BS 7430 / IEEE 142 / IEEE 808 min read

Earth Rod vs Ring vs Earth Mat: Which Gives the Lowest Resistance in 100 Ω·m Soil?

Part 2 of the earthing series. One rod gives 33.5 Ω, four rods 9.1 Ω, a 10 m ring 6.3 Ω and a 20 m × 20 m mat 2.7 Ω. Why size beats everything else.

Scenario

SoilUniform, ρ = 100 Ω·m
Burial depth0.6 m for horizontal conductors

Step-by-step calculation

Step 1: Single rod, 3 m × 16 mm (BS 7430 9.5.3)

R = ρ/(2πL) × [ln(8L/d) − 1]
R = 100/(2π × 3) × [ln(8 × 3/0.016) − 1]
R = 33.5 Ω

Step 2: Four rods in a line, 3 m apart

Rods closer together than about twice their length share the same soil, so the resistance does not fall in proportion to the number of rods.

Step 3: Ring, 10 m diameter, 10 mm conductor (IEEE 142)

R = ρ/(2π²D) × [ln(8D/d) + ln(4D/s)], s = 2h
R = 100/(2π² × 10) × [ln(8000) + ln(33.3)]
R = 6.33 Ω

Step 4: Earth mat 20 m × 20 m, 4 × 4 conductors (IEEE 80 Sverak)

Rg = ρ × [1/LT + 1/√(20A) × (1 + 1/(1 + h√(20/A)))]
LT = 160 m, A = 400 m², h = 0.6 m
Rg = 2.73 Ω (adding 8 rods of 3 m: 2.65 Ω)

Result summary

CheckRequirementActualStatus
Single rod—33.5 Ω✓ PASS
Four rods—9.14 Ω✓ PASS
10 m ring—6.33 Ω✓ PASS
20 m × 20 m mat—2.73 Ω✓ PASS
In 100 Ω·m soil the earth mat gives 2.7 Ω, the ring 6.3 Ω, four rods 9.1 Ω and a single rod 33.5 Ω. The area covered is what lowers resistance most.

Key insight: Resistance of a grid is roughly ρ/(4r) for an equivalent disc of radius r. Doubling the area lowers resistance by about 30 %; doubling conductor size barely changes it.

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Frequently asked questions

Why add rods to a mat if they change resistance so little?

Rods reach deeper, often wetter soil that stays stable through the seasons, and rods at the perimeter reduce step and touch voltages at the grid edge.

Is low resistance enough for a substation?

No. Touch and step voltages must also be checked — see Part 3.

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