explain gradients

[RSC Friends]

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

 

[najaB]

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?

It's a ratio so it's neither metric nor Imperial. It just means that there is a rise of 1 unit vertically for every 32 units you travel horizontally.

 

[EM2]

Think of it this way.
If you are at the bottom of the gradient, and walk 32m along it, you'll be 1m higher up than you were at the bottom.
EDIT - this isn't strictly accurate (Pythagoras and all that), but it's not far off.

 

[RSC Friends]

Thanks EM2. so it could be feet or metres. I get that.

 

[johnnychips]

I wonder why they changed the road signs, quite a few years ago now, from things like '1 in 4' to '25%'? Obviously, they have not done this on the railway.

 

[Bevan Price]

I wonder why they changed the road signs, quite a few years ago now, from things like '1 in 4' to '25%'? Obviously, they have not done this on the railway.

Some (mainland) European railways do it that way - but use "per thousand" than per cent. I cannot produce the "per thousand" symbol here, but it is approximately "o/oo". So a 20 "o/oo" gradient would be equivalent to 1 in 50.

 

[Howardh]

If it says 1;32 - is that the maximum or is that the average - you could have a half-mile climb where the gradient varies?

 

[najaB]

I cannot produce the "per thousand" symbol here...

It looks like this: ‰ - e.g. 20‰

If it says 1;32 - is that the maximum or is that the average - you could have a half-mile climb where the gradient varies?

I believe it is an average over at least a quarter mile, but happy to be corrected.

 

[Bevan Price]

If it says 1;32 - is that the maximum or is that the average - you could have a half-mile climb where the gradient varies?

Normally, there would be a new gradient post each time there is a significant change in gradient - although they probably would not bother for small changes, e.g. 1 in 32 to 1 in 34.

Note also that doubts have been expressed elsewhere about the accuracy of some published gradient information. Also, in former "mining" areas, subsidence may have resulted in changes of gradient that are not reflected in gradient posts or published gradient charts.

 

[brad465]

I wonder why they changed the road signs, quite a few years ago now, from things like '1 in 4' to '25%'? Obviously, they have not done this on the railway.

Might be because on the railway percentages above 2-3% are rarely feasible/used, and decimal point values would often be a common occurrence in gradient values. On the road ratios maybe too hard to grasp quickly for some road users, but % values would be easier to interpret and can be any number up to 25-30% usually.

 

[RSC Friends]

Yeh, see, you've lost me again!
I have what I need.
Over and out and thanks

 

[Cowley]

Hopefully you'll read this even though you've gone , it may help explain things visually a little.
I think the steepest bit of Dainton Bank is actually 1 in 36 and not 1 in 32. Another comparable gradient in the area that you may know is the climb from Exeter St David's up to Exeter Central which is 1 in 37, I mention this because you can clearly see the slope in comparison to the road that is on the same level as the railway at the station and which the railway then crosses on a substantial bridge in a fairly short distance later.

 

[pdeaves]

Some (mainland) European railways do it that way - but use "per thousand" than per cent. I cannot produce the "per thousand" symbol here, but it is approximately "o/oo". So a 20 "o/oo" gradient would be equivalent to 1 in 50.

Also referred to as 'permille'/'permil' in some quarters.

 

[30907]

I wonder why they changed the road signs, quite a few years ago now, from things like '1 in 4' to '25%'? Obviously, they have not done this on the railway.

With a percentage, the higher the number, the steeper the gradient. And it's standard across mainland Europe. OS maps have percentages, with ratios in brackets BTW.

 

[fairysdad]

Might be because on the railway percentages above 2-3% are rarely feasible/used, and decimal point values would often be a common occurrence in gradient values. On the road ratios maybe too hard to grasp quickly for some road users, but % values would be easier to interpret and can be any number up to 25-30% usually.

I actually find the ratio type roadsigns much easier to read quickly than the percentage roadsigns. I read 1:4 as 'one in four' without thinking about it, but have no idea what a sign reading '25%' means. 25% of what exactly? That said, I don't really need to know how steep a hill is when driving it - I see a gradient sign and know to expect a steep hill of some sort, doesn't really make a difference how steep!

 

[Cowley]

I actually find the ratio type roadsigns much easier to read quickly than the percentage roadsigns. I read 1:4 as 'one in four' without thinking about it, but have no idea what a sign reading '25%' means. 25% of what exactly? That said, I don't really need to know how steep a hill is when driving it - I see a gradient sign and know to expect a steep hill of some sort, doesn't really make a difference how steep!

Yes I'm the same

 

[swt_passenger]

I actually find the ratio type roadsigns much easier to read quickly than the percentage roadsigns. I read 1:4 as 'one in four' without thinking about it, but have no idea what a sign reading '25%' means. 25% of what exactly? That said, I don't really need to know how steep a hill is when driving it - I see a gradient sign and know to expect a steep hill of some sort, doesn't really make a difference how steep!

10% is 1 in 10, 25% is 1 in 4, 50% is 1 in 2 -

Or rise/run x 100

 

[The Ham]

With a percentage, the higher the number, the steeper the gradient. And it's standard across mainland Europe. OS maps have percentages, with ratios in brackets BTW.

The problem comes when trying to design very flat gradients as the difference in written form of 0.5% is very little to 0.25% yet that's 1:200 and 1:400 where the former could be a viable gradient (in that it would just drain depending on the surface finish) but the latter wouldn't be.

 

[jopsuk]

But for road signs, a simple "bigger number = steeper" is better. Neither the ratio not % are really that "intuitive" as to what the slope actually is- when you start translating into angles, 1:1, which is 100%, is a 45° or π/4 rad. Vertical, ie 90° or π/2, is 0/1 or ∞%.

 

[Joseph_Locke]

However, if anyone can find anything that gives the rules on the provision gradient posts on the railway, I'd be fascinated to hear about it (I know of no current legislation, rules or guidance).

 

[LNW-GW Joint]

But for road signs, a simple "bigger number = steeper" is better. Neither the ratio not % are really that "intuitive" as to what the slope actually is- when you start translating into angles, 1:1, which is 100%, is a 45° or π/4 rad. Vertical, ie 90° or π/2, is 0/1 or ∞%.

Ratio signs lose their accuracy as you get steeper, whereas percentages keep their accuracy (in numerical terms).
eg there is a big difference between roads of 1 in 5 and 1 in 4 which is hard to represent accurately on signs.
With percentages you have all the numbers from 20 to 25 to indicate the gradations.

We went to percentages to harmonise traffic signs across Europe.
No doubt the Daily Mail will want ratios back now, along with rods, poles and perches.
The ratio of height gain over distance is actually the tangent of the angle subtended, which as you say goes up to infinity for vertical.

 

[Supercoss]

Interesting thread,
signalboxes should have a gradient profile of their area of control such as this :
http://bed-pan.homestead.com/MCL-gradient.JPG
Out on the ground staff can refer to these:
http://bed-pan.homestead.com/DownCanalTunnelGradient.JPG
And the latest:
http://bed-pan.homestead.com/Down_Canal_Tunnel_CBI.JPG
primarily dsigned to remind staff in areas where rail trolleys are prohibited on gradients steeper than 1 in 50 with certain exceptions
and for all those previous 'steepest gradient' threads (away from Lickey Incline) a new one to consider in the mix

 

[Supercoss]

http://www.railsigns.uk/sect24page1/sect24page1.html
worth a read, most excellent source of info

 

[RSC Friends]

Can anyone direct me to a clear drawing of the gradient profile of the South Devon Banks, please?
I have access to the Railway Studies Collection in Newton Abbot, and it has most books, or a website?
Thanks

 

[John Webb]

Can anyone direct me to a clear drawing of the gradient profile of the South Devon Banks, please?
I have access to the Railway Studies Collection in Newton Abbot, and it has most books, or a website?
Thanks

There were gradient maps published by The Railway Magazine/The Railway Publishing Co. Ltd in book form from 1936 onwards; I have a 1947 edition. These were reprinted several times, eventually by Ian Allan in collaboration with the Tothill Press; I have a copy from the 1970s, ISBN 0 7110 0875 2.

In the 4.5 miles from Aller Junction to the other side of Dainton bank, there are no less than 23 changes of gradient in 15mm of print!

Regards,
John Webb

 

[Taunton]

There are various ways of measuring gradients. Victorian engineers often used a different approach again, feet per mile, that is the number of feet climbed per mile of length, which can account for the various oddball gradients you can find repeating on lines. The feet climbed were often a round sum, like 30. This over 5,280 feet in a mile gives 1 in 176, which was a common gradient on the old Great Central main line.

 

[RSC Friends]

Thanks John Webb, I will look up that book in the Railway Studies Collection.

 

[Taunton]

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!

 

[Deepgreen]

I actually find the ratio type roadsigns much easier to read quickly than the percentage roadsigns. I read 1:4 as 'one in four' without thinking about it, but have no idea what a sign reading '25%' means. 25% of what exactly? That said, I don't really need to know how steep a hill is when driving it - I see a gradient sign and know to expect a steep hill of some sort, doesn't really make a difference how steep!

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.

I would suggest that a gradient warning for a 1 in 10 hill might provoke a different driving style (gear selection, etc.) to a 1 in 3 hill.

 

[DynamicSpirit]

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 suspicion is that my brain must be judging horizontal distances differently from vertical distances (That would make sense: 10m horizontally is nothing: You can walk it in a few seconds. But 10m vertically is an impossibly high cliff). But I'm curious whether that's just me, or whether it's true of everyone.