Let the height be h, and let x = 1 mile, and the length increase d = 1 inch. Apply the Pythagorean theorem to a right triangle with hypoteneuse x/2 + d/2, base x/2, and height h: h^2 + (x/2)^2 = (x/2 + d/2)^2, or 4*h^2 + x^2 = (x+d)^2 = x^2 + 2dx + d^2 from which 4*h^2 ~ 2dx so h^2 ~ dx/2, h ~ sqrt(dx/2) ~ 178 inches ~ 14' 10"
rangerssuck wrote in news: snipped-for-privacy@googlegroups.com:
Nope.
Correct answer is 2 pi feet.
Nearly fifteen feet.
Looking at it simplistically, it's around 17 feet (somebody did the math; I checked it, and it was right).
However, in practice, what would it be? Probably less than a foot, because of the compressive elastic modulus of the rails, lifted up, and, once again, the catenary sag of the rails, which would consume almost all of the linear expansion in the curve.
That's my story and I'm sticking with it. d8-)
Makes a pretty good case for expansion joints.
Ed, in practice there'd be expansion joints or someone looking for a job. It would also probably make a hell of a noise.
True. But there have been alleged occassions of welded rail buckling from heat. I never checked this out, but I remember the question coming up when they converted much of the Northeast Corridor line to welded rail and concrete ties.
'Dunno. There are too many other things to check out.
On 08/13/2014 11:55 AM, rangerssuck wrote: ...
The new continuous rail rely simply on sufficient hold-down force to restrain it -- I was wondering not terribly long ago as was watching Union Pacific replacing a bunch of the main line thru here as were having not uncommon KS summer days of 105F or on occasion quite a bit higher than that...so I looked up and as far as I could find that's the way it's done. No magic low-expansion alloys, or other tricks I could find...
I was told that the new long rails that are used these days are installed under tension with some sort of winch like device to counteract expansion in hot weather.
Don't recalling finding that in the looking I did, but it certainly wasn't exhaustive. I don't see anything looking like it would serve that purpose on the UP work train here at the moment; will have to look more closely. Would be nice if they'd let me close enough to talk but doubt will before they get antsy...
Tracks are welded end to end to limit the wear and tear on the wheels. They have expansion spots that are switch joints and the long expansion runs down the spur. I talk to two different RR line members most every day.
Martin
David Billington posted for all of us...
And I know how to SNIP
Good sites for the OP to buy! Maybe get a free sample...
news:2JdHv.192264$ snipped-for-privacy@fx07.iad:
I wound up making my own -- no local sources, and I needed them faster than I could get them shipped in. Not to mention cheaper and more fun.
Thanks for all the replies, though.
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