Overhead Line Sag Calculator: Sag, Conductor Length and Ground Clearance with Ice and Wind

Find the sag, the conductor length and the ground clearance of an overhead line span.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the span, the conductor mass per metre and diameter, and the horizontal tension. Add the thickness of ice and the wind pressure if you want the loaded condition.

The calculator finds the weight of the conductor, adds the ice and wind loads as a resultant, and gives the sag S = w L squared over 8 T for a level span.

For supports at different heights enter the height difference. It finds the lowest point of the conductor and the sag from each support. It also gives the conductor length and the clearance above the ground.

Formulas used

  • S = \frac{wL^2}{8T}
  • \ell = L + \frac{8S^2}{3L}
  • x_{1,2} = \frac{L}{2} \mp \frac{Th}{wL}
  • w_t = \sqrt{(w + w_i)^2 + w_w^2}

Worked example

With the default numbers in the calculator above:

  1. Weight of the bare conductor: 8.83 N/m
  2. Resultant load on the conductor (weight and wind at right angles): 8.83 N/m, which is 1.00 times the bare weight
  3. Sag at the middle of the span: 3.97 m
  4. Length of the conductor in the span (parabola): 300.14 m, which is 0.14 m more than the span
  5. Ground clearance at the lowest point: 16.03 m

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Radial thickness of ice (0 = none) 10 mm; Wind pressure on the projected area (0 = none) 400 Pa; Height of the higher support above the lower one (0 = level span) 5 m.

  1. Weight of the bare conductor: 8.83 N/m
  2. Weight of the ice (density 913 kg/m3): 8.44 N/m
  3. Wind force on the conductor: 16.00 N/m
  4. Resultant load on the conductor (weight and wind at right angles): 23.54 N/m, which is 2.67 times the bare weight
  5. Distance from each support to the lowest point of the conductor: From the lower support 132.30 m, from the higher 167.70 m
  6. Sag below the lower support: 8.24 m
  7. Sag below the higher support: 13.24 m (check: S2 - S1 = 5.00 m, the height difference)
  8. Length of the conductor in the span (parabola): 301.00 m, which is 1.00 m more than the span
  9. Ground clearance at the lowest point: 11.76 m

Common questions

What does the tension mean?

It is the horizontal component of the tension in the conductor, which is the same everywhere in the span. The tension at the supports is a little higher.

Why does sag go up so fast with span?

Sag goes as the square of the span, so doubling the span multiplies the sag by four at the same tension.

When is the parabola not accurate?

When the sag is more than about 5 percent of the span. Use the catenary equations for that.

How do ice and wind affect the sag?

They add to the load per metre, so the resultant load rises and the sag rises with it at the same tension.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: AS/NZS 7000 Overhead line design; Weedy, Electric Power Systems (mechanical design of overhead lines).

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