# 15 Comparing Times Into Stage

How do our drivers compare based on the time it takes them to driver a particular distance into the stage?

Recall that we are using each carâ€™s own accumulated distance in to stage measure, rather than comparing times at distances into stage measured along some common, idealised route.

Sample common points to find the difference:

``````segment_length=100

# stage_length set in earlier section
segments = seq(from=0, to=stage_length, by = segment_length)

ogier_full_estimator = approxfun(trj_ogier\$cum_dist,
trj_ogier\$displacementTime)``````
``````## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## collapsing to unique 'x' values``````
``````evans_full_estimator = approxfun(trj_evans\$cum_dist,
trj_evans\$displacementTime)``````
``````## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## collapsing to unique 'x' values``````
``````ogier_time_points = ogier_full_estimator(segments)
evans_time_points = evans_full_estimator(segments)

ogier_evans_point_delta = ogier_time_points - evans_time_points

# Difference in time take to reach a particular point in the stage
ggplot()+geom_line(aes(x=segments, y=ogier_evans_point_delta))``````

Compare time into stage for a given distance into stage. Note that this is the distance into the stage as calculated from the trajectory, rather than by comparison of distances into the same (idealised) route.

``````ggplot() +
geom_line(data=(trj_ogier %>% mutate(dt=as.double(displacementTime)) %>% filter(dt >=0)),
aes(x=cum_dist,y=dt), color='blue') +
geom_line(data=(trj_evans %>% mutate(dt=as.double(displacementTime)) %>% filter(dt >=0)),
aes(x=cum_dist,y=dt), color='grey') ``````