2007 Q10 Headway

[ricky]

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 relativly simple.

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

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.

Thanks for the help

Rich

[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.

[jay.fitz]

I gave this one a try also.

JF

[PJW]

The diagram was useful.

Calculations for the first part seem fine, but a little more explanation called for; don't just quote the headway formula from thin air and even the conversion to m/s would have benefited from some hint why 140km/h = 350/9 m/s etc.

In the second part there were some more assumptions to state and explanation to give in order to gain more marks. For example you state that S31 is 125m clear of points, which I think means that the signal has a 125m overlap (presumably justified by the lower approach speed) and that it is this which is clear of the diamond crossing convergence with the opposite direction running line. It isn't actually clear therefore what you are taking as the distance beyond S31 where the train is assumed to have cleared the trailing points and therefore can start accelerating.

You state "distance to traverse" but you don't specify exactly what, but I guess the signal section S31 to S21 which is also being assumed to be 800m (even though the diagram by comparison with the mainline might suggest >1600m) plus the S31 sighting distance.

You did not state but it looks like another assumption that you judge that the rear of the branch train will be clear of the trailing points by the time the driver passes S21 (say S31 is 125m from CP, further 200m to tips of trailing point at convergence, a 125m train - looks to me like the driver might be 300m prior to S21 and would be able to start acceleration). The time and distance calculations to accelerate look ok.

You then seem to calculate (but don't really give quite enough explanation that this is what you are doing) the further time that the train will take when travelling at headway speed before covering the remaining distance to clear the overlap beyond S25 and thus allowing S19 to go to green for the next mainline train. I am pretty sure this is what you meant but the explanation was a little too brief and referred to overlap of S21 when I think you meant the overlap of the route from S23 (= overlap beyond S25).

You then state the time between M101 and B101 is 5+45+34+21 leaving the examiner to hunt around for what the significance of those numbers are. If you had identified these intermediate answers with a #1,#2,#3.#4 reference respectively then it woul have been quick to have cross referenced.
Alternatively could have said =
signalling system reaction time + 80kmh running + acceleration time + 140km/h running.

If you allowed 5 secs for S31 to step up in response to the overlap of S25 clearing (seems quite a lot even for SSI- the assumption you never stated was that the rout S31 to S21 would have been set as soon as mainline train had cleared points and therefore the route establishment time will have occurred well prior to the train moved outside aspect sequence range), then surely you should do the same for S19 stepping up and that this must occur before the next mainline train reaches its sighting point and therefore I'd have expected a further 5 + 8 seconds o be added on to your 105s figure.

I therefore didn't follow when you said that the next mainline train observing signal (I didn't understand which one!) should be 79s in rear of B?102. I had certainly lost you by now as your diagram shows M102 at signal 19 and surely if this is supposed to depict a moment in time when M102 just beyond S25 and B101 closely approaching S31 then M102 will be many minutes running time off the left hand end of the diagram and it would have been better to have depicted it as such or it suggests tht it is being brought to a stand at S19 so that the branch train can be run in front of it.

In fact it would probably have been clearer to refer to your trains as M101, B102 and M103 respectively- perhaps this is what your explanation was reflecting but you didn't revise diagram accordingly....

You are right that the question is asking for the time separation of your M101 and the next mainline train that can be run after the branch train has entered the line, but because of my confusion re what you meant as indicated above, you don't convince me that this is what you calculated.
Overall though you do convince me that you knew how to address the question and can do the maths. However you also seem to have ignored the very last part of the question, so suggest that you need to work on your question answering technique a bit as otherwise you will nt get all the credit that you would otherwise have achieved.

I gave this one a try also.

JF

[greatnessjason]

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!

[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!

[Alan Beavers]

Re not using 140kmh straight to 350/9 (which is actually a nice way of doing it, avoiding picking a calculator up until you have to), does that mean you can't use 0.447 to convert mph to m/s, you have to show 1609.344/3600?

Re your point 1 above PJW - at what point can the branch train enter the main line on a green. If you're using that signal as the starting point for the branch-train-following-main calculations, you're saying that no time has been lost before this i.e. the branch train has been able to keep up (that is keep hitting sighting points as the signals change to green) since 1 or 2 signals before (3 or 4 aspect).
So, if that is the case, could you extend that principle up to the 1st main line signal and use that as your starting point? Then all you need to calculate is 'time lost' accelerating then add that to the main line headway? (Assuming zero equipment response times etc.)
Time lost is: time taken to accelerate 80-140 & distance taken, versus time over that distance at 140.