For What It's Worth
"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 ft radius, or 23°. It is not difficult to apply spirals, in which the change of curvature is proportional to distance, to the ends of a circular curve. Circular curves are a good first approximation to an alignment.
The sharpest curve the Big Boys could negotiate was a 20 degree curve. The tenders, with their five rigid axles and one lead truck, were prone to causing problems on curves."
Therefore, a 20° curve will have a diameter of (5729.65/20x12/48x2=) 143.24 inches in 1:48 scale.
You can approximate what a real curve diameter in inches would be in O-Gauge 1:48 scale by dividing 2865 by the degree of curvature. (5729.65x12/48x2 = 2864.48)
Example of curvatures converted to diameter in inches for O-Gauge, 1:48 scale:
23° = 2865/23.3 = Ø124.6 inches (minimum for diesel locomotives)
20° = 2865/20 = Ø143 inches (Big Boy absolute tightest, slow speed)
14.4° = 2865/14.4 = Ø199 inches (sharp curve, early American railroad)
6° = 2865/60 = Ø477 inches (sharpest on mainline)
Alex