同济大学学报（自然科学版）2025，Vol.53Issue(2)：233-243,11.DOI:10.11908/j.issn.0253-374x.23223
基本型平曲线"两点法"设计计算原理
Design and Calculation Principles of the"Two-Point Method"for Basic Horizontal Curves
摘要
Abstract
To address the shortcomings of traditional traverse method such as significant deviation between the traverse and the horizontal curve,this paper proposes a"two-point method"for basic horizontal alignment design.It is only necessary to use the two endpoints named"point of tangent to spiral"and"point of spiral to tangent"to obtain the basic type horizontal curve family consisting of three elements including the transition curves and the circular curve.The total deflection angle(α)and total tangent length(T)of the horizontal curve family are known fixed parameters.First,the theoretical minimum and maximum values of the transition curve length(LS)or the radius of circular curve(R)are calculated using the iterative method(for symmetric type)or squeeze theorem analysis method(for asymmetric type),respectively.Then,the design value range of LS or R is determined based on the technical requirements of horizontal alignment.Afterwards,the traversal cycle is performed based on LS or R,and the corresponding deflection angle of the transition curve(β)is calculated using an iterative calculation method.Finally,the remaining parameters of each element is determined.The results indicate that,the"horizontal curve family"obtained through the"two-point method"has a regular distribution and does not overlap with each other,and all of the curves are located in"a specific design area"with narrow ends and wide-thick middle.The variation of parameters such as LS,R,circular curve length(LC),and total horizontal curve length(LH)is very regular.The increasing and decreasing of LS are opposite to those of R and LC,while the average of LH is approximately fixed.Furthermore,the ratio of the total tangent lengths is only solvable within the range from 0.5 to 2.0.The"two-point method"highlights the controlling role of coordinate location points,making the alignment layout efficient.The design outcome presents a series of horizontal curve families within a specific area,rather than a single curve.This is beneficial for comparing and selecting alignments based on actual topography and design intentions,thereby contributing to the advancement of intelligent route design.关键词
道路工程/基本型平曲线/两点法/迭代法/平曲线族/特定设计区域/线形优选Key words
road engineering/basic horizontal curve/two-point method/iterative calculation/horizontal curve family/specific design area/horizontal alignment optimization分类
交通工程引用本文复制引用
李玉华,王奥凯,刘佳音,马洋洋,吴树铭..基本型平曲线"两点法"设计计算原理[J].同济大学学报（自然科学版）,2025,53(2):233-243,11.基金项目
国家自然科学基金(51878121) （51878121）
