路线平面线形设计计算的两点线元法原理

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

摘要:

提出通过两点确定平面线形线元的设计计算方法。将平面线形线元分为切直线、圆曲线、正\反向完整型回旋线、正\反向非完整型回旋线共6种基本类型，均可由最多4个独立参数唯一确定。采用线元法顺次设计平面线形时，与起点相关的坐标、切向角、半径3个独立参数已知，故只需再拟定终点坐标即可唯一确定各基本型线元，均类似于两点确定一条直线。偏转角是线元其余参数计算的关键，圆曲线线元采用解析法，回旋线线元采用迭代法，亦可通过多项式拟合公式进行预估，误差不超过1.0%。两点线元法凸显坐标位置对线形的控制作用，适宜于立交、山岭区等复杂曲线线形设计及既有道路线形重构等。

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.