This paper considers the interaction between a train mounted pantograph and a railway overhead line, presenting results that could be used to reduce the cost of installing overhead electrification, for example, by reducing the need for expensive bridge reconstruction. Ideally, overhead wires would run at a constant height parallel to the track, however, gradients are often unavoidable due to clearance limitations requiring lower wire heights at bridges and tunnels, and higher heights above level crossings. In this study, the influence of a range of contact wire gradients on the contact force between the overhead line and pantograph has been studied using a validated finite element model. Introducing a windowing technique to identify discrete dynamic behaviours found that overhead wire gradients can be increased with minimal effect on the contact force, showing current wire gradient limits are conservative. This may open up opportunities for electrification, less disruptive than following current standards.