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Old road retracements - R.R. vs. Hwy Degree of Curve

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Strictly Surveying

Last Post by rankin_file 15 years ago

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mike-berry

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I’m not sure if this is a regional, state, or possibly just a county specific situation, but I’ll offer this up to see if others have run across it.

Most of the early (1920’s through 1940’s) road surveys in this area have curve information calculated in Railroad (or chord) Degree of Curvature rather than Highway (or arc) Degree of Curvature.

The curve data on these old plans usually included Delta Angle, Degree of Curve, Length and Tangent. The curve Radius is not given.

The pitfall is that surveyors will assume that the record degree of curve is the familiar Highway Degree of curve, divide it into 5729.578, and then run with that radius. Which is likely wrong.

When retracing these old roads, I use the following information to determine if the record curve information is Railroad or Highway Degree of Curvature.

We use AutoCAD LDT 2007 and it has some nice tools to analyze a curve’s data in either type of curve definition. You can calc the radius for both R.R. and Hwy, slap a curve in between two tangents using either radius, and then use the Inquiry tools for both “Railway” and “Roadway” curves to confirm which method they used.

Sometimes the original data doesn’t seem to follow either rule. They rounded a lot of these values back then. And in some cases the difference in the two methods is insignificant. But in others, you can start deviating from the record pretty darn quick.

I put the following graphics together to try to more clearly illustrate the method to my above madness:

It is worth noting that most of these 1920s-1940s survey maps have corresponding field books and the curve tables in the backs of these books are for Railroad curve calculations. Which is a good hint at what to expect.

(apologies for the poor quality images. This info is from a ,pdf file I’ve put together and copying the images into paint and then saving them as jpg’s really took its toll)

Posted : February 26, 2011 1:49 am

Gregg Bothell

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My experience has been that Railroads (including trolly lines) always used chord definition, while state roads could be either “Chord” or “Arc” definition. Calculations should always be done to verify which method was used.

I have worked over highway plans prepared in the 1920’s that used Arc definition and plans from the 1970’s that used chord definition. PennDot didn’t have a strict standard it seems.

Posted : February 26, 2011 10:11 am

Kevin Samuel

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Good topic Mike.

I just had a discussion with the former Public Works Director of Jefferson County about this very subject. Seems he had run across some similar situations on a rail line in WA that gave him some fits. Apparently it was one of the few rail lines that used spiral curves in the design and they apparently used a boutique method of calculating the curve.

I also recall the following tips from this website

A few reminders:

1. Neither ORS 209.015 nor ORS 672.047 (Right of Entry for surveyors) trumps Federal regulation 49 CFR 214. Google that CFR and read for yourself.

2. Railroad curves use a degree of curve definition based on a 100 foot chord length.

3. Railroad map stationing is based on track mileage and is slope chainage, not reduced to horizontal.

4. Center of Track in a mainline curve is most likely NOT the center of the right-of-way! (rails and ballasts move toward the radius point over time)

5. There are no such things as parallel spirals on rights-of-ways, and railroad alignments were very rarely laid out with spirals at all.

6. Visual mileposts are merely 'cues' for operators and were never intended to fix rights-of-ways or stationing.

7. Not all railroad property interests were acquired by strip maps.

8. Notations such as "SC" and "Pro" on maps when r/w's cross PLSS aliquot lines are mere guesses.

9. T-rails (vertically driven rail sections marking r/w limits) are to be measured in the center at the BASE of the T. These are sometimes seen on r/w lines.

10. Fences do not necessarily lie on right-of-way lines.

11. Do not rely solely on county records as the only legal documents of record, especially as they relate to railroad interests.

12. An appearance of an abandoned r/w is often times misleading.... "discontinuance of service", pulling up rails, culverts, bridges, etcetera do not constitute abandonment.

Abandonments: will not necessarily be found in county records are implemented under 49 USC 10903 and 49 CFR 1105 & 1152, which is the STB Abandonment process
County and State rulemaking does not kick in until the federal process has been completed.

13. Do not assume railroad rights-of-ways are easements... they are quite likely fee simple takings.

Posted : February 26, 2011 10:45 am

mike-berry

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RR length of curve vs. HWY length of curve

The concept of curve length as expressed in RR curves was hard for me to comprehend. I hope these graphics help anyone who has to retrace roads created with RR curves.

In the following examples, the original Dodds Road curve in the above post is used. It is stationed both in arc degree of curve (“HWY” stations) and chord degree of curve (“RR” stations).

Blue line = curve, Red dashed line = RR chord stations.

1. Beginning at PC 127+20.6, which is the same point and same station for both the HWY and RR stationing, the next even 100’ station is set as follows:
HWY station 128+00 is set 79.40’ along the curve’s arc from the PC (for a chord of 79.36’)
RR 128+00 is set 79.4’ from the PC along a chord which intersects the curve arc.

This places RR 128+00 the dreaded 0.04’ further along the arc than HWY 128+00:

The same goes for the next 100’ station.
HWY 129+00 is 100’ along the curve's arc from HWY 128+00
RR 129+00 is set on the curve at a 100’ chord distance from RR 129+00

(At this point RR 129+00 is 0.12’ further along the arc than HWY 129+00)

This continues through the curve:

Until the last even 100’ station in the curve (133+00, where RR is now 0.45’ further along the curve’s arc than the HWY stationing).

From HWY 133+00 you need to go an arc length of 98.18 feet to the PT.
From RR 133+00 you pull a straight-line chord distance of 97.7 feet to the PC

Same curve, same beginning and ending points, but a different form of stationing results in HWY PT 133+98.18 and RR PT 133+97.7.

That’s why the
HWY curve length = 677.58’ and
RR curve length = 677.1’

And, for the sake of full disclosure, it was reviewing the LDT RAILWAY CURVE LISTING that brought this realization to light for me. I wasn’t sure what the ARC LENGTH vs. TRUE ARC LENGTH values meant until I dug deeper into the old RR curve formulas. I wish Jobo was posting these days, I think he cut his eye teeth on RR curves and probably knows all the old transit tricks and rules of thumb for running them in.

Posted : February 27, 2011 12:55 am

bill93

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RR length of curve vs. HWY length of curve

It is interesting to rework the problem with PC=127+00 and 127+50 to compare the lengths. The highway curve doesn't change except the station numbers get the appropriate constant offset. The shape and length of the RR curve change very slightly due to the approximations falling differently. You have to decide if you want to hold the degree/radius, or the PT/outbound tangent since you can't match everything.

Posted : February 27, 2011 8:21 am

mg1944

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That's interesting because I just took a PENNDOT surveying exam and one of the questions involved a "highway curve" with a radius of 3000' and a 16 degree delta.
The PI station was given and the question was for the PC station.
The problem was that when the arc was calculated, divided by two and subtracted from the PI station, none of the 4 multiple choice awnsers matched.
It is now clear to me that that had to be a railroad curve.
It seems to me that this would screw up calc's for deflection angles if you based them on the arc station lenghts assuming arc definition.
Talk about a trick question.

Posted : November 19, 2011 5:15 pm

Doug Crawford

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The way I way taught, for highway curves, calculate the tangent of the curve, subtract from the PI station to get the PC station, but I'm old and from Ohio

Posted : November 19, 2011 5:51 pm