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2000 Headway Calcs and Layout
#1
Hello everyone,

I would like to post my calculations for the non-stopping and stopping headway requirements.

Please feel free to let me have your comments especially PJW.

Thanks & Regards


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.pdf   2000 Layout Calculations.pdf (Size: 15.68 KB / Downloads: 228)
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#2
(23-05-2010, 03:45 PM)alexgoei Wrote: Hello everyone,

I would like to post my calculations for the non-stopping and stopping headway requirements.

Please feel free to let me have your comments especially PJW.

Thanks & Regards

I'll give anyone else a few days to have their own attempt at these calcs before responding in detail.

However I have noticed your diagram for the stopping calculations; it is good that you have included one but I note that it suggests that section "e" which is the length of an overlap is sufficient distance for the train to reaccelerae to 33.33m/s yet the table below it states that the distance for that to occur is 450m.
Also you really cannot use DGR directly for stopping headway; headway is fundamentally about TIME not DISTANCE. For non-stop then these are directly related since speed is CONSTANT; for stopping then the dstance apart of the two trains constantly VARIES.

I think what you are trying to do (but you don't really explain it and that would be your downfall) is to consider the situation when both trains are running at their constant speed, the first having stopped and reaccelerated and the second still on clear aspects having yet to slow down. Certainly if trains are spaced like that then it is evident that the signalling can deliver that particular headway and if that is all which is needed to be demonstrated then that is fine; however to get the maximum capacity out of the railway it may be necessary to get the 2nd train that little bit closer- i.e. so that only just gets a clear aspect in the nick of time whilst the 1st train is still accelerating.
Certainly if this is your assumption of the meaning of stopping headway, then don't add anything more for contingency!

So if you stated your assumption that "Train 2 should never encounter any cautionary aspect due to Train 1" then getting it to the sighting point of the YY at the instant that train 1 clears the overlap beyond the 3rd signal ahead thus permitting Train2 to get a Green achieves that objective. Support your argument by referring to "defensive driving" and the fact that the YY is probably quite a bit further from the station than a train running at the timetabled speed would actually need to be able to stop and this makes logical sense.

Be aware though that it might be difficult to deliver the headway requested (as we have traditionally permitted Train 2 to encounter some restrictive aspects on the approach to the station. If the position of the YY in 4-aspect signalling or the Y in 3-aspect signalling is more or less where the driver needs to apply the brakes to stop in the station anyway, then in reality the aspect received wouldn't make much difference to how the train is driven). If, as often, there is a choice between
a) placing 3-aspect signals tight to braking distance or alternatively
b) upgrading to 4-aspect signals that are more widely spaced, then note that the distance of the "first caution" with the 4-asects is actually further from the station and therefore the warning will be more premature, so this would worsen headway if the driver following the defensive driving policy.
This is not the full story however because the next signal in rear in 3-aspect case would be further away than in the 4-aspect case.

So I suggest that you "tweak"your answer for this part of the question by amending the diagram, adding in some more words of explanation of what you are calculating, record and justify assumptions as per above and then I'll review that version.

See also this other solution

Note that I have now also now given comments on a previous posted example ; that which was written there could well have misled you, so hopefully my belated amendments will clarify.
PJW
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#3
Here's my attempt at the 2000 paper, taking into account comments from PJW on my 2004 calculations.

I'm not sure that I have done enough for the stopping headway, as you can probably tell by my last paragraph. I still feel like I'm missing a piece of the puzzle. I'm also wondering how I'll get all this down on paper in the 20 minutes in the exam!


Attached Files
.pdf   2000 headway calcs page1.pdf (Size: 101.8 KB / Downloads: 186)
.pdf   2000 headway calcs page2.pdf (Size: 123.69 KB / Downloads: 145)
.pdf   2000 headway calcs page3.pdf (Size: 111.22 KB / Downloads: 124)
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#4
(01-06-2010, 10:52 PM)interesting_signal Wrote: Here's my attempt at the 2000 paper, taking into account comments from PJW on my 2004 calculations.

I'm not sure that I have done enough for the stopping headway, as you can probably tell by my last paragraph. I still feel like I'm missing a piece of the puzzle. I'm also wondering how I'll get all this down on paper in the 20 minutes in the exam!

I have annotated and attached.

First thing to say is that you might find some comments "picky". Actually this is a very good sign; for the non-stop at least you did a good job. I have pointed out a few things that I wouldn't have mentioned if it was not otherwise so good, so take it as a compliment. If you had been struggling then I would have turned a blind eye (e.g. one is a repeat of something I noticed but didn't point out on your last paper), but since you have fundamentally "got it" then I have raised the bar a bit. The important thing initially was to get the engine running, now we can do a bit of fine tuning to improve performance and then we can move on to the sustained speed test of the exam.

Non stop headway
I think you have done enough to appease re your use of DGR method which is not the examiners' favourite methodology, apart from needing to amend diagram slightly to get rid of the potential bad impression that it might create otherwise.

In almost all other respects it was a model answer, but spoilt by two things:

a) a "silly" when talking about percentages. If an object sells for


Attached Files
.pdf   2000 calcs Int Sig.pdf (Size: 479.59 KB / Downloads: 221)
PJW
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#5
(03-06-2010, 12:03 AM)PJW Wrote:
(01-06-2010, 10:52 PM)interesting_signal Wrote: Here's my attempt at the 2000 paper, .....
I'm not sure that I have done enough for the stopping headway,....still feel like I'm missing a piece of the puzzle.

Stopping headway

I think I'd add to the diagram by putting a distance / time presentation underneath it.

The words relating to aspect sequence were o....the last sentence (as you realised) left things hanging and you didn't address- though by adding to your diagram would go some way towards this.

One thing that you need to make clear is that the minimum headway time is the interval between two consecutive trains passing the same physical location, when the 2nd train is as close to the first one as it can be without being affected by the aspect sequence created by it.

I am not sure if you had looked at the attempted 2004 calculations that were prreviously posted on this website; I have now given comments on those that may assist in understanding.

I hope the attached diagram helps explain. In retrospect I'd use graph paper or even the other A3 blank intended for Control Tables rather than this one- measurements were a pain (perhaps because I used A3 scaled to A4 so that I could then scan it, the boxes were not an easy number of mm to construct a decent scale). Even worse, the penultimate row was not as high as the rest (someone tell me this isn't the case on the paper really given out at the exam!). Anyway probably easier to read and I wasn't fighting exam time.

I used your signal numbering and was going to use your signalling with 3 aspects spaced at 2000m, but then realised that it wasn't going to work out even cose and therefore changed to 4-aspect signals 1000m apart. Diagram is primarily drawn showing train 1 entering the graph at bottom left at headway speed of 120km/hr then parcatically immediately on it braking curve to stop with its front at end of platform just prior to starting signal (assume this is the first train for a long time so gets Green aspects hroughout).
It stops for 30 seconds (between t=90 and t=120) before accelerating. By chance it achieves constant 120km/hr more or less as it passes signal 4 (but of course had I decided to place the signals at a greater spacing then it wil still have taken the 1115m / 67s but would not yet have reched the signal)- just coincidence and won't always be the case, dependent on headway speed c/f maximum permissible speed amongst other things.

When calculating the aspect sequence, it is the rear of the train that is relevant and in particular when it just clears the relavant overlap track circuits. It is important to realise that there is a potential for this train to affect the one following it at each individual signal and when looking at headway along the line then it is the worst case that dictates the capacity. In prnciple we therefore need to check each and work out which is the worst; however by going for constant signal spacing and with almost all the line constant speed then there is great similarity; the idea of putting a station stop in the exam paper is for the candidate to demonstrate that they can, in principle, deal with a departure from the simple.

On the diagram I have shown three of the possible "pinch points"
a) train 1 clearing O/L beyond sig 4 and at that time sig 3 changing to Y and sig 2 to YY and sig 1 to G
b) train 1 clearing O/L beyond sig 3 and at that time sig 2 changing to Y and sig 1 to YY
c) train 1 clearing O/L beyond sig 2 and at that time sig 1 changing to Y
Ideally I would have shown your signal 5 as well, but it was too tempting to make the grid boxes on the blnk 500m by 30s and I couldn't fit this in. Anyway I want to leave somthing as an exercise for the student- the way of ensuring understanding is to do it yourself, so suggest use a smaller scaleand extend by two signal sections on the approach to the station and an extra two beyond it as well to be able to see the full picture.

The diagram should make plain that sig 3 remains at Red for some 75s after passage of a train whereas sig 2 remains at Red for much longer- nearly 120s (not diagram isn't perfect scale and these figers are just judged by eye to get overview rather than claiming accuracy). There's not enough diagram drawn to show the situation for sig 1, but it is obviously going to be around 35-40s since most of the 1180m will be traversed at 33m/s- it is nearly far enough from the station not to be affected by trains slowing to stop at it.

What we are trying to work out is how close above (i.e. the same longitudinal position along the railway, later time) the identical curve for train 2 can be placed such that the driver does not see signal aspects that would make them drive more cautiously than they otherwise would.

I only just had spece to add train 2 and effectively it is only the "constant speed" portion at the extreme left hand end that shows. I placed it so that the front of the train 2 was 10 seconds running time on the approach to sig 1 at the instant that it first displays YY (previously it would have been displaying Y). For the moment don't worry what aspect train 2 would have rceived at the previous signal, but assume that the train is indeed travelling at 120km/hr. Sig 1 has been placed just over the SBD of 1975m from sig 3, but a train travelling at 120km/hr actually only needs 1115m to stop.
A) Had sig 1 shown a Green then the driver would not have started braking yet (in reality I expect they'd use the signal as a marker and probably start coasting until some other landmark at which they'd apply brakes to come to a stand- I suspect that in this case they'd learn that sig 2 would be that marker (the braking distance from 120km/hr is a little bit more than its distance from the station but by the time the train had coasted for 1km it would have actually lost significant speed gradually over that distance).
B) With sig 1 showing Double Yellow, the driver is trained to brake significantly even if not travelling at the maximum permissible speed- hence it will be affecting how the train is driven and train 2 will not reproduce the same curve as train 1 but take a bit longer through the section- hence can not claim even this as a sufficiently clear aspect sequence.

You'll note that there is no chance of this train 2 receiving a meaningful Double Yellow at sig 2; it might just be getting ready to improve aspect as the driver passed it. In a sense though, getting Single Yellow at sig 2 does not matter- it isn't telling the driver anything new given that previous aspect was Double Yellow; also now only 1m away from the station and train would always be travelling at a reduced speed by this position if it was going to be stopping.

The important consideration however is whether or not a train 2 getting to signal 1 at the first possible time to get a useful Double Yellow would have had a Green aspect at the signal in rear. To find out you need to extrapolate the diagram- however it doesn't take a genius to deduce that the train is likely to have had a Double Yellow previously and therefore would have been braking due to the presence of train 1 which at that timw would hace just been accelerating out of the station. Therefore the position in which I have drawn train 2 is not tenable; we'd need to timetable it later (i.e. move it up the page a bit more) to at least make sure that it got a Green at that previous signal- I guess that would be by around 30s.
Further away from the station stop, all will be fine' this is evident when you realise that a stoppng train will still be travelling at a good percentage of its normal speed on passing sig 2 and therefore the affect on trains an aspect sequence distance prior would be pretty small and nothing like those affected by the length of time that sig3 or sig2 are held to danger.

So what my diagram has shown is that my postulated train2 which is at a headway time of around 180secs is not tenable but that I'd need to schedule it more like 240 (and that is before I put any perturbation contingency in). Note also that I have put 4-aspect signals at effectively minimum spacing which is definitely overkill- the requirement was only for 360s stopping headway.
I did this:
a) for simplicity with showing on the diagram,
b) to show you how wrong your answer was since you reckoned that you could achieve 147s with 3 aspects!
It wasn't that your calculations were wrong or even that you calculated completely the wrong thing; it was that you didn't see the signalling significance and therefore do the whole job.

So to get into this, then I suggest you do the same sort of thing as I did but with a string of 8, 3-aspect signals at 2km spacing with a platform in the middle of the diagram- hence you will be halving both my distance and time scales I suspect.

Don't worry about drawing a pretty curve or its shape- just plot the two you really need re
i) where the front of the train reaches its constant speed
ii) where the back of the train clears the various overlaps
Remember that the train remains a constant length and travels at the same speed as the front (ignore both the effect of couplings and general relativity!)

I know that you won't have time to do all that in the exam itself, but by doing it you'll appreciate what you are trying to do and therefore be able to distill the essence to present in the exam.


Attached Files
.pdf   Stopping headway, time v distance diagram.pdf (Size: 996.86 KB / Downloads: 156)
PJW
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#6
(05-06-2010, 01:25 AM)PJW Wrote: It wasn't that your calculations were wrong or even that you calculated completely the wrong thing; it was that you didn't see the signalling significance and therefore do the whole job.

So to get into this, then I suggest you do the same sort of thing as I did but with a string of 8, 3-aspect signals at 2km spacing with a platform in the middle of the diagram- hence you will be halving both my distance and time scales I suspect.

Don't worry about drawing a pretty curve or its shape- just plot the two you really need re
i) where the front of the train reaches its constant speed
ii) where the back of the train clears the various overlaps
Remember that the train remains a constant length and travels at the same speed as the front (ignore both the effect of couplings and general relativity!)

I know that you won't have time to do all that in the exam itself, but by doing it you'll appreciate what you are trying to do and therefore be able to distill the essence to present in the exam.

OK, I've spent a bit more time on the stopping calcs and have had a go at drawing the graph for 3-aspect signalling, as per previous my calculations. Apologies in advance that it's a bit messy! Also, had to squash in signal 5, so that part's not quite to scale.

My conclusion was that 3 aspect signalling can meet the stopping headway requirement of 360s. My graphs shows that a headway of 242s can be achieved with this spacing.

Note, the aspect sequence only relates to (is caused by) the first train. I had added these on before I drew the second train. Was going to scribble them out, but concluded it might be less messy to leave them in. Anyways, I've got a better understanding of this now, but need a lot more practice.


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.pdf   2000_Timedistance_graph.pdf (Size: 825.4 KB / Downloads: 102)
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#7
(13-06-2010, 11:05 PM)interesting_signal Wrote: OK, I've spent a bit more time on the stopping calcs and have had a go at drawing the graph for 3-aspect signalling, as per previous my calculations. Apologies in advance that it's a bit messy! Also, had to squash in signal 5, so that part's not quite to scale.

My conclusion was that 3 aspect signalling can meet the stopping headway requirement of 360s. My graphs shows that a headway of 242s can be achieved with this spacing.

Note, the aspect sequence only relates to (is caused by) the first train. I had added these on before I drew the second train. Was going to scribble them out, but concluded it might be less messy to leave them in. Anyways, I've got a better understanding of this now, but need a lot more practice.

Yes, things are certainly coming together.
It is neat enough- there are only two things that I would advise
a) you draw with a rule the "constant speed" to more clearly differentiate this from the "changing speed free-hand" - in particular it loked quite odd for the first train near signal 4!
b) whilst you clearly took the aspect sequence line from the back of the first train clearing 3's overlap to give a G on sig 1, all the other lines seemed to be derived from the FRONT of the train but not necessarily passing an overlap joint- hence it looks confusing and I wasn't quite sure what to make of them, particularly since there seemed to be two different "times" at which the sequence changed to show sig 1@Y, sig2@R about 80 sec apart......

Re the aspect sequence- completely correct that relates to first train- the only thing is that the aspects would of course revert again once the 2nd train passes the relevant signal.
It was fine to leave them just as you did- just note that depicting the sequence as a result of train 1;
for best headway the aim is to place the "curve" for train 2 as low down the paper as possible whilst ensring that its driver gets sufficient sighting time of a signal displaying a sufficiently good aspect that can continue without unnecessary braking; aspect reversions as result of 2nd train not depicted.


I attach a couple of other sketches
a) a similar diagram to yours,
b) one of whch attempts to relate the headway achievable with 3-aspects to that achievable with 4-aspects.

a)We came to slightly different answers re the possible headway with 3-aspects; can you see why?
I think I am right- but tell me of you think otherwise. However getting the right answer isn't what's actually important- it is about demonstrating understanding. In the time pressure of the exam then you won't have time to do it as well as you did. So yes you will need to practice to get your marks-per-minute up, but I am definitely getting the impression that "the penny has dropped".

b) I am NOT suggesting that you do this in the exam, but just to have a look at it to attempt to deepen your understanding and "get an intuitive feel".
I have drawn the signal positions for 4 aspects and assumed that if signalled for 3 aspects these positions would coincide buit that alternate ones would be "missing". I have had to use red and blue pens to depict the different aspect sequence on the same aspect sequence lines which at least allows ready comaprison. There wasn't the space to draw much of the second train's path in (and ideed had I drawn in both the 3-aspect and 4-aspect case it would have become confusing, but the first portion is really the bit we need and it does show the difference in closeness reasonably well).


It is up to you as you'll know better than me how happy you feel, but I think that for now you have probably done enough on headway and ought to be moving on shortly to another exam element.
So why not now start placing your signals on the layout based on the results of your headway calcs and see how it starts working out in practice?


Attached Files
.pdf   3 aspect stopping headway diagram.pdf (Size: 162.99 KB / Downloads: 112)
.pdf   comparison of 3 and 4 aspect stopping headway.pdf (Size: 171.32 KB / Downloads: 120)
PJW
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#8
Thanks for all the feedback.

I'm working on the 2000 Layout now, and should have something to submit to the forum early next.
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#9
Quote:However I have noticed your diagram for the stopping calculations; it is good that you have included one but I note that it suggests that section "e" which is the length of an overlap is sufficient distance for the train to reaccelerate to 33.33m/s, yet the table below it states that the distance for that to occur is 450m.
Also you really cannot use DGR directly for stopping headway; headway is fundamentally about TIME not DISTANCE. For non-stop then these are directly related since speed is CONSTANT; for stopping then the dstance apart of the two trains constantly VARIES.
Hello PJW,

I am under the impression that accelerating to the timetabled speed of 33.33 ms-1 is not as critical as working out the time it takes for the first train to clear the overlap in order that the signals behind to clear for the second following train. I thought this is more critical as this actually limits the number of trains going through that section of the line.

Is my understanding incorrect?

Cheers
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#10
(26-06-2010, 07:30 AM)alexgoei Wrote: However I have noticed your diagram for the stopping calculations; it is good that you have included one but I note that it suggests that section "e" which is the length of an overlap is sufficient distance for the train to reaccelerate to 33.33m/s, yet the table below it states that the distance for that to occur is 450m.
Also you really cannot use DGR directly for stopping headway; headway is fundamentally about TIME not DISTANCE. For non-stop then these are directly related since speed is CONSTANT; for stopping then the dstance apart of the two trains constantly VARIES.

Hello PJW,

I am under the impression that accelerating to the timetabled speed of 33.33 ms-1 is not as critical as working out the time it takes for the first train to clear the overlap in order that the signals behind to clear for the second following train. I thought this is more critical as this actually limits the number of trains going through that section of the line.

Is my understanding incorrect?

Cheers
[/quote]

YES and NO!
You are absolutely correct that the headway along a line is limited by that of the worst section.
So when looking at the aspect sequence on the approach to the station, then the time at which the first train clears the overlap, thus allowing the signal in rear to step up to Y and the one behind that to YY and the one behind that to G (in the 4-aspect case) is indeed the critical factor. If train 2 encounters that signal displaying Green when they are still a reasonable distance prior to it, then the signalling certainly won't be impacting upon how they drive.
However this is just one consideration; the same evaluation in theory needs to be undertaken for each and every signal to check what aspect it would be displaying when a train encounters it; the signal that we have so far checked may not be the worst case.
In reality trains generally do not accelerate at the same rate as that at which they brake and indeed as speed increases their acceleration rate itself drops off vry significantly. The significance of knowing how long it takes for the first train to get back up to full headway speed is significant as one therefore knows that the train behind will not be catching it up any more.
In the IRSE Exam there is basically an oversimplification that the braking = acceleration = constant. You can get a feel what that means by looking at the graphs to recognise which are the critical sections GIVEN THAT ASSUMPTION and therefore "experience" can tell you which section is going to be the limiting one, which is why in the exam you concentrate purely on that. If however we had a question one year with a 0.5m/s/s deceleration rate but only a 0.25m/s/s acceleration rate, I suspect that this may change which is the critical section.
So like so much else, know what short cuts you are making, appreciate the implications of assumptions and explain what and why you are doing to the examiner.
Look at the question carefully. In the case of a "fast following stopping train" which does come up in certain exams, it is in fact when the first train regains headway speed which is significant, since up to that time the train behind (which of course is continuing at its own timetabled speed irrespective of the station) will be catching it up.
Also do be absolutely sure that whenever you attempt to convert a headway time into a headway distance (such as using DGR) that the trains of which the separation is being considered are in fact travelling at the same constant speed. One of the relatively "cheap and dirty" methods for getting an idea of the affect on a station stop is effectively treat it as non-stopping but add in a fudge. This calculates the extra time taken to slow down, dwell and accelerate again up to speed then converts it into what would be an equivalent thoretical distance for a train travelling at constant speed throughout. I can't say I like that method as to me it obfuscates what is really going on and it is all to easy to get confused when doing it- obviously if you do use it for "stopping following stopping trains" then it is acceleration back up tp headway speed that you must use. Using part of one method and part of another is a recipe for disaster!

Has that made it clearer or confused you now completely?
PJW
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