# Low voltage power lines - formula for spacing between poles?

What is the distance or separation between pole-pole in a 230 VAC distribution line?

Is there any formula for this, or we can take any distance?

• It's probably a mechanical problem with weight and bend of the cables plus cable strength. A bit like a suspension bridge but probably not an EE question. – Andy aka Jun 12 '15 at 11:37
• Yeah, the only other thing that comes to mind is that you want matching impedances on a three phase system. – Vladimir Cravero Jun 12 '15 at 11:49
• Its an electrical problem only. I know about bending of conductor. But i don't know about distance between poles. – Imran Ahmed Jun 12 '15 at 12:00
• Ya, i have to match the impedance. But will you plz relate your answer to my question? – Imran Ahmed Jun 12 '15 at 12:01
• What does "pole-pole" mean in this context? Are you talking about utility poles along a street, which is what Andy is assuming, or the distance between the conductors in a cable, which is what Vladimir is assuming? – Dave Tweed Jun 12 '15 at 12:37

## 2 Answers

The spacing between towers is a function of:

• The type of conductor used.

This is mainly determined by electrical design objectives (i.e. minimum current-carrying capacity). Environmental parameters also play a part.

Modern aluminium overhead conductor comes in several different alloy compositions, some optimised for electrical characteristics, others with steel reinforcement-wires for strength, and others specialised for harsh environments (i.e. marine salt spray, near coastlines.)

• The maximum permissible tension on the conductor.

This is limited by the tensile strength of the conductor, which has to support the conductor against the downwards force of gravity, and the sideways force of the wind, at the maximum wind speed for the geographic area.

If you live in cyclone/typhoon/hurricane country, the wind speed can exceed 200 km/h sustained or 278 km/h gusts (Australian Category 5 cyclone.)

• The maximum conductor sag.

The conductor's temperature varies depending on the ambient temperature and the load (amperes) being carried by the conductor. As the conductor heats up, it lengthens due to thermal expansion, and the conductor sags closer to the ground.

The transmission line must be designed to maintain a minimum clearance over the ground, at maximum sag. This is especially important when crossing roadways - if a transmission line sags too close to the road, a vehicle might hit the line as it drives past.

Transmission line design sits at the intersection of electrical engineering, mechanical engineering, civil/structural engineering, and materials science. There is no one "formula" that gives the tower spacing distance. The tower spacing distance is part of the overall transmission line design, and needs to be calculated with respect to many variables.

With that said, for common distribution lines, i.e. the 11kV HV + 415V LV distribution lines around my home-town, I would imagine the local distribution company might have a "typical" design. This might read something like: "8m wooden poles, with 6/1/3.75mm ACSR conductor, 4/3/2.5mm earth wire, tower spacing of 50 metres". Such a design would be conservatively engineered considering the local conditions (heavy salt spray and cyclonic winds, in my home town.) It wouldn't translate around the world.

In addition to Li-aung Yip's answer, identifying the span is based on some varying factors which he has mentioned. These can be tied together using the catenary equation (and by making some simplifying assumptions), which is a hyperbolic coshine function.

The catenary equation describes the shape of a free hanging chain or cable, and power lines can be modeled by these equations. The shape of the cable (due to its sag) is indirectly related to the span distance, because the shape of the cable is often determined by laws and regulations, e.g. what is the minimum height of the ground a conducting cable must be?

Therefore determining the span can involve the use of equations, but the variables defining this equation are only indirectly related to span. This paper http://home2.fvcc.edu/~dhicketh/DiffEqns/Spring11projects/Torrey_Seward_Kirk_Gordon/1Project/Kirk&ToreysDifEQ.pdf explains the derivation of the equation and this website has a useful calculator http://www.had2know.com/academics/catenary-equation-shape-hanging-chain.html