# Vertical Curves



## mrhsmith66 (Jan 27, 2017)

LargeScalers,

I'm wondering if there is a rule of thumb for vertical curves -- the transition track between a level and a grade -- in terms of radius. This would be of great help for someone like me who works out a track plan using one of those 3D CAD programs.

It seems to me there should be a rough relationship between the minimum/acceptable/pleasing radius you use for your rolling stock -- 80 foot passenger cars, Big Boy locomotives, etc., etc., and the vertical curve (another radius) you use to transition between level and sloped track. Say, for example, you use a 10 foot minimum radius then your rule of thumb -- this is hypothetical by the way -- might be twice that or a 20 foot radius for a vertical curves. Conversely, if your rolling stock is happy with 4 foot radius curves maybe an 8 foot radius vertical curve is all they need.

It would be great to hear from someone who came up with a quantitative rule of thumb. 

Thoughts, advice, suggestions?

Best hopes,

Hilary Smith
Pacific NW


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## David Leech (Dec 9, 2008)

Hilary,
I think that I would look at it around the other way.
What grade are you going into?
I only have around a 1% grade, so the transition from level to grade is really not measurable, it just happens.
If you are going from level to say 10% instantly, then there probably is a 'radius' of some sort, but you should really enter it gradually over a distance.
So, not sure this helps you, but good luck.
Cheers,
David Leech, Delta, Canada


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## armorsmith (Jun 1, 2008)

There are many factors to the question asked, none easily answered. David touched on is lightly with his example.Are you planning:

Mainline, branch line, loggin or mining?

Small short wheel base steam engines like an Aristo Rogers or a Bachmann 10 Wheeler?
Maybe narrow gauge equipment like Shays, Heislers or Climaxes?
Large longer wheel base stuff like a Big Boy or Challenger?
Big diesels like the SD70MAC?

How about rolling stock? Narrow gauge stuff in the 25 to 40 foot range?
Early to transition era 40 to 50 foot cars?
Modern in the 90 and up foot territory?

Heavy weight and streamline cars are longer and require larger radii curves and will require longer smoother vertical transitions than the turn of the century passenger equipment.

I will give the same general advice I usually give for track work. Use the largest radius curves your area will support. Same for vertical curves, a slow easy vertical curve will look great with small short equipment making the grade, however too sharp a vertical curve with longer rigid frames (steam mostly) will look terrible and quite possibly insert operational issues.

Look toward what you want the railroad to be first, that will help determine other factors along the way.


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## Greg Elmassian (Jan 3, 2008)

Also truck mounted couplers will take sharp vertical transitions way better than body mount.


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## MGates (Mar 16, 2016)

Easements aren't perfect arcs so it would be hard to give a simple radius or radii to use, I think it would have to be a mathematical formula to form an oblong curve over a certain run and rise? Not sure, I was never great with maths lol!

Lots of modelers typically choose a length to act as an gradual transition between level and constant grade and just try and make it as gradual as possible by eye, so in Z or N it would be a certain number of mm, in HO a handful of inches, and in large scale/G/Gauge 1 it would be feet. I did some drawings and it looks like 108in would give you a nice transition for a 3% grade, centered over the theoretical start of the grade.

I tried to find some sort of simple maths or rules that could work and came up with:

36"/3' easement length per 1% of grade that you transition to, centered over theoretical grade starting point from level plane.
Rise of approx. 0.6" per each 1% of grade that you transition to.
Here's an illustration I made:









Perhaps some data can be gathered about the curve that can be made under these parameters to get some sort of formula, someone much better at geometry and maths than me.

Best,
Mike


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## Ted Doskaris (Oct 7, 2008)

USA Trains 3 axle Diesels & Incline Transition Operation

The USA Trains 3 axle diesel locos (SD40-2, SD70 & ALCO PA/PB) are particularly sensitive to grade changes, especially with body mount couplers - mostly owing to how their trucks are inboard offset mounted toward the fuel tank. 










On the SD40-2, I had to raise up (remount) the front snow plow for dealing with a 1% incline change!



















See vignette, "_*USA Trains SD40 Snow Plow Relocation for Pragmatic Layout Operation*_"

-Ted


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## mrhsmith66 (Jan 27, 2017)

Many thanks to Ted, Mike (particularly good analysis), Greg, Armorsmith & David. All the comments and suggestions are quite welcome and informative.

What I should said upfront was my concern was for not only mainline vertical curves but also the vertical curves associated with a coal loader: what sort of vertical curves I should plan for coming out of the loader, bottoming out at the spring switch, and heading up the return kickback ramp?

Hilary


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