You actually responded when I was only half finished! I do tend to "bank" the first part of a long post as I have sometimes lost things in the past.
I have now concluded and post the full response here and deleted my earlier partial response
I am also going to move the post to be further down in the filing structure as the relevant year of calculations so that it is easier for everyone to find in the future
I see you have written out the question (or rather the figures on the layout diagram- did you actually check the precise wording of the actual question paper that year? this said:
Determine theoretically, either by calculation or graphically, appropriate signal spacings for the braking characteristics and the intensity of traffic on offer. All calculations and graphs must be shown.); very helpful to me for responding and others to look at, BUT DON'T DO IN EXAM ITSELF.
Perhaps the ratio 5/18 is regularly used in India for converting km/h to m/s but I feel a little more explanation is needed; to me showing initially as 1000/(60 x 60) is considerably more explanatory, costs little time and hence worth doing.
Fine until half way down sht 2, but then you quote an expression for Headway Distance without derivation or even explanation of the terms. Whereas Newton's laws of motion can be quoted (and here you "went the extra mile" by carefully explaining v,u and a), a specialised equation like this needs explanation.
[type v = u + at into Google and you get lots of relevant hits; type H3d = BD + S+ O + L and see what weird and wonderful things come up!]
It would have helped a bit if when you had stated assumption re Sighting Distance and Overlap lengths previously you had used also the abbreviations S and O there; it would be a more joined-up answer.
You need to show the examiner
a) you know what headway is
b) why constant speed headway can be expressed as a sum of these various distances.
I recommend a diagram for b) supported with a few words of explanation for a)
Otherwise it was good; in particular that you related your answer to the suitable form of signalling to use to achieve the requirement for non-stop headway.
I then find on sht 3 the diagram that I had been expecting earlier and now as an examiner would go back to give you nearly all of the marks I withheld earlier. Not all though for the following reasons:
1. It wasn't where it was most relevant or indeed cross referenced from that ("see later diagram" would have done)
2. The headway formula should have really quoted the signal spacing d rather than the BD; you diagram is good because it shows that you know the spacing must be at least braking distance but may be more than this; your formula is not aligned to this though.
3. there were no words relating to why H3d is drawn as it has been; indeed you do not even state that the open arrow heads represent trains.
Now looking at your stopping headway diagram.
I am a bit bemused by the annotation in terms of t on a one dimensional diagram where it is obvious that the depiction is in terms of distance. I sort of know what you mean, but I wonder whether you do; if the lines for the various t are supposed to be telling me that this is the time value for the front of the train to travel between the two places depiced, then t2 should have no "length" at all!
There is no explanation / justification why you are considering the particular group of 3 signals which you have chosen , rather than for example the section prior to and immediately after the station. Whereas in the non-stop case all signal sections are equal so any ones can be chosen, there is as-symmetry with the train slowing and accelerating . You need to be clear why the thing depicted is the "worst case".
Explanation of t1 and t2 are fine.
You have calculated t3 on the basis of a train from MAX PERMISSIBLE speed rather than the HEADWAY SPEED and also only braking at the very last minute to stop at the station. This last minute braking might (but even so I think they would leave some more "spare") be how a driver would drive if the signal prior to the station had been displaying Green- BUT it wasn't, your diagram shows it at Yellow.
You will find some old text books do take something of this approach, but it is not tenable today with greater awareness of SPADs and indeed the fact that there are On Board Data Recorders and these are interrogated routinely to check that every driver is actually driving as their instructions. Drivers will brake when seeing a caution aspect. In reality they will apply brake to approximately halve their speed, continue at this rate and then brake again to a stand. This is a bit time consuming to calculate, so I think that a reasonable approximation is to assume an even deceleration (i.e. at some rate lower than b) that will cause the train to stop within the distance of the signal section. You know initial speed, you know the distance, so you can calculate the time despite the fact that the rate is unknown.
From your diagram I would have anticipated t4 would have been calculated at the constant headway speed, yet your wording does not accord. Firstly it talks about maximum line speed ((so in this case 120km/h rather than the timetabled speed of the trains of 100km/h). Then it talks of the first cautionary aspect- yet your diagram shows Green. Then it talks about the delay in applying the brake (over an entire signal section!) having seen that cautionary aspect.
When look at the calculations for t4 it seems as if you are first calculating the distance travelled in time t3. (on the incorrect basis as described above).
Then you use the expression DGR which has come from nowhere and claim to be 2 x BD + X. But you diagram made clear that the signals are spaced at d which may be as small as BD but might be more......
You conclude with a clear statement of the Min and max spacings and in this you introduce the concept of a maximum of 150 percent BD which is not explained and then say the maximum is either the value of 1666.5m or d (that by now seems to be redefined as the MAXIMUM spacing that achieves headway) of 1880m, whichever is the greater. But you know that 1880m is greater than 1666.5m so you can be specific to the numbers in this example rather than state the generic rule. Moreover if there are two MAXIMUM constraints, both of which must be satisfied, then the actual constraint is the SMALLER of the two figures!
As an examiner therefore it is clear to me that you haven't quite understood everything. You have certainly got all the pieces that you need and they are all good in their own ways but they are not assembled to give a consistent whole .....
It looks like you are attempting to assemble a kit that can be configured in a number of different ways using alternative parts but have got a bit muddled up between them; hence things aren't quite fitting together correctly and sometimes you have had to force them to bodge it to make it apparently complete, but it doesn't all stand up to close scrutiny.
I suggest you review your answer against my comments and look back at other examples here and the comment made on them. Try to think for yourself WHAT IT ALL MEANS without worrying about the details of the maths- aim to improve the high level understanding first. You will then have no difficulty when it comes to "turning the handle" in any of these calculation questions.
Don't be discouraged; there are many exam candidates who make a worse attempt at the stopping headway than you have posted and you have plenty of time to improve.
I have now concluded and post the full response here and deleted my earlier partial response
I am also going to move the post to be further down in the filing structure as the relevant year of calculations so that it is easier for everyone to find in the future
I see you have written out the question (or rather the figures on the layout diagram- did you actually check the precise wording of the actual question paper that year? this said:
Determine theoretically, either by calculation or graphically, appropriate signal spacings for the braking characteristics and the intensity of traffic on offer. All calculations and graphs must be shown.); very helpful to me for responding and others to look at, BUT DON'T DO IN EXAM ITSELF.
Perhaps the ratio 5/18 is regularly used in India for converting km/h to m/s but I feel a little more explanation is needed; to me showing initially as 1000/(60 x 60) is considerably more explanatory, costs little time and hence worth doing.
Fine until half way down sht 2, but then you quote an expression for Headway Distance without derivation or even explanation of the terms. Whereas Newton's laws of motion can be quoted (and here you "went the extra mile" by carefully explaining v,u and a), a specialised equation like this needs explanation.
[type v = u + at into Google and you get lots of relevant hits; type H3d = BD + S+ O + L and see what weird and wonderful things come up!]
It would have helped a bit if when you had stated assumption re Sighting Distance and Overlap lengths previously you had used also the abbreviations S and O there; it would be a more joined-up answer.
You need to show the examiner
a) you know what headway is
b) why constant speed headway can be expressed as a sum of these various distances.
I recommend a diagram for b) supported with a few words of explanation for a)
Otherwise it was good; in particular that you related your answer to the suitable form of signalling to use to achieve the requirement for non-stop headway.
I then find on sht 3 the diagram that I had been expecting earlier and now as an examiner would go back to give you nearly all of the marks I withheld earlier. Not all though for the following reasons:
1. It wasn't where it was most relevant or indeed cross referenced from that ("see later diagram" would have done)
2. The headway formula should have really quoted the signal spacing d rather than the BD; you diagram is good because it shows that you know the spacing must be at least braking distance but may be more than this; your formula is not aligned to this though.
3. there were no words relating to why H3d is drawn as it has been; indeed you do not even state that the open arrow heads represent trains.
Now looking at your stopping headway diagram.
I am a bit bemused by the annotation in terms of t on a one dimensional diagram where it is obvious that the depiction is in terms of distance. I sort of know what you mean, but I wonder whether you do; if the lines for the various t are supposed to be telling me that this is the time value for the front of the train to travel between the two places depiced, then t2 should have no "length" at all!
There is no explanation / justification why you are considering the particular group of 3 signals which you have chosen , rather than for example the section prior to and immediately after the station. Whereas in the non-stop case all signal sections are equal so any ones can be chosen, there is as-symmetry with the train slowing and accelerating . You need to be clear why the thing depicted is the "worst case".
Explanation of t1 and t2 are fine.
You have calculated t3 on the basis of a train from MAX PERMISSIBLE speed rather than the HEADWAY SPEED and also only braking at the very last minute to stop at the station. This last minute braking might (but even so I think they would leave some more "spare") be how a driver would drive if the signal prior to the station had been displaying Green- BUT it wasn't, your diagram shows it at Yellow.
You will find some old text books do take something of this approach, but it is not tenable today with greater awareness of SPADs and indeed the fact that there are On Board Data Recorders and these are interrogated routinely to check that every driver is actually driving as their instructions. Drivers will brake when seeing a caution aspect. In reality they will apply brake to approximately halve their speed, continue at this rate and then brake again to a stand. This is a bit time consuming to calculate, so I think that a reasonable approximation is to assume an even deceleration (i.e. at some rate lower than b) that will cause the train to stop within the distance of the signal section. You know initial speed, you know the distance, so you can calculate the time despite the fact that the rate is unknown.
From your diagram I would have anticipated t4 would have been calculated at the constant headway speed, yet your wording does not accord. Firstly it talks about maximum line speed ((so in this case 120km/h rather than the timetabled speed of the trains of 100km/h). Then it talks of the first cautionary aspect- yet your diagram shows Green. Then it talks about the delay in applying the brake (over an entire signal section!) having seen that cautionary aspect.
When look at the calculations for t4 it seems as if you are first calculating the distance travelled in time t3. (on the incorrect basis as described above).
Then you use the expression DGR which has come from nowhere and claim to be 2 x BD + X. But you diagram made clear that the signals are spaced at d which may be as small as BD but might be more......
You conclude with a clear statement of the Min and max spacings and in this you introduce the concept of a maximum of 150 percent BD which is not explained and then say the maximum is either the value of 1666.5m or d (that by now seems to be redefined as the MAXIMUM spacing that achieves headway) of 1880m, whichever is the greater. But you know that 1880m is greater than 1666.5m so you can be specific to the numbers in this example rather than state the generic rule. Moreover if there are two MAXIMUM constraints, both of which must be satisfied, then the actual constraint is the SMALLER of the two figures!
As an examiner therefore it is clear to me that you haven't quite understood everything. You have certainly got all the pieces that you need and they are all good in their own ways but they are not assembled to give a consistent whole .....
It looks like you are attempting to assemble a kit that can be configured in a number of different ways using alternative parts but have got a bit muddled up between them; hence things aren't quite fitting together correctly and sometimes you have had to force them to bodge it to make it apparently complete, but it doesn't all stand up to close scrutiny.
I suggest you review your answer against my comments and look back at other examples here and the comment made on them. Try to think for yourself WHAT IT ALL MEANS without worrying about the details of the maths- aim to improve the high level understanding first. You will then have no difficulty when it comes to "turning the handle" in any of these calculation questions.
Don't be discouraged; there are many exam candidates who make a worse attempt at the stopping headway than you have posted and you have plenty of time to improve.
(11-03-2012, 10:26 AM)NJK Wrote: Dear Sir,
Thank you very much for your valuable comments.
Regards,
NJK
PJW