(16-07-2009, 03:11 PM)CMcGrory9 Wrote: Hello all,
Before I start asking any silly questions i'll offer up my attempts at the '98 Stopping Calcs. I was comparing my answers to those on they Model answer provided with the Study Pack.
Trying to investigate this; there could well be an error and if so it is not deliberate- however you are right that you would not be severely penalised by making one and carrying on appropriately.
One confusion is that there are actually two model answers and I am not sure to which you are referring. Looking at the "succinct" one this actually states:
"Since two signal sections (even at 150% braking) fit comfortably into the headway distance, the headway requirement at 80 kmh-1 is easily met by 3-aspect signalling. Signals would be best spaced at nominal 1.33 x 775 = 1030m to limit the amount of excess braking to that considered tolerable. For a line where there are only 4 contracted paths per hour, isolated 3-aspects with several km between stop signals would generally be perfectly sufficient unless the timetable required some trains to run in rapid succession".
so that seems to accord with what you are saying, so is it this one where you think there is an error or the other one?
I note that you have written that you are assuming that the freight will (and I can't quite read it but I guess it says not run at 100km/h), yet the question asks for a headway at 80km/h and permissible speed of all trains is stated as 100km/h so that means that you probably should count the freight and thus have L=400m. However given that there is only one of these an hour then definitely a good argument for ignoring it and using L=200m; in reality it makes very little difference in this question, you got 2410m and the given answer gave 2325m.
I then don't follow your answer. You are multiplying Vh by Ht and by selecting Vh = 22.2 you are obviously still looking at 80km/h running, but I don't see where the 144 figure comes from. Looking at the righthand portion you seem to be calculating the headway that would result from 3 aspect signals spaced at the maximum degree of overbraking recommended; you had a figure of 2920m which seemed to match your other figures but changed it to 3001m (which looks very odd as all the numbers in the addition are even numbers). You could certainly do with more explanation of what you are calculating at any place, but I don't violently disagree your figures.
The thing that I think you are missing is the # note that tells you that the portion of the line through the station area between the tunnel mouths has a maximum permissible speed of 40km/h. Hence even the non-stop trains will be decelerating , travelling slowly and then accelerating again. Any non-stopping headway calculations will only apply well away from the station where trains can actually run at the headway speed. The problem we have is that just outside the slow speed area the signals must be spaced for 100km/h but actually the trains will be doing a speed not that much greater than 40km/h as they have to be slowing down to respect that restriction or can only accelerate at a finite rate after it. You can't close up the signal spacing below 775m but you must still be able to deliver the headway; hence that's where 4 aspects for the relevant length of line at least become relevant.
However it is certainly possible that one or other of the model answers does have an error that needs correcting- can you give me more info in which one and where you think the error is. Did just wonder whether what you think is one times braking distance at 80km/h is actually twice braking distance at 40km/h- but that doesn't work out as braking distance is proportional to the square of the speed.
PJW