I have been sent privately by a member of this forum who I believe does not wish to be identified their answer to this question. Having given some limited feedback I decided the best way of doing was to re-do their answer (which was definitely on the right lines but VERY hard to follow- not helped by a few silly mistakes and the fact that most of the calcs were performed on almost scrap paper and not clearly linked to the main flow).
Instead of emailing my response directly to them, I feel it is best to post here so that others can look and comment. I did try to follow their assumptions and overall methodology as far as I could to make it easier for them to compare; hence recognise that I may have made some slightly different assumption for example in the layout (I have reflected this in the text- as you would have to if, as often happens, things only really get apparent when you are well into your answer). I did however change some of the assumptions if they seemed fundamentally wrong in a way that would lead me down a very wrong path.
Certainly not an easy question to do in the time available. Difficult particularly as not really sure what constraints there are on the optimum posiions of the points. Scenario suggests that the P-Way and signalling and station already exist, so taking about optimising point positions does seem a bit strange- if the points don't already exist then why is their speed fixed?
You just have not go time to consider the situation where the constraint is the station itself (my option 2 as I think that was what the examiners were after) or whether this is effectively conflict free and the constraint the approach release of the platform admission signal and the impact upon the block sections on its approach (my option 3 that didn't discuss in detail but that I think is the limiting factor IF you could actually optimise the position of the points).
Looking at the mark allocation it is clear that DESCRIPTION and EXPLANATION is far more important than the calculations themselves. I think therefore separating the production of the various numbers is a good idea (less disturbance to the flow of the argument) but have attempted to cross-reference to my "working scrap paper" in a way that I hope is clearer to the reader than the answer I got to look at (an attempt had been made but only served to confuse me!). This is a warning for those who are good at maths but don't actually understand Signalling Principles- these headway questions may not be such a good choice as they may at first appear, they are not an alternative to knowing your Principles.
So I hope the attached is a reasonable answer to the question but certainly not as complete as I would like. I really didn't do enough re the optimisation of the point positions (and indeed the layout given by my student wasn't exactly where I would have started from).
Not done any form of checking and you'll notice that I took a bit of a short cut by assuming that when using platforms alternately when it obviously isn't; the speed for trains using the Down Main is not constrained by the track (nor unless ROLs are provided neither is there approach release imposed on the junction signal) whereas a train routed via the Up Main would take longer arriving and departing due to approach release and the turnout speeds. I did some calculation of the increased time for departure but then failed to correctly incorporate at the relevant place so I later "bodged" the summary answer (as would have to do in the exam, explaining why).
If you look carefully you'll probably find some other mistakes and oversights but I hope it illustrates the general approach of what I think the examiners would want; feel free to post comments and corrections.
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In fact the thing that occurs to me once I have finished is that the figure obtained of 11 minutes for 2 trains following each other along the Down Main needs some interpretation. If we do a quick and dirty calculation:
train braking from max speed typically takes say a bit under 45 secs within the one block section,
dwell 120sec,
acceleration 55 sec, basically by the end of the O/L of the signal beyond the station
so say the first guess is 220sec to cover 2 block sections. Add in say 10 secs sighting and 10 secs for train to travel own length and we are up to 240 sec. Another train will get a non-restrictive aspect to enter station approx 4 minutes after the first one passed it, so even putting 20% contingency that is 12 trains per hour. Hence it looks like the original assumption that train would be starting from rest at platform admission signal may not have been the right one for the 1 platform case; at least theoretically if everything keeps perfectly to schedule then get more trains through than if starting with assumption that station is definitely the constraint. I think that there is an argument to be made that as soon as there is perturbation (like a longer dwell train because of someone unloading a bike for example!) the train service is likely to get into a "stop and wait for platform" mode. However I haven't quite convinced myself that my numbers are right; is there a fallacy or arithmetical slip somewhere?
PJW
Instead of emailing my response directly to them, I feel it is best to post here so that others can look and comment. I did try to follow their assumptions and overall methodology as far as I could to make it easier for them to compare; hence recognise that I may have made some slightly different assumption for example in the layout (I have reflected this in the text- as you would have to if, as often happens, things only really get apparent when you are well into your answer). I did however change some of the assumptions if they seemed fundamentally wrong in a way that would lead me down a very wrong path.
Certainly not an easy question to do in the time available. Difficult particularly as not really sure what constraints there are on the optimum posiions of the points. Scenario suggests that the P-Way and signalling and station already exist, so taking about optimising point positions does seem a bit strange- if the points don't already exist then why is their speed fixed?
You just have not go time to consider the situation where the constraint is the station itself (my option 2 as I think that was what the examiners were after) or whether this is effectively conflict free and the constraint the approach release of the platform admission signal and the impact upon the block sections on its approach (my option 3 that didn't discuss in detail but that I think is the limiting factor IF you could actually optimise the position of the points).
Looking at the mark allocation it is clear that DESCRIPTION and EXPLANATION is far more important than the calculations themselves. I think therefore separating the production of the various numbers is a good idea (less disturbance to the flow of the argument) but have attempted to cross-reference to my "working scrap paper" in a way that I hope is clearer to the reader than the answer I got to look at (an attempt had been made but only served to confuse me!). This is a warning for those who are good at maths but don't actually understand Signalling Principles- these headway questions may not be such a good choice as they may at first appear, they are not an alternative to knowing your Principles.
So I hope the attached is a reasonable answer to the question but certainly not as complete as I would like. I really didn't do enough re the optimisation of the point positions (and indeed the layout given by my student wasn't exactly where I would have started from).
Not done any form of checking and you'll notice that I took a bit of a short cut by assuming that when using platforms alternately when it obviously isn't; the speed for trains using the Down Main is not constrained by the track (nor unless ROLs are provided neither is there approach release imposed on the junction signal) whereas a train routed via the Up Main would take longer arriving and departing due to approach release and the turnout speeds. I did some calculation of the increased time for departure but then failed to correctly incorporate at the relevant place so I later "bodged" the summary answer (as would have to do in the exam, explaining why).
If you look carefully you'll probably find some other mistakes and oversights but I hope it illustrates the general approach of what I think the examiners would want; feel free to post comments and corrections.
-----------------------------------------------------------------
In fact the thing that occurs to me once I have finished is that the figure obtained of 11 minutes for 2 trains following each other along the Down Main needs some interpretation. If we do a quick and dirty calculation:
train braking from max speed typically takes say a bit under 45 secs within the one block section,
dwell 120sec,
acceleration 55 sec, basically by the end of the O/L of the signal beyond the station
so say the first guess is 220sec to cover 2 block sections. Add in say 10 secs sighting and 10 secs for train to travel own length and we are up to 240 sec. Another train will get a non-restrictive aspect to enter station approx 4 minutes after the first one passed it, so even putting 20% contingency that is 12 trains per hour. Hence it looks like the original assumption that train would be starting from rest at platform admission signal may not have been the right one for the 1 platform case; at least theoretically if everything keeps perfectly to schedule then get more trains through than if starting with assumption that station is definitely the constraint. I think that there is an argument to be made that as soon as there is perturbation (like a longer dwell train because of someone unloading a bike for example!) the train service is likely to get into a "stop and wait for platform" mode. However I haven't quite convinced myself that my numbers are right; is there a fallacy or arithmetical slip somewhere?
PJW