Establishment of Uniform Mathematics Model for Positioning the Center-line of Rail Transit

The positioning of the centerline is an important job in the process of rail transit.It is different from those common centerlines in the criterion and way of positioning.On one hand,the common ways can not be applied to the positioning of rail transit.The reason is that the location stand can not be set in the intersection point and circle center of curve due to the countercheck of building and the influence of peculiar urban surface.The condition of perspective is often limited even if the location stand can be set.On the other hand,besides the selected laying off measurements and the precision of the known points,the precision of positioning centerline depends on the coordinate preciseness of the stake points to a great extent.The coordinates are given in the local reference frame by intercepting a few finite terms from the progression expression,or making use of the approximate azimuth angles and the length of chords.So it is inevitably influenced in the accuracy degree for the result of the coordinates.It is disadvantageous for the high precision requirements of rapid rail transit so that it results in disconnecting the subsection of the whole engineer.Therefore,we provide the centerline integral mathematics model to compute coordinates of stake points,which can accurately and quickly get the results in the uniform reference frame.The quantity surveyors are able to lay off the points of the stake in the centerline through the pole-coordinate measurement and free location measurement with facility.Based on analyzing two existing mathematics models,which have been used in the middle of laying off centerline,the centerline integral mathematics model as well as its formulas is introduced in this paper.According to the characteristics of curvature radius,the mathematic relation between the coordinates and mileages for random stake points in the centerline is established.In the course of numerical calculation,the improved Romberg integral algorithm is used to get the coordinates,which is helpful to process a large number of calculation tasks and meets the high accuracy requirements of rapid rail transit.Based on the above model and algorithm,we program its software with C⁺⁺.In order to compare the integral mathematics model with other models,we also program the Tangent off-set method and the center of circle symmetry method.In practice,we respectively use three mathematics programs for Wuhan NO.1 Rapid Rail Transit Engineering.It proves that both the integral model and the center of circle symmetry method are superior to the Tangent off-set method in precision;while the integral model are superior to other models in practicability.