Converting Calculated headways to signal spaces.

[PJW]

Also I can calculate Braking times and distances to halt but how would you calculate the time and distance required for a train to brake from say 100km/h to 40km/h for a turnout ?

If you can calculate braking times and distances to a halt from 100km/h and also from 40km/h, then the times you require are the difference between those values. OK this may be a bit of a long winded way to get the answer, but when you think about it, it must work. This of course assumes that there is no "brake build up delay"; in the real world things aren't quite so simple as there is an elapsed time when little or no braking occurs following the driver's braking request.

Actually for constant braking rate thoughout the speed range, you can calculate the time taken to decelerate from initial speed "u" to final speed "v" by making use of the equation v=u+at; t=(v-u)/a (with the acceleration "a" of course being negative).

One of the very useful things of the IRSE so often using a=-0.5m/s/s is that it takes 2 seconds to reduce speed by 1 m/s; Hence if the initial speed is say 25 m/s then to reduce speed to 15m/s is a reduction of 10m/s which will take 20s. The average speed during the braking period is 20m/s and hence the distance travelled is 20 m/s x 20 s = 400m; hence you can often do in your head.