Earth Electrode Spacing Formulas

Earth electrode spacing formulas: two rods in parallel, the interaction factor, the combined resistance and the utilisation of each rod at a given spacing.

The formulas

ρ is the soil resistivity in Ω·m, L the driven length and d the diameter of the rod in metres, and s the distance between the two rods. The rods share the same ground, so their fields overlap and the pair is worth less than two separate rods, by the factor 1 + λ. The overlap falls as s rises, and a spacing of at least the length of the rod is the usual guide. The formulas assume a uniform soil and the same two rods, and a design with more rods or a grid needs a method for that layout. The resistivity and the sizes here are examples.

Worked example: two 3 m rods of 16 mm in soil of 100 Ω·m

1. R1 = 100 / (2π × 3) × (ln(8 × 3 / 0.016) − 1) = 33.49 Ω
2. At s = 3 m: λ = 100 / (2π × 33.49 × 3) = 0.1584
3. R2 = 33.49 / 2 × (1 + 0.1584) = 19.4 Ω
4. At s = 6 m: λ = 0.0792, so R2 = 18.07 Ω
5. Doubling the spacing from 3 m to 6 m lowers the pair from 19.4 Ω to 18.07 Ω

Two rods by spacing

Frequently asked questions

Why not put the rods close together?

Close rods share the same soil volume, so each one raises the potential near the other and the pair resists almost as much as one rod.

Is more spacing always better?

It helps, but with falling returns. Beyond about twice the length the gain is small, and the link between the rods gets longer and dearer.

Is a second rod better than a longer rod?

A deeper rod often does more where the lower layers of soil are wetter. A site test of the soil layers settles it.

Does this replace a measurement?

No. The formulas give a first estimate. The resistance of the finished earth must be measured, and the seasons change it.

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