[1]潘兵宏,王开明,赵胜林,等.可用作公路缓和曲线的K型曲线数学模型及其特点分析［[J].长安大学学报(自然科学版),2020,40(3):33-41.
　PAN Bing hong,WANG Kai ming,ZHAO Sheng lin,et al.Mathematical model and characteristics analysis of Kcurve thatcan be used as highway transition curve[J].Journal of Chang’an University (Natural Science Edition),2020,40(3):33-41.
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可用作公路缓和曲线的K型曲线数学模型及其特点分析［()
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长安大学学报（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
第40卷
期数:
2020年3期
页码:
33-41
栏目:
道路工程
出版日期:
2020-05-15

文章信息/Info

Title:
Mathematical model and characteristics analysis of Kcurve thatcan be used as highway transition curve
作者:
潘兵宏; 王开明; 赵胜林; 陈林圻; 胡炜; 温长鹏
（1. 长安大学 公路学院，陕西 西安 710064； 2. 安康市交通规划设计院，陕西 安康 725000；3. 陕西省交通规划设计研究院，陕西 西安 710065）
Author(s):
PAN Binghong1;  WANG Kaiming2;  ZHAO Shenglin3;  CHEN Linqi1; HU Wei1;  WEN Changpeng1
（1. School of Highway, Changan University, Xian 710064, Shaanxi, China; 2. Ankang TransportPlanning and Design Institute, Ankang 725000, Shaanxi, China; 3. Shaanxi Provincial TransportPlanning Design and Research Institute, Xian 710065, Shaanxi, China）
关键词:
道路工程; 路线设计; 曲线设计; K型曲线; 公路线形; 公路设计新技术
Keywords:
road engineering;  line design;  curve design;  Kcurve;  highway alignment;  new road design technology
文献标志码:
A
摘要:
为了克服曲线法设计的局限性，解决长期困扰公路线形设计中的一些技术难题，以传统回旋线数学模型为基础，提出一种适应能力更强、更符合车辆行驶轨迹与驾驶人行为特征的K型曲线以代替传统回旋线作为公路用缓和曲线。首先，对传统回旋线的参数特点、曲率变化特点及航向角与弦切角的变化关系进行分析，并以航向角与弦切角的变化关系为基础建立了K型曲线参数方程，对方程中各参数对其影响进行分析；其次，通过K型曲线的参数方程推导得出任意点曲率半径的数学表达式；最后，通过数值解法讨论在不同参数取值情况下，K型曲线曲率半径与弧长之间的关系。研究结果表明：当弦长m值与弦切角a值固定时，选取适当的航向角与弦切角的比值k值，可调节K型曲线曲率半径随弧长的变化速率，提高了在地形困难地区公路线形设计的灵活性；在公路线形设计中采用K型曲线代替传统回旋线作为缓和曲线，不仅能够改善不良线形、增加车辆行驶的安全性，同时其便捷、适应性强等特点还可显著提高公路线形的设计效率与设计质量。〖
Abstract:
In order to overcome the limitation of curve method and some technical problems in highway geometric design, based on the traditional mathematical model of the gyro line, a Kshaped curve with stronger adaptability and more in line with the vehicles driving trajectory and drivers behavior characteristics which could replace the traditional gyro line as the highway mitigation curve was proposed. First, the parameters of the traditional gyro line, the characteristics of curvature change and the relationships between the heading angle and the chord angle were analyzed. Based on the relationships between the heading angle and the chord angle, the Kcurve parameter equation was established. The influence of various parameters on the Kcurve were analysis in detail. Then the mathematical expression of the curvature radius of any point by the parametric equation formula of the curve was derived. Finally, the relationships between the curvature radius of the Kcurve and the arc length under different parameters values were discussed by numerical solution. The results show that when the m value and the a value are fixed, the appropriate k value can be selected to adjust the change rate of the curvature radius of the Kcurve with the arc length, which improves the flexibility of highway alignment design in difficult terrain area. In the highway alignment design, the Kshaped curve is used to instead of the traditional gyro line as the mitigation curve, which not only can improve the poor alignment combination and increase the safety of the vehicle. Its convenience and adaptability can greatly improve the design efficiency and design quality. 2 tabs, 9 figs, 26 refs.

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更新日期/Last Update: 2020-06-03