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Exercise 1A, Appendix W of the Study Pack - interesting_signal - 30-03-2010
Ok, here's what I have done so far. I'm still working on questions 8, 9 and 16.
I feel a bit silly but I'm struggling with question 16. Can anyone point me in the right direction? Or perhaps a fresh look at it tomorrow will make it clear.
There was quite a lot of work involved in working through all of these questions so it will take me a bit longer to attempt activity G23 for the 2004. For anyone starting this module I would recommend these exercises as they force you to think and not just calculate!
RE: Exercise 1A, Appendix W of the Study Pack - PJW - 31-03-2010
(30-03-2010, 10:48 PM)interesting_signal Wrote: Ok, here's what I have done so far. I'm still working on questions 8, 9 and 16.
I feel a bit silly but I'm struggling with question 16. Can anyone point me in the right direction? Or perhaps a fresh look at it tomorrow will make it clear.
There was quite a lot of work involved in working through all of these questions so it will take me a bit longer to attempt activity G23 for the 2004. For anyone starting this module I would recommend these exercises as they force you to think and not just calculate!
Don't feel silly- as you have realised, these were designed to make you think about what to calculate and therefore see what you understand and what you don't. There would be no value in proving that you can use an electronic calculator many times over.
Re Q16. Uniform deceleration makes it easy in that when decelerating from 60mph to a stand the average speed is 30mph. [Odd that this didn't seem to give you a problem when attempting Q11....??]
So what about putting yourself to the test- is anyone else going to have an attempt at these?
RE: Exercise 1A, Appendix W of the Study Pack - PJW - 31-03-2010
(30-03-2010, 10:48 PM)interesting_signal Wrote: Ok, here's what I have done so far. I'm still working on questions 8, 9 and 16.It is evident that you have read and understood the Study Pack and also avoided a few of the "traps". You also generally did a good job of explaining your answers. However some brief comments on those that I have looked at so far:
Q1. You made the unstated assumption that the headway time calculated was to be at the maximum permissible speed. Also you calculated the headway at MINIMUM signal spacing, not "maximum" as requested.
Q3 (and others). You used symbol "S" both for the braaking distance and the Sighting Distance; ok you didn't confuse yourself, but do beware of mixing and matching between different conventions and make sure any answer is self consistent!
Also Q3 shows a slight confusion I think- but whether of expression or understanding I do not know. Third sentence should read If the ratio had been less than 2, then 3 aspect signalling would not have been capable of delivering the required headway and therefore 4 aspect signalling would be a necessity. Last sentence should have stated .... as this gives the most economical means of achieving the required headway (MAXIMUM signal spacing, so minimum number of signals required for given distance)
Q4. You surely meant that the distant signal would be prior to (on the approach to) the stop signal; the nomenclature is NOT in advance but in rear
Q5. Err- all the figures seem to be the same as Q4 with a slightly different end wording; not an answer to Q5????
Q7. THINK. Does a train going down hill need a longer or shorter distance to stop than one on the level......? Lesson: firstly take a bit more care re the maths; secondly do a "common sense" check.
Q10. Only quibble is use of the word "speed" rather than "velocity"; it is a vector quantity and the "sign" is important [relevant to Q7 of course]
RE: Exercise 1A, Appendix W of the Study Pack - interesting_signal - 31-03-2010
Thanks for the quick response.
Q1 - Ok, I'll have another look at that.
Q4 - yes that's what I meant!
Q5 - Silly copy/paste mistake. I will (re)do the answer.
Q7 - Longer. Noted.
RE: Exercise 1A, Appendix W Headway - PJW - 31-03-2010
Q17. Bit of a surprise this one!
It may just be that you used a wrong word carelessly, but I am going to assume that you wrote what you meant- in which case it reveals a misunderstanding which I'll now attempt to correct. However I'd be interested to know if there is anything in the Study Pack etc that gave you the wrong impression, so that I can attempt to cure the problem at source for others.
Headway is not about safe separation of trains. Think about it; I am sure that you know that in 3 aspect signalling a train can be just clear of the overlap joint of one signal (at red) and a train can be safely approaching the signal in rear (at yellow). There is at least braking distance between the signals so the second train ought to stop at the red signal and there would still be an additional safety distance- the overlap- between the trains.
Your answer to Q18 states that for trains to be at minimum non-stop headway there must be more than two signal sections between them. This is indeed correct; the driver of the second of the two trains must see a Green- i.e. they can drive their train in a manner unaffected by the presence of the first train. Hence headway is all about capacity ; if the trains become closer that the minimum headway separation, then the second of them will encounter cautionary aspects and therefore it must brake, therefore lose time compared to the timetable and indeed waste line capacity by not using to the optimum for the speed for which it is signalled.
I think it is best to think of headway as a TIME; it only equates to a DISTANCE on the assumption of constant speed. Where the speed of the line fluctuates (as all really do), or where trains need to slow to pass over pointwork, or indeed slow and stop at a station, a pair of trains doing the same thing will remain a constant headway time apart ( the time interval between them measured at any site along their route is the same), but NOT a constant distance apart. Imagine train 1 slowing for a station whilst train 2 behind it will be travelling at full speed- their distance separation will be reducing. When train 1 is stopped at the station, train 2 will be catching it up fast. However train 1 will eventually accelerate to maximum speed again whilst train 2 will itself need to slow down for the station; hence their separation will then be increasing again. Since the trains do identical things, then once both are travelling at full speed again, their distance separation will return to its original value. This is obviously a key difference; "headway distance" can be a useful concept for non-stop, but is meaningless otherwise.
Your last para is tolerably right but, as above, measurement in metres is only sensible when placing signals on constant speed running line. Measurement in seconds is far more useful and is what mainline railways tend to use. Measurement in trains per hour is generally used for metros. The rationale is when a line is used at maximum capacity then it is the total number of trains that the "pipe" can accommodate which is important (as you say for the TOC). On those lines that are not so heavily used then this is not a useful measure, but what is far more significant is the minimum time interval between successive trains that is important.
Take Paddington; a TOC wants to run an HST to Bristol, one to South Wales and then one the West Country leaving at 5 minute intervals in a "flight" and then no more until the next half hour. The remainder of the time within the hour is used for slower trains- this maximises the use of the line. There is a mix of traffic and capacity is lost when two trains of different speeds are timetabled adjacent to each other, which is why the "flighting" of similar trains is economical of capacity. "Trains per hour" is only a useful measure when all trains are "the same".
Another rather different example; Machynlleth. Generally a 4 car train arrives from Birmingham with one driver (for economy) and it then splits into a 2 car set going north to Pwllheli and one going the other way along the coast to Aberystwth with a separate driver. The few miles between the station and the subsequent junction needs to be signalled to permit two relatively closely following trains- or else the passengers in the second train would have a long delay on their through journey. However there may well not be another train along the line in that direction for another 2 hours; you can see that "trains per hour" is a meaningless concept here, but that there i a need to signal that line with a headway of only a few minutes.
Q18/19.
Look at what you wrote again; can you see your mistake.
Hint: I don't think you a Physicist- your dimensions are wrong!
RE: Exercise 1A, Appendix W of the Study Pack - interesting_signal - 07-04-2010
Here's my updated answers. Note, I have left out question 9 for now as I haven't studied the stopping calculations yet.
RE: Exercise 1A, Appendix W of the Study Pack - PJW - 08-04-2010
(07-04-2010, 10:36 PM)interesting_signal Wrote: Here's my updated answers. Note, I have left out question 9 for now as I haven't studied the stopping calculations yet.
Suggest leave stopping headway calcs for now then; there will be relevant example at Signet.
Q4 additional
To achieve headway requirement you are correct that following trains need to be able to be signalled within 2040m of each other; you then calculated that this meant adjacent block signals should be no more than 1460m apart. You made an error in your conclusion (which I failed to point out) when you stated that distance to be 2040m.
To achieve the braking requirement you correctly state that distant signals should be a minimum of 300m in rear of the block signals. In isolated 3 aspect signalling there would not normally be a reason to place the distant signals much further than this, except perhaps to give better sighting due to track alignment, bridges etc.
If you decided (for the reasons you stated) that you wanted to provide 3 aspect continuous signalling then you'd need to decide what overbraking would be acceptable. If you simply placed the same number of signals evenly (and thus actually provided nearly twice the capacity demanded but at a cost not hugely more than that of the isolated 3 aspect solution) then each signal would be approx 730m apart; that would make the sections some 250% overbraked- you'd need to decide whether you could live with that.
Perhaps you meant provide more signals (i.e an extra one between the positions of the R/Gs and then space them all out evenly) even though this would add significantly to costs- on a simplistic "pure SEU" basis some 25% increase in costs. This would place them at approx 485m intervals which would be some 160% of braking- in percentage terms that still sounds an awful lot but in absolute terms it isn't a huge distance. At the permissible speed it would be approx 24seconds. In terms of sighting, it may well be possible to see one signal from the next- certainly it is not likely to be long before it comes into view- the signals are spaced at not much more than twice the AWS distance apart. I think I would be comfortable with that spacing; however I wouldn't feel it reasonable to have provided a 3 aspect signal every 1460m to provide the bare minimum capacity with each section some 480% braking; you did not really describe what you were proposing when talking about 3 aspect signalling.
Hence you need to think about why there is an "overbraking rule", the risk which it is seeking to mitigate and therefore what would be the consequences of breaking the rule. Perhaps you feel that this is unfair comment since that is what you meant by what you wrote; I do agree that you seemed to mention the right considerations, but really I wasn't fully convinced. Seemed to me that you were quoting what you had picked up from reading rather than demonstrating that you really understood. You would have got credit for what you did write, but not as much as if you had worded more convincingly. So learn from this- whether by improving your understanding or by improving your demonstration that you do understand, because it is the impression you give the examiner that counts.
Conversely I was far happier re your description re Q5- I believe that you understand the issue.
Q8
Fine to start with, determining what the headway time would be for 3 and 4 aspects with signals placed at minimum spacing suitable for the passenger trains (though a little explanation in words like this of what you were calculating would have been advantageous).
Then I wasn't very sure what you were doing- you seemed to derive the HD again from the HT and because of rounding errors the 3678m changed to 3672m. You then seemed to use the DGR method on the figures and almost be surprised that you came to the same answer. You didn't explain what the significance of calculating the signal spacing both by 2025/2 and also 3032/3 was, or indeed what is the significance of the the ratio of DGR/S being 1.5. A little more clarity in what you are calculating, what is a maximum and what is a minimum figure would help.
Re the freight train- note that you have to provide signalling on this line for these two different train types. An easy way of thinking about this is that during the day there is a need to run passenger services at 80mph at 120s timetabled headway, yet during the night the same line and same signalling is to be able to support a train service of freight trains running at 60mph at timetabled headway of 180s.
Which trains have the longest braking distance?- this fixes the MINIMUM signal spacing
which trains have the more onerous headway requirement?- this fixes the MAXIMUM signal spacing
Overall feeling is that you haven't quite seen "the wood for the trees"- the mechanism seems to be whirling away quite nicely, yet the penny didn't quite drop! Hopefully the above will give it a jolt......
As you yourself said, the role of these exercises is to get you to think and really appreciate what it is all about- you are well on the way and once it has truly sunk in you'll not forget it, so persevere!
Q18/19
Yes one error corrected but still one silly!
You are calculating a TIME [T] which as you correctly say is a DISTANCE [L] divided by a VELOCITY [L/T]
Hence all the terms in the brackets on the right of your equation must have the dimensions of LENGTH [L]. However you wrote "Sighting Time"which I imagine was just a silly slip for "Sighting Distance".
Always worth a 2nd look at any equations to make sure that all quantities are in the same units and that the formula is DIMENSIONALLY correct.
RE: Exercise 1A, Appendix W of the Study Pack - merlin89 - 21-12-2010
I have included my calcs for question 1 below I have a query is the maximum permitted spacing for 3 aspect SBD + 33%?
Convert Line Speed into ms-1: 80 x (1609/3600) = 35.75ms-1
say 36ms-1
Find Braking Distance using the following formula BD = u2/2b, where b is the deceleration rate (usually given in the notes, assume 0.5ms-2 if not stated), and u is the train speed.
BD= (36)2 / (2 x 0.72) = 1296 / 1.44
BD = 900m
Maximum permitted spacing is SBD + 33%
SBD = 1258m + 33% = 1673 m
Sighting distance is 12 sec at headway speed = 12 x 36 = 432 m
Overlap = 180 m
Hd3 = (2B + S + O + L)
Hd3 = ( (2 x 1673) + 432 + 180 + 100 )
Hd3 = 4058 m
Ht3 = Hd3/V
Ht3 = 4058/36= 113secs round up to 115secs
Answer:
Headway time for 3-aspects at maximum permitted spacing = 115 seconds
Also is it best to submit my answer to the appendix as a job lot or can I submit them in this thread as I o them one at a time?
RE: Exercise 1A, Appendix W of the Study Pack - PJW - 21-12-2010
(21-12-2010, 03:09 PM)merlin89 Wrote: I have included my calcs for question 1 below I have a query is the maximum permitted spacing for 3 aspect SBD + 33%?
Convert Line Speed into ms-1: 80 x (1609/3600) = 35.75ms-1
say 36ms-1
Find Braking Distance using the following formula BD = u2/2b, where b is the deceleration rate (usually given in the notes, assume 0.5ms-2 if not stated), and u is the train speed.
BD= (36)2 / (2 x 0.72) = 1296 / 1.44
BD = 900m
Maximum permitted spacing is SBD + 33%
SBD = 1258m + 33% = 1673 m
Sighting distance is 12 sec at headway speed = 12 x 36 = 432 m
Overlap = 180 m
Hd3 = (2B + S + O + L)
Hd3 = ( (2 x 1673) + 432 + 180 + 100 )
Hd3 = 4058 m
Ht3 = Hd3/V
Ht3 = 4058/36= 113secs round up to 115secs
Answer:
Headway time for 3-aspects at maximum permitted spacing = 115 seconds
Also is it best to submit my answer to the appendix as a job lot or can I submit them in this thread as I o them one at a time?
From my perspective I still have design for the commissioning starting on 24/12/10 to sign off as CRE and there are a million and one things to do to try to stop the whole job going very pearshaped; therefore I shall not have time to look at until 2011 so I suggest that you do as a combined lot.
Yes 133% braking is a typical maximum spacing, although in some circumstances this can be exceeeded it is a suitable value to utilise in this context.
RE: Exercise 1A, Appendix W of the Study Pack - reuben - 22-12-2010
(21-12-2010, 07:50 PM)PJW Wrote:(21-12-2010, 03:09 PM)merlin89 Wrote: I have included my calcs for question 1 below I have a query is the maximum permitted spacing for 3 aspect SBD + 33%?
Convert Line Speed into ms-1: 80 x (1609/3600) = 35.75ms-1
say 36ms-1
Find Braking Distance using the following formula BD = u2/2b, where b is the deceleration rate (usually given in the notes, assume 0.5ms-2 if not stated), and u is the train speed.
BD= (36)2 / (2 x 0.72) = 1296 / 1.44
BD = 900m
Maximum permitted spacing is SBD + 33%
SBD = 1258m + 33% = 1673 m
Sighting distance is 12 sec at headway speed = 12 x 36 = 432 m
Overlap = 180 m
Hd3 = (2B + S + O + L)
Hd3 = ( (2 x 1673) + 432 + 180 + 100 )
Hd3 = 4058 m
Ht3 = Hd3/V
Ht3 = 4058/36= 113secs round up to 115secs
Answer:
Headway time for 3-aspects at maximum permitted spacing = 115 seconds
Also is it best to submit my answer to the appendix as a job lot or can I submit them in this thread as I o them one at a time?
From my perspective I still have design for the commissioning starting on 24/12/10 to sign off as CRE and there are a million and one things to do to try to stop the whole job going very pearshaped; therefore I shall not have time to look at until 2011 so I suggest that you do as a combined lot.
Yes 133% braking is a typical maximum spacing, although in some circumstances this can be exceeeded it is a suitable value to utilise in this context.
Merlin
Good calcs.
Not sure where you got the figure of 1258m from? - you just calculated braking distance on the previous line as 900m. It appears that you've added ??% and 33% to the minimum safe braking distance.
The current railway group standard GK/RT0034 states the (typical) figure of 33% allowed overbraking. However, the figure used in the past was 50%, and there is a "temporary non compliance" issued against the standard, allowing the old 50% figure to remain. In general, using the 50% figure gives you more flexibility in positioning signals, so use this to your advantage in the exam!
Looking at your equations, you have used quantities "BD", SBD" and "B" at different times, not clear which is which.
regarding the equation for 3 aspect headway time, i always think it's worthwhile drawing a sketch (much quicker on paper than on a website!) showing the position of the 2 succesive trains, and all the dimensions. This justifies the equation, instead of just plucking it out of the air.
In this question, you can save a little time by directly adding the sighting allowance as a time: looking at the maths, you've multiplied 12 by V, then added this to a figure which you then divided by V. it would be quicker to initially ignore sighting in the distance equation, and simplly add 12s to your calculated answer.
reuben