As a followup to my question, I guess the concept or the question is
no different than if it referred to a dipole instead of radials on a
vertical. The concern is protection from the high voltage at the end
of the wire, and the potential of it causing a fire.
So it is really a very general question, considering the numbers of
antennas hams are having to disguise or hide inside their homes these
days.

Rick K2XT

Rick K2XT wrote:
As a followup to my question, I guess the concept or the question is
no different than if it referred to a dipole instead of radials on a
vertical. The concern is protection from the high voltage at the end
of the wire, and the potential of it causing a fire.
So it is really a very general question, considering the numbers of
antennas hams are having to disguise or hide inside their homes these
days.

In a vertical dipole, you have only one "radial" which carries
the same currents and voltages as the upper vertical element.
Seems to me, when one has multiple radials, the energy in each
radial has to be the total energy available divided by the number
of radials. Therefore, the voltage at the ends of 1/4WL radials
should decrease as the number of radials is increased.

This seems to be another way that distributed networks differ
from lumped circuits. We might even be able to calculate the
voltage at the ends of the radials, given the number of radials
and the total power available to the radial system.
--
73, Cecil http://www.qsl.net/w5dxp


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Cec, don't you think you should take diameter of radials as well as
their number into account. Also their angle, and the height above
ground, or their distance from the brickwork, roof beams and rafters
when in an attic.

Do you have an equation for Volts = Function( number, frequency,
watts, length, diameter, angle, height, etc ) ?
----
Reg, G4FGQ

Reg Edwards wrote:
Cec, don't you think you should take diameter of radials as well as
their number into account. Also their angle, and the height above
ground, or their distance from the brickwork, roof beams and rafters
when in an attic.

Actually, I was thinking free space when I wrote that. It
was a qualitative answer, Reg, not a quantitative one.

Do you have an equation for Volts = Function( number, frequency,
watts, length, diameter, angle, height, etc ) ?

Only a ballpark figure, Reg, which should be good enough.
Since balanced radials don't radiate (much), it should
be a piece of cake for you to come up with a piece of
software that calculates voltage at the tips Vs number
of radials. Let me know if you need any help. :-)
--
73, Cecil http://www.qsl.net/w5dxp

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"Cecil Moore" wrote:
Reg Edwards wrote:
Do you have an equation for Volts = Function( number, frequency,
watts, length, diameter, angle, height, etc ) ?

Only a ballpark figure, Reg, which should be good enough.
Since balanced radials don't radiate (much), it should
be a piece of cake for you to come up with a piece of
software that calculates voltage at the tips Vs number
of radials. Let me know if you need any help. :-)
________________

Reg,

The 1937 Brown, Lewis and Epstein IRE paper "Ground Systems as a Factor in
Antenna Efficiency" include an analysis of the currents in radial ground
systems, along with equations and graphs for it in various configurations.
All you need to do to apply them to a system of raised radials is to modify
these basic equations.

Of course, you will have to read the paper first to do that (wink, nudge).
But then you might also see why knowledge of ground conductivity was
unimportant to the conclusions of this paper, and refrain from saying so in
the future.

RF

Richard Fry wrote:

Reg,

The 1937 Brown, Lewis and Epstein IRE paper "Ground Systems as a Factor
in Antenna Efficiency" include an analysis of the currents in radial
ground systems, along with equations and graphs for it in various
configurations. All you need to do to apply them to a system of raised
radials is to modify these basic equations.

Of course, you will have to read the paper first to do that (wink,
nudge). But then you might also see why knowledge of ground conductivity
was unimportant to the conclusions of this paper, and refrain from
saying so in the future.

RF

Unfortunately, the mathematical analysis in that paper was found to be
in error. A search of the literature shows that quite a number of people
worked on this problem well after publication of the BL&E paper. Some
notable work was done by J.R. Wait and W.A. Pope of the Radiation
Physics Laboratory, Defence Research Branch, in Canada. Two papers in
particular give equations for the impedance of radial systems which
appear to be valid -- "The Characteristics of a Vertical Antenna With a
Radial Conductor Ground System", Appl. Sci. Res. B, Vol. 4, 1954; and
"Input Resistance of L.F. Unipole Aerials With Radial Wire Earth
Systems", Wireless Engineer, May, 1955. The equations involve multiple
integral equations which can't be solved in closed form. In papers I've
read which do involve equations which can be solved in closed form, even
approximately, the results have deviated greatly from BL&E's measured
results, making the accuracy of the method doubtful. This holds true for
Reg's program, also, which apparently depends on some simplifying
assumptions which aren't valid.

NEC-2, which is readily available in numerous forms, does about as good
a calculation as any of elevated radial systems. Its major limitation,
in my opinion, is the inability to deal with stratified ground. Of
course, even if it could handle stratified ground, the user would
somehow have to determine the properties and locations of the various
strata. NEC-4 can, in addition to NEC-2's capabilities, include buried
radials in its models. A few tests show reasonable agreement between it
and BL&E's results. Incidentally, the equations in the first Wait and
Pope paper I mentioned resemble those used in NEC-4, but I haven't
studied them in enough detail to determine if they are indeed the same.

Elevated radial systems have been somewhat controversial, with some
indications that modeled results don't imitate actual results very well,
particularly at low frequencies. But there's very little really good
measurement data available to make a valid judgement. Besides the
possibility of stratified ground, some people have reported difficulty
in maintaining equal currents in near-resonant elevated radial wires in
real installations. This would have a substantial effect on a system,
and would definitely cause deviation between modeled and measured results.

There's considerable work to be done in this field, but what really
needs to be done is the making of good, well documented and carefully
done measurements of elevated radial systems -- not more calculations
based on invalid assumptions.

Roy Lewallen, W7EL

On Mon, 08 Aug 2005 12:27:09 -0700, Roy Lewallen
wrote:

There's considerable work to be done in this field, but what really
needs to be done is the making of good, well documented and carefully
done measurements of elevated radial systems -- not more calculations
based on invalid assumptions.

Hi Roy,

That inspired me to reach for The ARRL Antenna Compendium, Volume 2.

Within it, the very first article, is
"Vertical Antennas: New Design and Construction Data"
By Doty, K8CFU; Frey, W3ESU; and Mills, K4HU

Their 10M vertical(s) above an elevated radial system of 64 wires
presents some interesting results. Albeit, they perhaps do not answer
the questions you've offered, but it does reveal the quality of work
possible.

73's
Richard Clark, KB7QHC

On Mon, 08 Aug 2005 12:27:09 -0700, Roy Lewallen
wrote:

Unfortunately, the mathematical analysis in that paper was found to be
in error. A search of the literature shows that quite a number of people
worked on this problem well after publication of the BL&E paper. Some
notable work was done by J.R. Wait and W.A. Pope of the Radiation
Physics Laboratory, Defence Research Branch, in Canada. Two papers in
particular give equations for the impedance of radial systems which
appear to be valid -- "The Characteristics of a Vertical Antenna With a
Radial Conductor Ground System", Appl. Sci. Res. B, Vol. 4, 1954; and
"Input Resistance of L.F. Unipole Aerials With Radial Wire Earth
Systems", Wireless Engineer, May, 1955. The equations involve multiple
integral equations which can't be solved in closed form. In papers I've
read which do involve equations which can be solved in closed form, even
approximately, the results have deviated greatly from BL&E's measured
results, making the accuracy of the method doubtful. This holds true for
Reg's program, also, which apparently depends on some simplifying
assumptions which aren't valid.

snip

Roy Lewallen, W7EL

Roy, I don't have the Wait and Pope paper for review, but I'm
concerned over the validity of their equations that you say render
BL&E's measurements invalid. How can their measurements be invalid
when field-strength measurements of literally thousands of AM BC
antennas agree with BL&E's? Keep in mind that every BC station that
uses a directional array is required to prove the performance of the
array with field strength measurements that assure the measured values
agree with the calculated values.

It was only after verifying BL&E's measurements by comparing their
data with those obtained from many subsequent measurements of BC
antennas that the FCC used the BL&E data in standardizing the
requirements for radial systems for new BC stations.

Isn't it possible that Wait and Pope's equations relate to some other
aspects of BC antennas than those of BL&E? I simply cannot accept the
notion that BL&E's data is wrong.

Walt,W2DU

On Mon, 8 Aug 2005 06:39:47 -0500, "Richard Fry"
wrote:

Of course, you will have to read the paper first to do that (wink, nudge).
But then you might also see why knowledge of ground conductivity was
unimportant to the conclusions of this paper, and refrain from saying so in
the future.

Hi OM,

In fact those authors took great care to consider the condition of
ground conductivity and documented it for very good reasons. One of
the hallmarks of their work reveals that the phase shift between the
RF in the Wire, and that induced into the ground causes the lateral
flow of currents, increasing power dissipation. This is a major
reason why the density and spacing are important.

Elevating the radials creates an entirely different situation.

73's
Richard Clark, KB7QHC

"Richard Clark" wrote
"Richard Fry" wrote:
But then you might also see why knowledge of ground conductivity was
unimportant to the conclusions of this paper, ...
Hi OM,
In fact those authors took great care to consider the condition of
ground conductivity and documented it for very good reasons.
__________________

Nowhere in Brown, Lewis and Epstein's IRE paper titled "Ground Systems as a
Factor in Antenna Efficiency" is there ANY documentation of the actual
ground conductivity that was measured, or even calculated for the antenna
site and/or the propagation path used. It was unimportant for the construct
and relevancy of the tests and conclusions which the paper reported.

This is the paper I was referring to in my previous posts.

RF