A Theoretical Approach to Catenary Uplift calculation in Railway OLE/OHE/OCS

In this article I will provide a theoretical approach on the catenary uplift that occurs during a dynamic situation in rail overhead lines when the pantograph pushes the contact system to perform its basic function of current collection, this effects the clearances between catenary and bridge soffit near the overbridges (Free running).

Clearance assessment to overbridges (flat decks / arched bridges / Foot overbridges) is crucial to maintain sufficient static & dynamic mechanical/electrical clearances against the Rail overhead contact systems which can be either 25kV AC or 1500V DC or 750V DC etc.

Pantograph mounted on the train exerts pressure on the contact wire to maintain continuous contact with it for safe & efficient current collection. In this process it lifts the contact wire, an intuitive question might arise “why would the catenary wire rise when the contact wire is lifted by pantograph as the droppers are flexible stranded wires” (considering there is sufficient vertical distance between contact & catenary). Well, the whole system of catenary wire & contact wire each tensioned & suspended between the supports forms a coupled mechanical system. The catenary supports the weight of the contact wire through droppers. The droppers are pre-tensioned due to the weight of contact wire, when the pantograph pushes the contact wire, the tension in the dropper reduces (at high uplifts the droppers even become slack & unload the contact wire weight on catenary), allowing the catenary to spring back upward to its natural position because of its tensioned state.

The catenary uplift function y(x)?with respect to x (along the track) behaves close to parabolic curve, with maximum uplift occurring at mid-span and zero uplift at catenary supports.

Equation of a parabolic curve is:

Here,

The Point A is lowest point in catenary.

Point B is the position where the uplift is to be checked.

Lb?is the distance from support to point B.

The uplift value calculated using the above-mentioned formula is subtracted from the static clearance value to determine the passing clearance at point B.

As per NR regulations, Minimum passing electrical clearance to be maintained is 200mm & the static electrical clearance is 600mm for stranded conductor (catenary) & 270mm for contenary. These values can vary if any control measures are taken for special situations.

Conclusion:

This uplift value, obtained from the results, is utilized to evaluate the dynamic passing clearances between the catenary/contenary and the overbridge soffit height. ?

This analytical method provides quick results for smaller deflections, one can also consider Dynamic simulation methods which involve computational modeling (FEM) of pantograph-catenary system with appropriate mechanical properties for more detailed & accurate results. This approach accounts for the dynamics of the system which includes oscillations/vibrations, elasticity & damping.

Note:

At arched bridges, it is important to check the minimum passing clearance between the uplifted/swayed pantograph and the arch soffit as well.

Assumptions:

• The deflection is considered small, so that the wires elastic deformation in axial geometry is considered negligible.
• Elastic modulus of the cable is ignored as this is more of a geometrical deformation rather than an elastic deformation, where the Elasticity Modulus influence is less on the results.

References: UKMS B14/B10

*Pantograph contact force (P) is generally 90N (at 125mph).

*static clearances between catenary/contenary & bridge soffit are calculated with similar analytical approach using sag formula. (stay tuned. I would like to share that article soon).