Calculation
f = q·L²/(8·H)
For small sag relative to span, the true catenary is very closely approximated by a parabola.
Dubbel Mechanik B 1.9.2 Seil unter konstanter Streckenlast: FH = q·x2²/(8f)
Sag of a cable between two equal-height supports
For small sag relative to span, the true catenary is very closely approximated by a parabola.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Sag f — Largest vertical distance of the cable from the line joining the two support points.
- Distributed load q — Uniformly distributed self-weight or additional load per unit cable length.
- Span L — Horizontal distance between the two equal-height support points.
- Horizontal tension H — Horizontal component of cable tension, equal to the full cable tension at the lowest point.
Example
q=10 N/m, L=50 m and H=5,000 N give f=10·2,500/(8·5,000)=0.625 m.
Assumptions and limits
Slack, inextensible cable with uniform load and equal-height supports, small sag (parabolic approximation); cable stretch, temperature effects, ice and wind load are excluded.
Understand Sag of a cable between two equal-height supports
This calculator determines the sag of a slack cable, overhead line or drive belt under uniform distributed load using the classic parabolic approximation.
What does this quantity describe?
For small sag relative to span, the true catenary is very closely approximated by a parabola: f=q·L²/(8·H), with q the distributed load, L the span and H the horizontal cable tension.
Formula and variables
f = q·L²/(8·H)
f = q·L²/(8·H)H = q·L²/(8·f)
| Symbol / input | Meaning |
|---|---|
| Sag f | Largest vertical distance of the cable from the line joining the two support points. |
| Distributed load q | Uniformly distributed self-weight or additional load per unit cable length. |
| Span L | Horizontal distance between the two equal-height support points. |
| Horizontal tension H | Horizontal component of cable tension, equal to the full cable tension at the lowest point. |
Choose the inputs correctly
q is the uniformly distributed load per unit length, L the span between the two equal-height supports, H the horizontal component of cable tension.
How to use the calculator
Determine q from the cable's or line's self-weight (plus ice or wind load where applicable), L from support spacing, H from the set cable tension.
Worked example
q=10 N/m, L=50 m and H=5,000 N give f=10·2,500/(8·5,000)=0.625 m.
Understand the result and units
Greater horizontal tension H reduces sag; a larger span L increases it quadratically.
q is a distributed load, L and f are lengths, H is a force.
Typical applications
Rough sizing of overhead lines, cableways, clotheslines and similar freely hanging cables under uniform distributed load.
Assumptions, limits and common mistakes
Slack, inextensible cable with uniform load, equal-height supports and small sag relative to span (parabolic approximation rather than exact catenary); cable stretch, temperature effects, and additional ice or wind load are excluded unless already included in q.
Common mistake: Do not confuse the tension at the lowest point (H, horizontal) with the maximum cable tension at the supports; the latter is somewhat larger there due to the slope.
Frequently asked questions
What is “Sag of a cable between two equal-height supports” used for?
Rough sizing of overhead lines, cableways, clotheslines and similar freely hanging cables under uniform distributed load.
Where do the input values come from?
q is the uniformly distributed load per unit length, L the span between the two equal-height supports, H the horizontal component of cable tension.
What does the result not cover?
Slack, inextensible cable with uniform load, equal-height supports and small sag relative to span (parabolic approximation rather than exact catenary); cable stretch, temperature effects, and additional ice or wind load are excluded unless already included in q.