Methodology

Earthing, Fault Current and Working Clearance

Why a ground rod cannot clear a fault, why doubling a rod's diameter achieves almost nothing, and why a LOWER available fault current can produce a more dangerous arc flash.
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Two different jobs, routinely confused

The single most consequential confusion in this subject is that earthing and bonding are treated as one thing. They are two, they use different paths, and only one of them clears faults.

BONDING joins all the metalwork and provides a low-impedance return to the SOURCE — the transformer winding or the generator — through a conductor. When a live part touches an enclosure, it is this metallic path that carries enough current to operate a fuse or breaker quickly. The size of that current, and therefore the speed of disconnection, depends on the impedance of the conductors, not on the ground.

EARTHING connects the installation to the mass of the earth. Its jobs are to hold the system near earth potential, to give lightning and static somewhere to go, and to limit the voltage that appears on exposed metal. It is not, and cannot be, a fault path in a low-voltage system.

The arithmetic settles it. A ground electrode meeting a common twenty-five ohm target, on a two-hundred-and-thirty-volt system, can pass about nine amperes through the soil. A sixteen-ampere breaker will sit there indefinitely while the enclosure stays live. That is the whole argument for the protective conductor, and it is why a system relying on earth return needs residual-current protection rather than overcurrent protection.

A rod's resistance is nearly all in the first few centimetres of soil

Almost all of an electrode's resistance comes from the soil immediately around it, because that is where the current density is highest — the current spreads out into ever larger shells, and once it has, the remaining resistance is negligible. This one fact explains the entire shape of electrode design.

It explains why length beats diameter, decisively. In the standard expression the diameter appears inside a logarithm, so DOUBLING a rod's diameter improves its resistance by only a few per cent, while doubling its length improves it by roughly forty. A thicker rod is bought for mechanical strength during driving, not for electrical performance.

It explains why multiple rods must be spaced apart. Two rods closer together than their own length have overlapping shells of soil, are competing for the same current path, and deliver far less than the halving that parallel resistances suggest. The conventional minimum spacing is one rod length, and more is better.

And it explains the seasonal problem. Soil resistivity depends on moisture, dissolved salts and temperature, all of which move through the year, and it can change by an order of magnitude between a wet spring and a dry or frozen month. A measurement taken once is a measurement of one day; where the value matters, electrodes are driven below the seasonally active zone and the test is repeated in the worst season rather than the convenient one.

R=ρ2⁢π⁢L⁢(ln⁡4⁢La−1)
Resistance of a driven rod. Soil resistivity is a direct multiplier; length divides AND appears in the logarithm; radius appears only inside the logarithm, which is why diameter barely matters.
ρ
soil resistivity — the dominant term, and seasonally variable by an order of magnitude
L
driven length of the rod
a
rod radius — buried in a logarithm, so doubling it changes little

Fault current is set by the source, not by the load

The current available into a bolted short circuit is limited by the impedance between the fault and the source, and at a service entrance that is dominated by the supply transformer. Its rating and its percentage impedance set the ceiling: a large transformer with a low impedance can deliver tens of thousands of amperes into a fault, and the connected load is irrelevant to that figure.

Available fault current FALLS with distance, because every metre of conductor adds impedance. So the worst case in a building is at the service equipment and it reduces downstream — which is the opposite of the intuition that danger accumulates away from the supply, and it is why the interrupting ratings required at a main switchboard are so much higher than those at a final distribution board.

Two consequences follow, and both are commonly missed. A device must be able to INTERRUPT the current available at its location; installing one with a lower rating is not a reduced margin but a device that may fail destructively while trying to open. And the downstream conductors must survive the let-through energy during the clearing time — a breaker that interrupts successfully has still failed if the cable behind it was damaged getting there. That is the check the protective conductor sizing calculation performs, and it is an energy check rather than a current check.

The one change that raises fault current across a whole installation is an upgraded supply transformer. A utility replacing a unit with a larger one can invalidate the interrupting ratings of equipment that was correct the day it was installed, without anyone inside the building touching anything.

Where it turns around: less fault current can be more dangerous

Arc flash energy is not the fault current. It is the ENERGY delivered at the working distance, which is the arc power multiplied by the time the protection takes to clear it — and clearing time depends on the current in a way that can reverse the result.

A protective device on its instantaneous region clears an enormous fault in milliseconds. Reduce the available current — a longer run, a smaller transformer, a weaker source — and the same device may fall onto its inverse-time curve, where clearing takes hundreds of milliseconds or seconds. The arc power is lower and the duration is far longer, and the product can be substantially WORSE.

This is why arc-flash results cannot be reasoned about from fault current alone, why the analysis needs the actual protective device characteristics and settings, and why turning maintenance-mode settings on — which trade selectivity for speed — reduces incident energy without changing the current at all.

Working clearance dimensions are a related but separate provision, and they are about people rather than insulation. The depth, width and headroom in front of equipment exist so that a worker can operate it, step back and escape, and so that a second person can reach them. They are absolute dimensions rather than calculated ones, they must be clear at all times rather than at the moment of work, and the most common violation — storage — is invisible on every drawing.

Busbar ampacity is a temperature limit, not a current formula

A busbar's rating is the current at which its temperature rise reaches the limit its insulation, its supports and its terminations can tolerate. That makes it a HEAT BALANCE — losses in the conductor against heat leaving by conduction, convection and radiation — and it is why an identical bar has different ratings in free air, in an enclosure, and stacked with others.

Two effects make the alternating-current rating lower than the direct-current one. SKIN EFFECT pushes current towards the surface, so the interior of a thick bar carries less than its share; PROXIMITY EFFECT distorts the distribution further when bars are close together. Both mean that cross-sectional area alone over-predicts capacity, and that several thin bars outperform one thick bar of the same total area.

Because the rating is thermal, ambient temperature enters directly: a switchroom running hot has derated every bar in it. And because the losses are resistive and grow with the square of current, a bar operating near its limit is producing four times the heat it produced at half load — which is the origin of the electrical room heat load that has to be removed, and of the joints that loosen through thermal cycling and then run hotter still.

Published ratings come from tested assemblies for exactly these reasons. An estimate from a formula places a bar in the right region; the rating that can be relied on is the one established by a temperature-rise test on the actual construction.

Lightning: a volume of protection, not a cone

The older way of describing what an air terminal protects was a cone at a fixed angle. The method in current standards is the ROLLING SPHERE: imagine a sphere of a radius set by the protection level rolled over the structure, and whatever it cannot touch is protected. Where it does touch is where a strike can attach.

The two disagree in a way that matters. A cone implies that a taller rod protects proportionally more, and the sphere shows that it does not — beyond a point the sphere simply touches the roof edge between terminals, so the answer to a large roof is more terminals rather than a taller one. It also predicts the failure that the cone hides: strikes to the SIDES of tall structures, below the tip, which is why tall buildings have terminals on their upper flanks and not only on the roof.

The air terminal is also the least important part of the system. A strike must reach earth through down conductors with enough cross-section and few enough sharp bends to carry it, and a path with a high inductance will simply be bypassed — the current side-flashes to nearby metalwork, which is what puts it into services and electronics. Bonding of all incoming services at entry is what actually protects a building's contents, and surge protective devices are what protect the electronics on those services.

The honest summary for the estimator on this page is that it returns a geometric radius under a stated protection level. It is a first-pass screening figure. A lightning protection design is a whole-system matter — terminals, down conductors, earth termination, bonding and surge protection — and none of the last four is a radius.

What has to be measured

Every quantity on this page has a measurement that supersedes it. Soil resistivity comes from a four-point survey rather than a table; an installed electrode's resistance from a fall-of-potential test, which needs real distance and gives a wrong answer if the test probes are inside the electrode's own resistance area. Clamp-on testers are convenient and measure something different — a loop, which requires a parallel return path to exist at all.

Available fault current is established by a short-circuit study using the utility's actual source data, not by a rule of thumb, and incident energy by an arc-flash study using the installed protective devices and their settings. Both are documents that have to be revised when the supply or the protection changes.

The calculators here estimate. They are for checking whether a design is in the right region, for sanity-checking a figure someone has quoted, and for understanding which variable actually moves the answer. They are not evidence of compliance, and the pages say so, because in this subject the difference between an estimate and a study is measured in injuries.

Calculators that use this method

Basis

  • IEEE Std 80, Guide for Safety in AC Substation Grounding — grid resistance, step and touch voltage, and the soil model behind them.
  • IEEE Std 81, Guide for Measuring Earth Resistivity, Ground Impedance and Earth Surface Potentials — the four-point survey and fall-of-potential method.
  • IEEE Std 142 (Green Book), Grounding of Industrial and Commercial Power Systems, for the distinction between bonding and earthing set out above.
  • Dwight, H.B. (1936), Calculation of Resistances to Ground — the rod expression used in the formula above.
  • NFPA 70 (National Electrical Code) Article 250 for grounding and bonding conductor sizing, and Article 110 for working space dimensions.
  • IEC 60364-4-41 and 60364-5-54 for the European treatment of earthing arrangements and protective conductor sizing, including the adiabatic energy check.
  • IEEE Std 1584, Guide for Performing Arc-Flash Hazard Calculations, and NFPA 70E — the incident-energy model in which clearing time, not current alone, governs.
  • NFPA 780 and IEC 62305 for lightning protection, including the rolling sphere method, down conductor requirements, side flash and bonding of services.
  • IEEE Std C37.20.1 and UL 891 for switchgear and switchboard temperature-rise testing, the basis of published busbar ratings.
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