The first thing to say is that this is a model of good explanation with clear and neat presentation. Inevitably when answering a question in exam, time is of the essence and such an effort cannot be expected, but excellent whilst learning.
Just be a bit careful of rounding too early and make sure you do so "on the safe side". Calling 50mph = 22m/s rather than 22.3m/s slightly underestimates and when you go on to calculate the braking distance it gives you 484m whereas if you'd kept the extra digit then it would have given you 497.3m which would then best be rounded up to 500m. Since having enough braking distance is vitally important, make sure you round things up rather than down.
Not sure why you stated L was given as 200m. Perfectly ok to assume 200m as it wasn't stated explicitly, although I note in part c you used 100m as was stated for the stopping trains. I suspect this to be a minor unintentional slip.
The definition of stopping headway in part b might be ok in a low speed metro environment with just Red /Green signals, but there is a problem in using it in a higher speed environment. You are basically claiming that train 2 would be travelling at 50mph when approaching signal 3, even though it remains at red until the train is only 10 seconds from it. Given that you calculate that to brake to a stand would take 44sec (I'd have calculated 44.6 and therefore rounded up to 45sec) then clearly this is dangerous driving; if the signal didn't actually clear then there would certainly be a SPAD and very likely to be a collision with the rear of the train 1 which might still be in the platform, perhaps delayed by signal 5 or perhaps because some passenger is holding a door open.
Broadly your calculations were fine (but actually a driver in the UK should definitely brake immediately when passing a yellow signal even if they know they have more than adequate distance- it is more realistic to assume that they will brake at an average rate less than the maximum and thus utilise the distance they have available), for what you said you were calculating. In reality though, train 1 would not be doing 50mph on the approach anyway, since it would have received a restrictive aspect at signal 1- consider your diagram but drawn slightly earlier: train 1 would have been on signal 5's overlap track and thus signal 3 at red and signal 1 could, at most, be showing yellow. Hence train 2 would have been braking once it had passed signal 1, expecting to stop at signal 3.
You could have said that the driver knows they need 500m to stop and therefore would only need to make the decision to apply brakes when seeing signal 3 at red. This certainly would not comply with the UK's "defensive driving" policy and obviously would require that signal to have a sighting distance exceeding 500m by at least the distance covered during the driver's reaction time. A sighting distance of 725m is more than that usually achieved but not totally impossible, but even if that is your assertion then distance x would start well prior to the signal and the related time t4 would be quite a lot more than your calculation implied!
So the answer you gave isn't actually credible, but you have shown that you are comfortable with the maths and physics of the situation and a reasonable grip of how this relates to signalling headway, so you would still have scored well.
Remember that when trains are at headway separation that the first train must not affect the way that the following train is driven. The way to calculate it therefore is to ensure that train 2 does not get a restrictive aspect on signal 1 caused by train 1 leaving the platform.
A small point is that it would be mopre realistic to assume that a train stopping at signal 5 would almost certainly stop a little way (10-25m) prior to it- otherwise can't see it's aspect when time to depart the station!
Part d. Actually you went to quite a lot of work to get to the same number as part b. If you'd thought about it a bit before launching in to the calculations, it should have been obvious that you were actually calculating the same thing- a train timed from 10sec prior to apssing a signal 1200m from the platform starter and then accelerating to clear its overlap. Actually if you calculated b and d on more realistic assumptions, you would have got different answers.
So a useful exercise; basically sound but some learning points to assist you improve.
You may find looking at this thread for 2000 stopping calculations helpful , particularly the attachments for stopping headway graphs.
Just be a bit careful of rounding too early and make sure you do so "on the safe side". Calling 50mph = 22m/s rather than 22.3m/s slightly underestimates and when you go on to calculate the braking distance it gives you 484m whereas if you'd kept the extra digit then it would have given you 497.3m which would then best be rounded up to 500m. Since having enough braking distance is vitally important, make sure you round things up rather than down.
Not sure why you stated L was given as 200m. Perfectly ok to assume 200m as it wasn't stated explicitly, although I note in part c you used 100m as was stated for the stopping trains. I suspect this to be a minor unintentional slip.
The definition of stopping headway in part b might be ok in a low speed metro environment with just Red /Green signals, but there is a problem in using it in a higher speed environment. You are basically claiming that train 2 would be travelling at 50mph when approaching signal 3, even though it remains at red until the train is only 10 seconds from it. Given that you calculate that to brake to a stand would take 44sec (I'd have calculated 44.6 and therefore rounded up to 45sec) then clearly this is dangerous driving; if the signal didn't actually clear then there would certainly be a SPAD and very likely to be a collision with the rear of the train 1 which might still be in the platform, perhaps delayed by signal 5 or perhaps because some passenger is holding a door open.
Broadly your calculations were fine (but actually a driver in the UK should definitely brake immediately when passing a yellow signal even if they know they have more than adequate distance- it is more realistic to assume that they will brake at an average rate less than the maximum and thus utilise the distance they have available), for what you said you were calculating. In reality though, train 1 would not be doing 50mph on the approach anyway, since it would have received a restrictive aspect at signal 1- consider your diagram but drawn slightly earlier: train 1 would have been on signal 5's overlap track and thus signal 3 at red and signal 1 could, at most, be showing yellow. Hence train 2 would have been braking once it had passed signal 1, expecting to stop at signal 3.
You could have said that the driver knows they need 500m to stop and therefore would only need to make the decision to apply brakes when seeing signal 3 at red. This certainly would not comply with the UK's "defensive driving" policy and obviously would require that signal to have a sighting distance exceeding 500m by at least the distance covered during the driver's reaction time. A sighting distance of 725m is more than that usually achieved but not totally impossible, but even if that is your assertion then distance x would start well prior to the signal and the related time t4 would be quite a lot more than your calculation implied!
So the answer you gave isn't actually credible, but you have shown that you are comfortable with the maths and physics of the situation and a reasonable grip of how this relates to signalling headway, so you would still have scored well.
Remember that when trains are at headway separation that the first train must not affect the way that the following train is driven. The way to calculate it therefore is to ensure that train 2 does not get a restrictive aspect on signal 1 caused by train 1 leaving the platform.
A small point is that it would be mopre realistic to assume that a train stopping at signal 5 would almost certainly stop a little way (10-25m) prior to it- otherwise can't see it's aspect when time to depart the station!
Part d. Actually you went to quite a lot of work to get to the same number as part b. If you'd thought about it a bit before launching in to the calculations, it should have been obvious that you were actually calculating the same thing- a train timed from 10sec prior to apssing a signal 1200m from the platform starter and then accelerating to clear its overlap. Actually if you calculated b and d on more realistic assumptions, you would have got different answers.
So a useful exercise; basically sound but some learning points to assist you improve.
You may find looking at this thread for 2000 stopping calculations helpful , particularly the attachments for stopping headway graphs.
(06-07-2012, 04:34 AM)savitha kandasamy Wrote: Dear Members,
I solved Q9 in Appendix W, Activity 1A from study pack. Kindly review it.
savitha
PJW