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On things such as the 5 Mile or Signalling Diagrams, what measurement is used for gradients i.e. 1 in 100, is it metres, feet or yards? I've made an assumption it's metres when calculating elevation (length of track divided by gradient or 137.2m / 100).
How do they typically measure gradients? I read somewhere it's possibly signal to signal or when a significant change is detected.
On things such as the 5 Mile or Signalling Diagrams, what measurement is used for gradients i.e. 1 in 100, is it metres, feet or yards? I've made an assumption it's metres when calculating elevation (length of track divided by gradient or 137.2m / 100).
In your example for every 100 <units> horizontally, the track rises or falls by 1 <unit>. It doesn't matter whether the <unit> is a foot, metre, furlong or nautical mile, the angle subtended at the origin will be the same.
In your example for every 100 <units> horizontally, the track rises or falls by 1 <unit>. It doesn't matter whether the <unit> is a foot, metre, furlong or nautical mile, the angle subtended at the origin will be the same.
Surely I need to know what unit Network Rail used to then calculate elevation? If Network Rail use 1ft rise every 100ft, I then need to make sure I convert my track length to feet as well otherwise I'll be doing 137.2m / 100ft instead of 450.13ft / 100ft. Happy to be wrong!
I didn't really have a choice in the school I went to (which wasn't great) and my parents weren't that well off - so that came across as snobby if I'm honest. I also find it completely acceptable to ask for advice when I'm not an expert in that field.
Surely I need to know what unit Network Rail used to then calculate elevation? If Network Rail use 1ft rise every 100ft, I then need to make sure I convert my track length to feet as well otherwise I'll be doing 137.2m / 100ft instead of 450.13ft / 100ft. Happy to be wrong!
As long as both parts are the same unit then the rise or fall will be in the same unit. So 1 in 100 will give a 1 metre rise or fall for every 100 metres if you are working in metres or a 1 foot rise or fall for every 100 feet if you are working in feet. Just don't mix the units.
I didn't really have a choice in the school I went to (which wasn't great) and my parents weren't that well off - so that came across as snobby if I'm honest. I also find it completely acceptable to ask for advice when I'm not an expert in that field.
It wasn't intended to be 'snobby', it's just that I left school 60 years ago and basic arithmetic and geometry was a given. Maybe they teach computer science now instead, I just don't know.
Surely I need to know what unit Network Rail used to then calculate elevation? If Network Rail use 1ft rise every 100ft, I then need to make sure I convert my track length to feet as well otherwise I'll be doing 137.2m / 100ft instead of 450.13ft / 100ft. Happy to be wrong!
No, a ratio is a ratio, 1ft rise in 100ft is the same slope as a 1m rise in 100m - converting ft to metres you'd get .3048m rise in 30.48m, or dividing both through by 0.3048 you get back to 1 in 100
The only pitfall would be if they mix units and started doing a 1ft rise in 100m (or other combination), but they don't.
As coppercapped said, for gradients the ratio has to be both units the same or it would never work, so 1 in 100 could be any unit of measurement at all, the angle would always be the same.
On maps it's the same - 1 inch (or cm, or metre even, on paper in front of you) : represents 50,000 inches (in real life) - hence they are sometimes referred to as "representative fractions".
At the risk of causing confusion, it may be worth knowing that gradients are also measured in % or even in 0/00. I think I am correct in saying that gradients on roads are now measured in % but they used to be shown as 1 in x. A gradient of 1 in 100 would be 1% and 1 in 4 is 25%. In European railway documents gradients are measured in 0/00 so I in 25 is shown as 40 0/00 or in Britain as 4%.
All dimensions are ratios and do not have units.
Another point is that length over which the height change is measured is usually along the slope. This is the length that can be measured whereas the true horizontal length cannot be measured easily. On a shallow gradient this will not make a significant difference but on a road with say a 25% gradient this will make a significant difference against the true horizontal.
It wasn't intended to be 'snobby', it's just that I left school 60 years ago and basic arithmetic and geometry was a given. Maybe they teach computer science now instead, I just don't know.
Apologies that I misread your post. They taught it back when I was in school (late 90s to mid-2000s) and they only just started to teach IT skills at that time instead of foreign languages. They probably do more computer science these days but I don't know either. I read articles that suggested some basic programming classes.
No, a ratio is a ratio, 1ft rise in 100ft is the same slope as a 1m rise in 100m - converting ft to metres you'd get .3048m rise in 30.48m, or dividing both through by 0.3048 you get back to 1 in 100
The only pitfall would be if they mix units and started doing a 1ft rise in 100m (or other combination), but they don't.
As coppercapped said, for gradients the ratio has to be both units the same or it would never work, so 1 in 100 could be any unit of measurement at all, the angle would always be the same.
On maps it's the same - 1 inch (or cm, or metre even, on paper in front of you) : represents 50,000 inches (in real life) - hence they are sometimes referred to as "representative fractions".
At the risk of causing confusion, it may be worth knowing that gradients are also measured in % or even in 0/00. I think I am correct in saying that gradients on roads are now measured in % but they used to be shown as 1 in x. A gradient of 1 in 100 would be 1% and 1 in 4 is 25%. In European railway documents gradients are measured in 0/00 so I in 25 is shown as 40 0/00 or in Britain as 4%.
All dimensions are ratios and do not have units.
Gradients on rail and road are measured slightly differently, as I understand it. On roads "1 in 10" means a 1 foot change in elevation for every ten feet of horizontal distance (substitute your units of choice). On rail it means a 1 foot change in elevation for every ten feet along the slope. (In trigonometrical terms, roads use the tangent of the angle, rail uses the sine). However, it makes little practical difference at the sort of gradients used on roads and rail - even at 1 in 7 the difference is less than 1%.
== Doublepost prevention - post automatically merged: ==
Another point is that length over which the height change is measured is usually along the slope. This is the length that can be measured whereas the true horizontal length cannot be measured easily. On a shallow gradient this will not make a significant difference but on a road with say a 25% gradient this will make a significant difference against the true horizontal.
The horizontal distance can be measured on a map (and the elevation can be taken from the contours). A 25% gradient along the slope will be tan (arcsin 0.25) = 0.258 or a little under 26% if measured against the (shorter) horizontal distance.
For those who have forgotten their geometry lessons, (or weren't paying attention)
tan (tangent) is the ratio of the vertical distance to the horizontal distance for a given angle
sin (sine) is the ratio of the vertical distance to the slope distance (hypotenuse) for a given angle
arcsin is the inverse function - given a value for the sine, what is the angle
Gradients on rail and road are measured slightly differently, as I understand it. On roads "1 in 10" means a 1 foot change in elevation for every ten feet of horizontal distance (substitute your units of choice). On rail it means a 1 foot change in elevation for every ten feet along the slope. (In trigonometrical terms, roads use the tangent of the angle, rail uses the sine). However, it makes little practical difference at the sort of gradients used on roads and rail - even at 1 in 7 the difference is less than 1%.
== Doublepost prevention - post automatically merged: ==
The horizontal distance can be measured on a map (and the elevation can be taken from the contours). A 25% gradient along the slope will be tan (arcsin 0.25) = 0.258 or a little under 26% if measured against the (shorter) horizontal distance.
For those who have forgotten their geometry lessons, (or weren't paying attention)
tan (tangent) is the ratio of the vertical distance to the horizontal distance for a given angle
sin (sine) is the ratio of the vertical distance to the slope distance (hypotenuse) for a given angle
arcsin is the inverse function - given a value for the sine, what is the angle
I recall reading somewhere that different countries expressing (railway) gradients in per cent (%) or per mille (‰ (or 0/00), i.e. per thousand) terms did not all calculate them the same way (I think the distinction was between America and Europe, but I forget the details)
Yes. Better indicated as ‰, but that's not an easily entered charcter here. Widely (but not I think universally) used in Europe, and useful as many gradients are between 1 & 10‰, or if you prefer 0.1 & 1% or 1 in 1000 and 1 in 100.
I think the symbol possibly seems intuitively wrong because we usually think about thousands and 3 places? But then if you follow that logic you would start wondering about the familiar percent sign and why it’s drawn like a fraction?
IIRC from a maths lesson long ago, the percent sign isn’t really based on a fraction symbol, it gradually developed from a shorthand way of writing “per cento” in the original Italian.
Concepts such as percentages, fractions, and ratios are certainly on the curriculums of respective parts of the UK.
The fact that they're listed separately (along with so many other individual aspects of maths) means that there can be a tendency to teach then in individual sessions, even though they're just different ways of expressing the same thing: a ratio. I know from experience that getting some pupils to make the connection between them can be a hard task. These days I'm digging up students' distant recollections of ratios when introducing them to the likes of voltage divider circuits.
As with so many things, the teacher you have, their style of delivery, and the conduct of the rest of the classroom has a big influence on what aspects of your education click, and which don't.
An older colleague of mine observed that pupils these days (or the past decade) weren't as comfortable in doing calculations in fractions, and were more at home with decimal values. (This was when delivering a special session to high-flyers too.) I have a personal suspicion that it corresponds to the loss of familiarity with imperial measurements (no more 12ths of an inch to work with) and greater use of calculator which present answers as decimals.* I'll leave it to the reader to consider how much of a good or bad thing this is.
*Recent scientific models tend to give answers as fractions, but students are then asking how to get a decimal value out of it instead.
I recall reading somewhere that different countries expressing (railway) gradients in per cent (%) or per mille (‰ (or 0/00), i.e. per thousand) terms did not all calculate them the same way (I think the distinction was between America and Europe, but I forget the details)
Yes. Better indicated as ‰, but that's not an easily entered charcter here. Widely (but not I think universally) used in Europe, and useful as many gradients are between 1 & 10‰, or if you prefer 0.1 & 1% or 1 in 1000 and 1 in 100.
Thanks. I couldn’t find a way to enter the character correctly using my iPad.
I also came to the conclusion that the mille rather than percentage gave a whole number and was therefore perhaps easier to read. We are now in the position where Railway Group Standards refer to TSIs and Euronorms which are written using the European terminology. I have found myself comparing the RGS standard for parking brake requirements of holding the train on a 1 in 30 gradient (shown as 33‰) with the Euronorm requirement of holding on a 40‰ gradient I.e. 1 in 25. In the UK we still need to comply with some European railway standards even though we have left the EU.
I think the symbol possibly seems intuitively wrong because we usually think about thousands and 3 places? But then if you follow that logic you would start wondering about the familiar percent sign and why it’s drawn like a fraction?
IIRC from a maths lesson long ago, the percent sign isn’t really based on a fraction symbol, it gradually developed from a shorthand way of writing “per cento” in the original Italian.
I always assumed the % character came from taking 100 and putting the one on a slope between the two zeros, but I don't actually know this. Per mille does the same with 1000.
I recall some in East Anglia that use the infinity symbol (8 lying on its side) for level. It's a bit strange but strictly correct because level can be thought of as "1 in infinity".
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Good explanation of the different road and rail gradient methods BTW.
