(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.