📌 1) Basic Sag–Tension
Relationship (Parabolic Approximation)
This is the most commonly used quick estimate formula
for sag and horizontal tension:
where:
= Sag (vertical drop,
m) 
= weight per unit
length of conductor (N/m) 
= span length (m) 
= horizontal component
of tension (N)
This approximation assumes the conductor behaves like a parabola — good for moderate spans/sags.
📌 2) Exact Catenary Sag
Formula
For more accurate calculation (especially with long spans or
larger sag), the conductor forms a catenary curve:
where:
= horizontal tension
(N)
This exact form accounts for the true physics of a hanging cable.
📌 3) Horizontal Tension
vs Total Tension
The horizontal component is often what sag formulas
use. The actual tension at the supports (the force the structure sees)
is:
So if you know sag and horizontal tension, you can find the
total support tension.
📌 4) Conductor Length and
Slack
If you know the actual conductor length 
(between supports), the
relationship with sag is:
Then the sag can be approximated from length:
This comes from approximating the catenary near its
midpoint.
📌 Summary of What These
Show
|
Parameter |
Typical Formula |
|
Sag vs Tension |
|
|
Tension vs Sag |
|
|
Exact Catenary Sag |
|
|
Total Support Tension |
|
|
Conductor Length Relationship |
|
