Suppose there's a fairly isolated well grounded antenna mast. Or a power
pylon in the middle of a field. There may be people or animals wandering in
the vicinity. Sooner or later lightning will strike a high mast.
The question arises at what distance from the base of the mast should a
safety fence be erected to protect people and animals from electrocution. Or
to provide some other greater degree of protection.
The situation can be translated into your back yard. There are then
subsidiary questions such as at what distance should the mast-grounding
system be bonded to the domestic house ground? Or to another mast?
It's obvious that risks, probabilities, choice of safety factors, soil
resistivity, strength of lighting strokes are involved. It's entirely up to
YOU what you do about it.
There are ball-parks within ball-parks. Nevertheless, to keep you in the
right set of ball parks a few simple calculations can be made. Without
numbers bafflegab will prevail.
The local ground system at the base of the mast can be represented or
modelled by a hemispherical electrode impressed into the ground surface.
The electrical characteristics of this simple electrode are very easily
calculated from its radius and soil resistivity.
Suppose the antenna mast with its buried legs and set of ground rods extends
out to a radius Rh metres from the centre of the small system. Even if the
mast consists only of a 2" diameter aluminium tube buried to a depth of 2
feet without any rods you will now have a number Rh. For this exceptional
simple case of a single fat rod call Rh = 1/2 depth. It turns out to be
very non-critical anyway.
A hemispherical bowl of low-resistivity concrete is very well represented by
the mathematical model of course. The concrete becomes the ground electrode.
The resistivity of the material forming the ground electrode does not enter
into the argument because the lightning stroke is assumed to be a current
source.
It is not difficult to show that the voltage at the edge of the electrode,
at a distance Rh from the mast itself, relative to the voltage of the mass
of the Earth at a great distance is given by -
V = S * I / 2 / Pi / Rh volts
where S is soil resistivity in ohm/metres,
I = current in lightning stroke in amps,
and Rh is the hemispherical radius.
However, we are not greatly interested in the volts at the electrode. What
matters is the VOLTAGE GRADIENT along the surface of the soil as the current
streams away from the base of the antenna in all radial directions
uniformly.
It should be noted, and is intuitively fairly obvious, that at a short
distance beyond Rh the current flows away from the antenna mast in radial
directions through the soil regardless of the actual shape and construction
of the ground electrode system.
Suppose a cow is facing the antenna and the distance between the animal's
front and rear legs is 1.5 metres. Insofar as the cow is concerned what
really matters is the voltage gradient along the soil surface. With a little
integration it can be shown the voltage difference Vd between two points on
the soil surface at distances R1 and R2 from the mast is given by -
Vd = S * I / 2 / Pi * ( R1 - R2 ) / R1 / R2 volts,
If soil resistivity S = 100 ohm.metres,
( Soil conductivity = 10 mS )
Stroke current = 50,000 amps,
Rear legs distance from mast, R1 = 6 metres,
Front legs distance from mast = 4.5 metres,
Neglecting the resistance of a cow, the potential difference between the
poor animal's front and rear legs would rise in a matter of milli-seconds to
Vd = 44,000 volts without time being allowed even to say "Moo". Current and
voltage then subside more slowly.
Whereas the radio station owner, at the same location, standing on one leg
wearing a rubber boot would very likely survive unscathed.
As a matter of interest the voltage gradient G at a distance of R metres
from the mast is given by -
G = S * I / 2 / Pi / Square( R ) volts-per-metre.
The foregoing calculations are exact when the ground electrode is a true
hemisphere. There are other applications.
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Reg, G4FGQ
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Regards from Reg, G4FGQ
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