## 4 Modeling Results  
The optimal length of a short section of the traction network was selected by comparing the calculated EMF strengths at a height of 1.8 m for the middle of the short section and the beginning of the next two-kilometer section (nodes 38-45 according to the diagram in Figure 8a). The EMF for this section was determined in a plane-parallel formulation. In doing so, the elements modeling the overpass were removed from the diagram. As a result, the optimal length of the short section was chosen to be 40 m, which was divided into 200 line elements according to the methodology proposed in [33]. The results of EMF calculations for a point with coordinates \(x=0\) and \(z=0\) are given in Table 1.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Method** & \(\mathbf{E_{max}}\)\(\frac{\mathbf{kV}}{\mathbf{m}}\) & \(\mathbf{H_{max}}\)\(\frac{\mathbf{A}}{\mathbf{m}}\) \\ \hline EMF of short wires & 3.20 \(\pm\) 0.04 & 77.67 \(\pm\) 0.9 \\ \hline Plane-parallel EMF & 3.26 \(\pm\) 0.04 & 80.07 \(\pm\) 0.9 \\ \hline Difference between the EMF of short wires and the & \(-\)1.8 & \(-\)3.0 \\ plane-parallel field, \% & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of comparative EMF calculations for a height of 1.8 m.  
Figure 9: Coordinates of the location of current-carrying parts and elements of the overpass: (a) CNW—contact wires; (b) CW—catenary wires.  
As seen in Figures 14-17, the presence of the overpass leads to a considerable reduction in the amplitudes of EMF strengths compared to its absence; at \(z=0\), the amplitude Emax decreases by 64% due to the shielding effect of the railings, while the curve \(H_{max}=H_{max}(x)\) remains virtually unchanged.  
Figure 18 shows the results of modeling EMF at a height of 8 m, i.e., directly under the overpass. Both curves coincide for the magnetic field. This analysis is crucial because sensitive equipment, such as video surveillance cameras, may be affected by EMF when installed on the overpass.  
Figure 16: Comparative graphs of dependences of the electric (**a**) and magnetic (**b**) field amplitudes at a height of 10.8 m on the x coordinate at \(z=0\): 1—with overpass; 2—without overpass.  
Figure 17: Three-dimensional diagrams of strength amplitudes at a height of 10.8 m for electrical (**a**) and magnetic (**b**) fields in the presence of overpass.  
Based on Figure 12, it can be concluded that in the presence of a grounded structure, the electric field strength at a height of 8 m increases by a maximum of 75%. The magnetic field remains unaffected by the overpass.  
The described method of modeling EMF allows the following factors to be taken into account:  
* The presence of rolling stock in the form of metal wagons and tanks under the overpass, which can have a noticeable effect on the distribution of electromagnetic field strengths in the space surrounding the overpass;
* Pipelines, reinforced concrete platforms, and metal fences, which also affect the nature of the distribution of EMF.  
Based on the proposed method, it is possible to correctly account for the artificial structures of railways in the form of bridges with traffic above and below, galleries, and tunnels with a large number of metal structures that affect the values of field strengths. In addition to the normal mode considered in the article, the proposed method allows determining the EMF strengths in short-circuit modes of the contact suspension on the rails through the elements of the overpass structure.