Calculate furthest distance in given time or best time for given distance - r

Question

I have imported data from my GPS tracker and I am trying to figure out how to best calculate furthest distance ran in given time (e.g. 12-minutes) or best time for given distence (e.g. 5 miles). Given the observations are taken in unequal intervals and my speed is also not constant, I will have data like the table below:
x <- read.table(header=T, sep="", stringsAsFactors = FALSE,text="
time dist
4 3
5 4
5 6
3 2
5 5
4 5
4 3
4 2
5 6")
My best attempt so far is to generate new dataset where times go by one time unit. It is then relatively easy to calculate furthest distance in given time. The downside of this is that a) I would need to repeat the same logic for best time (generate data with unit distance), b) it seems to be quite sub-optimal solution for data with thousands data points.
# Generate data frame where each row represents one unit of time
z_adj <- data.frame(
time = unlist(sapply(x$time, function(s) rep(s, each = s))),
dist = unlist(sapply(seq_along(x$dist), function(s) rep(x$dist[s], each = x$time[s])))
)
z_adj$seq_time <- seq_along(z_adj$time)
z_adj$time_dist <- z_adj$dist / z_adj$time
# Furthest distance given time
# Time 10
z_adj$in_t10 <- sapply(z_adj$seq_time, function(s) sum(z_adj$dist[s:(s+9)]))
z_adj$in_t10[which(z_adj$in_t10 == max(z_adj$in_t10, na.rm = T))]
# Fastest time given distance
# ... would need to do the above again with constant distance :/
Is there a more straightforward approach to accomplish this?

Answer 1

You could use something like this:
x <- read.table(header=T, sep="", stringsAsFactors = FALSE,text="
time dist
4 3
5 4
5 6
3 2
5 5
4 5
4 3
4 2
5 6")
# Add starting point and cumulatice time/distance
x <- rbind(c(0,0), x)
x$total_time <- cumsum(x$time)
x$total_dist <- cumsum(x$dist)
# function to interpolate and calculate lagging differences
foo <- function(x, y, n) {
interpolation <- approx(x, y, xout = seq(min(x), max(x)))
diff(interpolation$y, lag = n)
}
# Max distance in ten units of time
max(foo(x$total_time, x$total_dist, 10))
# Min time for ten units of distance
min(foo(x$total_dist, x$total_time, 10))
BTW, in your code you should sum over z_adj$time_dist instead of z_adj$distto get the correct result.