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App W , Activity 1A , Q9 from study pack
#1
Dear Members,

I solved Q9 in Appendix W, Activity 1A from study pack. Kindly review it.


savitha


Attached Files
.docx   App W Activity 1A Q9 of study pack.docx (Size: 11.68 KB / Downloads: 96)
.pdf   App W , Activity 1A Ans 9 of study pack.pdf (Size: 862.05 KB / Downloads: 124)
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#2
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.

(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
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#3
hi,

I made modifications to the answer & tried to understand the concept by plotting in graph. Kindly review it.

savitha


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.pdf   Ans 9 - rework.pdf (Size: 1.32 MB / Downloads: 62)
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#4
Broadly this looks ok and certainly you have got the answers to be different from each other this time which is good!
Hopefully drawing the graphs have strengthened your understanding.

The manner in which you have calculated t2 however does basically say:
a) the distance over which the train is given warning to brake is 2400m [TRUE]
b) the driver knows they only need 500m to come to a stand at their maximum service braking rate [TRUE]
c) therefore the driver will not act upon the cautionary aspects and will carry on at the norma speed regardless until the very lst instant when they will apply the brakes and come to a stand at the signal [NOT TRUE].

In reality drivers will always be more cautious than that and nowadays they are tauht that they must brake at cautionary aspects, significantly reduce speed, then coast buntil they get closer to their stopping place and then brake again but not at their maximum rate so that they have "something in hand" so as to be certain that even in poor conditions that they will indeed be able to stop by the required place.

The easiest way to make some approximation to this braking profile is to say instead:
a) the distance over which the train is given warning to brake is 2400m [TRUE]
b) the driver knows they only need 500m to come to a stand at their maximum service braking rate [TRUE],
c) the driver will utilise all the 2400m to stop by selecting a lower average braking rate than their train would be capable and hence have a more gentle reduction in speed (and is defensive in that this technique places lower reliance on friction between wheel and rail so less liable to slide in poor adhesion conditions, also if the driver has misjudged his position slightly or weight of the train and runs the risk of not being able to stop in time, can always select a higher brake rate and thus recover the situation- if they left braking to what they judged the last possibloe instant but had misjudged then they would have no escape and they would SPAD!)
Therefore you can calculate the time taken (t1+t2) by saying that d =2400, a= unknown, v=22.35m/s and u=0.


Another small thing is that t6 is actually the ADDITIONAL time after having cleared the overlap in order to regain full speed. Actually you didn't need to calculate t5 and t6 separately (as you'll see you actually deducted the value for t5 when calculating t6 but then add t5 to t6 in your end equation!). Also what you calculated isn't quite the stopping headway- you have calculated the time taken for a train to travel the distance commencing at the sighting point of the relevant signal approaching the station stop until regaining normal speed afterwards. What you need to do is compare this to the time the train would have taken to trravel the same distance if it had not been stopping to calculate how much EXTRA time is needed.

This is the time that a stopping train loses. To calculate the initial separation between trains needed prior to the stop in order that they are still separated by the minimum non-stop hyeadway after the station then you must add your calculated figure to the non-stop headway figure.
This is the "fast train following stopping train" headway.

If however you are wanting to calculate the "stopping train following another stopping train" headway, then you do not need to worry about the place at which the train has reaccelerated to its normal speed but just look at the separation in time between a train being at the sighting point for the restrictive signal, slowing down, dwelling, reaccelerating again to clear the overlap which then permits the following train to be driven in the same manner.

You actually got very close to obtaining the answe and certainly in the exam would have got a lot of credit for your explanation and working out, but you didn't quite calculate what you were intending to.



(17-07-2012, 05:23 AM)savitha kandasamy Wrote: hi,

I made modifications to the answer & tried to understand the concept by plotting in graph. Kindly review it.

savitha
PJW
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