IEEE Std 142 ring formula6 min read

Worked Example: Can a Perimeter Ring Electrode Reach 10 Ω in 200 Ω·m Soil?

A buried ring around a small building, checked against the 10 Ω usually aimed for in lightning protection earthing. A 12 m ring falls short; a 20 m ring passes.

Scenario

Soil resistivity200 Ω·m (measured, Wenner method)
ConductorBare copper, 10 mm diameter
Burial depth0.6 m
Target10 Ω (low-frequency earth resistance aimed for in BS EN 62305-3)
OptionsRing of 12 m diameter (close to the building) or 20 m diameter (around the site)

BS 7430:2011 does not give a ring formula, so the ring-of-wire formula from IEEE Std 142 (Dwight) is used, with s equal to twice the burial depth.

Step-by-step calculation

Step 1: Ring formula

D is the ring diameter, d the conductor diameter and h the burial depth.

R = ρ / (2π²D) × [ln(8D/d) + ln(4D/s)], s = 2h

Step 2: 12 m ring

Step 3: 20 m ring

Step 4: Other ways to lower the resistance

Instead of a larger ring, earth rods can be added to the 12 m ring, driven deep where the soil is wetter. The conductor size has only a small effect: doubling the diameter lowers the 12 m ring by about 0.6 Ω.

Result summary

CheckRequirementActualStatus
12 m ring≤ 10 Ω10.86 Ω✗ FAIL
20 m ring≤ 10 Ω7.03 Ω✓ PASS
In 200 Ω·m soil a 12 m ring gives about 10.9 Ω and misses the 10 Ω target; a 20 m ring gives 7.0 Ω and meets it. Confirm the installed value with a fall-of-potential test.

Key insight: Ring resistance falls roughly in inverse proportion to the ring diameter. Size matters far more than conductor thickness.

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Frequently asked questions

Why not use BS 7430 for the ring?

BS 7430:2011 gives formulas for rods, plates, straight strips, meshes and some star and cruciform layouts, but not for a ring. IEEE Std 142's ring-of-wire formula is the usual reference.

Is the 10 Ω target mandatory?

BS EN 62305-3 recommends a low earth resistance, if possible below 10 Ω, for a lightning protection earth. Electrical safety requirements for the installation are set separately, for example by disconnection times and touch voltages.

More in Earthing, Lightning & Static Safety

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