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Big radius curves and transition curves, by Dr. Norbert Aust (Switchdoc) 
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Posted Sun Apr 20 2003 10:47pm 
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Step 1: Computing of points
To define the different points I prefer computational methods but this might be depending on my profession. To do this computation use my ExcelSheets that sould be downloadable from this site Trainz_Tracks.xls. Just fill in the fields indicated green:
 angle from westeast direction to the track end starting due east being zero counting positive counterclockwise (north: 90, west: 180, south 270 or 90)
 radius of the curve
 desired angle of deflection starting zero being straight ahead counted positive counterclockwise
 length of the piece of streight track to be connected to the distant end.
fig.02
As a result you receive within the fields marked in blue the centre of the circle, the distant endpoint of the curve, the auxiliary points necessary and endpoint of the straight track connected to the curve's endpoint. You get these data as coordinates starting with 0 from the splinepoint at the track end you have. This all sounds mighty complicated but application of this is fairly easy. You get
dx: distance you have to go due east, if negative due west
dy: distance you have to go due north, if negative due south.
In this example you find the terminal splinepoint of the curve by applying the rulers 337.2 m due east and from there onwards 227.4 m due north.



