Abstract
This paper describes the correct procedure for calculating the lateral displacements necessary to realign a railway curve. The procedure is based on the traditional assumptions, uses versine measure, and is easy to apply. The paper shows that for a set of design versines to be achievable they must satisfy two conditions. First, the sum of the design versines must equal the sum of existing versines, and second, the centroid of the new versine diagram must coincide with the centroid of the old versine diagram. The mathematical basis of the method is derived and the problems with traditional procedures are highlighted. The versine corrections which are necessary in transition curves are given. Methods are discussed for finding optimal valid solutions to realignment problems. The use of linear programming in curve realignment and a number of linear programming formulations are described.
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