2004 Headway Calcs

[Peter]

Here are my headway calcs for the 2004 paper, I've considered the stopping and non-stopping headways.

Consideration of branch/single line to follow.

There does not seen to be an attachment here. Can you please post it.

Peter

This particular thread is moderated by PJW, so my attachment won't be available until he makes it visible. And I believe he's on holidays until next week.

You are right, I forgot which thread we were in!

[PJW]

This particular thread is moderated by PJW, so my attachment won't be available until he makes it visible. And I believe he's on holidays until next week.

Only set it up like this so that we could have multiple people doing the same thing working to a common deadline and once it had expired then making all attempts visible to review together. Not really working out like that at the moment, so have made visible- will look at over the weekend once I've sorted myself out after the weeks holiday!

[Peter]

Only set it up like this so that we could have multiple people doing the same thing working to a common deadline and once it had expired then making all attempts visible to review together. Not really working out like that at the moment, so have made visible- will look at over the weekend once I've sorted myself out after the weeks holiday!

Yes, the idea is a good one. Not quite sure if the settings are right - if you have made it visible, it still does not show up. I'll try to have a look when I'm not being badgered to get off the computer.....

[PJW]

Only set it up like this so that we could have multiple people doing the same thing working to a common deadline and once it had expired then making all attempts visible to review together. Not really working out like that at the moment, so have made visible- will look at over the weekend once I've sorted myself out after the weeks holiday!

Yes, the idea is a good one. Not quite sure if the settings are right - if you have made it visible, it still does not show up. I'll try to have a look when I'm not being badgered to get off the computer.....

It has worked before OK; I think that it could have been operator error by me. I certainly had the options in Admin CP but may have not selected the right one before actioning. They have disappeared from the "awaiting moderation" but the good news is that they were not entirely deleted so I have downloaded and post here with my annotations.
I take that back- seems to have been some delay but the attachments have now magically appeared without me doing anything- but perhaps the other Peter did something

Basically the stopping calculations were fine and reasonably well explained. One of the examiners is particularly adverse to the DGR method, so you do need to be especially careful with your explanations if using this. I would advise use of a diagram annotated with the abbrievations that you are going to use and just a few more words of explanation (as I have shown in blue)- it was towards the end when you started to use abbrieviations that (although I grant pretty obvious) you hadn't actually defined.
I used Red text to indicate the "compulsory" rather than "advisable" comments / corrections.

The stopping headway wasn't so good; the elements included are basically sound, but the answer stopped short of proving that 3 aspects at minimum (or indeed some greater spacing) would be adequate to deliver required headway. You didn't state your assumptions- such as that it was "stopping following stopping" that you were being asked to calculate rather than "fast following stopping"- either of which I'd regard as plausible given the question set.

Its main defect is that it did not relate the times t1-t4 calculated to the actual stopping headway which would be achieved. A subsidiary defect is that the t4 calculated did not match the t4 of the diagram provided.
Hence I'd give you some marks for being able to use Newton;'s laws of motion and for being vaguely on the right lines; however your answer does NOT convince me that you understand the impact that the first stopping train would be having on the aspect sequence behind it and therefore on the manner in which the drver of the following train (not even mentioned in your answer to either part of the question!!) would be driving. The fact that the t4's don't match, suggests that you have mix-and-matched bits from various sources but not properly integrated them in your brain and hence don't fully understand the significance of what you are doing.
All the bits are good; but they do need to be bolted together correctly!
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As an overview of what you are trying to do:
1) Initial condition; two trains following each other at constant speed (it not actually stated whether this is the max 120km/h or some lower timetabled speed, so you should explicitly state your assumption- you chose 100km/hr which is perfectly reasonable, but did you really think enough about this and choose for the right reason)
2) Train 1 slows down to stop at station; Train 2 catches it up slowly at first and then quite quickly once first is stopped.
3) Unless Train 1 has cleared the overlap of the station starter before Train 2 reaches the sighting point of the second 3-aspect signal in rear, then it will receive a caution aspect at it. Question is whether this will affect how Train 2 is driven- what do you think?
4) Unless Train 1 has cleared the overlap of the signal beyond the station starter by the time that Train 2 reaches the signal reading into the station, then it will receive a caution aspect at it. Question is whether this will affect how Train 2 is driven- what do you think?
5) Unless Train 1 has cleared the overlap of the second signal beyond the station starter by the time that Train 2 is ready to depart from the station, then it will receive a caution aspect at the station starter. Question is whether this will affect how Train 2 is driven- what do you think?

Remember that "headway" is all about one train NOT impacting on another. Not a perfect analogy by any means, but perhaps easier to think about; a stream of traffic progressing smoothly on a motorway. Another similar motorway merges; if traffic on both is sufficiently light then although the resultant traffic is heavier than it was, it carries on flowing quite freely and no one really minds or notices. However as the level of traffic on both gradually increases later on in the day, what often happens is that a capacity limit is reached and then average speeds drop- indeed there can be quite a pronounced tipping point and it can get very slow stop-start with big build ups for many miles.
Traffic jams on the railway tend to be far less visible (until we get ETCS L3 or at least virtual blocks) as instead of getting vehicles bumper to bumper we keep them a full block section apart, but they happen none-the-less.
Stopping headway has no clear analogy with roads since it is normally so easy to overtake and relatively quick to brake and accelerate. I suppose "Fast following Stopping" could be a bit like a car driver who would catch up a bus on a stretch of lightly used narrow road where overtaking isn't an option; the calculation would then be how much head-start would the bus need over length x with y bus stops for it to have cleared the narrow section before a car which travels faster and without any requirement to stop just reaches it at the first overtaking opportunity.

So taking an overview of your answers I'd say all the "mechanics" are ok but you largely failed to demonstrate to me that you had grasped the "big picture" of what the activity is all about and why it is such an important part of signalling the layout- i.e. the throughput of traffic. Hence suggest you need to do more work in that regard to be able to gain the marks on offer.

See also
my response to Alex

[PJW]

Hello Peter,

Here is the appended work sheet

Regards

Having defined SBD as Service Braking Distance in the table, then you should stick with it thrughout; you didn't define B in the formula for Hd3 but that seems to be the same. Alternatively you could have defined a quantity such as "d" as the signal spacing for the general formula for headway and then said that the best headway is when d is as small as possible and that its minimum value is the SBD.
You should NOT just quote this formula
a) you must define the individual terms "B", "S","O", "L"- both giving them names and showing that you know what is meant by the term; I would advise use of a diagram for this. In particular you have not stated your implicit assumption relarting to "S"; where does the 340m come from- how many seconds are you allowing the driver, at what speed?
b) you must show WHY the equation is true- again I believe that the quickest easiest way is to use a diagram which shows two trains at minimum spacing with the second one just achieving a clear aspect sequence in time for the driver to avoid needing to brake. This would demonstrate your understanding as to why each of the factors influence achievable headway.

Looks to me that the "V" you used when calculating Ht3 was the maximum permissible rather than the correct headway speed.

Certainly in your "alternative" calculation you certainly used 33.33 even though you had written Vh. Otherwise I think this methodology is a good approach, but you need to explicitly state, having calculated your value of "d" which just provides enough CAPACITY, that it also satisfies the minimum of SBD which is necessary for SAFETY. You were right that in this example the constraint of 133% overbraking is in fact more onerous than that imposed by the headway requirement, but you should have stated this more clearly and obviously.

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In this paper I wouldn't have complicated by worrying about the speed restriction over the points from the branch- just have caculated for following trains on the mainline straight approach. However it is a valuable thing to include as a comment as one of the things justifying the level of "contingency" that you propose.

I think it is reasonable to assume that stopping trains will run at most at the timetabled speed of the non-stop service- however you need to state whatever assumption you are making. Since the question isn't 100% unambiguous you'd be wise to state your assumption that you are considering two following trains both stopping at the station. Your diagram shows deceleration from around 100km/hr, but I believe that you based this on the deceleration from 120km/hr to respect the turnout speed.

You have calculated the time for a train would take from passing the platform protecting signal, then brake to a stand int he station and then reaccelerateup to 40km/hr and then continue at that constant speed to clear the overlap. Although a useful constituent, this isn't quite what is wanted.

a) I think you may have been considering the use of the platform loop; that is a good thing in that you are relating te calculations to thee layout but it does add a layer of complexity; probably best to state assumption of use of the mainline platform, but include a comment re the additional time needed if the loop used- another reason for the need of a bit of contingency.
Also remember that if we are able to use freely two lines through the station (and that means that the overlap arrangements are such that a train can be signalled into the one at the same timeas a trai is leaving the other), then the stopping headway constraint is rather less onerous.

b) So you know for how long the station protecting signal will be held to danger. That is useful knowledge (and indeed for a Metro which I know you are more used to) is a fair bit of the answer- but it is not the whole answer. If Train 2 were at that signal then it certainly (hopefully!!) wouldn't be travelling at 100km/hr; it would be completely stopped at a red signal that was just about to change to yellow. So it would need to react (human delay to notice spect change, take the brakes off delay) then accelerate up to 40km/hr so the value of time "a" would be different to that calculated. This also indeed wouldn't strictly be "headway" as Train 2 has had to stop due to the presence of train 1; the optimum situation would be that Train 2 would be slightly further behind, so that it would see the signal clear before it needs to commence its braking if it should need to stop at it.
In a "Metro" environment then one would assume 2-aspect signals with a train able to come to a stand within the distance of direct observation, hence provided this signal had cleared before the driver felt he needed to act then that would be good enough to achieve the headway.
However in a mainline environment with 3-aspect signals, the message that the driver needs to brake to stop at a signal is NOT conveyed by that signal but the one behind (on the aproach thereof). So you need to factor this into your calculations: the previous signal should show Green by the time that Train 2 is within Sighting Distance of it or else the driver would be braking to stop at the platform protecting signal. Similarly one could argue that this signal should itself then have cleared to Green by the time Train 2 closely approaches it with Train 1 still accelerating away from the station; however this is rather too conservative because in reality the driver of a stopping train will need to be braking soon for the station stop, regardless of the position of Train 1. There is no hard and fast answer; if the headway speed of the train equals the maximum permissible speed and the signal spacing is the bare minimum of SBD then clearly the protecting signal clearing to yellow as soon as the driver of Train 2 can see it is good enough- the distance needed for braking is efffectively the length of the signal section. Conversely if the headway speed of the train service is not as high as "linespeed" or if the signals are actually spaced at distance in excess of SBD, then Train 2 could and would delay its braking later if given a Green (driver only needs to stop in the station, an overrun by a few metres of the ideal stopping position is not critical) than if given a Yellow (driver by training MUST make a meaningful brake application prior to passing the caution signal and will be more cautious as an overrun by a metre of the next signal could be career threatening).
So you need to relate this part of the answer to the signal spacing determined from the non-stop calculations and state what your assumptions are with some indicative justification of what "counts" as a resttrictive aspect on which signals within the aspect sequence which results from the relative positions of the two trains at different times in the sequence.
See also my response to Interesting Signal

and also look back at history

[alexgoei]

Hello PJW,

Thank you for the reply.

Will go through your comments as the two other postings on this website which yyou mentioned.

Cheers

[PJW]

I have been sent another person's version of the calculations for this year, to which I have added "sticky note" comments within the pdf file that show up on the scan and reveal themselves when you hover over them.

Pretty similar attempt to another one recently and hence my comments are very similar:
It is very clearly set out and goes through logically.
It is "going through a process" and therefore not necessarily directly answering the actual question which was set.
It quotes the headway formula without a diagram to explain derivation.
It uses what is termed an "aspect ratio" which is not explained or justified.
It calculates the minimum headway for 3 aspect signals which was not required in the 2004 paper.
It does however also determine the acceptable range of spacing that does answer the question related to signalling the layout.
It attempts to use the same short cut method for stopping headway, doesn't completely explain what trying to do, but it was a bit better because the "penny did actually drop" with me this time. However it is based upon the 3 aspects being placed at minimum spacing rather than any greater figure that matches what was declared would be used.

Assumption were placed at the end as an after thought, although they had previously been utilised. No comment was made regarding the necessity or not of designing any contingency into the signalling relating
to the declared headway requirement and level of utilisation.

[chitrajanarthanan]

Can u please go thorugh this calculation and comment on above calculations???

[PJW]

Can u please go thorugh this calculation and comment on above calculations???

I can see no attachment.......?
Aarh Have now sussed it. This subForm inhereted some properties from when we were attempting to run a virtual study group and had been configured to require attachments to be moderated. Have now done that and hopefully corrected, so that doesn't reoccur in future.

Tomorow evening is my first chance to do so, unless someone else hasd the chance to do so earlier.

I'll also move this post so that adds to the previous thread on 2004 calcs

[Zaphod]

Can u please go thorugh this calculation and comment on above calculations???

I have only looked through this pretty briefly but my impression is that it's pretty good. A couple of points I noticed:

One of your assumptions states "absolute track circuit block section". I assume that "track circuit block" is meant, as absolute block is something different.

On the second graph on page 5, I think the x-axis is actually depicting time and the y-axis distance. In this case, the line for the stopping train should be below the non-stopping train. They certainly should not converge in the way shown. The figures seem to be right, it's just that the graph needs to be redrawn to make it clear what the figures actually mean.

The sentence "After 189 secs we can pass the fast passenger train" is possibly ambiguous. Does it mean that a fast train can be run 189 seconds after the stopping one? I would possibly reword to avoid the possibility that it means that the two trains should pass one another (which looks like it might be happening based on the graph).