ok...so lets go in oncemore.....
first, lets talk about ways to name inclines.
1.) the degree-method
1a.) old degrees:
in old-degrees, a circle has 360 degrees, a "right" angle 90 degrees.
1b.) new degrees:
a circle has 400 degrees, what gives the advantage of easier parts: 200 for a hlaf, 100 for a quater 50 for 1/8, 25 for 1/16 circle. this is just used in surveyors community , but not really to name inciles, nor the 360 degrees version.
2.) the relativity method:
it is based on a fixed amount of height-difference of "1", no matter what the unit is: inches, meters, kilometers, miles...as far as u use the same on the length!
So:
1: 100 means: for a (topgraphical) lentgh of 100 units u raise 1 unit.
1: 30 means on 30 units un raise 1 unit.
As far as we use "normal" Railroad-gradients, the topgraphic length and the related length (real length) can be considered the same.
up from 1:40 or 1: 30 gradients it may be intersting to calculate the real track length.
3.) the "percent"-method
most people get puzzeled with this, because they consider a housewall as a 100% gradient: the steepest thing they imagine.
But thats just another "writing" for the degree-methods: 100% would be 90 degrees, 50% would be 45 degrees.
BUT THAT IS NOT!
the percent-method gives another length-raise-relation:
this time the base is always the same: 100 units of topographic length raises the given amount of units.
10% means: on a base of 100 units u raise 10 units. 10 units per 100 units....per 100...per cent.
4.) the permille-method
its exactly the same as the percent-method, but based on 1000 units length. thas done because many RR have fine differences in gradients that gives broken percentages: 3,3% 5,1% 1,3% this is the same as 33‰ 51‰ 13‰
prototypical RR are like this:
mainlines: tried to be held on a max of 1-1,5 %, on about 2 % the operations become difficult with long trains and because of security questions (brakes) most lines over 2% are named "steep-line" with special instructions.
average lines: the lines are often more smooth "on the landscape" and often have inclines of 2 or 3 % up and down, with less affect to the operations with mostly short trains and less goods-transports.
branchlines: some branchlines going to the bottom of the mountains out from the plains have incines of 3 or 4 % as a standard.
mountainlines: engineers found out that on about 7% theres a savety-line for operations, whats going steeper needs to have a rack. but there are tram-lines (modern ones) with 12 or 13 % inclines over kilometers, but the light cars have heavy brakes (magnet-line-brake). The onyl "old" line i know with 13 % without rack is in portugal with a streettram going down along a church.
fastlines:
because of the good traction and kinetic energy the inclines on fastlines are sometimes heavy (up to 4%). Thats no problem for the ICE-train, but for the builders-trains bringing material to the building lot.
a max of 4-5% , reduced to 2 % the sharper curves get is a good advice for the gardenrailroad. it was told here before.
Frank