calcualting minimum radius

Hi,

With the question brought on an earlier thread, I have finally found a simple solution. It took me a while to find it since I forgot one piece of information I had as a constant and was not a variable.

The basic equation has to do with geometry and similar triangles. However the two known distances are the rigid wheel base and the gauge difference between the wheel set gauge and the track gauge.

For example, a standard gauge wheel set (from what I could piece together from several sources) is 56.125". The standard track gauge is 56.5". This leaves a distance of 3/8" (0.375") or 0.031 feet. I will call this variable E.

I will define the variable C as being 1/2 the rigid wheel base.

The radius (R) is then R = C²/E + E.

To allow for a wider gauge in the curve, The equation becomes:

R = C²/(E + W) + E.
where: W is the extra width in the gauge.

W may also be considered the sum of all allowances for allowing a locomotive to round a sharper curve. In addition to gauge widening, this would include blind drivers and extra side play on driving axles.

To keep the math simple, I made the assumption that the chord length of the rigid wheel base on the outside rail and the track centerline would be the same which is not true. This gives a slightly larger answer for minimum curve.

For reasons of error in calculation and the probable changes in track alignment due to age in the field, I would add 5% to the minimum radius.

For a locomotive with a 10 foot wheelbase and the standard gauge gauge difference of 0.375" :

C = 10/2 = 5' = 60"
E = .375"
R = 60²/.375+.375 = 9600.375" = 800 feet.

To convert to the degree of curvature, use D = 5730/R.

This yield a 7.16 degree curve (about 7 degrees and 10 minutes).

With a 5% safety factor added in, the minimum radius would be 840 feet (6.8 degree maximum curve).

If you have a .125" gauge widening in the curve, E = .375"+.125" = 0.5"

This would yield a minimum radius of 600 feet. With a 5% safety factor, this is 630 feet.

I hope this helps out.

Doug vV