Implement different walking times

[mpadge]

Currently uses Naismith's Rule, but i found out from this tweet by @michaeldorman about the movecost package which implements several alternative cost functions. Some of these could also be implemented.

[mpadge]

Looks like this is really worth implementing, especially in the Tobler or Marquez-Perez versions, which appropriately penalise even flat walking compared with slightly downhill. The formulas all come directly from ?movecost::movecost.

tref <- 1
dz <- -20:20 / 100
cost0 <- tref * (1 + dz / 10) # current naismith implementation
cost1 <- tref / (6 * exp (-3.5 * abs (dz + 0.05)))
cost2 <- tref / (4.8 * exp (-5.3 * abs (dz * 0.7 + 0.03)))
cost3 <- tref / (1 / ((0.0277 * abs (dz) * 100) + 0.6115))

cost1 <- cost1 / min (cost1)
cost2 <- cost2 / min (cost2)
cost3 <- cost3 / min (cost3)

n <- length (dz)
dat <- data.frame (
    slope = rep (dz, 4),
    cost_fn = c (
        rep ("Naismith", n),
        rep ("Tobler", n),
        rep ("Marquez-Perez", n),
        rep ("Uriarte Gonzalez", n)),
    cost = c (cost0, cost1, cost2, cost3)
)
library (ggplot2)
ggplot (dat, aes (x = slope, y = cost, colour = cost_fn)) +
    geom_line ()

^{Created on 2022-08-24 with reprex v2.0.2}

[mpadge]

That commit dropped Naismith in favour of Tobler. Exposing choices between the variants shown above would be highly unlikely to ever make a discernible difference, particularly as errors in interpolating elevation differences from a raster will always far outweight the kinds of minor differences between the functions shown above. This single improvement should be plenty sufficient to make walking times far more realistic.