another try at double line layout

[onestrangeday]

Hi PJW:

Thank you for taking time to review my attempt and your suggestions are very valuable for me for learning. I have attached my revised version for headway calculations of Q2-4 and the layout, please have a look to see whether I am on the track or not.

I would like to ask more questions if it is ok:

1. I think I need to understand the question clearly before I can put on signals on the layout especially to meet the operational requirement.

So my question is On the question it described “Freight - Line A to Line B reversing at Station C, running around via crossovers at Station A and Station C - 1 per night (0100-0600)”.

My interpretation is that the freight train first travel from line A and stop at station C. After that it reverses from the loop in station C and make a cross to the lower line using the crossover at station C and return back to Station A. When it arrives at station A, the freight train makes another cross to the upper line using the crossover at station A.

Or does it depends on how you comprehend the question, I mean the description ?? or may be I pay too much concentration on this ?

2. You have mentioned the following
“You should also have considered the maximum spacing constraint dictated by the degree of excess braking considered acceptable (as above) in case it is more onerous than that given by headway consideration; in this case it is not the constraint but a statement to that effect should have been included.”

Do you mean that when design the signalling layout, in real situation the maximum spacing will be shorter than the theoretical value because of excess braking taken as a major factor ?

3. The result I’ve calculated for Question 4 is differ to what you have presumed (the distance is greater than 3500m), can you check my result ?



Thanks

Q2.
Should justify your statement why non-stop headway requirement of 3 mins is more onerous than 6 mins stopping headway. Only needs to be brief and consider the additional time penalty that a station stop imposes (i.e. time lost decelerating, time lost dwelling, time lost accelerating back to the through headway speed).

Always round up braking distances; it was sensible to choose a nice round number such as 2000m for a nominal signal spacing. Firstly it is always good to have a bit of margin over the bare minimum, so there is “somewhere to go” is placing a particular signal in a certain position is not possible / practicable / sensible. Secondly it makes your life much easier in exam conditions- quicker and less prone to error.

Good statement of assumptions and clear presentation.

Having shown that headway requirement met by 3 aspects, no need to consider 4 aspects on those grounds. If you end up needing to put 4 aspects for signal positioning on the layout reasons, then self evident that headway requirement will be met so do not even have to mention this.

In this instance I do not believe that you needed to repeat calculations for freight trains; there is only one train per hour. In this example we already know that the passenger service needs signals about 2km apart, so the only stretch of line where the freight headway could be the determining factor is on the line from A to the junction. With a max speed of 100km/h, even if we consider the need to slow over various junctions etc., it must be reasonable to assume that it will average no less than 50km/h, so the headway signals could be very nearly that far apart. In the UK major towns are rarely further apart than that, so obviously it just isn’t going to be the thing that determines how close signals need to be.
Certainly if there had been more freight trains then it could have been a factor. The very important thing of which to be aware is that in reality the freight braking rate is often much less than that of passenger trains; it is not an issue given the numbers given in this question, but otherwise it could be that the freight braking distance from 100km/h might exceed the passenger braking distance from 160km/h and in such circumstances would be the determining factor for the minimum signal spacing for the line.

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Q3. You should always show the derivation of the formulae used (other than standard ones such as Newton’s laws of motion), define the various abbreviations / quantities involved and explain (oftn a diagram is helpful). This comment applies actually to Q2; obviously if done there then could just have quoted subsequently.
For example, you have never actually stated that St means Sighting Time etc.

In explanation you said that “For 3 aspect signalling, the distance d equals service braking distance D…..”; this is only true for signals at MINIMUM spacing; they can be more widely spaced than this (often as much as 33% extra, sometimes 50% extra).

The equation for DMAX could do with some further explanation; you need to state that it is the headway time specification Ht which gives the constraint (the fact that it immediately follows the text re the 3 aspect signals at minimum spacing means that the logic of the presentation isn’t easy to follow).

You should also have considered the maximum spacing constraint dictated by the degree of excess braking considered acceptable (as above) in case it is more onerous than that given by headway consideration; in this case it is not the constraint but a statement to that effect should have been included.

Only a minor issue but you should ROUND DOWN the maximum spacing constraint; I’d have been tempted to quote the range as 2000m – 3500m.

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Q4.
For this part of the question you seem to need to make a choice whether to “start with a clean sheet of paper” or adopt the signal positions as drawn in response to Q1. The way I read it is that you should ignore the proposed position of signal C27 (even though I think you were right to place where you did and worry about the aspect sequence separately). The answer will then be telling you where you COULD place C27 on purely headway and braking grounds, rather than where you SHOULD place C27 when other considerations are taken into account (which is where you have placed it).

Hence I would initially assume signals 2000m on the approach and 2000m beyond the platform starter and work out what headway would be achieved. Assuming that this is less than the required 6 minutes than could determine how much “margin” existed in terms of spare time, then convert this into a distance at the headway speed. This will then tell you by how much the signal spacing could be increased and yet still satisfy the 6 minute constraint. If this figure is greater than 3500m then clearly the stopping headway is less onerous than the non-stop headway; however I would presume that this is not the case and some lower maximum limit would need to apply and this would be the answer to Q4.

In order to calculate the headway between two trains both of which stop at station C, need to work out the time difference between the trains passing the same place. If we choose the place where the front of the train stops at the station platform then it is the easiest to imagine and describe (obviously the time difference at any place is the same).
Start the clock as the train comes to rest.

1. There is then a period of station dwell during which the doors are opened, passengers get out and in, the doors close and the brakes are released prior to the train accelerating. The station dwell time is given as 30 seconds.

2. There is then the time during which the train is leaving the station and travelling sufficiently far that the rear of the train clears the overlap beyond the platform starting signal. Use Newton’s Laws to determine how long the train takes to travel a distance equal to its length L, the overlap length O plus any distance between the front of the train when stationary and the signal (25m is a good assumption). During this time the train will be constantly accelerating.

3. Once this has occurred the signal in rear of the station clears from red to yellow; also at this time the signal further in rear change from yellow to green (actually this all may take several seconds depending whether the track circuits are deliberately slow acting and on the technology used- a relay based system with normal acting tracks may take 0.5 second and therefore really negligible, but an electronic interlocking with slow to pick tracks may well take in excess of 5 seconds so adding this in as a factor is a reasonable assumption.

4. At the minimum headway the following train would by now just be getting to the sighting point of the outer signal; had it been closer then its driver would have seen the restrictive yellow aspect and may have started to brake. The time which has to be calculated is how long it will be before that train then reaches the station and stops in the same place as the earlier train at which time the clock is stopped and will be showing the sum of the times described in 1+2+3+4. The time calculation for 4 is itself composed of several different times, the one to be calculated first is that to stop the train from the headway speed and the associated distance for this to occur. This distance will clearly be much smaller than the train has left to travel and there is a need to state some assumptions re how the deceleration would occur. Given that the outer signal is green then the train has no need to slow, so the length of the sighting distance and the inter-signal spacing will be covered at headway speed. Indeed provided the next signal had become green by the time the train encounters it then it too may be passed at headways speed- even if it is spaced at minimum braking this would be for the maximum permissible speed which is greater than that which the train is travelling. However the driver is unlikely to leave the braking until the very last possible minute, so it may be reasonable to suggest that the braking would start when passing it and continue until the train moving reasonably slowly (say 15m/s) and then the final brake application made to stop in the correct place Hence the difference between the signal spacing and that distance actually needed to stop is calculated; this is then converted into a time based on the 15m/s running. i.e. add
a) the time taken to travel from the sighting point of the outer signal to the inner signal
b) the time to brake to a stand from headway speed
c) the time for the slow speed running within the overall braking activity.