Vertical Curves - The Penultimate Word

Vertical Curves - The Penultimate Word

Postby gerhard_k » Wed Jun 01, 2016 5:47 pm

In Kalmbach's Model Railroad Planning 2016 annual, which came out about 2 months ago, way in the back on page 86 is a very thorough 4-page article about vertical curves, by Van S. Fehr. This topic has always interested me, mostly because of the casual rules-of-thumb that are bandied about (including by me in earlier topics on this board: Bernd's Otter Creek Falls Coal & Lumber Rwy. and Juup's Building Eisenbach :wave: ), and the absence of any kind of rational analysis in the past.

Btw, although I'm a mechanical engineer, I have always considered myself a bit of a language geek, perhaps partly brought on by coming over from Germany at age 14 and encountering this mess of a language that is American English :whistle: . So I felt a bit sheepish when I got to my 40's before I learned that 'penultimate' is not an emphasized version of 'ultimate', sort-of like saying 'singularly unique', but that instead it means the one last step before the ultimate version of something. And that's why I titled this thread the way I did, because on such a topic there is surely never The Ultimate Answer. But I digress (which I am told I do a lot :roll: )...

So Mr. Fehr, after searching the modeling literature and finding only 2 articles back in the 1970's that really didn't have any solid information, decided to do some serious work. He identified causes of problems from too-sharp vertical curves: derailing from wheel flanges lifting above the railhead, uncoupling from differential motion of car ends, and short circuits from (metal) loco pilots touching the rails. He selected 76 models of freight and passenger cars, and steam and diesel locos. He worked with the measurements of HO models, but that's no problem because vertical curves are scale-independent if they are related to loco and car dimensions. By combining the various possibilities in a big Excel spreadsheet, he had 1216 separate cases for minimum functional vertical curve radius. Plotting the results, he derived a limiting value for sharpest vertical curvature to be safely used on a layout.

In some earlier posts on this board, I had quoted an old rule, to plan for a vertical curve length equal to one car length for each % of grade change. As it turns out, that will certainly keep you out of trouble, but actually results in much longer vertical curves than are necessary, and we all know how tight space is on most model railroads. Van Fehr's data conclude that the minimum necessary vertical curve length is one car or loco length (the longest on your layout) for each 2.5% of grade change, a much more agreeable result for track planning.

He also has some practical suggestions for using the bending stiffness of the subroadbed to sort-of auto-create the vertical bend between two constant-grade sections. Finally, he points out that this minimum-length vertical curve can seem quite abrupt and toy-like, and if you have the available space, especially if you run long trains, that stretching the curve out to, say, twice the minimum will be more visually pleasing.

So it appears we finally have a rationally-based rule for designing the vertical curves on our model railroads. Does anyone have experience with intentionally-designed vertical curves that are sharper (shorter) than this new guideline, and still worked out ok? Inquiring minds want to know... :ugeek:
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Re: Vertical Curves - The Penultimate Word

Postby sacto-tt » Thu Jun 02, 2016 6:14 pm

Have you looked on line for prototype information on vertical curves? Both BNSF and NS provide online docs regarding calculating permissible vertical curves. Being a Computer Scientist, the math was over my head. :mrgreen:
-Joe-
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Re: Vertical Curves - The Penultimate Word

Postby oldtrainguy » Fri Jun 03, 2016 2:02 pm

Thats a lot of useful information. Thanks.

Im a little confused about how the car length fits in with the 2.5% grade. I know what the 2.5% is, the rise over the run but im not sure where the car length fits into that.
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Re: Vertical Curves - The Penultimate Word

Postby ctxmf74 » Fri Jun 03, 2016 2:21 pm

"how the car length fits in with the 2.5% grade"

It's rate of change. The grade should not go from level to 2.5% in less than one car length. Actually even though it can work I'd use a more gradual rate of change for appearance sake. Two car lengths for 2% is not very far in TT scale and just 4 car lengths would get one up to 4% grade which is plenty steep for trains......DaveB
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Re: Vertical Curves - The Penultimate Word

Postby gerhard_k » Fri Jun 03, 2016 10:29 pm

sacto-tt wrote:Have you looked on line for prototype information on vertical curves? Both BNSF and NS provide online docs regarding calculating permissible vertical curves. Being a Computer Scientist, the math was over my head. :mrgreen:

The author, in fact, starts by talking about prototype practice, and quotes Am. Railway Eng'g. Assn guidelines that require a 1075-foot (= 12 89' cars!) length for a 2% grade change at 50mph. At that rate, very few model railroads would ever be able to have any grades at all! So it turns out that, as with horizontal curves, selective compression is necessary for vertical curves on model railroads.
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Re: Vertical Curves - The Penultimate Word

Postby krokodil » Sat Jun 04, 2016 1:59 am

image.jpeg
Curve


In my practice I use for the vertical curve roughly two lengths of a standard locomotive (cca 30-40 cm). It is not a rule just a practice, if there is enough space the curve can be longer (better).
Especially in our scale with the new couplers it is extremely critical because in downhill ride the cars will push the locomotive and bring the coupler to decoupling. The former BTTB couplers or KADEEs are much better from this perspective. For that reason I replaced all new couplers (close couplers) with the older ones. Unfortunately the change for KADEE is to complex for my big and old fleet... :grin:
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