An algorithm for the parabo1ic approximation of the catenary applicable in both inclined and level spans

When planning overhead lines either the catenary or the parabola model is in use for drawing the conductor curve. Originally the conductor in the span takes the shape of the catenary but in certain cases it can be replaced by the parabola. The question arises what the difference between these two curves is. Relating to the catenary approximation by the parabola, professional literature gives a mathematical algorithm for the case of the level span only. This paper presents a universal algorithm which is applicable in inclined and level spans as well. Besides the mathematical background of the mentioned algorithm, the paper also shows its practical application and evaluation of the results obtained in a relevant numerical example.