Railroad Curve-101

By my computations using my trusty ole hp-48 I get the following information:

CHORD definition curve.

Radius=1763.183
L=707.787
Chord=703.044
D=(given)3.15
delta=(given)23.0000
T=358.724
E=36.122

I am assuming the information is for the centerline of the railway, hope this provides the number you need to get it into ACAD. It wouldn't hurt to have someone double check my results.:-)

I get the same numbers. For most railroad I encounter it's a simple process. Locate the tangents from best evidence. That's usually rails and bridges. Fillet off the curve using the radius that matches degree of curve by chord definition. Check against the curve information and reliable stationing on the plans. It's fairly rare that I need to do more...

If you start with 3-15-00 railroad degree of curve, and 23 degree delta, I concur with Robert Locke's numbers except that his length is the arc length, whereas the calculated railroad stationing length would be 707.69. I haven't taken the time to calculate the actual value starting with the exact fractional starting and ending stations; it will be close but not exactly that.

Whether the data would be for the centerline, inside rail, or outside rail depends on the practice of that railroad line. I think it may be more common to use the inside rail, but I'm not sure of that.

Someone re-stationed the rail-line and re-measured the degree of curvature as significantly different from the original design. The curvature could have drifted over the decades since the line was originally built as rails and ties settled in and as they were replaced.

What I don't understand is the increased degree of curvature. Some of the curvature would tend to work its way into the original tangent sections to lengthen the curve and reduce the degree of curvature. Somehow it has been rebuilt with greater curvature?

See below for my calculation of the original curve design.
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Tutorial:
With a degree of curvature only about 3 degrees, there isn't a lot of difference between a highway (arc definition) and railroad (chord definition) curve. Nevertheless, you will want to use the railroad formulas.

I find my homebrew calculator to be quite useful.
https://dl.dropboxusercontent.com/u/25124076/CurveCalc.exe

Recognize that degree of curvature has two definitions. Convert either of them to radius using the appropriate formula. A circular curve has only one radius but two measures of curvature, sort of like a room has one temperature but Fahrenheit and Celcius degree readings, only not as much different.

The other thing that is different is the railroad stationing is based on chords between PC, even stations, and PT whereas highway curve stationing is based on arc length. One annoying result of the RR stationing is that the curve you end up with is very slightly different depending on where the PC happens to fall between even 100 ft stations. That difference may of course be lost in the overall imprecision of layout.

Everything else you know about horizontal curves applies to both.
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Calculation with original data: It is a little confusing how someone has marked up the original data. If I read the struck out numbers correctly, the original design was
RR degree of curvature 3 degrees
Delta 23-00-00

From those I calculate:
Radius 1910.08 ft
Railroad pseudo-length Lrr=766.67
The pseudo-length is approximately the sum of the stationing chords.
Long Chord 761.62

And I read the struck out stationing as
3443+29 PT
3435+62 PC
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767 ft RR pseudo length (approx sum of chords)

This matches the calculated Lrr within 0.33 ft, so things are close.

ok, so I got the same curve calculations. here is where my problem comes in...when I put them into AutoCAD and have it create the curve the curve line does not fall inline with my field shots. There was very little error in the survey so I am confident that they should coincide. Thus I did not know if I was missing a bit of information about rr curves. In the field we took shoots along the each rail. I did a best fit line along the strait away and the largest error was 0.01. I then placed the centerline of the rail between the two rails. With that I figured the curve should be rather close.

that's cause the rails will be in spiral-curve-spiral, the curve should not fit the right of way. put in a spiral, 200' maybe 300' and see if your rail shots fit then

If the plans showed a Point of Spiral, Point of Curve to Spiral I would agree. The begin and end are labeled PC and PT. It is possible the rails were constructed with a spiral in and out but the right of way is a simple curve.
You may notice a consistent offset through the curve due to construction methods or distortion from use. That's the prime reason I stay in the tangents for the alignment locations...

Yes just about every railroad row is a simple curve, and all rail curves are spiral-cruve-spiral. They should me following a track that moves them to the inside of the centerline oh the row

vl

Be*, of* dang phone

If No Spiral Specified, The Track Gang Would Field It In

Simple Way for a 200' spiral, assuming 0.5' offset?, measure back from PC on tangent 100', measure to inside of curve, 0.5', layout out curve, measure 100' chord on curve. mark mid-point of 0.5' offset, i.e. 0.25', hold 100' back from PC, mid point of offset at PC and 100' point along curve. eyeball in the rail through those 3 points and you have a good enough spiral for non main line tracks.

As explained by my father, who worked the DL&W RR track gang from 1927-1930, or thereabouts. After DL&W abandonment we walked the track he laid and picked up a few tie nails from those years.

Paul in PA

If No Spiral Specified, The Track Gang Would Field It In

And if they didn't build it with a spiral, the moving train would do it for them;-)

If No Spiral Specified, The Track Gang Would Field It In

> And if they didn't build it with a spiral, the moving train would do it for them;-)

Yep, similar to setting the gauge..we'd set it a 4'-8 1/4" and let the train take care of the other 1/4"

Mike, not so fast

Assuming that the rails were laid out, as the plans said, in a simple curve. The train itself would make the sprial, curve, and spiral, which is why, today, we lay out spiral, curve, spiral, so that it best fits what the train wheels are going to do in the first place.

Joe Glidden explained this much better than I, and upon a great deal of research, I agree with his findings. For this reason, when replacing RR, I use tangents and PI's and radius and the center of the track through the curve is just where ever in the hell it happens to be. 🙂

We use the tangents to fit the curves as best we can. Even with locating the rail every 5 feet with the trolley. Another thing to be aware of is the interval at which the rail is located. In the tangents, 50 to 100 foot stationing might be ok, but we always make it shorter going into the curve and through the curve/spirals.

Mike, not so fast

Yes, I think we agree, except that the plans have little to do with the track location in the curve and that wasn't an accident.

Maybe in the early days of railroad design, but it probably didn't take long to realize that simple curves wouldn't work.

So the railroads (in my area for sure) intentionally laid out the rights of ways with simple curves and laid out the tracks spiral-curve-spiral. They understood that the centerline of the track through the curve would slide to the inside.

I just wish highway engineers would do the same.:-/

There are of course exceptions, I'm working on two different boundaries, one with simple curve right of way (legals filed in the courthouse 1900's showing simple curves), and spiral-curve-spiral track (valuation maps showing spiral-curve-spiral which I can ignore for right of way). The other boundary has a railroad with that rare document acquiring right of way using spiral-curve-spiral.