(Disclaimer: To make things clear I'm talking about adhesion railways and excluding rack railways as those are an entirely different technology and requires specially equipped vehicles. Also I'm looking for examples as how this is engineered.)
I was surprised recently as I visited the Wutachtal railway in southern Germany. A particular section of this railway makes extremes detours with multiple bridges and tunnels in order to climb 231m while having a railway steep of only 1%.
According to the museum's explaination, the steep of 1% was required because they wanted to allow heavy military freight trains to circulate on this railway. However, steeper railways are very common, including rails which allows heavy freight trains. For instance, according to German language Wikipedia:
- The Gotthard railway has a max steepness of 2.8%
- The Simplon railway as well as the Neuchâtel–Pontarlier railway a max steepness of 2.5%
- The Arlberg railway in Austria has a steepness of 3%.
- The line between Vevey and Chexbres has a steepness of 4% and light freight trains circulates on this line.
Some trains which only allows passenger train and have narrow gauge have much steepers rails:
- The Uetli train in Zürich has a steepness of almost 8%
- The Pöstlingbergbahn has a steepness of 11.6%, (narrow gauge)
- Lisbon tramway has a steepness of 13.5%
Since the maximum allowed steepness is a major factor when designing a train line, I really wonder what factors determined it.
- What kind of problems appears when the rail is too steep for a train, is it a problem when going uphill (train slip and can't advance) or when going downhill (train slips and can't break)
- Does the weight of the train, or the power of the locomotive play a role
- Did technology allow steeper trains as time passed, or is there a hard physical limit that can't be overcome
- Why could Switzerland and Austria allows freight trains on 3% or even 4% steep tracks while Germany needed to limit itself 1%
EDIT: Since I asked the question, I've learn about a very interesting thing on the subject : In Geneva, 1904 a tramway line with a steepness of 11.8% was ready for usage but an accident when doing tests, where the tramway slipped and was unable to break, cancelled the line. So apparently the major problem is being able to break when going down. But the Lisbon tramway seems even steeper and didn't have similar accident as far as I'm aware.