On The Spatial Characteristics Of Highway Geometric Alignment Under Frenet Frame

the main point of traditional highway alignment design is to do the horizontal and vertical projection design respectively, and then to combine the two parts. While the projection separates the intrinsic link between plane and profile, Ever worse, there isn’t rigorous analytical model to guide horizontal and vertical curve combination, which lead to inevitable differences between the designed alignment and the combined one. The first division, then combination design ignores the three-dimensional curve nature of highway alignment and results a series of problems to the combined alignment such as spatial discontinuity, mismatch of alignment geometric condition and vehicle kinematics, and inconsistent between drivers’perception and designed line.In order to solve problems exit in traditional highway alignment design method, the thesis first define the key elements that determine nature features of spatial curves based on the study of their basic geometric features, then these elements are used to analyze relationship between spatial geometry and kinematics. On the basis of spatial curve study, analysis and comparison of geometric continuity and kinematics features between traditional design alignment and spatial alignment are carried out, which provides useful ideas for constraints design of spatial alignment. The study includes the following three aspects:(1) Traditional alignment design is based on the combination theory of horizontal and vertical alignment which defines three-dimension alignment in two-dimension plan and profile respectively in nature, it leads to problems in traditional design models that the two-dimension continuity can not ensure spatial continuity by simple combination. So on the basis of studying geometric and kinematical features of spatial curve, the key factors that determine curves’ spatial characteristics are defined, that’s frenet frame, curvature and torsion; and the factors are used to describe spatial continuity and geometric-kinematic relation of highway alignment.(2) Two-dimension curvature is used to analyze alignment continuity in traditional design, while it can no more describe spatial continuity features completely in three-dimension space. From the point of view of differential geometry, the basic elements that define spatial curves are spatial curvature and torsion, that is, a spatial curve can be uniquely determined with given curvature and torsion. For this, the thesis firstly builds quantitative calculation models of spatial curvature and torsion for highway alignment under frenet frame, then uses geometric continuity as evaluation indexes to quantitatively study spatial continuity features of highway alignment is three-dimension space. The results show that the highway alignment designed with combination theories will show different sudden changes in different combinations in three-dimension space.(3) It is known that vehicle running stability reflects the quality of alignment directly, so studying the relation between alignment and vehicle kinematics is in great need for the purpose of building three-dimension alignment model that is optimal for both vehicles and occupants. For three-dimension alignment is the expansion of two-dimension alignment, the thesis clears the main alignment parameters that affect vehicle stability and the corresponding three-dimension alignment parameters, it help to build constraint for spatial curvature and torsion; then uses spatial curvature and torsion to represent kinematic indexes in three-dimension; lastly, the thesis carry out preliminary exploration on building three-dimension alignment model. All the above lays foundation for future research.