Calculation of Sag for Catenary Shape of Conductor

Calculation of Sag for Catenary Shape of Conductor

For earlier derivations we have assumed that the sag is small compared to the span and hence conductor takes the form of parabola. With this assumption, we have derived the expression of sag under various conditions. But if the sag is comparable with the span then conductor takes the form of catenary. And the expressions derived earlier are no longer valid for such a case.

Consider a conductor, supported at the points A and B with O as the lowest point on the conductor, as shown in the Fig. 4.6.1.

Let P be the point on the conductor such that l (OP) = c. The point O is origin and the co-ordinates of point P are (x, y). The tension T is acting tangentially at point P.

The various forces acting on the curve portion OP of the wire are,

1. The horizontal tension H acting at O.

2. The weight of the portion OP which is wc acting vertically downwards through centre of gravity.

3. The horizontal and vertical components of tension T in the conductor i.e. T_x and T_y acting at P.

The assumption that l(OP) = Distance x along horizontal direction is no longer valid.

In the equilibrium condition, horizontal and vertical components will balance each other.

This is the required equation of the catenary form of conductor.

1. Calculation of Tension T and Conductor Half Span Length

The tension T at any point P is,

and the supports A and B are at same level then,

This is length of curved conductor in half span.

While the sag S can be obtained by putting y = S in equation (4.6.11).

Review Question

1. Show that a transmission line conductor suspended between level support assumes the shape of catenary. Derive the expression for sag.