Adding an appropriate pre-sag to the geometry of simple catenary systems for electric railways can improve their performance in dynamic interaction with the pantographs of trains operating under them. The value of pre-sag can be obtained by empirical approximation or computationally expensive optimisation. This study aims to define a simple but accurate method to determine a suitable pre-sag without dynamic simulations and to find its limitations.

A quasi-static method to determine the ideal value of pre-sag is described based on elasticity variations. It considers variations of the static contact force. The limits of this method are investigated by comparing it to a parametric dynamic simulation study. In the dynamic simulation, an optimal level of pre-sag is identified for each contact force level. The influence of the speed in the dynamic simulation results is expressed in two parameters: the quasi-static influence in the mean contact force and the dynamic influence in the ratio between the vehicle speed and the wave propagation speed in the contact wire.

The comparison between the suggested method and the dynamic simulations shows a high consistency up to a speed limit of around 40 % of the wave propagation speed. The best agreement with the dynamic results is achieved by calculating the optimal pre-sag based on the absolute elasticity variation.

The simplified approach for determining the pre-sag is valid for low-speed applications, such as suburban railway lines. For these cases, a highly suitable geometry can be obtained with the suggested method, meaning a significantly reduced computational effort. As a case study for this work, the results are applied to a Swedish suburban rail line upgrade case.

The static uplift force is added as a varied parameter in dynamic simulations. The shift in system behaviour from low to high dynamics is described, and how the benefits from pre-sag are visible and then disappear. The limit value of the low-dynamics regime is identified to be 40 %.