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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