Degrees of CurveModelers use radius when describing curves, but the real world uses Degrees of Curve. What is a degree of curve, it is the degree of offset per 100 feet. It would not be practical to draw a 300 or 400 foot radius curve in the real world, we can do this in the modeling.
There are 360 degrees in a circle, if you offset by 10 degrees per segment,
you will form a circle in 18 segments, 180/10=18. It then follows that 18
degrees of curve will take 10 segments and 45 degrees of curve will take 8
segments. See the following PDF files for a diagram of this. 

Translating from Real World Degrees of Curve to HO radius is easy if you
know just a little Trigonometry. If it takes X segments, at X degrees of
offset to form a circle, then each segment is X degrees of a circle.
Trigonometry tells use that in a right triangle, sin(Alpha)= Opposite
divided by the hypotenuse. If we draw a line from the center of the circle
and perpendicular to the segment we get a right triangle. So,


Using these equations we get two tables.Degrees of Curve to Radius Interesting Number From the above Tables
In real life the railroads use 1, 2 and 3 degree curves. Looking at the last three line, to make an HO scale 1, 2 or 3 degree curve takes a 65, 32 or 21 foot radius curve. 

Page Last Updated 12/19/2004 