**2.2 Calculation method for ballastless track coordinate cluster under complex line conditions**

Accurate measurement is the most important and difficult process to control in the construction of ballastless track. The whole measurement technology requires high precision and is influenced by many factors. The azimuth of the track slab centerline and the three-dimensional coordinates of the rail top center at the rail support platform used in the measurement process need to be accurately calculated, and digital results are automatically generated to guide the construction and laying of the base, track slab, etc.

According to the plane data of the route, the tangent offset method (i.e. rectangular coordinate method) is used to calculate the coordinate values of each point on the

#### **Figure 4.** *Schematic diagram of track layout algorithm.*

route. As shown in the figure, take the calculation of any point coordinates. The mileage of the starting and ending points (HZ/ZH) of the curve and the coordinates of the intersection point (JD) are known. The azimuth of the line conductor is expressed in *A*, the radius of the circular curve is expressed in R, and the length of the transition curve is expressed in *l0*. The coordinates of the straight-line segment, the transition curve segment (front/back), and the circular curve segment are calculated section by section to form the track design data file.

The horizontal and vertical relative coordinates of each calculation point within the straight line are fixed, and the longitudinal coordinates are the cumulative value of the fastener spacings. The coordinates and azimuth of the main point and control point of the plane curve are calculated through the plane design data of the line, including the coordinates of the intersection point, the curve radius and the length of the transition curve. The elevation of the main point and control point of the vertical curve is calculated through the design data of the line profile, including the elevation of gradient change point, slope, grade length and radius of the vertical curve. At the same time, the coordinates of track slab rough laying position point and base corner point are calculated.

Each point of the transition curve is a gradually changing three-dimensional coordinate, the plane takes the starting point of the plate as the coordinate origin, and the vertical takes the midpoint of the rail top line of the starting point of the plate as the coordinate origin.

The horizontal coordinate of each point within the circle curve has an offset value, the vertical coordinate is fixed, and the longitudinal coordinate is the cumulative value of fastener spacings.

*Perspective Chapter: Intelligent Construction Technology of Ballastless Track for High-Speed… DOI: http://dx.doi.org/10.5772/intechopen.109611*

**Figure 5.** *Generated digital results.*

After calculation, the system will automatically generate the digital results guiding the construction survey, as shown in the **Figure 5**.

Description of relevant figures of track slab data file

Line 1: Slab number; Coordinates of the starting point of the slab, X coordinate perpendicular to the line direction; Y coordinate along the line direction; Elevation Z coordinate; Type of track slab; Mileage; Radius of plane circular curve; Vertical curve radius; Superelevation;

Line 2: Slab number and control point; X coordinate perpendicular to the line direction; Y coordinate along the line direction; Elevation Z coordinate; Type of fastener;

…

The last line: Slab number; Coordinates of the ending point of the slab, X coordinate perpendicular to the line direction; Y coordinate along the line direction; Elevation Z coordinate; Type of track slab; Mileage; Radius of plane circular curve; Vertical curve radius; Superelevation.
