(23-05-2010, 03:45 PM)alexgoei Wrote: Hello everyone,
I would like to post my calculations for the non-stopping and stopping headway requirements.
Please feel free to let me have your comments especially PJW.
Thanks & Regards
I'll give anyone else a few days to have their own attempt at these calcs before responding in detail.
However I have noticed your diagram for the stopping calculations; it is good that you have included one but I note that it suggests that section "e" which is the length of an overlap is sufficient distance for the train to reaccelerae to 33.33m/s yet the table below it states that the distance for that to occur is 450m.
Also you really cannot use DGR directly for stopping headway; headway is fundamentally about TIME not DISTANCE. For non-stop then these are directly related since speed is CONSTANT; for stopping then the dstance apart of the two trains constantly VARIES.
I think what you are trying to do (but you don't really explain it and that would be your downfall) is to consider the situation when both trains are running at their constant speed, the first having stopped and reaccelerated and the second still on clear aspects having yet to slow down. Certainly if trains are spaced like that then it is evident that the signalling can deliver that particular headway and if that is all which is needed to be demonstrated then that is fine; however to get the maximum capacity out of the railway it may be necessary to get the 2nd train that little bit closer- i.e. so that only just gets a clear aspect in the nick of time whilst the 1st train is still accelerating.
Certainly if this is your assumption of the meaning of stopping headway, then don't add anything more for contingency!
So if you stated your assumption that "Train 2 should never encounter any cautionary aspect due to Train 1" then getting it to the sighting point of the YY at the instant that train 1 clears the overlap beyond the 3rd signal ahead thus permitting Train2 to get a Green achieves that objective. Support your argument by referring to "defensive driving" and the fact that the YY is probably quite a bit further from the station than a train running at the timetabled speed would actually need to be able to stop and this makes logical sense.
Be aware though that it might be difficult to deliver the headway requested (as we have traditionally permitted Train 2 to encounter some restrictive aspects on the approach to the station. If the position of the YY in 4-aspect signalling or the Y in 3-aspect signalling is more or less where the driver needs to apply the brakes to stop in the station anyway, then in reality the aspect received wouldn't make much difference to how the train is driven). If, as often, there is a choice between
a) placing 3-aspect signals tight to braking distance or alternatively
b) upgrading to 4-aspect signals that are more widely spaced, then note that the distance of the "first caution" with the 4-asects is actually further from the station and therefore the warning will be more premature, so this would worsen headway if the driver following the defensive driving policy.
This is not the full story however because the next signal in rear in 3-aspect case would be further away than in the 4-aspect case.
So I suggest that you "tweak"your answer for this part of the question by amending the diagram, adding in some more words of explanation of what you are calculating, record and justify assumptions as per above and then I'll review that version.
See also this other solution
Note that I have now also now given comments on a previous posted example ; that which was written there could well have misled you, so hopefully my belated amendments will clarify.
PJW