There are some step-by-step examples included in the Study Pack on the DVD.
Also there are some pretty good attempts on this forum, for example
this one which is certainly good for the non-stop headway. Then, if you follow the thread down, there is a detailed demonstration of stopping headway is included.
HOWEVER BEWARE.
It is not a question of finding a good example and memorising how to reproduce in the exam. The actual question asked does change subtly from one year's paper to another. Hence you do need to understand, so that you can interpret correctly.
You asked for simplified; I do not see how I can do this and still give enough detail. As an overview though for a TYPICAL question:
1/ Calculate using Newton's Laws of motion the distance to decelerate to a stand from the MAXIMUM PERMISSIBLE speed. This gives MINIMUM SPACING for 3 aspect signals.
2/ Take the required timetable headway time and assess whether there is a need to deduct a contingency allowance from it (based on level of traffic) in order to determine the signalling design headway. Suggest that a figure of 5% - 10% is often appropriate for the mainline layout.
3/ Convert the headway distance to headway time for a train travelling at uniform speed for which the non-stop headway is defined.
4/ Draw a diagram to show how this headway distance relates to signal spacing, overlap length, train length and sighting distance.
From here on it does very much depend on wording of the question.
5/ State assumption re extent of overbraking considered acceptable to address the risk that a driver may become accustomed to signals spaced widely and thus defers braking, then encountering a section which is tightly braked. A figure of 133% is often reasonable. From this work out what this constrains the MAXIMUM spacing of the signals to be.
6/ You now have a MIN/MAX range for signals based on safety braking considerations; also a MAX limit dictated by operability to achieve the required headway. Determine the more restrictive MAX constraint and then you have the permissible range of signal spacings.
7/ If there is an adequate range between MIN and MAX that in practice you ought to be able to place signals in places which
a) respect these values AND
b) fall in sensible places on the layout (i.e. correctly signal junctions and does not force signals in stupid places with respect to stations or standage needs)
then you have your 3 aspect solution which will work.
Note though if the headway need to not onerous (i.e. the period between trains is quite long), this would over-signal and therefore not be economical. In this case, decide on isolated 3 aspect signalling with the red/green signals spaced to suit headway requirement and each having its yellow/green signal on its approach separated by a distance based on the braking distance (I'd aim to place at approximately 105% but choose a nice round number easy to measure)
8/ If you find that the MIN is very close to the MAX then there is so little flexibility where signals can be placed that in reality it isn't practicable solution; see 9.
9/ If you find that the MIN is actually bigger than the MAX then clearly 3 aspects are not tenable. Therefore need to select 4 aspects because this gives two signal sections over which to brake.
10/ Might then need to determine a suitable spacing for the 4 aspects; to keep solution as economical as possible then these would need to be as widely spaced as they can be whilst satisfying their other constraints.
The question may sometimes require the student to determine what is the headway for signals placed at minimum spacing, sometimes to select an optimum spacing which economically just achieves the headway and satisfies the braking constraints, sometimes to determine the headway that would result from signals at their maximum spacing permitted by braking constraints etc.
Then there is the issue of the stopping headway calculations. Again the wording does change, so precisely what you do will need to vary accordingly.
I would often take the spacing determined as suitable for the non-stopping and use this to derive the consequential stopping headway; generally not asked to determine what the value actually is but only that
it achieves a specific value.
However do not try to run before you can walk; you need to be confident about the non-stop scenario first.
Also there are some pretty good attempts on this forum, for example
this one which is certainly good for the non-stop headway. Then, if you follow the thread down, there is a detailed demonstration of stopping headway is included.
HOWEVER BEWARE.
It is not a question of finding a good example and memorising how to reproduce in the exam. The actual question asked does change subtly from one year's paper to another. Hence you do need to understand, so that you can interpret correctly.
You asked for simplified; I do not see how I can do this and still give enough detail. As an overview though for a TYPICAL question:
1/ Calculate using Newton's Laws of motion the distance to decelerate to a stand from the MAXIMUM PERMISSIBLE speed. This gives MINIMUM SPACING for 3 aspect signals.
2/ Take the required timetable headway time and assess whether there is a need to deduct a contingency allowance from it (based on level of traffic) in order to determine the signalling design headway. Suggest that a figure of 5% - 10% is often appropriate for the mainline layout.
3/ Convert the headway distance to headway time for a train travelling at uniform speed for which the non-stop headway is defined.
4/ Draw a diagram to show how this headway distance relates to signal spacing, overlap length, train length and sighting distance.
From here on it does very much depend on wording of the question.
5/ State assumption re extent of overbraking considered acceptable to address the risk that a driver may become accustomed to signals spaced widely and thus defers braking, then encountering a section which is tightly braked. A figure of 133% is often reasonable. From this work out what this constrains the MAXIMUM spacing of the signals to be.
6/ You now have a MIN/MAX range for signals based on safety braking considerations; also a MAX limit dictated by operability to achieve the required headway. Determine the more restrictive MAX constraint and then you have the permissible range of signal spacings.
7/ If there is an adequate range between MIN and MAX that in practice you ought to be able to place signals in places which
a) respect these values AND
b) fall in sensible places on the layout (i.e. correctly signal junctions and does not force signals in stupid places with respect to stations or standage needs)
then you have your 3 aspect solution which will work.
Note though if the headway need to not onerous (i.e. the period between trains is quite long), this would over-signal and therefore not be economical. In this case, decide on isolated 3 aspect signalling with the red/green signals spaced to suit headway requirement and each having its yellow/green signal on its approach separated by a distance based on the braking distance (I'd aim to place at approximately 105% but choose a nice round number easy to measure)
8/ If you find that the MIN is very close to the MAX then there is so little flexibility where signals can be placed that in reality it isn't practicable solution; see 9.
9/ If you find that the MIN is actually bigger than the MAX then clearly 3 aspects are not tenable. Therefore need to select 4 aspects because this gives two signal sections over which to brake.
10/ Might then need to determine a suitable spacing for the 4 aspects; to keep solution as economical as possible then these would need to be as widely spaced as they can be whilst satisfying their other constraints.
The question may sometimes require the student to determine what is the headway for signals placed at minimum spacing, sometimes to select an optimum spacing which economically just achieves the headway and satisfies the braking constraints, sometimes to determine the headway that would result from signals at their maximum spacing permitted by braking constraints etc.
Then there is the issue of the stopping headway calculations. Again the wording does change, so precisely what you do will need to vary accordingly.
I would often take the spacing determined as suitable for the non-stopping and use this to derive the consequential stopping headway; generally not asked to determine what the value actually is but only that
it achieves a specific value.
However do not try to run before you can walk; you need to be confident about the non-stop scenario first.
(24-08-2011, 01:39 PM)ganeshg10 Wrote: thanks for the reply,
can you give me simplified method(formulas) to find the aspect selection,headway & breaking distance calculation.
if you can give step by step answers,it will be good for me to understand.
PJW