John --
I have already posted how to create spiral easements without math.
Here's a repeat of that message:
The key to good performance with any body-mounted coupler is your
trackage alignment. There is no real minimum radius for body-mounted
couplers IF you design curve transitions (spiral easements) into your
alignment. You can do this without math simply by using a length of
rail as a spline to plot your track centerline. First draw your
circular arc offset by about a half inch from your straight track
centerline. (Use a larger offset for very small radii, a smaller one
for very large radii.) Then place your rail spline so that its center
is approximately where the straight track should join the curve. Then
spike one end of the spline aling the straight-track line and the other
end along the circular arc. Spike each end in three places to ensure
conformance to both the straight line and the circular arc. Then use
the location of the spline as a template to draw your transition
centerline.
If you wish to have gently undulating alignment instead of perfectly
straight track, connect three lengths of rail (code 125 or heavier) with
rail joiners and solder them together so you have a perfectly straight
9-foot length. Spike this down in just four or five places and let the
rail take its natural shape between the spiked locations, then draw your
line along the edge of the rail.
There is a scientific/mathematical foundation for this based on
minimum-energy configurations of splines. Four our purposes, it's
enough to know that such an alignment for trackage minimized lateral
offset between the ends of railroad cars.
Dick Karnes
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