Is there an equation for slack in power lines?

Answer 1

Slack, in high power transmission lines, refers to the difference between the length, L, of a conductor hanging between two towers, and the direct distance (span length), S, between the attachment points on those towers.

Rather than give slack its own variable, it is simply written (L-S).

In his book "Electric Power Generation, Transmission and Distribution, Vol 1", Leonard L. Grigsby gives the following approximate equations for slack:

L-S = 8D^2/3S, where:

- D is the mid-span sag (how far the conductor sags below a line drawn directly between the attachment points at mid-span)

The alternate equation is:

L-S = S^3/(24*W^2) = S^3*w*2/(24*H^2), where:

- w is the conductor weight per unit length

- H is the horizontal tension (constant) throughout the conductor catenary, and

- W = H/w is known as the "catenary constant"

These equations are only approximations. Exact catenary equations involve hyperbolic sines and cosines, and these parabolic equations are approximations for those. The are relatively accurate as long as sag is less than 5% of span length.