Just to add a little to Richard's quite correct advice.

A single well-elevated 1/4-wave radial has a resistive input impedance
of very roughly 25 ohms. It is, in effect, a horizontal 1/4-wave
antenna and forms, with a 1/4-wave vertical, a bent half-wave dipole
which will radiate just as efficiently as a straight wholely vertical
dipole. The radiation pattern, of course, will be different.

With two or more equi-distributed radials the radiation pattern
changes again and the resistive impedance presented to the base of the
antenna reduces still further.

When the height of radials above ground is of the order of 1/10th of
their length the resonant length begins to decrease. So when the
radials are lying on the surface of the ground the propagation
velocity is about only half of the free space value. Consequently, to
maintain the 1/4-wave resonant length, their physical length should be
reduced.

On the other hand, when the radials are lying on the ground surface,
ground loss damps down resonance and dimensions are no longer very
critical. A collection of surface radials can be of various lengths.
They can be investigated/selected by using a hand-held antenna
analyser.

Shallow-buried radials, in average sorts of soils, are practically
non-resonant and their lengths can be reduced without detriment to
small fractions of the free-space wavelength.

The attenuation at HF along buried radials is quite high. There is not
much point in having radials longer than the distance at which very
little current is flowing in them.

For the behaviour of buried radials in various soils see program
RADIALS2 from website below.
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Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
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