Integral calculus usage for conductor length determination on the basis of known maximal sag of a parabola

Abstract

This paper shows a mathematic solution for calculation of conductor length using integral calculus on a parabola. The presented method can be used for spans approximately up to 400 metres. In that case the catenary may be approximated by a parabola (quadratic function), while the difference between the catenary and the parabola is negligible. The necessary data are the span length, the heights of the suspension points and the value of the maximal sag. The algorithm is prepared for in- clined spans, but it is applicable for levelled spans too, because it is just one special case when the conductor suspension points on two supports are on the same height level. Naturally, the conductor length changes with temperature, so it is possible to calculate it for a chosen temperature, using a conductor sag for that temperature, chosen tension and conductor type.