2000 Mainline calcs

[alexgoei]

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

[PJW]

(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.

[alexgoei]

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

[PJW]

(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?

[alexgoei]

Quote:Has that made it clearer or confused you now completely?

Hello PJW,

Thanks for clarifying when to use (a) clearing the overlap in order for signals to clear for the next following train as part of identifying pinch points and (b) non stopping train following stopping train (not stopping following stopping).

The DGR from the Non Stopping Headway computation was used as the starting point for determining signal spacing for computing the stopping headway although this may subsequently change to meet the stopping headway requirements. Is this incorrect?

I have had a chance to compare the workings of two other students on this forum; one by "interesting signals" which is 3 aspect and the other by "douglas" which is 4 aspect. Both after some reworking and your comments give almost identical headways of about 244 secs. I am trying to determine which is operationally superior. Will let you know.

Regards

Alex

[PJW]

(26-06-2010 05:18 PM)alexgoei Wrote:  

Quote:Has that made it clearer or confused you now completely?

The DGR from the Non Stopping Headway computation was used as the starting point for determining signal spacing for computing the stopping headway although this may subsequently change to meet the stopping headway requirements. Is this incorrect?

Certainly need to prove that THE SAME proposed signalling meets BOTH requirements. It may be that you can get a good idea from looking at the respective figures which is the likely to be the more onerous- typically (in questions set in IRSE Exam) a stopping train will lose approx 30s during braking, 30s dwell and approx 30s during acceleration. Hence is the Non-stop requirement is 2.5mins and Stopping is 3.5mins then it is obvious that the latter is dominant; if the Stopping however is 5 mins then it is unlikely to be the important factor.

I'd generally worry about the Non Stop requirement first- after all that would allows you to signal a good proportion of the layout reasonably. Note that you may be asked to calculate the best possible headway that could be achieved, but when placing your signals you would probably aim to do so in a way that was economical- i.e. only just meets the headway requirement. However you would also need to decide how to protect junctions and this may well imply that you need closer signals that the headway itseld demands. Similarly where you have a station / other slow speed area, it is sensible to make the sections in that area shorter if the stopping requirement looks at all "tight" to achieve.

By now you have probably placed in indicative positions little arrows on your track diagram representing the places in which your first guess is that you'd probably put signals. That is the time to do your stopping calculations; I'd work from my embryonic solution, look for the worst vase (there my be several staions, certainly two directions) and prove that the worst one would deliver the requirement. Note that I am not expecting to be asked what is the best stopping headway that could be achieved by signals at minimum spacing? or even what i the value of the headway that your signalling solution achieves?. If the task is just to provide a compliant solution, them my approach would be to work from my solution to check it works. If I find that it doesn't, then I need to rethink my initial signal positions by closing the spacing more or decide to put in a stretch of 4 aspects in what is otherwise 3 aspects. However, provided your first guess is right (that's where the inital comparison of the two headways comes in useful), it is quicker and easier since just doing calculations from "known" positions; also give more realistic result where signals are spaced at greater than minimum spacing as I assume that drivers start braking at the first caution and brake evenly to come to a stand within that entire distance (i.e. at an average deceleration rather less than the max value specified in the question). This confirms to me that I have still met the requirement if I felt I could get away with widely spaced signals; obviously if I assessed that the NS requirement was onerous then even if the rest of the line had signals spaced generally at 130% braking then I'd have closed the spacing around the station to be much closer to the minimum.

Quote:I have had a chance to compare the workings of two other students on this forum; one by "interesting signals" which is 3 aspect and the other by "douglas" which is 4 aspect. Both after some reworking and your comments give almost identical headways of about 244 secs. I am trying to determine which is operationally superior. Will let you know.
Regards
Alex

Look at the comparison graph I did. For simplicity this compares 3 aspects spaced at 2000m with 4 aspects spaced at 1000m. The first caution to instruct the driver to brake falls in the same location (obviously when you think about it!). Hence the difference is that
a) in the 4 aspect case the previous signal is 1000m earlier, whereas i
b)n the 3 aspect case it is 2000m earlier
Therefore the 4 aspects have achieved the 2nd train being 1000m closer.

However suppose the option was more realistically between 3 aspects signals spaced at 1000m and 4 aspects spaced at 1300m.
In the diagram the 3 aspect signal (301) two in rear of platform starter (307) would be at 4000m from it.
The 4 aspect signal (401) three in rear of the platform starter (407) would be at 3900m and hence effectively in the same position (i.e. 403 wouldn't fall at same position as 303 being 600m further away and 401 is 1300m prior to this); therefore giving no significant advantage in terms of distance. Indeed it has probably made things noticeably worse since a driver would brake on seeing 403 at YY, 600m earlier than they would have done when seeing 303 at Y.

Where 4 aspects do score though, is by limiting the impact of a small perturbation of train service. The fact that there are two warnings of the red ansd the signals are closer does mean that if train 1 is slightly late away and train 2 getsa restictive aspect and has to brake, there is a chance to give updated information as soon as the next signal comes into view and, if that signal is by now showing YY, then the driver knows that they can ease off the brakes having already reduced their speed. Conversely in the 3 aspect case they would still have to be braking until the following signal comes into view and, since they have been expecting to stop at it, will be travelling quite slowly. It is things like this that give you "hidden contingency", so I suppose one way of reflecting that numerically is to insist that there is a 10% contingency margin if using 3 aspects but waive that need in the 4 aspect case.