Profile Intersection of Contact Wires in Overlap

(This article was co-authored with Valery Iuleu )

In the previous article, we examined the key criteria for selecting overlap parameters. However, one important aspect of the contact wire geometry was deliberately left unaddressed—crossing wires within the overlap profile. This factor becomes increasingly critical as pantograph speed rises, affecting the stability of the overhead contact system and the quality of current collection performance.

Problem Statement

As the pantograph passes through the overlap, an angle β is formed at the point where it simultaneously contacts both the uplifted and freely hanging contact wires. This angle directly affects the performance and longevity of the overhead contact system, as it determines the quality of pantograph-wire interaction and the stability of the contact suspension. The larger this angle, the higher the probability of an "impact" at the considered point.

At first glance, in a static state (without pantograph force), angle β may appear to be zero in some cases. However, when the effect of the pantograph is considered, the situation changes: the contact wires deflect, altering their relative positioning.

Our goal is to determine the optimal geometry of the contact wires in a static state and analyze how angle β, which forms under pantograph force, changes under different overlap configurations.

International HSR Design Practices

🐉 China

When designing high-speed railway lines with speeds up to 300 km/h, Chinese specialists recommend raising the contact wire crossing point by 40 mm above the nominal height.

🐻 Russia

Theoretical studies by Russian engineers for HSR lines with speeds up to 400 km/h indicate the following:

• In overlaps with an odd number of spans (where the crossing occurs closer to the middle of a span), the contact wire crossing point is raised by 40 mm.
• In overlaps with an even number of spans, the wires are overlaid at the nominal height.

💃 Spain

As far as the authors are aware, when designing lines for speeds of 350 km/h, Spanish engineers raised the contact wire crossing point by 35 mm above the nominal height.

Technical Specification and Calculation Results

Initial Data

This study examines the optimal contact wire (CW) geometry for a 4-span overlap. According to the authors, this type of overlap is the most common in contemporary HSR projects. The calculation will be performed for the Spanish C-350 catenary.

• Contact wire elevation at the end of the transition span – 600 mm.
• Distance from the steady arm axis to the first dropper in the transition span – 4.5 m.

Calculation Methodology

A two-dimensional finite element method (FEM) model of the static state of the overhead contact system, developed by the authors in MATLAB, is used for the analysis. This model has been validated on multiple projects and has demonstrated strong accuracy in determining catenary elasticity. Additionally, its correctness has been confirmed through comparison with benchmark calculations provided in EN50318:2018.

The pantograph contact force is determined according to the methodology outlined in EN50367:2020, using the average value between the maximum and minimum forces. For speeds up to 350 km/h (AC, >200 km/h):

F_(m,max)= 0,00097·350^2+70≈189N
F_(m,min)= 0,00047·350^2+60≈118N
F_(m,aver)= 0,5(F_(m,max)+F_(m,min))≈153N        

Contact Wire Positioning in the Central Transition Area

For different geometric configurations, the attack angle (β) of the pantograph as it transitions to the adjacent catenary will be calculated.

Three configurations of contact wire positioning will be analyzed:

• Option #1: Contact wire rising starts from the first dropper towards the anchoring point.
• Option #2: Contact wire rising starts from the steady arms.
• Option #3: Contact wire rising starts from the third dropper away from the anchoring point.

As a result of the calculations, diagrams were obtained showing the positions of the contact wires in overlapping catenaries when one of them is uplifted by the moving pantograph, meeting the contact wire of the adjacent tensioning section.

Calculations were performed for two cases of contact wire pre-sag: 0‰ and 0.5‰

Contact Wire Positions – Contact Wire Pre-Sag 0‰

Contact Wire Positions – Contact Wire Pre-Sag 0.5‰

* dashed line indicates the uplifted contact point trajectory in the static approximation.

Based on these results, attack angles (β) were calculated for all six cases and are presented in the summary table.

Conclusions

1. The minimum attack angle (β) is observed in Option #3 (where the contact wire is raised in the previous span, forming an "x"). This configuration reduces the dynamic impact of the pantograph on the approaching contact wire, improving current collection quality and reducing wear on the contact strips.
2. As the contact wire's pre-sag decreases, the attack angle (β) also reduces. This is explained by the fact that, in the presence of sag, the wire lifted by the pantograph tends to assume a horizontal position. In contrast, without sag, the wire forms a "descending arch," which reduces the attack angle.

Thus, the presented analysis confirms the validity of choosing Option #3 for arranging overlaps on HSR. The authors hope that this material will also be useful to readers in understanding the background of various technical decisions.

Recommendations

• It is recommended to apply a certain vertical distance from the contact wire at the transition mast. The optimal value of this distance should be determined based on a comparative analysis, considering the span parameters, the rise of the contact wire, and the wire characteristics.
• In the transition span of the overlap, it is advised to avoid any pre-sag of the contact wire.

These measures will significantly improve the interaction between the pantograph and the contact wires in the overlap areas of the tensioning sections and extend the lifespan of the contact wires.

Towards a More Detailed Analysis

Our analysis is based on calculating the trajectory of the contact point in a static approximation. However, to fully understand the underlying processes, it is necessary to consider the dynamic effects influencing the interaction between the pantograph and the contact wires.

The next step in the research will be a dynamic analysis of the catenary, which will allow us to assess its behavior under real-world conditions. We plan to explore this aspect in detail in the future article.