How the Line Sag Calculator Works
The Line Sag Calculator estimates the sag of a suspended line or cable using the common parabolic approximation. This approximation is useful when the sag is small relative to the span.
Unlike the old version, this calculator does not assume an arbitrary 1 m sag to calculate tension. Instead, it asks for the horizontal tension directly and calculates sag from that value.
Line Sag Formula
For supports at the same height and small sag:
where:
- w = line weight per unit horizontal length, N/m
- L = span length, m
- H = horizontal tension, N
Support Tension
For unequal support heights, the calculator estimates the slope at each support and calculates approximate support tension:
Thermal Expansion
Free thermal expansion is estimated as:
This is the free length change. Real installed-line sag and tension change with temperature depends on the restraint condition, initial stringing tension, material, creep, wind, ice, and load history.
Example Calculation
Span length = 50 m Line weight = 0.5 kg/m Horizontal tension = 5000 N Support height difference = 0 m
Convert line weight:
Calculate sag:
When the Parabolic Approximation Is Not Enough
Frequently Asked Questions
Why does higher tension reduce sag?
Higher horizontal tension pulls the cable flatter, reducing the vertical sag.
Why does heavier cable increase sag?
A heavier line has a larger distributed load, which increases sag for the same span and tension.
Can this handle supports at different heights?
Yes, it includes a height difference input and estimates the low-point location and support tensions.
Is this exact catenary analysis?
No. This is a parabolic approximation. Exact cable shape follows a catenary, especially for large sag.