Principle of Two-point Segmentary Element Method for Horizontal Alignment Design and Calculation

Abstract:

A design and calculation method was proposed for determining horizontal linear elements through two points. The segmentary elements of the horizontal alignment can be divided into six classifications： tangential straight line， circular curve， and four types of clothoids. There are no more than 4 dependent parameters for each segmentary element. When designing horizontal alignment by the segmentary element method， the three parameters related to the origin point are known. Thus， once the coordinate of the destination point is available， the six basic types of segmentary elements and the remaining parameters can be uniquely determined simply by using the origin and destination points of the segmentary element， which is similar to the determination of a straight line through two points. The calculation of the deflection angle of the segmentary element is the key to solving the parameters. For the circular curves the analytical method is employed， whereas for the clothoids the iterative method is recommended. The deflection angle can be estimated by fitting formula of polynomial， with the error which is less than 1.0%. The two-point segmentary element method emphasizes the control effect of the coordinates’ location on the alignment， in which the alignment is easy to control through the destination location of the segmentary elements. The method is applicable to the complex horizontal alignment design for roads at the interchange ramp and hilly area as well as the reconstruction of the existing road alignments.

Key words:road engineering;horizontal alignment;two-point segmentary element method;deflection angle;iterative method