In principle OK, but don't quite agree.
The headway speed is 140km/h which, to your level of approximation, is 40m/s and the braking distance therefore under 1600m rather than the 2000m shown which reflects braking from maximum permissible speed.
Since you were only interested in the differential time between the 2 trains then the consideration of the Sighting Distance SD and the Clearance Distance CD are irrelevant since they are the same in each case. Indeed introducing these just complicates things, particularly as the reference to train length and overlap in an area unrelated to the platform starting signal displays a certain level of confusion.
When on page 7 you state "a non-stopping train would have travelled in the same time 4600m" you do not mean that! Rather you ought to say that "a non stopping train would cover the same 4600m in a shorter time", as indeed you go on to calculate to be 115 seconds compared to the 205 seconds.
Obviously since you have used 2000m rather than 1600m then your relative times of the two trains are out; you have actually made the non-stop one go a distance of 4000m in the time that you claim the stopping train travels 4000m yet the time calculated is consistent with real 3200m.
For the stopping, I agree BDt and ADt are 80 sec; since constant acceleration / deceleration, then the average speed is 20m/s. The non-stop train is travelling at 40m/s so it will catch up by a total of 40+30+40 = 110 seconds. You made it 90 seconds (which is explained by the 800m error at 40m/s = 20 seconds).
As ever don't mix up Max permissible Speed and headway Speed
So Ht4(ns-s) = 90 + 110 = 200s
Ht3(ns-s) = 115 + 110 = 225s
and thus the stopping headway requirement is met by either comfortably, but the non-stop requirement is too onerous for 3 aspect signalling to achieve in practice given that there are bound to be other constraints on placing signals and there is not much tolerance.
The headway speed is 140km/h which, to your level of approximation, is 40m/s and the braking distance therefore under 1600m rather than the 2000m shown which reflects braking from maximum permissible speed.
Since you were only interested in the differential time between the 2 trains then the consideration of the Sighting Distance SD and the Clearance Distance CD are irrelevant since they are the same in each case. Indeed introducing these just complicates things, particularly as the reference to train length and overlap in an area unrelated to the platform starting signal displays a certain level of confusion.
When on page 7 you state "a non-stopping train would have travelled in the same time 4600m" you do not mean that! Rather you ought to say that "a non stopping train would cover the same 4600m in a shorter time", as indeed you go on to calculate to be 115 seconds compared to the 205 seconds.
Obviously since you have used 2000m rather than 1600m then your relative times of the two trains are out; you have actually made the non-stop one go a distance of 4000m in the time that you claim the stopping train travels 4000m yet the time calculated is consistent with real 3200m.
For the stopping, I agree BDt and ADt are 80 sec; since constant acceleration / deceleration, then the average speed is 20m/s. The non-stop train is travelling at 40m/s so it will catch up by a total of 40+30+40 = 110 seconds. You made it 90 seconds (which is explained by the 800m error at 40m/s = 20 seconds).
As ever don't mix up Max permissible Speed and headway Speed
So Ht4(ns-s) = 90 + 110 = 200s
Ht3(ns-s) = 115 + 110 = 225s
and thus the stopping headway requirement is met by either comfortably, but the non-stop requirement is too onerous for 3 aspect signalling to achieve in practice given that there are bound to be other constraints on placing signals and there is not much tolerance.
(14-03-2012, 02:56 PM)kball Wrote: Thank you again for your comments.
I have updated my answer to version 4.
Tha main change being the revised calcs for a non stopping train following a stopping.
If this looks alright, albeit too much for the exam time allowed, I will have a go at using this information to mark up the layout.
Many thanks
KJB
PJW