(01-07-2009, 06:46 PM)PJW Wrote: We are beginning to get attempted answers for the mod5 Exam Workshop later on this month and got a bit of a surprise; we got some "bonus extra" track circuit calculations from other past papers. Hence posting them here.

OK

Taking them in the order PJW listed them:

1995 (actually I think this is 1999, but that does not really matter as you have written the question out - incidentally something that is not necessary in the exam and only wastes time). This one was a pretty sparkling attempt. Your diagrams are correct and your logic is sound and the answer you get is spot on what I had previously calculated in a post for a similar

question. The only comment I would make by the way of improvement would be for there to be a few more words in there about what you are calculating eg some words about the fact that you are looking to find the value for the fault which causes the rail voltage to fall to the point at which the relays will drop away.

2003 - A good start. You correctly got to the point where you worked out that for the relay to pick up, the value of the ballast resistance was 2.14ohms, although from what you did in the last part and what you did in the 2005 question, I suspect that is more my luck than actually realising what you needed to calculate. I would start off my saying what you meant by "reliable operation" - something like the point at which the relay will re-pick after a train, maybe noting that this was the limit of reliable operation, not a realistic situation in which to leave the track.

Having worked out the critical point to be where the ballast resistance is 2.14ohms you fluffed converting this to a length which surprised me because in the other questions where you had to go the other way (ie were given a figure and a length you correctly came up with the Rb figure). You had a value in ohms and needed to translate that to a figure in km and the linking constant is measured in ohm km. Considering the dimensional units of each we must have

ohm km / ohm = km

ie you have to divide the given value of 3 ohm km by the ohmic value you calculated to give the corresponding length. The fact that you got a 6km DC track circuit should have rung some alarm bells with you. It should be more like 1.4km.

You then tried to calculate the drop shunt but made the same error here as you did in the 2005 question. You used the figure given as the pick up current around which to calculate the drop away. Deliberately they have not told you that for a typical track relay, the drop away current is about 68% of the pickup hence you need to calculate the value of shunt that will reduce the rail voltage to a point much less than you did. Again, an alarm bell here in that you stated that the drop shunt was an open circuit.

In 2005 your maths (with one exception, see later) and layout are spot on apart from the fact that you were trying to calculate the drop shunt using the rail voltage value for the pickup. The 3 ohm drop shunt you calculated is not unsafe, but is higher than a typical value. Carrying on using this erroneously high rail voltage, you try to calculate the drop shunt required and come up with a value of 38 ohms (which is to be expected as the TC is easy to shunt and likely to right side fail), however, look at the line in the middle of page 3. You have:

15Rs = 15.57Rs + 21.9 (correct for the numbers that you have)

But you then say

0.57Rs = 21.9, hence Rs = 38.43.

The flaw is that you should have written

- 0.57Rs = 21.9

This, of course gives you a negative value for the drop shunt which is meaningless, but in fact what you are describing is a situation where, under steady state, the TC will already have dropped and maths being what it is, is helpfully telling you that to get to the point at which the relay would drop (if it were not already down!) you have to apply a negative resistance. This is of course the point at which you say "this cannot be right", look back in your working and realise there is a mistake higher up.

I think you also missed the part where you were asked to comment on the reliability and how it can be improved (oh and note that you showed a variable feed resistor in your diagram when the text specifically states this is fixed, a significant fact if you are then going to comment about how to improve the performance of the wet track).

In summary, they are three pretty good attempts in terms of circuit analysis, but you do need to gen up on the characteristics and performance of track relays (pick and drop points), get comfortable working out ballast resistance and watch out for arithmetic slips.

If there is anything that does not make sense, please let me know and I'll try to explain it better.

Peter