2007 Q10 Headway

[PJW]

You need to find the headway separation between the two trains coming from the mainline but when there is a train to insert between them coming from the branch. Therefore it breaks down into various calculations-
1. How soon after the first mainline train can the branch train enter the line with a green
2. How long does it take for the branch train to accelerate to the mainline headway speed
3. How much more time does this train take to reach the place at which it has travelled far enough that the next mainline train can get a green when reaching the sighting point of its signal and thus running at minimum headway behind it.

This clearly is the bare minimum and therefore unless timekeeping to timetable perfect then it won't work out, so an element of contingency in the planning is called for. The last part of the question adds in the other factor that there is the traffic on the opposite running line also to cross and therefore a greater allowance may be needed.

Hi PJW,
From the thread above, what I understand (correct me if I'm wrong) is that to calculate mainline headway for part B of the question, is to add the first mainline headway calculation from part A and add to the converging headway calculation ?

I've attempted this question as well and would appreciate any comments. Thanks!