The Transition Curve whose Curvature Varies Directly as its Length from the P. C. or Point where it Connects with the Tangent

The ideal transition curve, to pass from a tangent to a circular curve of given degree, is one whose curvature is zero at the point where it leaves the tangent (P. C.) and increases directly as its length, measured along the curve, to where it connects with the circular curve, at which point it should have the same tangent and rate of curvature as the circular curve. By the use of such curves on railroads or street car lines to ease off the ends of circular curves, the super-elevation of the outer rail for the circular part is gradually attained without shock, and the sudden change from the tangent to a circular curve, so often experienced on unadjusted railroad curves, with its annoying and damaging lurch, is avoided