Gradients...

https://www.sabre-roads.org.uk/forum/viewtopic.php?f=1&t=37346#p896795 claims that (in a UK context) rail gradients are 'track distance'  (i.e actual distance along the track) rather than map distance ( I.E absoloute  horizontal).

For most typical main-line rail gradients the approximations are broadly the same, but it would nice to know which is actually used in actual practice and in Open BVE ( which seems to follow the per mille convention used in Europe).

Do the professionals use track distance, or map distance, and if so how do I translate between the two?.

As you say, in continental Europe (for sure in Germany) railway gradients are expressed in "per mille" and are the [radial] tangent of the gradient, contrary to road gradients expressed in "per cent" and calculated as the [radial] sine of the gradient. However, as you also say correctly, the difference is not noteworthy. The steepest adhesive railway of the world is the Pöstlingbergbahn in Austria with a maximal gradient of 116 per mille, the steepest adhesive tramway of the world is the line 28E in Lisboa, Portugal with a maximal gradient of 135 per mille. arctan(0.135) is 7.68°, arcsin(0.135) is 7.75°. In other words: The difference is negligible.

OpenBVE it would seem used the per mille value.  Thanks .