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 Geometric Design: Theory and Concepts

 
Transition Segments

Often, horizontal curves are more comfortable and more aesthetically pleasing if the change in roadway cross-section and curvature is effected over a short transitional segment. 

The gradual change in curvature is produced by using a spiral curve. The radius of the spiral curve starts at infinity and is gradually reduced to the radius of the circular curve that you designed originally.  Adding the spiral curve causes the centripetal acceleration to build up gradually, which is more comfortable for vehicle occupants.   The equation commonly employed to calculate the minimum length of the spiral transition segment is given below.

L = (3.15*v3)/(RC)

Where:
L = Minimum length of the spiral curve (ft)
v = Speed (mph)
R = Circular curve radius (ft)
C = Centripetal acceleration development rate (usually between 1 and 3 ft/sec3)

The other purpose of the transition segment is to gradually change the cross-section of the roadway from normal to superelevated. This can be accomplished by rotating the cross-section around any line parallel to the roadway.  The engineer should keep water drainage in mind while considering all of the available cross-section options. Opinions vary as to how fast the pavement cross-section should change, but most people agree that the change in curvature and the change in cross-section should occur in concert with one another. You should look at your local geometric design policy for more specific information regarding transition segments.