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A Sensible Ruling Gradient?

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Diplodicus

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8 Mar 2013
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When constructing a '1 11½" narrow gauge line, climbing a long valley, what would be:

  1. a sensible ruling gradient over five miles;
  2. a maximum gradient for 880 yards;
  3. minimum radius curve?:
Many thanks
 
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Tim M

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When constructing a '1 11½" narrow gauge line, climbing a long valley, what would be:

  1. a sensible ruling gradient over five miles;
  2. a maximum gradient for 880 yards;
  3. minimum radius curve?:
Many thanks
This really depends on height difference between the start and end of your railway.

Taking the Ffestiniog Railway as an example, over the 7 and a half miles from Porthmadog to Tan-y-Bwlch the height difference is about 130m using an average grade of 1:80. Tyler’s Curve is the sharpest at just under 50m. Those clever pre Victorians designed the railway 190 years ago with a constant gradient ensuring unchanging (literally) horse power requirement.

A short steep hill might mean larger and more expensive motive power, for example the Welsh Highland Railway with long stretches of 1:40 has locos twice the power output of the FR. When the FR built the Deviation in the 1960’s/1970’s it included a spiral to maintain a constant gradient to gain height.

You need to look at your railway as a system, matching your motive power requirements to the route, avoiding short hills and sharp curves at all costs.

Google ‘Festipedia’ for more details of the Ffestiniog and Welsh Highland Railways where there’s nearly 200 years of history to explore. Tyler’s Curve has its own page as does the Deviation.
 

Magdalia

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You need to reframe your questions to think this through properly.

As Tim M says, your most important constraint is the height difference between the bottom end and the top end of the railway. The gentlest ruling gradient you can have is constant. Any variation in gradient makes the ruling gradient steeper.

But anyone with a rudimentary knowledge of geography will appreciate the river valleys are usually concave, very steep at the top end and almost flat at the bottom end.

This mean that most railway lines in river valleys climb up the side of the valley at the bottom end, are high above the valley in the middle, and then return to river level at the top. This requires either expensive engineering work or sharp curves, in order to cross the tributary streams coming down the valley sides.

I'm more familiar with standard gauge than narrow gauge, but the principles are the same. A good expensive engineering work example is the Settle and Carlisle in the upper Eden Vale between Appleby and Ais Gill. A good sharp curves example is the climb from Bridge of Orchy to the County March on the West Highland.

As Tim M says steeper ruling gradients come with motive power costs. Steep gradients and sharp curves also affect journey times. The answers to your questions then become trade offs between initial construction costs, and ongoing costs and revenues.
 
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