Well, I must have missed your earlier post, 'cause I don't remember seeing any 
of this before.  But I'm not sure I completely understand it all, anyway (I 
didn't pay much attention in math class).  So maybe I'll just try to build 
myself a large version of an old drafter's tool called a "French Curve" 
(http://mathworld.wolfram.com/FrenchCurve.html) out of a thin sheet of plywood 
or a thick sheet of styrene, and cut out the curve starting with a wider radius 
and gradually tighten it to the desired 40" (or smaller) radius... then just 
lay it where I want it on the layout and trace around it for placing the 
center-line for the track/roadbed.

HECK with all the math...how's that for simple!?


John Degnan


  ----- Original Message ----- 
  From: Richard Karnes 
  To: [email protected] 
  Sent: Saturday, December 09, 2006 1:02 PM
  Subject: {S-Scale List} Re: NASG/AM Heavyweight Operation


  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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