(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
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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