Design and Calculation Principles of the “Two-Point Method” for Basic Horizontal Curves

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 （L_S） 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 L_S or R is determined based on the technical requirements of horizontal alignment. Afterwards， the traversal cycle is performed based on L_S 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 L_S， R， circular curve length （L_C）， and total horizontal curve length （L_H） is very regular. The increasing and decreasing of LS are opposite to those of R and L_C， while the average of L_H 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.