From High Voltage Engineering and Testing, 2nd Edition
Appendix 5.1: : Conductor Sag and Tension Calculations
Referring to the diagram in Section 5.3 the true length of the conductor from C to B may be calculated from:
Hence the complete conductor length S from A to B is obtained by substituting
and the conductor sag is:
and cosh x can be expanded:
The equation for sag, D, can also be expanded as follows:
Typically, a 400 m span and a tension of 2500 kg with a conductor of mass 1.74 kg/m will have a sag of:
The second term of the calculation is only 0.15% of the first term and, therefore, to a first approximation it is usual to ignore it. Accordingly, the equation:
is used to calculate sags and tensions for level spans when the sag is less than about 10% of the span. This equation describes the shape of a parabola.
For use in the case of supports on sloping ground, i.e. with supports at A and B in the following diagram, the parabolic equation for sag and tension is adapted as follows:
where, as shown in Figure 5.15. X is the distance from the lower support B.
Figure 5.15: Parabola for line conductor supported at unequal heights.
It should be noted that the parabola follows the same curve from A to B as for a parabola with level supports fixed at A and C. The above equation is sufficiently accurate for determining sags and tensions of slack spans from the terminal...
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