2007 Q10 Headway

[PJW]

Hi Guys,

I have had ago at 2007 Q10 from Module 3 which is about headway.

I am pretty confident on the first part of the question which seems relatively simple.

A double track railway is signalled using 4 aspect signalling (G – YY – Y - R) for trains of 125m length travelling at a nominal 140km/h. Signals are spaced at an average of 800m and a 225m overlap is provided at each signal. Calculate the theoretical headway for following trains. [7 marks]


Good approach but you forgo to make any allowance for the sighting distance between the front of the nd train and the signal which just changes to green when the 1st train clears the overlap as shown.

Another thing is that the headway is dictated not by the average spacing but the longest total spacing of 3 consecutive signals along the line- this will become the line limit for capacity. Not suggesting you change the numbers, but a point worth making, perhaps by stating the assumption that the average works out on each group of 3 signals such that the spacing from Green to Red in each case is 2400m.

The second part of the question I am less confident on. I think the maths is correct but I may have misinterpreted the question.

A double track junction is added in the middle of the line, clear of the overlaps of the protecting signals, with a divergence speed of 80km/h.
Determine by calculation, or graphically, the effect on headway for a train converging with the mainline and accelerating to line speed. Assume an acceleration rate of 0.5ms-2 and state any other assumptions regarding relative positions of signals to the junction (with the aid of a
diagram). [14 marks]

You probably did it to make your calculations easier, but it is not good layout design to have the trailing connection immediately on the approach to signal A2. However it was good to state that acceleration wouldn't commence until the rear of the train has passed completely over the connection.

Although what you did looks ok and reasonably well explained, I don't think you finished calculating what was needed. I interpret the question as meaning how closely can the 3rd train (from the main) follow the 1st train (from the main) given that there is a need to interleave the 2nd train (from the converging branch) between them.

Hence you need to decide where train 2 would need to be with respect to signal B1 at the instant that train 1 has passed (and you need to consider if this means the overlap of signal A2 or A3 or A4!) and also consider whether there is a need to add any allowance for the points to move and be detected.

Then basically the calculations you have performed but including the time it takes for train 2 to clear the overlap of signal A4 as you have shown. Then you add in the figure which was calculated in the first part of the question (as by that time train 2 is moving at maximum speed and thus it is irrelevant that it came from the branch and it is just normal constant speed plain line headway consideration again); obviously the points have to be thrown and gain detection but it would be reasonable to state the assumption that this will occur whilst the train from the branch is moving between signals A2 and A4 so does not add any extra time.

Obviously there are assumptions to state / show in your diagram.

The final part was only four marks and asks about timetabling, I have no experience of this so if any one can offer any points on this it would be appreciated.
Converging trains have to cross the other line. What timetabling rules should be applied to minimise the impact on mainline trains in both directions? [4 marks]

To fit the last part of the question better (always read the WHOLE question before starting!), you should have shown the converging line BELOW rather than above the straight line given that you have traffic from right to left and you are assuming (as reasonable in the UK) left-hand running on double track lines. In the diagram as you have drawn it is actually the main line train which crosses both direction tracks of the diverging route, rather than vice versa.

However slightly modifying the question to suit your diagram, the railway would attempt to timetable a train to pass A1 at a time when there was due to be no train using the facing lead and diamond crossing as well of course as no train from signal B1. A good answer would point out that the route over the junction need to be set and points have time to throw, gain detection, aspect clear and aspect sequence respond before the approaching train gets to the relevant sighting point; indeed would want a margin so that the route would be established with a bit of time to spare.
The junction would need to be maintained locked until the rear of the longest train travelling at perhaps slightly less than its usual ideal speed had cleared the pointwork, plus a small allowance for the signaller to become aware and set up the route for the next train taking a conflicting path through the junction.
Also should have an allowance for trains not running precisely on train , so that if one is slightly delayed there is a bit of a buffer before the junction is required to be committed for the next train. Often railways specify "junction margins" or "junction reoccupation times". I think therefore the examiners were expecting reference to "junction headway" separate to "plain line headway". The important thing to emphasis is that a train requires the junction committed to it not only whilst any part of it is traversing the area, but sufficiently prior to its arrival that it can be signalled appropriately and thus not be impeded by restrictive aspects as a consequence.

Clearly if the trains needing to join the main line and in the opposite direction diverge from the mainline are timetabled to pass each other at the junction, then they impact on the through mainline traffic less as get "2 for the price of 1". Even if the up and down train aren't exactly simultaneous, it is more efficient to the flow of mainline traffic to have one slightly extended interruption caused by the branch traffic rather than two separate shorter ones.