The term “minimum radius” can be very confusing to model railroaders, particularly those of us who want to make our outdoor layouts look more prototypical and less toy-like in appearance. As a necessity, manufacturers talk about minimum radius when they specify how their products will operate on our layouts. Sectional curved track are specified in radius. Most of us use radii when we are laying out our curves for our layouts.
Unfortunately, the real railroads do not measure curves in terms of radii. That would be impractical for them. Rather, railroad surveyors use basic trigonometry to layout prototype curves. They reference curves using a term called “Degree of Curvature”.
A 1° curve has a radius of 5729.65 feet. Curves of 1° or 2° are found on high-speed lines. A 6° curve, about the sharpest that would be generally found on a main line, has a radius of 955.37 feet. On early American railroads, some curves were as sharp as 400 ft radius, or 14.4°. Street railways have even sharper curves. The sharpest curve that can be negotiated by normal diesel locomotives is not less than 250 feet radius, or 23°. Even narrow gauge lines like the Rio Grande Southern had maximum curvatures of 24°, and there were only two curves that sharp … one at the Ophir Loop and the other at Trout Lake.
To convert degree of curvature into an actual curve radius, simply take the sine of ½ the degree of curvature and divide it into 50 feet. The result will be the prototype radius in feet. To find the model radius, just divide the prototype radius by the model scale.
Sound confusing? It is … unless you are a math major. A much simpler approximation is to divide the degree of curvature into 5729.65. The resulting number is the prototype radius in feet. Then divide that number by your scale and you have the model radius.
The following table does the math for you. I have converted standard track radii in one foot increments from 4 to 20 feet into degree of curvature for the five most common large scales. The curvatures are rounded to two decimal places. Degree of Curvature Table
As an example, if you are using 10 foot as your radius and you are modeling in 1:29 scale, then your curvature is slightly less than 20°. If you model in 1:20.32 scale and you want to layout a 20° curve, then your radius should be approximately 14 feet.
Hope this helps take some of the mystery out of curvature for both newbies and seasoned veterans alike.