Hi,
I published some about this topic on the old NGLS server. Basically, the use of spirals or easements were not in general use until the 1880's. The need for a spiral (and superelevation) is based on the maximum track speed. With narrow gauge speeds (with a few exceptions like the Boston, Revere Beach and Lynn) being very slow, they are not needed.
In my book "Civil Engineering for Outdoor Railroads Volume 1", I cover the history and the how and why of easements and super elevation and "degrees of curvature".
For an excerpt from my book, please visit [
douglasvanveelen.home.mindspring.com]
The Friends of the C&TS has a copy in their library. I believe I also sent copies to TVRM, the NMRA library, SCRM, and CRRM among the museums.
If you would like to purchase a book that includes programs to generate the tables I published in the book, the list price is $25.49 and $2.50 shipping. If you mention the Friends of the C&TS, I'll donate $2.50 of the purchase price of each book to the Friends of the C&TS.
If you would like a book but would like the $2.50 donated to another organization (like the Friends of the EBT) please contact me before making the purchase.
If you have any short questions, I'll be glad to answer them.
Your Chord method of laying out a spiral has to do with the geometric properties of a spiral and can be laid out that way for a good approximation of a spiral.
Doug