Transition curves
A transition curve is laid out so that the curve gradually increases (or the radius decreases) as the track goes from a straight into a curve. It means that the sideways force (the centripetal force) on the rolling stock of a train gradually increases from zero on the straight to that experienced on the sharpest part of the curve. This reduces the sideways lurching of the train.
According to Charles E Lee, referring to the Festiniog Railway, the "The curves were all carefully laid out on parabolic lines, and so eased into the reversing curves or the straights." This was before standard gauges lines accepted the advantages of transition curves (around 1890) and was the first use of transition curves in the UK when Charles Easton Spooner relayed sections of the FR for locomotives running and new rails around 1869.[1]
With transition curves it is necessary to gradually increase the superelevation as the radius of the curve decreases. The track cannot be superelevated on the straight in anticipation of the curve without undesirable consequences for vehicle ride.