# 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:

```
=100
segment_length
# stage_length set in earlier section
= seq(from=0, to=stage_length, by = segment_length)
segments
= approxfun(trj_ogier$cum_dist,
ogier_full_estimator $displacementTime) trj_ogier
```

```
## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## collapsing to unique 'x' values
```

```
= approxfun(trj_evans$cum_dist,
evans_full_estimator $displacementTime) trj_evans
```

```
## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## collapsing to unique 'x' values
```

```
= ogier_full_estimator(segments)
ogier_time_points = evans_full_estimator(segments)
evans_time_points
= ogier_time_points - evans_time_points
ogier_evans_point_delta
# 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')
```