Civil Engineering for Outdoor Railroads Volume 1

The AREA (American Railroad Engineering Association) manual states that passenger cars "... will ride comfortably around a curve at a speed which will require an elevation about 3 inches higher for equilibrium" (Route Surveying and Design, page 287).

In these definitions, an item called the degree of curvature has caused lots of discussion over the years. What is the degree of curvature and how is it used?

To understand the degree of curvature, an understanding of how and why it came to be used is important. In the days when civil engineers only had pencil and paper (even before slide rules), civil engineers had to lay out railroads and curves were an integral part of that design. The tools they had included a 100'' length “chain (or measuring tape). With broad railroad curves of 2,000-10,000 feet in radius and with probable trees and rocks and rivers in the way between the center of the curve and the centerline of the proposed track, a system was developed to allow field crews to lay out a curve with the minimum of hassle using a transit.

Surveyors use stations for measuring length in the field. One station is 100 feet. Frequently a surveyor''s chain is also 100'' or one station. A measurement using stations is usually represented as 11+43.25 This means that the point in question is 11 stations and 43.25 feet from some arbitrary beginning point or 1143.25 feet from the same origin (beginning point). Therefor one mile is station 52+80 from the origin. It can also be seen that one mile is 52.8 100'' chains.

When all calculations (even the computation of the tables of sine and cosine) were done by hand, approximations were acceptable. For example, if you are laying out the Union Pacific Railroad and are in the middle of hostile territory, you want to make the quickest calculations possible.

So the civil engineer would go out and eyeball the route to take (this is called route surveying). Then he would get a survey crew to take measurements of the existing untouched land and the civil engineer would reduce the notes to a set of drawings that showed the existing terrain well enough so that he could design the new track. He would then lay out the proposed track using angles and trigonometry and geometry. When he got the design he wanted, he created field notes for the survey crew.

So far, we have no need for degree of curvature.

The curves most railroads use are so broad that there is little difference between a 100 foot chord and a 100 foot arc. So in the early years of designing the railroads, the 100 foot chord was used to make it easier to calculate and easier to lay out. This is where the “railroad” or chord definition and a “highway” or arc definition  of a degree of curvature come from. By the time roads and highways were designed instead of just paving over dirt paths, abilities to calculate the results had improved enough for the arc definition to be easier to calculate and use.

The railroads had always used chord definitions and continued to use them so as not to have to alter all their records and plans. This is similar to my Aunt Cor in Holland. She loved trading recipes with my mom (her sister-in-law). The problem was metric and english measurement systems. Instead of converting all the recipes, she purchased a set of english measuring cups and spoons to avoid the conversions.

So what is the degree of curvature used for? It is used by survey crews.