Each individual radial is obviously a single-wire transmission line buried
in a lossy medium.

As with all lines, it has Zo and attenuation, and when length is being
considered its propagation velocity is of great importance.

Due to the very high permittivity of water (80) and the water content of all
soils, rocks even, the velocity factor VF along a buried wire is much
smaller than the free space value. Even when just resting on a slightly damp
soil surface the VF roughly falls to 0.5 which can be easily checked with a
hand-held antenna analyser. A 1/8-wavelength of wire behaves as a
1/4-wavelength when on the soil surface but with a poor Q.

Soil permittivity K is tabled alongside soil resistivity (conductivity).
Velocity in a transmission line is proportional to 1/Sqrt(K). So a typical
value of K of 14 results in a velocity factor of 1/Sqrt(14) = 0.267 i.e.,
only 27 percent of the free space velocity.

Attenuation along a buried wire is quite high. Typically it is 8 to 10 dB
per 1/4 wavelength at its own velocity depending on soil composition.

Therefore, not only is a buried radial VERY much shorter than its free-space
value, there's not a lot of current flowing in it near its end - and if
there's little current flowing in it, it may just as well not be there.

There is not much point in increasing length of radials beyond that when
input impedance of the line is already Zo.

The moral is - if you have any wire remaining after laying some short
radials then don't use it to increase their length - increase their number!

For performance of radials in quantitative terms there are 4 programs which
may be of interest at my website.

EARTHRES analyses DC and VLF performance of ground rods, plates, etc., and
of a system of ground radials of any number and length.

RADIOETH demonstrates behaviour versus length at VLF to HF of a single
radial wire.

ENDFEED and TANT136 integrate the calculations of the first two programs by
incorporating them in working models of inverted-L and T-antennas
respectively.

Remember the accuracy of performance predictions depends on how accurate you
know the soil resistivity and permittivity in the vicinity of your antenna.
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

Hi Reg,

Very interesting opinion Reg and as usual your software are very useless
;-).
Here are some more commentaries
http://www.astrosurf.com/lombry/qsl-radials.htm

73
Thierry, ON4SKY


"Reg Edwards" wrote in message
...
Each individual radial is obviously a single-wire transmission line
buried
in a lossy medium.

As with all lines, it has Zo and attenuation, and when length is being
considered its propagation velocity is of great importance.

Due to the very high permittivity of water (80) and the water content of
all
soils, rocks even, the velocity factor VF along a buried wire is much
smaller than the free space value. Even when just resting on a slightly
damp
soil surface the VF roughly falls to 0.5 which can be easily checked with
a
hand-held antenna analyser. A 1/8-wavelength of wire behaves as a
1/4-wavelength when on the soil surface but with a poor Q.

Soil permittivity K is tabled alongside soil resistivity (conductivity).
Velocity in a transmission line is proportional to 1/Sqrt(K). So a
typical
value of K of 14 results in a velocity factor of 1/Sqrt(14) = 0.267
i.e.,
only 27 percent of the free space velocity.

Attenuation along a buried wire is quite high. Typically it is 8 to 10 dB
per 1/4 wavelength at its own velocity depending on soil composition.

Therefore, not only is a buried radial VERY much shorter than its
free-space
value, there's not a lot of current flowing in it near its end - and if
there's little current flowing in it, it may just as well not be there.

There is not much point in increasing length of radials beyond that when
input impedance of the line is already Zo.

The moral is - if you have any wire remaining after laying some short
radials then don't use it to increase their length - increase their
number!

For performance of radials in quantitative terms there are 4 programs
which
may be of interest at my website.

EARTHRES analyses DC and VLF performance of ground rods, plates, etc., and
of a system of ground radials of any number and length.

RADIOETH demonstrates behaviour versus length at VLF to HF of a single
radial wire.

ENDFEED and TANT136 integrate the calculations of the first two programs
by
incorporating them in working models of inverted-L and T-antennas
respectively.

Remember the accuracy of performance predictions depends on how accurate
you
know the soil resistivity and permittivity in the vicinity of your
antenna.
----
.................................................. .........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. .........