bartman-tn
[clip] While the railroad can install additional ballast, better condition ties and fasteners, and other items such as anchors, the rail will still expand. The hope is that the rail grows vertically instead of lengthwise.
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emphasis added - PDN]
Well, not quite - perhaps you meant to post instead that "the rail may still expand". In an ideal world - which is often achieved on the well-maintained lines - the ballast, ties, fasteners, and anchors, etc. would work together so well that the rail doesn't move at all as it heats up. What happens to the rail is that it experiences thermally induced compression stress - it is pushing against itself, but not going anyplace. As an analogy, think of an isometric exercise where you push against a solid wall. If you do it perfectly, neither you nor any of your appendages move at all, but you can sure feel the load / pressure /stress in your hands, arms, and muscles. It's the same with the rail. The trouble starts when the rail expands - then it starts to move longitudinally. That motion - often called "running" - can be fairly harmless if it is small in magnitude and remains in the same direction as the track. But if the movement starts to or wants to get large in magnitude, and then is or becomes constrained in both directions - such as by a grade crossing, a turnout (switch), bridge, or even the weight (mass) of the adjoining length of track - then the rail and track will take the "path of least resistance" to relieve that stress. In this context, the concern is that would be buckling into a sun kink at an (in)opportune location.
Next, technically, the rail will grow vertically when under such heat-induced stress, but only on a microscopic scale, per Poisson's Ratio (typically around 0.3 for steel, I recall). Without getting into all of the aspects of the theory of elasticity that pertain here ( a very difficult 3rd year spring course at Lafayette College, thanks to the challenging but enjoyable now-retired Dr. B. Vincent Viscomi !), that means that for every unit of deformation in the longitudinal direction, a corresponding ratio of deformation occurs in the other orthogonal directions - think of how a chunk of Jello would respond under similar pressures. To illustrate this with a very exaggerated example, if a very large chunk of steel is compressed by 1" in a certain direction (say, the X axis), it will typically expand in both of the other directions (Y axis and Z axis) by an amount equal to Poisson's Ratio x the amount of the deformation in the X axis direction, which is 0.3 x 1" = 0.3 inch.
To more clearly illustrate this, the pertinent length of rail would be 1 inch long. For a change in the rail's temperature ("/\ T" or "Delta T") from the "neutral temperature" that the rail should have been laid at - say 90 degrees F, to a typical maximum temperature - say, 150 degrees F, the /\ T would be 60 degrees F. Per the formula (see the excerpt from Railway Man's post below), the change in length would be:
Length of rail (in inches) x Coefficient of Thermal Expansion for Steel x /\ T (in degrees F), or here:
1" x 0.00000645in/in/degree Fahrenheit x 60 degrees F = 0.000387 inch, which is a little less than 4 / 10,000 of an inch, per inch of length of rail.
Multiplying this dimension by Poisson's Ratio gives the change in dimension of a 1" cube of steel in the other 2 directions/ dimensions/ axes, or:
0.000387 in. x 0.3 = 0.000116 in. per inch of distance, which is a little more than 1 / 10,000 of an inch, per inch of height or width of the rail section.
Since we're talking mainline here, let's use the height of 141AB rail, which is 7-7/16" = 7.44". So the amount of vertical "growth" (expansion) would be the "strain" in that direction per Poisson''s Ratio (above), times the rail's length or dimension in that direction, or:
0.000116 in. / in. x 7.44 in. = 0.000863 inch - a little less than 1 / 1,000 of an inch of vertical growth. So yes, technically the rail does grow vertically under heat-induced constrained expansive stress, but not by amounts that anyone would care about, I think.
Alternatively, the track could buckle upwards instead of sideways - that's rare, but I believe it has happened from time to time in odd places. I doubt if that's what you meant either, though.
Also, the following illustrative example is from Railway Man's post of 12-19-2008 at 12:41 AM to the thread "Re: Thermal Expansion and its Effects on Train Lengths" at - http://cs.trains.com/trccs/forums/t/143682.aspx - the distances, changes, analysis, and comments are the same for rails and track, except that the "neutral temperature" for adjusting the length and the residual thermal stress in Continuous Welded Rail ("CWR") is not 70 degrees - more often, it is a specific value in the range of 85 to 95 degrees Fahrenheit - which varies by railroad, territory, and the official making the determination:
"The thermal expansion coefficient of steel is 0.00000645in/in/degree Fahrenheit.
For a 10,000 foot train, the difference between -30 degrees in North Dakota in January and +120 degrees in Arizona in August is 150 degrees x 12 x 10,0000 x 0.00000645 = 116" = 9.675'
But "nominal lengths" of cars over pulling faces are not measured in North Dakota in January at -30, they're measured on a ~70 degree F day at the car builder, so the difference is only ~ 50 degrees or 3.225' between the average day and the hottest possible day. And this is for a 10,000-foot train. Few trains are of that length."
Finally, you're right about the railroad industry's efforts at finding automated or better methods to monitor levels of heat compression in rails/ track to detect and provide a warning before it gets severe enough to cause a sun kink. Although I'm not real familiar with that, it seems to be making some progress. While simply installing a "strain gage" type of approach may seem to be enough, I understand that a very big challenge with that - since all it really measures is the change in length / strain / stress - is accurately defining and measuring the inital state or starting value of the compressive stress in the rails. Without knowing that, you don't have the actual absolute value of that stress, so you can't know how much of a margin of safety is left before the risk of buckling becomes unacceptable. And that depends on defining and measuring the stability and stiffness of the track structure, which is a whole 'nother discussion for a later time.
- Paul North.
"This Fascinating Railroad Business"
(title of 1943 book by Robert Selph Henry of the AAR)