Degrees of Curve
Modelers 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.
Degrees of Curve 10.pdf,
Degrees of Curve 18.pdf,
Degrees of Curve 45.pdf |
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,
-
sin (1/2 A) = 50/R - Multiple each side by R
-
R * sin(1/2 A) = 50 - Divide each side by sin(1/2 A)
-
R = 50/sin(1/2 A) - Replace 12/ A with A/2 (makes it
easier to read)
-
R = 50/sin(A/2) - This is
our first equation. How to find the Radius from the degrees of Curvature.
-
R * sin(A/2) = 50 - Starting with the equation from step
2, Divide each side by R.
-
sin(A/2) = 50/R - Take the Arc Sin of each side.
-
A/2 = arcsin(50/2) - Multiple each side by 2.
-
A = 2 * arcsin(50/2) -
This is our second equation. How to find the degrees of curvature from the
radius.
 |
Using these equations we get two tables.
Degrees of Curve to Radius
Radius to Degrees of Curve
Interesting Number From the above Tables
| |
Degree of Curve
(Degrees) |
Radius (Feet) Scale Feet |
Radius (Inches) for HO |
| Minimum Free-Mo curve for a branch line |
22.063 |
261.300 |
36.000 |
| Minimum Free-Mo curve |
18.880 |
304.850 |
42.000 |
| 100 foot radius curve |
60.000 |
100.000 |
13.777 |
| |
1.000 |
5729.651 |
789.389 (65.78 feet) |
| |
2.000 |
2864.934 |
394.710 (32.89 feet) |
| |
3.000 |
1910.078 |
263.156 (21.93 feet) |
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. |
