What is the formula for conductor sag?

For a level span the parabolic formula is S = w·L² ÷ (8·T), where w is the conductor load per metre (N/m), L is the span in metres and T is the horizontal tension in newtons. Sag rises with the square of the span, so doubling the span quadruples the sag.

What factor of safety is used for overhead line conductors?

IS 5613 practice is a minimum factor of safety of 2 against the ultimate tensile strength under the worst loaded condition, and everyday tension limited to roughly 22–25% of UTS to control creep and aeolian vibration.

Does sag increase with temperature?

Yes. The conductor expands as it heats, tension falls and sag increases. This calculator solves the change-of-state equation so you can see sag at the stringing temperature and at maximum operating temperature.

How do ice and wind change sag and tension?

Ice adds vertical weight and wind adds a horizontal force on the projected area. The resultant load per metre is the vector sum, which raises tension and increases the resultant sag in the direction of the load.

Conductor Sag and Tension Calculator

Pick a standard ACSR, AAAC or AAC conductor, enter the span and design conditions, and get mid-span sag, horizontal tension, tension as a percentage of breaking load, a temperature sag table and a ground clearance check. Sag uses S = w·L² ÷ (8·T) with the classical change-of-state equation for temperature, ice and wind.

Design inputs

Conductor & span

ConductorSpan length (m)Factor of safety (on UTS)

Temperature & loading

Stringing temperature (°C)Final / maximum temperature (°C)Radial ice thickness (mm)Wind pressure (N/m²)

Clearance check

Attachment height above ground (m)Required ground clearance (m)

Indian Electricity Rules minimum clearance across open country: 5.8 m for lines up to 11 kV, 6.1 m for 33 kV.

Results

Maximum sag

3.68 m

Governed by the final condition

Final tension

5.26 kN

16.2% of 32.41 kN UTS

Initial sag

2.38 m

at 32 °C, still air

Conductor length in span

200.18 m

Span 200 m

Condition	Load (N/m)	Tension (kN)	% of UTS	Sag (m)
Initial — 32 °C, still air	3.86	8.10	25.0%	2.38
Final — 75 °C, still air	3.86	5.26	16.2%	3.68

Ground clearance: 7.32 m available vs 5.80 m required — OK

Margin +1.52 m at the maximum-sag condition.

Stringing sag table (still air)

Sag and tension for DOG on a 200 m level span, strung at 32 °C with a factor of safety of 4.

Temperature (°C)	Tension (kN)	Sag (m)
0	11.93	1.62
10	10.58	1.83
20	9.36	2.06
30	8.30	2.33
40	7.39	2.62
50	6.63	2.92
60	6.00	3.22
75	5.26	3.68

Conductor data used

DOG (ACSR), 6/4.72 mm Al + 7/1.57 mm steel, total area 118.55 mm², diameter 14.15 mm, weight 394 kg/km (3.86 N/m), breaking load 32.41 kN. Modulus 78 GPa, coefficient of expansion 19.3 × 10⁻⁶ /°C — Composite aluminium/steel final modulus (IS 398 Part 2 practice).

Sag formula

For a level span the conductor takes a catenary shape, closely approximated by a parabola when sag is under about 10% of the span: S = w·L² ÷ (8·T). Conductor length in the span is L + 8S²/(3L). For inclined spans, sag is measured from the chord and the low point shifts towards the lower support.

Change of state

When temperature or loading changes, tension is found from T₂³ + T₂²[E·A·α·(t₂−t₁) + w₁²L²EA/(24T₁²) − T₁] = w₂²L²EA/24. Heating lowers tension and increases sag; ice and wind raise the load per metre and therefore the tension.

Ice and wind loading

Ice is treated as a radial annulus at 913 kg/m³ added to the conductor weight. Wind acts horizontally on the projected area (diameter + twice the ice thickness). The resultant load per metre is the vector sum of the vertical and horizontal components.

Tension limits

IS 5613 keeps the worst-condition tension below 50% of UTS and everyday tension near 22–25% of UTS. Higher everyday tension increases creep and aeolian vibration damage at the clamps; lower tension increases sag and the required pole height.

Clearance

Check clearance at maximum sag, which is usually the maximum-temperature still-air case for distribution lines and the ice case in cold regions. Indian Electricity Rules require 5.8 m across open country up to 11 kV and 6.1 m at 33 kV, with extra clearance over roads and crossings.

Limitations

This is a preliminary design tool: it uses a parabolic level span, a single final modulus and no creep or stress-strain curve. Final stringing charts and sag boards must come from a full catenary sag-tension run with the supplier's data and the actual span profile.