What is Cable Sag?
Cable sag is the vertical deflection of a suspended cable or wire below its support points due to gravity and applied loads. When a cable is strung between two points at the same elevation, it forms a catenary curve. For most practical calculations where sag is small relative to span, the parabolic approximation is sufficiently accurate.
Sag calculations are critical in power line design, suspension bridges, zip lines, clotheslines, fence wire tensioning, and any application where cables span between supports. Too much sag can cause clearance problems, while too little sag creates excessive tension that can break the cable or damage supports.
Sag Formula
Where w = weight per unit length, L = span length, T = horizontal tension. The actual cable length is approximated by:
Factors Affecting Sag
- Temperature: Cables expand in heat and contract in cold, changing sag by 10–20%
- Ice loading: Ice accumulation adds significant weight, increasing sag substantially
- Wind: Wind causes horizontal displacement and can increase effective cable tension
- Creep: Over time, cables stretch permanently under sustained load
- Elevation difference: Unequal support heights shift the lowest point of the catenary
Acceptable Sag Limits
| Application | Typical Sag Ratio | Notes |
|---|---|---|
| Power Lines | 3–5% | Must maintain ground clearance |
| Suspension Cables | 5–10% | Structural consideration |
| Fence Wire | 1–3% | Tight for containment |
| Zip Lines | 3–6% | Must ensure safe clearance |
Worked Example
A 100-ft cable span with weight of 0.5 lb/ft and 500 lbs horizontal tension:
Cable Length ≈ 100 + (8 × 1.25²) / (3 × 100) = 100.04 ft
Frequently Asked Questions
How do I reduce cable sag?
Increase the horizontal tension, use a lighter cable, reduce the span length, or add intermediate supports. Be careful not to exceed the cable's rated breaking strength when increasing tension.
What is the sag-to-span ratio?
The sag-to-span ratio is the maximum sag divided by the span length, expressed as a percentage. For power lines, this is typically kept between 3% and 5% to maintain adequate ground clearance.
Does temperature affect cable sag?
Yes, significantly. Cables expand when heated and contract when cooled. A steel cable can change length by about 6.5 × 10&supmin;&sup6; per degree Fahrenheit, which noticeably affects sag over long spans.