How to calculate a scale gradient

Joe · Post by **Joe** » Sun Jul 05, 2015 6:46 pm

Hi I model in the standard sm32 scale so i wondered how do i work out the gradients on my line in scale terms? would be useful to compare them to real life inclines
cheers
Joe

AFGadd · Post by **AFGadd** » Sun Jul 05, 2015 7:15 pm

Hi Joe,

Simple answer is - A gradient does not scale.

Let's take the Rheidol as an example, the gradient on the final miles of the line stiffens to a fearsome 1 in 50. This simply means that for every 50 units of distance travelled the line rises 1 of the same units.
So every 50 feet the line rises 1 foot, or every 50 metres the line rises 1 metre. It amounts to the same gradient and the same angle.

And exactly the same rules apply on a model, whether 009 or SM32 scales.

Soar Valley Light · Post by **Soar Valley Light** » Sun Jul 05, 2015 7:15 pm

Joe,

Gradients are a ratio of amount of rise against distance travelled. As such they hold good for any scale.

1 in 30 (for instance) is 1 foot rise in 30 feet travelled, or 2 feet in 60, 3 feet in ninety, and so on. In 16mm scale a 16mm rise in 480mm travelled is a gradient of 1 in 480mm divided by 16mm the result of which is 30, i.e 1 in 30, just the same in any scale you see.

I hope this helps (more than it hinders!)

Andrew

AFGadd · Post by **AFGadd** » Sun Jul 05, 2015 7:19 pm

Soar Valley Light:111897 wrote:Joe,

Gradients are a ratio of amount of rise against distance travelled. As such they hold good for any scale.

Andrew

We both posted at the same tome Andrew...

Soar Valley Light · Post by **Soar Valley Light** » Sun Jul 05, 2015 7:20 pm

Great minds think alike - especially when they share the same name!

I think your explanation was a little clearer!

AFGadd · Post by **AFGadd** » Sun Jul 05, 2015 7:28 pm

Soar Valley Light:111900 wrote:Great minds think alike - especially when they share the same name!

I think your explanation was a little clearer!

Of course Andrew!

However, I have NEVER understood (or tried to understand) measuring gradients using percentages???

Soar Valley Light · Post by **Soar Valley Light** » Sun Jul 05, 2015 9:44 pm

Me neither!

I can deal with the maths but the value is meaningless to me!

Andrew

MDLR · Post by **MDLR** » Sun Jul 05, 2015 10:22 pm

Soar Valley Light:111903 wrote:I can deal with the maths but the value is meaningless to me!

I can't do the maths, but as we are all brought up with "1 in XXX" gradients in the UK, I also have no conception of what a percentage gradient might represent. Perhaps on of our members across the Channel or on The Left Hand Side of the Pond could provide equivalents for (say) 1 in 50 and 1 in 100 to give us an idea.

ikcdab · Post by **ikcdab** » Sun Jul 05, 2015 10:28 pm

Actually percentages are much easier. Its just the percentage rise against the distance. so 25% means that the rise is 25% of the distance - so its the same as 1 in 4.
so 1 in 100 equates to 1% and 1 in 50 equals 2%.
so to test you, what would 1 in 30 be?

invicta280 · Post by **invicta280** » Sun Jul 05, 2015 10:29 pm

I always assumed a 10% gradient was 10/100 =1/10 or 1 ft rise or fall per 100 feet horizontal. i.e, 1 in 10. Is it something else then?

ikcdab · Post by **ikcdab** » Sun Jul 05, 2015 10:31 pm

invicta280:111910 wrote:I always assumed a 10% gradient was 10/100 =1/10 or 1 ft rise or fall per 100 feet horizontal. i.e, 1 in 10. Is it something else then?

No, thats correct but 1 in 10 would be a TEN foot rise or fall per 100 feet horizontal.

This is why percentages are much easier!

MDLR · Post by **MDLR** » Sun Jul 05, 2015 10:34 pm

ikcdab:111909 wrote:Actually percentages are much easier. Its just the percentage rise against the distance. so 25% means that the rise is 25% of the distance - so its the same as 1 in 4.
so 1 in 100 equates to 1% and 1 in 50 equals 2%.
so to test you, what would 1 in 30 be?

3.33%?

steampig · Post by **steampig** » Mon Jul 06, 2015 12:05 am

Somewhere or other I have acquired the idea that gradient measurement quoted in % is the fraction (vertical distance travelled)/(road distance travelled) - the denominator being the hypotenuse of the right-angled triangle with the other two side being horizontal and vertical distances travelled. It is therefore the sine of the angle of the road to the horizontal (expressed as a percentage), whereas the x-in-y measure is the tangent of that angle (as a ratio). However for railway gradients, and all but the most extreme road ones, the difference is probably negligible.

invicta280 · Post by **invicta280** » Mon Jul 06, 2015 6:50 am

ikcdab:111911 wrote:
No, thats correct but 1 in 10 would be a TEN foot rise or fall per 100 feet horizontal.

This is why percentages are much easier!

Doh! yes of course. (It was late in the day when I posted)

Post by **ge_rik** » Mon Jul 06, 2015 7:27 am

MDLR:111912 wrote:
ikcdab:111909 wrote:Actually percentages are much easier. Its just the percentage rise against the distance. so 25% means that the rise is 25% of the distance - so its the same as 1 in 4.
so 1 in 100 equates to 1% and 1 in 50 equals 2%.
so to test you, what would 1 in 30 be?
3.33%?

So, would that be just under a penny ha'penny in old money?? ;)

Rik

Soar Valley Light · Post by **Soar Valley Light** » Mon Jul 06, 2015 8:19 pm

Just when I thought I was getting the hang of it - I worked it out to be one pence farthing!

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