CP, Wprime.kJ = NULL, data = NULL, smooth = FALSE)

`time.s, power.W`	numeric vectors of similar length describing elapsed time and corresponding power output recordings.
`CP, Wprime.kJ`	numerics (scalar) describing the two parameters of the basic critical power model, given in units of watts and kilojoules, respectively.
`data`	optional; a `data.frame` in which to find `time.s` and `power.W` arguments. If provided (i.e. not `NULL`), `time.s` and `power.W` arguments should be bare, unquoted column names.
`smooth`	logical; should power data be averaged into sections of sub- and supra-CP power output?

If the Wprime.kJ argument is supplied, W' balance per se is returned; that is, the output starts at "Wprime.kJ" and will decline with periods of supra-CP power output. This approach, while most familiar, relies on a valid estimate of total W' in order that W' balance is not seen to go < 0. This requirement can be circumvented by simply returning W' expended; that is, the ongoing work expended above CP. W' expended will be returned if the Wprime.kJ argument is left as NULL (default).

A numeric vector of W' expended/balance values.

Skiba PF, Chidnok W, Vanhatalo A, Jones AM. Modeling the Expenditure and Reconstitution of Work Capacity above Critical Power. Medicine & Science in Sports & Exercise 44: 1526–1532, 2012.

Skiba PF, Jackman S, Clarke D, Vanhatalo A, Jones AM. Effect of Work and Recovery Durations on W' Reconstitution during Intermittent Exercise. Medicine & Science in Sports & Exercise 46: 1433–1440, 2014.

Skiba PF, Fulford J, Clarke DC, Vanhatalo A, Jones AM. Intramuscular determinants of the ability to recover work capacity above critical power. European Journal of Applied Physiology ( November 26, 2014). doi: 10.1007/s00421-014-3050-3.

library(dplyr, warn.conflicts = FALSE)
data(chaingang)

chaingang <- mutate(chaingang,
                    Wbal = Wbalance(time.s, power.W, CP = 325))

# For an estimate of W'
max(chaingang$Wbal)

# This is probably being inflated by passing raw power data
# to the function. A solution:
chaingang <- mutate(chaingang,
                    power.W = roll_mean(power.W, 25, ema = TRUE),
                    Wbal = Wbalance(time.s, power.W, CP = 325))

max(chaingang$Wbal)  # 19.4 is more realistic.

plot(Wbal ~ time.s, type = "l", col = "red", data = chaingang)

# This representation is probably unintuitive to most.
# Hence, some modified approaches:

# Reverse the y axis...
ylim <- extendrange(chaingang$Wbal) %>% rev
plot(Wbal ~ time.s, type = "l", col = "red", ylim = ylim, data = chaingang)
title("Flipped y axis")

# Subtract an estimate of W'
Wprime <- max(chaingang$Wbal)
plot(Wprime - Wbal ~ time.s, type = "l", col = "red", data = chaingang)
title("W' subtracted")