Keepin' ON TRACK
Technical Data

HOW TO MEASURE THE CURVE IN DEGREES FOR HO:

Real railroads measure curves in the real world using the following method. Since there is no nice flat table top on which someone can map out a radius from a given center point in the real world engineers used the following:

Real railroad engineers measure a curve based on 100 foot cords. That is a distance of 100 feet is measured out and the difference (divergence) in the rail at that point from the starting point is the degrees of curvature of the track. In the prototype 10 degrees is a sharp curve, and this equates to about 88" radius in HO scale. 10 degrees in the real world is the smallest an SD45 can negotiate. The D&RGW had some 18 degree curves on the Monarch Branch and some 24 degree curves on the narrow gauge.

Why 100 foot cords? No body is certain, but some literature states that it is the length of chain that was practical for the early surveyors to use. It just became the standard.

Railroad data is listed as:


Remember in high school when the geometry teacher said to pay attention because some day you were going to need this? Now is the time to drag up your old memory bank and apply it to the problem. This assumes a 10 degree curve is needed and the math is below.

R = Radius

D = degree of curvature

R= 50/sin (D/2)

For a 10 degree curve, sin (10/2) = sin 5 = .0872

50/.0872 = 573 ft.

We don't have enough information to solve using the Pythagorean theorem, but simple trig should do. The angle is 10 degrees. The number we want would be the adjacent side of the triangle. Adjacent is the cos 0, so the cosine of 10 degrees is 0.984. Multiply that by 100 for 98.4 feet. Or if you want to know how far from the original center the track has moved it would be the sine of 10 degrees or 17.3 feet.

Since you do not want to go through all of that math, look at this NMRA web site (another free service of the NMRA): "http://www.nmra.org/standards/sandrp/s-8.html"

The chart in Standard S-8 shows the prototype degree of curvature, the prototype radius in feet, and below that the radius in inches for each of the major scales.

Edited from MR Forums in current editions.

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