What is the steepest incline a locomotive can make. And also what are the incline laws for other counties.?

Question

What is the steepest incline a locomotive can make. And also what are the incline laws for other counties.?

Answer 1

It is not a question of legality, but physics.

Metal on metal is one of the most effiecent use of energy in transportation tems, because it minimises the frictional forces. But the downside is that as the gradient increases, more power is needed to produce forward motion and to prevent slipping backwards. Even so, there is a limit and I remember that calculating this was a problem that we were set in my University lectures

In general terms, railways are built with gradents of up to 1 in 100 (1%). From memory, the steepest sustained gradient on a UK main line is about 1 in 40. (2.5%).

Rack and pinion railways can climb far steeper gradients because the rack prevents slippage.

Answer 2

For US class 1 railroads, the now absorbed Southern Pacific's Siskiyou Branch of the Oregon (Shasta) Division boasted a grade of 3.1%.  There was another grade as steep, if not slightly steeper, near La Junta, Colorado, of the old Santa Fe.

The Siskiyou line has been short-lined and is now operated by CORP (California Oregon And Pacific).  I believe the trackage near La Junta is now a part of the BNSF or has itself been short lined.

There are other secondary and tourist railroads that have considerably heavier grade, particularly where "shay" type steam locomotives are employed.  Two that come to mind, although I am not sure the percent of the grade, includes Roaring Camp and Big Trees, near Felton, California, and the Cass Scenic Railway.

In addition, within this genre there is a steam powered "cog driven" tourist road where grades exceed 8%, although I don't recall the name or location.

There is (or was, as of 1962) a steam/diesel electric powered short line between Sao Paulo and Bela Horizante, Brazil, where trains on heaviest grades are assisted by cable, both ascending and descending.

I have worked the Siskiyou Branch, and ridden with my father at the throttle of the shay of BT&RC, and ridden on a steam engine of the cable railway in Brazil.  All very interesting.

I am sure that the funicular railways of the Alps, Andes, as well as other places in and through the mountains of the world are equally impressive in their design.  The many logging railroads of the US regularly traversed heavy grade with heavy log trains, again with Shays, Heislers and the Climax type, all steam powered with the cylinders drving geared trucks, as opposed to the conventional "side rod" arrangement so many are familiar with.

Though I am repeating myself, there is a formula to calculate power needs for given tonnages up a given grade, known as "The Rolling Train Resistance Formula".  It is calculated by taking the horsepwer per ton (total trailing tonnage divided by available horesepower), multiplying by 12 then dividing by the percentage of the grade, which will give you the speed this train would travel.  Put another way, HPT x 12 / %G = S, as long as the capacity of the draft gear is not exceeded, when a train separation will occur.

The "incline laws" are governed by gravity, which is pretty much the same everywhere on the planet.

A very good question.  I am sure there are some very good answers to follow.  Thanks for asking.

Answer 3

The steepest rack railway is the Pilatusbahn in Switzerland with a gradient of 1 in 2.