explain gradients

[swt_passenger]

1 in 4 is 25% of a vertical climb (i.e. 1 in 0 is 100%) 1 in 1 would be 50%, 1 in 2 = 41.5%, 1 in 3 = 33% and so on.

No, 1 in 1 (a 45 degree slope) is 100% expressed as a percentage, as has already been pointed out twice.

 

[Deepgreen]

No, 1 in 1 (a 45 degree slope) is 100% expressed as a percentage, as has already been pointed out twice.

Oops - not only did I mess up the conversions, I failed to read the thread properly!

 

[ian1944]

I sometimes think that it's a pity that gradients aren't expressed as degrees, which would have the double advantage of the value increasing with the steepness, and there being no possible confusion between sine and tangent which can arise in the "1 in ..." or "%" styles. As 1 degree is about 1 in 57, track gradients would best be expressed as tenths or hundredths of a degree.

 

[daikilo]

Newton Abbot Museum: Explaining the need for extra engines at NA: Sorry to be dumb, but if a track gradient is 1:32 (Dainton Bank) how do I explain that to a child? Is it metric? If not, how do I convert it to something a metric child would understand?
Thanks

As it happens, here we are looking at ratios which are independent of the unit of measurement, so your child may well understand it without a problem. The difference is whether the vertical axis (1 unit in x units) or the horizontal (z units in 100 units) is the fixed value.

What is important is that the ratios used are never along the straight line between the two points although that is what the vehicule will actually follow. Your child will need to understand triangles to get to that, and a bit more to be able to work out the actual angle to the horizontal (or vertical) of the road/track (which is never on signs but very important if you want to look at energy use)..

Coming back to the question of a data source, obviously Network Rail has it, but I have not yet found how to extract it from their public files. I would not be surprised if a local railway group can help, or even find someone on Newton Abbot station.

 

[swt_passenger]

Slightly off topic but did anyone notice the BBC did a thing about 'steep streets' around the country yesterday?

http://www.bbc.co.uk/news/uk-england-38568893

Noticeably they used degrees to two decimal places for their gradients, rather than either of the usual road sign options... :roll:

 

[daikilo]

Slightly off topic but did anyone notice the BBC did a thing about 'steep streets' around the country yesterday?

http://www.bbc.co.uk/news/uk-england-38568893

Noticeably they used degrees to two decimal places for their gradients, rather than either of the usual road sign options... :roll:

Yes, it is called spurious accuracy.

That said, tan16.09 (~40%/1 in ~2.5) is very steep. If I recall correctly, hardknot pass is 1 in 3 at its steepest.

 

[DelW]

On the subject of gradients, does anyone else notice that gradients often look steeper than they actually are? For example, if I'm standing at the top (or the bottom) of a 1 in 5 gradient, then if I look along it casually (without trying to actually measure any angles), it might visually give me the impression of a 45 degree slope (1 in 1), even when I know perfectly well it isn't anything like that

I think that most people over estimate the steepness of slopes - climbing a 1:2 hill path feels more like 1:1, whereas climbing a true 1:1 you'd probably be using hands as well as feet. I recently climbed a Victorian stone staircase up the side of a valley which was at about 41° to horizontal, yet looking down from the top it felt precipitous.

 

[GRALISTAIR]

My simple mind thought that gradient equals tan theta .

 

[Bevan Price]

Coming back to the question of a data source, obviously Network Rail has it, but I have not yet found how to extract it from their public files. I would not be surprised if a local railway group can help, or even find someone on Newton Abbot station.

Some railway company history books contain gradient profiles. Complete profiles for almost every line on the Great Central Railway, and Lancashire & Yorkshire Railways are in the books by George Dow (GCR) & John Marshall (L&YR) .

The North Eastern Railway Association has reprinted complete profiles for that railway.

https://drive.google.com/file/d/0B8TQ0uMwUhO9dFRlYy1NQ1RFazA/view

(look for title called "gradient sections".)

The people who reprinted the Midland Railway system maps also reprinted the Midland gradient profiles. Copies (second hand from here, and possibly elsewhere):

http://www.lindatinkerrailwaybooks.co.uk/index.php?route=product/product&product_id=1789

Elsewhere, coverage in public sources is patchy. NRM (York) may be the best place to look for public information - but expect it to take plenty of time to find what you are looking for.

I assume gradient information exists at NR somewhere within detailed line surveys, but I would be surprised if is ever released into the public realm - unless someone has a lot of money to pay them for the time & effort in locating and compiling all the information. (Freedom of Information requests can be rejected if huge costs would be incurred in provision of data - even when there is no need for secrecy.)

 

[John Webb]

Regarding getting information from Network Rail, I'm certain that they have detailed gradient diagrams available. Certainly BR did - around 1960, prior to my family's first trip to Cornwall on the WR main line and being in my early teens, I wrote to the office at Paddington asking for a sight of the gradient diagrams; I was invited up to a drawing office at Paddington, given a drawing board and spent two hours copying the said diagrams by hand - great fun!

 

[Joseph_Locke]

Some railway company history books contain gradient profiles. Complete profiles for almost every line on the Great Central Railway, and Lancashire & Yorkshire Railways are in the books by George Dow (GCR) & John Marshall (L&YR) .

The North Eastern Railway Association has reprinted complete profiles for that railway.

https://drive.google.com/file/d/0B8TQ0uMwUhO9dFRlYy1NQ1RFazA/view

(look for title called "gradient sections".)

The people who reprinted the Midland Railway system maps also reprinted the Midland gradient profiles. Copies (second hand from here, and possibly elsewhere):

http://www.lindatinkerrailwaybooks.co.uk/index.php?route=product/product&product_id=1789

Elsewhere, coverage in public sources is patchy. NRM (York) may be the best place to look for public information - but expect it to take plenty of time to find what you are looking for.

I assume gradient information exists at NR somewhere within detailed line surveys, but I would be surprised if is ever released into the public realm - unless someone has a lot of money to pay them for the time & effort in locating and compiling all the information. (Freedom of Information requests can be rejected if huge costs would be incurred in provision of data - even when there is no need for secrecy.)

Regarding getting information from Network Rail, I'm certain that they have detailed gradient diagrams available. Certainly BR did - around 1960, prior to my family's first trip to Cornwall on the WR main line and being in my early teens, I wrote to the office at Paddington asking for a sight of the gradient diagrams; I was invited up to a drawing office at Paddington, given a drawing board and spent two hours copying the said diagrams by hand - great fun!

Recent (professional) experience would suggest that NR do not have comprehensive and accurate records of gradient (it's normally comprehensive but old and inaccurate, or new and patchy). Even the signalling plans can't be relied on as the data is often just copied from the previous plan. We've been using measured data from things like RiLA to verify them.

 

[edwin_m]

There is a set of what are known as Five Mile Diagrams produced by an external party from NR records, including gradients and quite a lot of other useful stuff. But they are only available by licence from that company (which is no doubt expensive) and NR can't even give them out to their suppliers. I suspect the external company offered to do this and make them available to NR for free, as a commercial venture funded by charging third parties.

I agree with Mr Locke the gradient information has probably not been updated for years, perhaps not even since the lines were originally built.

 

[Joseph_Locke]

There is a set of what are known as Five Mile Diagrams ...

I agree with Mr Locke the gradient information has probably not been updated for years, perhaps not even since the lines were originally built.

The gradient data on the 5-mile plans is either missing or based on the signalling plans anyway (so not always current / right). I believe NR train planning has a database, but the name escapes me.

As to accuracy, the line through Bryn is still shown quite flat, despite the major lift that was applied to go over the new motorway bridge nearby!

 

[rebmcr]

Do the measurement trains not have the capability to build a dataset of the gradients they pass over?

 

[Deepgreen]

Yes, it is called spurious accuracy.

That said, tan16.09 (~40%/1 in ~2.5) is very steep. If I recall correctly, hardknot pass is 1 in 3 at its steepest.

It isn't spurious if the data is used for comparisons of steepness, as the BBC item did. Whether there is any point in the comparison being undertaken is another question. It's also worth mentioning that the streets in question had very short sections which were much steeper than their averages.

 

[Deepgreen]

There is a set of what are known as Five Mile Diagrams produced by an external party from NR records, including gradients and quite a lot of other useful stuff. But they are only available by licence from that company (which is no doubt expensive) and NR can't even give them out to their suppliers. I suspect the external company offered to do this and make them available to NR for free, as a commercial venture funded by charging third parties.

I agree with Mr Locke the gradient information has probably not been updated for years, perhaps not even since the lines were originally built.

The vast majority of railway gradients have not changed since the lines were built. There are a very few lines where infrastructure changes (mainly flyovers, etc.) have changed gradients, but extremely few on plain line (I can't actually think of any off-hand).

 

[ComUtoR]

We have had new gradient markers installed on one of our routes. There doesn't appear to be any rhyme or reason to their placement.

 

[furnessvale]

Do the measurement trains not have the capability to build a dataset of the gradients they pass over?

Just thinking about this when I read your post.

Sounds like a fairly simple clinometer would be of assistance.

 

[Joseph_Locke]

Just thinking about this when I read your post.

Sounds like a fairly simple clinometer would be of assistance.

Apart from when the train is accelerating or braking ?

 

[RSC Friends]

Just to add to the OP, when the South Devon gradients were designed by Brunel, he intended to use the Atmospheric Railway on them (probably features elsewhere in your museum, especially the rats story) and considered gradients were thus not important (not actually correct, but off-topic - Brunel was sometimes brilliant, but at other times had an extraordinary mechanical naïveté) and thus laid out some extremely steep gradients to save on construction costs, its principal claimed benefit.

Ironically, the system was only installed and got working (sort of) on the level section from Exeter to Newton Abbot, beyond there the atmospheric machinery was abandoned only part-completed, but the original steep alignments had already been built and were kept for locomotive use.

The gradients were (are) some of the steepest on main lines in Britain, and were challenging in a number of aspects. Dainton was a particular problem because, unlike other steep gradients like Lickey, it changes at the summit from 1 in 36 up to immediately 1 in 36 down the other side. Steam locomotives needed to maintain their water level at all times over the firebox top, at the rear of the boiler, and the effort in climbing the hill could cause the boiler water level to fall. The gradients were sufficient to start to be noticeable in the water level in the boiler (this rarely happens elsewhere on railways) and when the loco tipped from going up to going down there was a chance for this to happen, the safety fusible plug might then blow, and that was the end of this trip for the engine.

At least they could coast down the other side to Totnes!

Thanks Taunton, I can use this working knowledge.

Off topic reply:
NA Museum has a piece of atmospheric pipe, a visually accurate, but technically imperfect, running model of the atmospheric railway, a full size Brunel image (take your photo next to the man), as well as a letter from him. We don't mention the rats! When NA ran its Brunel 150 celebrations, modern materials and technology had an atmospheric model carrying people at a brisk walking pace in the grounds of Forde House. Health & Safety man blanched!

 

[furnessvale]

Apart from when the train is accelerating or braking ?

Given that the forces involved in both those movements can be measured and incorporated into the system, I don't see that as insurmountable.

The real question is, do we NEED gradient information?

If the answer is yes, then the measurement train would seem the ideal vehicle to deliver it economically.

 

[Railsigns]

The real question is, do we NEED gradient information?

The answer is YES, unless you think braking calculations (for signal spacing, etc.) need not take account of gradients?

 

[The Planner]

The gradient data on the 5-mile plans is either missing or based on the signalling plans anyway (so not always current / right). I believe NR train planning has a database, but the name escapes me.

If we do then Ive never seen it, we have always gone off signalling diagrams and 5 mile diagrams, even an old Ian Allen gradient map book!

 

[The Planner]

The real question is, do we NEED gradient information?

If the answer is yes, then the measurement train would seem the ideal vehicle to deliver it economically.

Too right we do, cannot model SRTs etc without them. We can't assume everything is flat.

 

[Railsigns]

the gradient data on the 5-mile plans is either missing or based on the signalling plans anyway (so not always current / right). I believe nr train planning has a database, but the name escapes me.

tratim?

 

[The Planner]

TRATIM is the old method of calaculating SRTs and thats going back a bit.

 

[edwin_m]

I shared an office with the TRATIM people for a while. I seem to recall a full set of gradient profiles in rather nice leather-bound volumes.

The gradient won't change much when measured over a distance of hundreds of metres or more, which is all that really matters for running time calculations most of the time. If a "dip" has appeared due to subsidence the train will run a bit faster on the way down and slower on the way up, which will roughly cancel out. I guess it could be significant when trying to assess whether a train is at risk of stalling on a severe gradient.

 

[furnessvale]

Too right we do, cannot model SRTs etc without them. We can't assume everything is flat.

Exactly. So the measurement train would appear to be the ideal vehicle to deliver that information.

How do we get that information at present?

 

[Joseph_Locke]

Exactly. So the measurement train would appear to be the ideal vehicle to deliver that information.

How do we get that information at present?

We don't, routinely. The NMT can measure altitude and location, but does hiccup at times. The trouble is that the measured track profile is smoothed out by tampers over the years and has no dclearly efined "changes"; it's OK to measure level changes between any two points though.

 

[Joseph_Locke]

If we do then Ive never seen it, we have always gone off signalling diagrams and 5 mile diagrams, even an old Ian Allen gradient map book!

Forgive me, but I now understand the truth about SRTs!