2011 Headway calculation

[kball]

Hello,
I have recently joined the IRSE forum with the intention to sit the IRSE exam this year.
It's been a while since I tried any headway/ braking distance calculations and I would be grateful if someone would be kind enough to look over my calcultions and provide some feedback.

Kind regards
KJB

[Jerry1237]

Hello,

I have not checked the maths or algebra as others are more qualified to do that. However, I do have some comments on your comprehensive answer and some of the conclusions.

1) Time is a killer in exams and what you've written seems to be a little excessive for the marks awarded. There is no need to repeat equations. Derive them once and give answers for other examples.
2) The definition of headway time is incorrect but the maths seems good. Headway is equal to Overlap plus sighting distance plus distance from first green aspect to the red...
3) 10% margin on 1972m does not make 2000m but 2169.2m - however, the question states no margins.
4) There is no need to discuss other options such as two aspect (which is unlikely to support the quoted service anyhow).

That said, it was a good attempt but brevity with detail and clarity is what gets marks and supports exam technique for this question.

[Zaphod]

Hello,
I have recently joined the IRSE forum with the intention to sit the IRSE exam this year.
It's been a while since I tried any headway/ braking distance calculations and I would be grateful if someone would be kind enough to look over my calcultions and provide some feedback.

Kind regards
KJB

Hi KJB,

I noticed in your answer that the headway for 4-aspect signalling is greater than that for 3-aspect, which is the opposite of what I would have expected. I think the reason this has happened is because you have set BD1,2,3 equal to the required braking distance. Under 4-aspect, the distance between signals only needs to be half of this value. So BD1,2,3 need to be set to something like 986 m (for 4-aspect only).

I think your definition of the headway time in your equation is correct, but where you have written it out in words you have omitted a couple of terms, as Jerry said.

For part b, I am not sure how valid the assumption is that the time taken to accelerate back up to line speed can be disregarded. In reality, I would expect this, as well as the time taken to come to a stop at the station, to be an important component of the additional headway time. I would suggest that the best way of addressing this in the exam would be to add a (v-u)/t term, which covers both the time taken to decelerate and subsequently accelerate.

I think that adding a contingency of say 5% is not a bad idea (indeed it is exactly what we do in reality!). However, what you have added is more like 1%.

Overall I think it's a pretty solid answer and just requires a couple of tweaks and additions.

ZB

[PJW]

[quote='kball' pid='3438' dateline='1330550186']
Hello,
I have recently joined the IRSE forum with the intention to sit the IRSE exam this year.
It's been a while since I tried any headway/ braking distance calculations and I would be grateful if someone would be kind enough to look over my calcultions and provide some feedback.

Kind regards
KJB

I agree with Jerry that this is too long for examination timescales; you really need to get all the calculations done within 20-25 minutes and this means also the stopping headway ones which you have not really attempted.
Be aware that there should be differences between:
a) Textbook explaining to students
b) A student’s preparatory work produced as practice to help them absorb the information
c) An exam candidate’s response.

Answer (ignoring the repeated question) started well, but do not give braking distances allegedly to the centimetre! Round up to the next higher 5m or 10m; suitable level of precision.
Since freight train braking rate is given as the same as passenger, do not need to consider separately; worth stating the (rather unjustified) assumption of no significant brake build up time though! Not sure why felt need to calculate for what you called “trains” 4 & 5.
Headway is “required” (not “defined”) to be 2 minutes
Headway is not the distance between Green and Red; it is the time (which at constant speed can be converted to a distance) between the sighting point of the Green to the end of the overlap beyond the Red, (as the other respondents have already pointed out). Similarly as Zaphod has said, in 4 aspect signalling for signals at minimum spacing it is the double yellow which has to be braking distance from the red. Again when giving the calculated times then quote them to suitable precision.

Your answer showed lack of experience / comprehension by presenting 4 aspect signalling giving a worse headway than 3 aspects; getting a wrong answer is one thing, not recognising and acknowledging that it is ridiculous is what will lose you lots of marks.
Having calculated that 3 aspects just meet the constant 140km/h headway specification, you then state that such signalling is suitable; the fact that it is barely sufficient even with the signals at absolute minimum means that in practice you just couldn’t achieve a real scheme when there are other constraints re signal positioning. By adding on your arbitrary allowance for “unknown factors” you clearly will no longer be able to satisfy the headway requirement; you do not seem to have recognised that.

As others have pointed out, you can’t ignore the deceleration and acceleration times for the stopping trains; these are greater than the 30 seconds which you have added. Hence rather missed the whole point of this part of the question. The question actually asked for the situation where a non-stopping train was catching up an earlier stopping train.
So overall as an initial activity t start to get to grips with the subject then you have made a useful start. There are some useful components here, but it is not yet close to an exam answer.

Zaphod was right that you have some useful stuff to build upon but I feel he was being far too kind in an attempt to encourage you. Whereas this is a good thing, I think that I need to balance this by being rather more blunt.

You have shown you can read the question and put some numbers into equations, but you have not demonstrated signalling knowledge and understanding, rather the contrary. For example (in addition to what I have written prior) if 3 aspects barely deliver headway, then 2 aspects certainly wouldn’t (though of course might be just what is needed on some lighter used portions of the layout such as a branch). Note that 2 aspect signals are still generally used as a 3 aspect sequence and does not require Absolute Block Working.

So when reading your answer, I do not get the feeling of “competent signal engineer” but “someone who can do maths but doesn’t understand the signalling they are attempting to describe”. I might give you 5 of the 20 marks available for being able to calculate braking and have some idea about what non-stop headway is.

However it is early days and there is plenty of time to learn; by looking at other attempts on this website and looking at the comments on these as well as being prepared to try again and submit further attempts for more comments you’ll be able to improve.

[mangeshwakankar]

I tried to calculate (this being my very first calculation for Module 2).
I also assumed 10 percent contingency, so the headway requirement changes from 120s to 108 sec for non-stopping headway.

With 4 Aspect I got 93 sec and with 3 Aspect I got 118 sec, assuming the "B" to be 1972m (value corresponding to 160kph).
Also, for Fast train following a stopping train the headway is met by 4 Aspect signal.
I will post my calculation soon to have a check.

Hello,
I have recently joined the IRSE forum with the intention to sit the IRSE exam this year.
It's been a while since I tried any headway/ braking distance calculations and I would be grateful if someone would be kind enough to look over my calculations and provide some feedback.

Kind regards
KJB

[Jerry1237]

mangeshwakankar,

You need to be a little careful where speeds/distances are altered and whether the value is added or subtracted. I would suggest that 108s whislt notionally correct would be better written as adding to the minimum headway distance as kball's attempt at the question.

In effect, headway can be thought of in two ways.
1) signal braking distance is a safety measure
2) headway time is an operational requirement.

Signalling means we ensure safety first, we satisfy the operational requirement secondly. The distinction is very important and shows an understanding of the principles.

[kball]

Hello again,
I am attaching my second attempt at the signalling the layout calculations for module 2 2011.

I would especially like PJWs comments on this, as I clearly hadn't thought it through on the first attempt.

I am still unsure if I have the 4 aspect headway right, but at least this time I have the logic the right way around.
I hope that my answer is clear enough to follow.

I have still showed the braking distances for all the trains listed, as the question does ask for the braking distances for the permissible speeds. I took this to mean all the trains listed.

I appreciate that my answer is on the long side, and would take up too much time in the exam, but my aim is to get it right first, then try fitting it into the time allowed.

Thanks
KJB

[kball]

I have just realised that in b)ii) I divided 40 by 0.5 and got 20!
looing at it again now, I would need to add 160 seconds to the headway time for both 4 and 3 aspect which would exceed the 4 min required headway on both.
In conclusion I susupect that I do not need to calculate the time taken to reaccelerate back to line speed, but insteat the time taken for a departing train to clear the overlap.
I will take another look this eveneing and recalculate.
Your comments on the rest will still be appreciated.
Thanks
KJB

[kball]

Managed to find time in my lunch break.
I have updated the doc to vers 03 and re calculated the time for the stopping train accelerating past the OL.
It is still very tight to the required headway.
I would appreciate your comments.
KJB

[PJW]

Looking at v3.
I would state for Ans 1 a)
S1= 1975m
S2,3,4 = 775m
S5(!) = 125m

Ans b 1
Conversely beware rounding up too early, particularly if you will be squaring the result; at least be cogniscent of having done so and when subsequently get a number recognise the degree of precision that it has.

Need just a little more explanation why headway is from the sighting point of the Green to the overlap of the red; describe the effect of the position of one train on how the following train will be driven.

Diagram of 4 aspects is confusing to use the abbreviation for signal separation as BD- the signals will be spaced at half braking and therefore (given your rounding which I do not disagree with) 1000m.

Otherwise OK, although I'd have said
for 4 aspects "30 seconds within the non-stop headway requirement of 2 minutes) to emphasise that it is satisfied with a comfortable margin,
for 3 aspects "barely achieves the non-stop requirement of 2 minutes and therefore not practicable solution given other signal sighting constraints that will arise when applying to a given track layout and geography".


Ans b2
Need to explain how the elements you are calculating (time for train to come to rest, time for train to accelerate the length of the overlap and its own length) contribute to the overall consideration of stopping headway.

I think that I wouldn't have bothered with the 3 aspect stopping calcs having already decided that 3 aspects not suitable for the non-stop scenario, though I admit that the wording of the question arguably requires you to do so.
The question was
Determine graphically or by calculation the theoretical best headway (without any allowances) at minimum signal spacing and the given speed for application on layout 1 for:
i) a fast passenger train following another fast passenger train
and
ii) a fast passenger train following a stopping passenger train.


I'd argue that having decided that the 3 aspect option was out for i) that the only interpretation I need apply to the question for part ii) was 4 aspects.

Your answer for this is getting there, but not there yet.

There are 2 possible approaches:
a) disregarding the figures for non stop headway and considering the aspect sequence seen by the 2nd train (non-stop) following a train which has stopped. It must only see Green aspects, so the important thing is that it shall not get to the sighting point of a restrictive signal until that signal just steps up; the time you need is the time that the first train previously took from being at the same place,
1. some constant speed running until,
2, slowing to stop at the station (it would presumably have been following a fast train and thus would only have itself seen green aspects so the driver could leave their braking last minute to stop at the station since its platform starter will always have been Green sufficiently early during the approach),
3. station dwell,
4. accelerating up to the headway speed again,
5. continuing to run at this speed so that it just clears the overlap of the signal (think carefully which signal this would need to be for a 4 aspect sequence) which permits the signal which the 2nd train is approaching to step up to Green.

b) consider the differential time between the 2 trains.
1. take the figure for the non-stop headway that reflects the situation AFTER the station when the 2nd train has now caught up the 1st to be just at the headway distance
2. work out how much than this the 1st train must have previously been running ahead of the 2nd, because of the need to stop at the station.
This would entail the time to slow down from the constant speed , the dwell time plus the time to accelerate up to the constant headway speed again
3. work out how long the 2nd train would take to travel the same distance.
4. from 2 & 3 you work out the differential time and you add THIS to the NON-STOP HEADWAY figure.

I think your first attempt was on the right lines for approach b) yet you simply added the time for the stopping train to cover two section without ensuring that it was actually running at headway speed at these two places, neither did you take into account that the non-stop train would take a certain time to travel that distance.
Your revised attempt went some way towards the approach a), yet you got confused with "stopping train following another stopping train" which has some of the same components but is subtly different.

So a bit more work in understanding the logic of what you are trying to do before getting stuck into the maths is what I'd advise; understand the BIG PICTURE first and beware that the question asked in the paper does vary a bit from year to year, so taking stuff for one worked example may not be completely applicable to another.

Your last section was ok as far as it went, but didn't consider the various portions of the layout separately:
A-D
C-D
D-E
D-F
Does "one size fit all"?
it would be a very unusual IRSE layout when it did........

Managed to find time in my lunch break.
I have updated the doc to vers 03 and re calculated the time for the stopping train accelerating past the OL.
It is still very tight to the required headway.
I would appreciate your comments.
KJB