railroad curve

[VANCE]

Can anyone help me out here?

Attached is a map of a railroad in Ukiah. The curve or spiral in question starts at station 5841+49.9 and ends at 5847+47.0.

Thanks

[Steve Martin]

It looks like a Taper curve to me, Taper #1 per the standard Taper curve table in use by whichever railroad that built that line. A Taper curve is where they taper or change the degree of curvature (Railroad definition & probably based upon 50' chord lengths) for every 30' of centerline arc length. That is my recollection anyway. It seems to me that this has been brought up on this forum before. Try searching the archives for railroad curves or spirals as taper curves are a simple approximation of a spiral.

[VANCE]

no bearing are shown.

[mpallamary]

Hi,

Please be advised that there are several methods to calculating a spiral curve. Do you know the name of the Railroad Line? They did not use uniform methods. Most were field derived to facilitate layout.

As a general rule, set the PI intersection and then back out from there. There is a simple station and offset method as this relies on a compound calculation method, again to facilitate layout. I spent several years laying these buggers out throughout New England back in the '70's. If you use the X-Y method, you can fix the coordinate values by station/offset and then drop it in to your net. Is this for a layout or interpretation for a description?

I have other formulae but these are pretty standard. The various methods may vary as to the spiral formulae but as long as you hit the transition points into the circular curve, you should be okay. They usually rely on the chord method, again to facilitate their layout as the survey crew could stretch a 100-foot chord but not an arc. The 4 degree probably is a chord reference.

Hope this helps. Good luck.

PS, there are actually 3 of the spiral files. pdf images goot too large.

[Steve Martin]

Vance,

I read the T.1. portion at the end of the stationing to mean a #1 Taper Curve. On the Southern Pacific line and it's tributaries, a #1 taper means that the degree of curvature changes by 30 minutes for every 30' of arc length.

The length of the tapers in and out of that curve are 210' or 7 changes of degree of curvature in and 7 changes of degree of curvature out. It works like this: the first 30' of arc length has a degre of curvature of 0 degrees 30', the 2nd 30' of arc length has a degre of curvature of 1 degree 0' ... the 7th 30' of arc length has a degree of curvature of 3 degrees 30' and the central angle has a degree of curvature of 4 degrees. This curve has equal tapers in and out so the same applies to the taper out of the curve.

Take a look at the attached Southern Pacific Taper Curve Table. A #1 Taper in a 4 degree of Curvature curve
corresponds to the 210' taper length. That fits the stationing length listed on your curve.

Also attached is some information regarding the San Diego & Arizona Eastern Railroad Taper Curves and a deed from a property adjoining the SD&AE right of way.

I hope this helps. Let me know how you work it out.

[Steve Martin]

Here is a book that you can read online about Taper Curves:

http://www.archive.org/details/railroad ... 00perkrich

[E_Page]

Looks to me that you have 7 30' transition sections of curve in, and 7 out (7 x 30' = 210'). You have a 4 degree central curve, each section of transition should be another 30' degree of curve.

So going from tangent to central curve:
TC1 = 30' D of C
TC2 = 1 Degree D of C
TC3 = 1D30' D of C
.
.
.
TC7 = 3D30' D of C

Central Curve = 4 Degree curve

Mirror that on the way out.

Chord definition all the way through of course.


Which RR built this line? That will have a bearing upon which is the correct method to use.

[VANCE]

Thanks for the help.

[Lee Hixson]

Although I've never run into the situation, I've read that in a lot of cases where you have spiral curves for the tracks, the R/W lines are just regular curves. They purposely did not want to complicate the geometry of ownership or easement lines. Regretablly, I missed the RR seminar that was held recently. Can anyone who attended offer insight as to which companies did it this way, did they always do it this way, and any tips as to how you can recognize/confirm that it was done this way?

[E_Page]

Lee,

As I recall from Charlie Tucker's railraod surveying seminar last year, the RW curves are ALWAYS circular curves... except when they aren't.


I hope you find that more helpful than I did.


Edit: Oh, yeah, also from the RR seminar - And if you don't know the difference, you should be shot! - Charlie apparently believes in harsh penalties for one's ignorance.

[Steve Martin]

The deed I posted above is proof that Right of Way can be acquired on the Taper.

It does make the calculations more complicated and with what may be a few feet of offset to the projected main curve between tangents, I can see why Right of Way agent would prefer to use the simple curve.

How you prove it one way or the other should begin with research into the original Right of Way deed and the adjoiners deeds.

[McGee]

This is not a timely response, as this posting was only recently brought to my attention. I offer my interpretation of the attached RR Map as I believe it may be of interest to others. The initial posting does not indicate whether the author’s intent is to re-establish the center of the tracks or the center of the railroad right-of-way. It is my understanding they are not usually the same.

While working on a project for Union Pacific to reconstruct a slip out in Santa Barbara County between 2000 and 2002, we were requested to stake the railroad R/W. We were advised by Union Pacific Railroad at the Omaha, Nebraska office that the center of the R/W follows a circular curve as defined in the Southern Pacific Taper Tables and not the spiral curves as shown on the track map. We were supplied a copy of the Tables and an explanation of how they were to be used to establish the circular center of the R/W. At a CLSA Seminar in October 2009 titled “Railroad Surveying 101â€￾, speaker Charlie Tucker re-iterated this concept numerous times.

The following interpretations of the railroad map attached to the initial posting are made with reference to the attached Southern Pacific Taper Tables titled “S.P. Taper Curve Tables, Corrected March 1924â€￾.

The curve shown on the railroad map is a “Simple Curve – Equal Tapers at Both Endsâ€￾ (see attached diagram). The begin of curve station “5841+49.9 B.C.T.1â€￾ is the begin of a No. 1 Taper spiral curve which is defined as changing 30 minutes of arc for each 30 foot chord. The length of the spiral is 210 feet or 7, 30 foot chords ending at a point of compound curve where the spiral becomes a circular curve at station “5843+59.9 C.C.4°Rt.â€￾. The circular curve is a 4 degree curve based on two 50 foot chords enclosing 4 degrees of curvature. The radius “Râ€￾ of the track circular curve (NOT the same curve as the center of the right of way) is given in the Tables on Page 13 and 19 as 1432.467 (=25/sine(degree of curve/4). The radius “Dâ€￾ of the center of the R/W (NOT the same curve as the center of the track circular curve) is given in the Tables on Page 19 for a No. 1 Taper with 7 chords as 1434.116. The offset between the two curves is given as “dâ€￾ in the same Table as 1.649. The begin and end of the circular curve for the center of the R/W (again, NOT the same curve as the center of the track circular curve) is located 104.969 towards the PI on the semi-tangent from the BC and from the EC, respectively listed as “tâ€￾ in the Tables on Page 18 for a No. 1 Taper with 7 chords. The total semi-tangent shown on the map is 299.9 which agrees with the sum of 104.969 plus the semi-tangent of 194.96 (=D*tan(15°29’/2)). Assuming there is nothing in the deeds that would contradict this solution, using the track centerline for the R/W centerline would result in a 1.65 foot error in the R/W location in the circular portion of the curve.

The following link was offered up by and by Steve Martin in March 2010 as part of this thread, and by Evan Page, PLS in a 2008 thread titled Spirals who stated “The definitive reference on these curves was written by Lee Perkins, a SPRR field engineer, in 1915. A PDF version of this book can be found here: http://www.archive.org/details/railroad ... erkrichâ€￾.
A cursory inspection found the Tables in this publication to be in agreement with the Southern Pacific Taper Tables.

Michael McGee, PLS3945

[pls7809]

What a wealth of information!! Thanks to everyone who has posted in this thread.

[Stephen Johnson]

Lee,

As I recall from Charlie Tucker's railraod surveying seminar last year, the RW curves are ALWAYS circular curves... except when they aren't.


I hope you find that more helpful than I did.


Edit: Oh, yeah, also from the RR seminar - And if you don't know the difference, you should be shot! - Charlie apparently believes in harsh penalties for one's ignorance.

That is about a perfect description of RR ROW Curves.

BTW, I have rarely seen one that wasn't a regular circular curve instead of a spiral on the row. Though I found a US highway in Santa Fe, NM, that used a spiral.

[Steve Martin]

Taper curves came up in another thread.

Attached is some more information on Taper Curves and a copy of a deed for those who beleive that right of way was alway acquired on a simple curve as opposed to concentric with the mainline track centerline on Taper Curves

[pls7809]

Charlie Tucker's RR Seminar is coming in August. From the CLSA website homepage:

Railroads 101
Speaker: Charlie Tucker

August 7 - Santa Rosa, CA
August 14 - Ontario, CA

Mark Your Calendar! Registration for Railroad 101 will open soon!