Prapoorna,
Actually I did notice your question and thought I had answered. However I will now try to do so more clearly.
NO and NOT EXACTLY.
First you need to recognise that there are two different situations:
a) "stopping headway for following stopping trains"- all trains do the same thing, they all stop at the station as a regular service pattern;
b "fast train following stopping train"- there is a stopping train within the stream of non-stopping train and hence, because of its lower speed through the relevant section of line, uses up more than a single train path as given by the non-stop headway calculations.
For situation a) SERVICE OF STOPPING TRAINS
1, Consider train1 about to leave the station; work out how long it will take to clear the overlap of the station staring signal (almost certainly it will continue to be accelerating here as not yet moving at the headway speed, but this is not important)
2. Work out how close to train1 the driver of train2 can be without having to change their driving as a result of seeing a restrictive aspect caused by train1. This will depend on whether there is 3-aspect or 4-aspect signalling, also assumptions about how drivers are trained to drive. A driver due to stop at the station would have to brake for it regardless of any aspect displayed at a signal, but is likely to leave to almost the last moment and therefore utilise their max braking rate. However if they think the platform starter is at red they would be more cautious and since in general signals are spaced at more than braking and also the headway speed may be lower than the max permissible speed the train would not need all of a 3-aspect signal section to stop if the only concern was the station stop, yet if the outer signal were yellow then the driver would brake at it (or even the sighting distance prior to it) and use the whole available length to slow down; thus the actual brake rate would be less than the maximum. Hence I suggest using the distance from the sighting point of the first caution to the station and assume uniform braking over that distance from the initial headway speed to a stand. Work out the time taken to stop over that length.
3. Add the station dwell time, after which train2 is ready to start accelerating. that is a complete cycle as train2 now needs to clear the overlap before the driving of train3 is too adversely affected.
This gives the "succession of stopping trains" headway.
For situation b) STOPPING TRAIN AMONGST NON-STOP SERVICE"
1. Work out how long it takes a train to slow down from its maximum headway speed at its declared maximum brake rate, then dwell in the station and then re-accelerate up to the original headway speed again. [Note this has nothing to do with clearing the overlap]
2. Work out how long a train that WAS NOT STOPPING would have taken to travel the same distance. Clearly to work this out you need to know from your calculations in 1 how far the train travelled during its acceleration and re-acceleration time.
3. Now calculate the difference between time 1 and time 2; this tell you how much ADDITIONAL time is needed because of the train needing to call at the station.
4. it is the time in 3 which you add to the non-stop headway time. This tels you how much "head-start" time train3 (a non stop) needs to allow train2 (a stopping service) in order that it does not catch it up too much. What we want is that once train 2 has lost the time because of its stop, it is then running just sufficiently ahead of train3 that train3 does not encounter restrictive aspects- we have two non-stop trains again but we needed to allow a bigger gap between them initially so that we still had enough gap left after the stopping train had experienced the associated delay.
Hence I think your problem is that you have taken bits of a) and bits of b), haven't realised they are different an muddled them. Hence you "have your wires crossed" and need to untangle. Separate out the two different things.
When you are doing the exam be very careful to read the question to find out what they are asking. The 2012 paper was very unusual and the examiners may try a new twist for 2013.
It will always be testing
i) Your knowledge of aspect sequence and headway
ii) Your knowledge of Newton's equations of motion
but the precise question may vary. If you actually understand the concepts, you'll be able to cope, but do not try to learn standard answers as they may well be inappropriate to the question encountered
Hope this helps a bit
Actually I did notice your question and thought I had answered. However I will now try to do so more clearly.
NO and NOT EXACTLY.
First you need to recognise that there are two different situations:
a) "stopping headway for following stopping trains"- all trains do the same thing, they all stop at the station as a regular service pattern;
b "fast train following stopping train"- there is a stopping train within the stream of non-stopping train and hence, because of its lower speed through the relevant section of line, uses up more than a single train path as given by the non-stop headway calculations.
For situation a) SERVICE OF STOPPING TRAINS
1, Consider train1 about to leave the station; work out how long it will take to clear the overlap of the station staring signal (almost certainly it will continue to be accelerating here as not yet moving at the headway speed, but this is not important)
2. Work out how close to train1 the driver of train2 can be without having to change their driving as a result of seeing a restrictive aspect caused by train1. This will depend on whether there is 3-aspect or 4-aspect signalling, also assumptions about how drivers are trained to drive. A driver due to stop at the station would have to brake for it regardless of any aspect displayed at a signal, but is likely to leave to almost the last moment and therefore utilise their max braking rate. However if they think the platform starter is at red they would be more cautious and since in general signals are spaced at more than braking and also the headway speed may be lower than the max permissible speed the train would not need all of a 3-aspect signal section to stop if the only concern was the station stop, yet if the outer signal were yellow then the driver would brake at it (or even the sighting distance prior to it) and use the whole available length to slow down; thus the actual brake rate would be less than the maximum. Hence I suggest using the distance from the sighting point of the first caution to the station and assume uniform braking over that distance from the initial headway speed to a stand. Work out the time taken to stop over that length.
3. Add the station dwell time, after which train2 is ready to start accelerating. that is a complete cycle as train2 now needs to clear the overlap before the driving of train3 is too adversely affected.
This gives the "succession of stopping trains" headway.
For situation b) STOPPING TRAIN AMONGST NON-STOP SERVICE"
1. Work out how long it takes a train to slow down from its maximum headway speed at its declared maximum brake rate, then dwell in the station and then re-accelerate up to the original headway speed again. [Note this has nothing to do with clearing the overlap]
2. Work out how long a train that WAS NOT STOPPING would have taken to travel the same distance. Clearly to work this out you need to know from your calculations in 1 how far the train travelled during its acceleration and re-acceleration time.
3. Now calculate the difference between time 1 and time 2; this tell you how much ADDITIONAL time is needed because of the train needing to call at the station.
4. it is the time in 3 which you add to the non-stop headway time. This tels you how much "head-start" time train3 (a non stop) needs to allow train2 (a stopping service) in order that it does not catch it up too much. What we want is that once train 2 has lost the time because of its stop, it is then running just sufficiently ahead of train3 that train3 does not encounter restrictive aspects- we have two non-stop trains again but we needed to allow a bigger gap between them initially so that we still had enough gap left after the stopping train had experienced the associated delay.
Hence I think your problem is that you have taken bits of a) and bits of b), haven't realised they are different an muddled them. Hence you "have your wires crossed" and need to untangle. Separate out the two different things.
When you are doing the exam be very careful to read the question to find out what they are asking. The 2012 paper was very unusual and the examiners may try a new twist for 2013.
It will always be testing
i) Your knowledge of aspect sequence and headway
ii) Your knowledge of Newton's equations of motion
but the precise question may vary. If you actually understand the concepts, you'll be able to cope, but do not try to learn standard answers as they may well be inappropriate to the question encountered
Hope this helps a bit
(02-09-2013, 05:51 AM)prpaoorna Wrote: It would be helpful for us if you answer my earlier question in this thread that you haven't noticed.
"While doing stopping headway calculations, do we need to add non stopping headway time to the stopping headway time?"
Thanks & Regards,
Prapoorna N
PJW