Calculating Railway Height

[edwin_m]

I suspect that gradient profiles are really an idealised version of a more complicated situation on the ground. All the profiles I've ever seen show straight lines between angular change-of-grade points. Even if a line could be built like that, it would be most uncomfortable to travel over.

In reality, there will be a vertical transition curve at each change of grade. In modern computer-calculated road alignments, such curves follow precise mathematical equations, and the lengths and levels along the curve are calculated to millimetre accuracy. But when railways were built, I imagine the surveyors just set out the main gradients, and the transitions were probably eyed-in during tracklaying.

When there are long straight grades, like the Lickey, those curves wouldn't have too much effect, but where a line has multiple changes of grade in a short distance, the cumulative effect could be that actual ground levels AOD might end up rather different from values calculated from gradient profiles.

Although they act as transitions between gradients, they are vertical curves of constant radius. In railway alignment transition curves only occur horizontally, and are sections where the radius and cant varies along the track to give a smooth, er, transition between the main (constant radius) curve and the straight or another curve. This isn't necessary vertically because vertical curves are of much larger radius than horizontal ones.

However, vertical curves only affect the elevation in the area of the curve itself. The elevation of the track beyond the ends of the vertical curve is just the same as if the curve didn't exist and the gradient changed abruptly at the position of the gradient post.

 

[Rescars]

In reality, there will be a vertical transition curve at each change of grade. In modern computer-calculated road alignments, such curves follow precise mathematical equations, and the lengths and levels along the curve are calculated to millimetre accuracy. But when railways were built, I imagine the surveyors just set out the main gradients, and the transitions were probably eyed-in during tracklaying.

When lines were first built, I'd guess some of the finer details were left to local interpretation. Presumably continuous rail is easier to lay accurately than pointed track. At the outset, not all rails were even connected with fishplates. As an example, there was no fishplated track anywhere between Castle Douglas and Portpatrick when this line in SW Scotland first opened (that's about 60 miles).