Gradient Transitions (again) and accommodation

[Steve Taylor]

Would anyone out there have knowledge of how P-Way and Civils in the mid-Victorian era calculated and laid out changes in gradient?

I'm currently at the stage of dividing up the engineer's 1:500 OS (re-scaled to 4mm) to give me the sizes and shapes for my baseboards.

 

The whole trackbed is on a gradient. From the east it runs as single track at 1:81, under an over bridge and through the single platform, however just of the west end of the platform there was a gradient board for a change to 1:100. This then gives 700mm of plain line from the gradient board to the switch tips of the crossover onto double track. I understand that a gradient change cannot take place exactly and completely at the point of the marker board and must be spread out and eased. Given that this is comparable to a change from level to falling at 1:18 could I take the marker board as an approximation and smooth the change in the 700mm of plain track, or should i double it and extend the easement back through the platform too making the transition in 1400mm? I'd like to get my head round this  asap since smoothing this transition across a board joint could be a major pain. The board joints are also subject to the position of earthworks, s&c work and rodding runs too.

 

Also........ bridges over lines with a gradient. Given the structure guage would the bridge be built strictly to the guage and incorporate any gradient in the design of its arch or would it simply be built as if on flat ground but with enough clearance for the structure guage on the side closest to the sloping trackbed?

 

If anyone has any thoughts I can post up the details of the sectional appendix giving the measurements for the prototype location if that would help.

 

Ps. Photographs give evidence that the up line through the crossover into plain single line had a cant though the down line to the west of the crossover did not. It must have been a hell of a racket with a 20 wagon mineral train crawling through, smacking across the crossover and opening up once clear, conversely the squealing of brakes, clanging of buffers and couplings on the down grade must have been a bit of an industrial orchestra at times. No speeding through this point even on a clear road since there was also a token change to consider.

[Grovenor]

A change from 1:81 to 1:100 is barely noticeable, and although it should certainly be spread out, ie use a vertical curve, 700mm of length will be more than enough. The prototype has specified minimum radii for vertical curve radius as it affects design of couplings, overhangs, underbody clearances etc. For relatively low speeds such as your case a suitable minimum radius would be in the region of 1000 metres full size, ie about 13m in 4mm scale.  Any normal bridge, eg for a road over would just be built level with clearances for the uphill end as you suggest, only a very long/wide bridge, approaching a tunnel would be built on the grade.

Keith

PS. You can use Templot to draw a 13m curve and overlay it on two lines intersecting at your 1:81 and 1:100 grades to determine the length of the curve and the tangent points.

[Steve Taylor]

Thanks for the confirmation that it is a practical consideration in 1:1 scale and worth examining in 4mm - even if perhaps not particularly easy to execute. Also thanks for the confirmation of the bridge design question.

 

Now to get this to work over a foamboard substrate.

 

Steve