I found a document on the WWW by someone from Mi. DOT explaining how their highway spiral curves are constructed, but because it is based on an arc defined degree of curve instead of chord defined I wondered if the construction is the same.
I have a long tangent passing through the property I am surveying with similar Spiral curves at both ends. Both curves are 3 degree curves with 3*30' spirals in and out and exit the tangent turning to the right. Stationing is next to impossible to read on the map copy I have, but my best guess is that the TS to SC by stationing is 228 feet for both curves. One curve has a delta of 24*22' and the other is 40*44'. Here is a snippet of the map;
The tangent line in question is highlighted with a red line and is the only active line on site. The other line was abandoned many moons ago. The stationing and curve data is on the plan but is written so light it is next to impossible to read.
As I understand the construction of a Spiral Curve, you fillet the tangents with a radius to define the simple curve, then that is moved toward the radius point based on a calculation of the 3*30' Spiral, this is where I am getting lost. I can't seem to figure out that calculation.
Go online and try to find "The Railroad Spiral by William Searles". This should help you define what you are trying to do.
Sometime ago, I downloaded a copy from Google.
Jim Crume has an excellent publication regarding spirals. Everyone should have it...
I found his online Spiral Calculator but I can't get it to give me anything close to the verifiable answers. Leads me to believe there are more than one or two ways to skin a Spiral cat.
I found this book image online. The answers I am looking for seems to be there and I am working on getting it downloaded and printed.
I am not sure about Colorado, but in Texas, where they used a spiral, either on a RR or on a highway, it was used only on the railway or the roadway and not on the right-of-way. B-)
Spiral Curve, American Railway Engineering Association, D&RG
About 40 years ago, I was involved in staking a couple spirals on the Denver & Rio Grande Railroad. The Rio Grande engineer gave to me copies of pages from the American Railway Engineering Association Engineering Manual and said that was the method the Rio Grande used. At the time, I used an HP45 to do the calculations. Today, I'd use a spread sheet. The formulae were, as a matter of convenience for slide rule calculations, dependent upon the versine(delta/2) which is equal to [1 - cos(delta/2)].
Tables as well as discussion from "Route Location and Design" by Thomas F Hickerson provided additional useful information.
See:
Manual of the American Railway Engineering Association
By American Railway Engineering Association
http://books.google.com/books?id=aMkFwx490QUC&pg=PA100&focus=viewport&vq=spiral
From the current manual
In staking by deflections, considerable convenience is sometimes found in dividing the spiral in ten equal chords, conforming to the theory upon which the formulas are based.
From the 1965 manual
In staking by deflections, it is sometimes convenient to divide the spiral into a number of equal chords.
Spiral Curve calculator has been my goto program.
I have SMI V7 DOT on an HP48 that does spiral curves also.
Hickerson Route Location and Design is a good source of anything in that category.
I use simple curves for the ROWs around here.
Using best fit usually works very good on RR r/w that involve curves. They have few r/w markers if any and not so many things on the maps can be found in the same place.
Center of bridges and tresses usually match and road crossings. The mile markers that can be found are usually in the same place anymore.
0.02
Get the book...
Spiral Curve, railroad definition, questions? Thanks all!
The links were helpful and will get me through the current situation. Some day I fully intend to discover how these curves are constructed so I don't have to use "by guess and/or by God" methods. If one knew how they are supposed to be, he could easily recognize when they are not as they should be.