Comparison of the Length of the Catenary Curve and its Parabolic Approximation in the Span of an Overhead Line

Taking into consideration the fact that both the catenary and the parabola curves occur in plans of overhead lines, it is very important for electrical design engineers to clearly know what the mathematical differences are of the two mentioned curves, which are regularly in use for drawing the conductor curve. The parabola is generally applicable in short spans while the catenary can be used in any spans. This paper deals with the difference between the lengths of the catenary and its mathematical approximation with the parabola operating with universal formulas, which are valid for both inclined and level spans. Suitable algorithm of a parabolic approximation of the catenary is considered relevant from the aspect of overhead line design. It means that both the parabola and the catenary always have the same support points in a span. In order to draw concrete conclusions a complex practical example and their numerical results have been presented and adequately analysed.