Electric Fence Pulse Decay Under Vegetation Leakage: Maximum Effective Length, Far-End Voltage, and a Design Rule by Vegetation Class

Vegetation touching an electric fence leaks current to ground along the whole line. This paper models that leakage as a distributed shunt conductance and derives how far an energizer pulse can travel before the voltage at the far end falls below a deterrent level. The wire is treated as a line with series resistance of 40.0 ohm/km, a peak open-circuit energizer voltage of 9000 V, and a rectangular-equivalent pulse width of 30 microseconds. Minimum deterrent voltages are taken as 2000 V for cattle and 4000 V for sheep and goats. Six vegetation classes are studied, from clean, dry and maintained, with a leakage resistance of 5000 ohm for a 1-km length, to extreme brush, with a leakage resistance of 50 ohm for a 1-km length. Two limits act together. The first is source sag: leakage drains the pulse energy, so a small energizer cannot hold its open-circuit voltage into a heavy load. The second is a voltage ceiling that no energizer size can pass: the far-end voltage cannot exceed 9000 V divided by cosh(gamma L), where gamma is the propagation constant and L is the length. Under wet-season heavy brush, the ceiling alone limits a cattle fence to 3.45 km and a sheep and goat fence to 2.29 km, at any energizer size. At 5 km in that class a 20 J energizer gives only 550 V at the far end, and even an energizer with unlimited energy gives only 761 V. At 10 km the values are 23 V and 32 V. By contrast, on a clean, dry, maintained fence a 5 J energizer reaches 24.10 km for cattle and 16.21 km for sheep and goats. A design rule is given as the output energy required to hold deterrent voltage at 5 km and at 10 km for each vegetation class. Where the table entry is impossible, buying a larger energizer is not an answer. Clearing the line or subdividing the fence into shorter separately fed lengths is the only answer in the model. AI disclosure: This paper was prepared with the assistance of Dave, an AI system. Dave carried out the modelling calculations, produced the computed results, and assisted with drafting, under the direction of the named author. All results are SIMULATED, NOT MEASURED. No fence was built, no energizer was tested on a fence, and no animal was tested for this work.