Counterpoise and Radial Ground Array Resistance

A transmission or distribution structure on a ridgeline, on frozen ground, or in shallow soil over bedrock is grounded with buried horizontal wire instead, and the counterpoise relation has a different length dependence from a rod's -- which is the whole reason to reach for it. A buried horizontal conductor sheds current along its entire length, so its resistance falls roughly as one over length with a logarithmic correction: DOUBLING A COUNTERPOISE NEARLY HALVES THE RESISTANCE, where doubling a driven rod barely helps, because each additional foot of rod reaches ground no less resistive than the last. Multiple radials do not divide the resistance by their count, and assuming they do is the ordinary way this gets oversold. Each wire sits in the others' potential field, so the current it sheds has to fight ground that its neighbours have already raised. The mutual-coupling penalty grows with the number of radials and shrinks as they are spread further apart, which is why four long radials beat eight short ones of the same total wire almost every time. Both numbers are reported -- the ideal parallel value and the coupled one -- so the penalty is visible rather than assumed away, and the penalty itself is entered because it depends on the geometry of the particular array. Resistivity is read in ohm-cm, the same unit the driven-rod and four-pin resistivity calculations use, so two grounding answers for one structure cannot disagree about the dirt. A horizontal electrode in UNIFORM soil at power frequency. Soil is almost never uniform, and a two-layer structure -- conductive topsoil over rock, or the reverse -- changes the answer substantially; a four-pin survey run at several spacings is what reveals it, and one spacing does not. This gives power-frequency resistance and NOT the impulse impedance that governs lightning performance, which is lower than this for a short counterpoise and HIGHER for a long one, because a surge does not have time to reach the far end before the stroke is over. Seasonal variation with moisture and frost is large and is not modeled, and a resistivity measured in a wet spring is not the number the line lives with in February. It does not evaluate step and touch potential or ground potential rise, which are separate screens, and it does not size the conductor for fault current. IEEE 80, IEEE 81 for measurement, and the utility's grounding standard govern.

R = rho / (pi L) x [ ln( 2 L / sqrt(d x h) ) - 1 ] with rho in ohm-cm and L, d and h in centimetres; the array value is the single-wire resistance divided by the radial count and multiplied by an entered mutual-coupling penalty; the length for a target resistance is that relation bisected.

The buried horizontal electrode (counterpoise) resistance relation, by name, with IEEE 80 and IEEE 81 named for measurement. Resistivity is read in ohm-cm to match the driven-rod and four-pin resistivity calculations. The mutual-coupling penalty is ENTERED, not modeled. Power-frequency resistance in uniform soil, NOT impulse impedance. IEEE 80, IEEE 81, and the utility's grounding standard govern.

One logarithm on a resistivity the reader measures; no soil table or grounding standard text is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: soil_resistivity_ohm_cm, length_ft, burial_depth_in, wire_diameter_in, radials, coupling_penalty, target_resistance_ohm, single_wire_ohm, ideal_parallel_ohm, array_ohm, coupling_cost_ohm, double_length_ohm, doubling_improvement_x, length_for_target_ft

• Uniform soil a two-layer structure changes the answer substantiallyIEEE 81, a four-pin survey at several spacings
• Power frequency, not impulse a surge does not have time to reach the far end of a long counterpoiseIEEE 80
• The mutual-coupling penalty is entered it depends on radial length and spreadthe utility's grounding standard