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, 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

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

Rest easy, Walt. To my knowledge, no one has ever shown BL&E's
*measurements* to be invalid, or the conclusions reached from those
measurements. It's their mathematical treatment of what they expected to
happen, in the first part of their paper (Part II: Theoretical
Considerations), that wasn't correct. I don't believe I have a paper
that details the errors they made, but it was regarded my later authors
as being in error, prompting a great deal of more rigorous work. Later
authors don't generally even reference that BL&E theoretical
mathematical work. Nearly all reference their measurements, however, as
they should.

Roy Lewallen, W7EL

Walter Maxwell wrote:

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 Tue, 9 Aug 2005 08:03:53 -0500, "Richard Fry"
wrote:
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.

Hi OM,

Both Reg and you would do well to obtain and read a copy.

On page 757 is introduced the necessary discussion of:
Is = Iw + Ie
"The we will denote the total earth current flowing radially inward
.... as Is, ... where Iw is the component flowing in the wires, and Ie
is the part which actually flows in the earth.

The discussion of earth conductivity (quite specifically named as
such) within the paper spans pages 757, 758, 759, 760, with numerous
citations and graphings against specific conductivity values applied
to related figures in page 761, 762, 763, and 764.

On page 758:
"The actual earth current and the current flowing in the radial wires
are given by..." introducing formula (8).
Followed on page 759 with:
"while the current actually flowing in the earth is...." introducing
formula (10).
"Thus from (8), (9), and (10), together with Fig. 4. we may obtain the
actual current in the earth...."

As for explicit conductivity:
"Fig. 5 shows the current in the wires for the following conditions
.... 0.2X10^-4 mhos per cm cube"
"Fig. 6 shows the actual current in the earth for the same
conditions."

"shown for the following conditions..." and four specifications of
conductivity follow.

Now, specifically to a comment I offered as to the importance of
noting conductivity:
"When the earth is of good conductivity, the current leaves the wires
and enters the earth closer to the antenna than does when the earth is
a poor conductor."

There is also a formulation for Fig. 17 (page 766) that is introduced
as "The current is flowing toward the antenna through a ring of earth
of radius..." which computes the power lost to ground for a known
conductivity (with examples abounding).

In this short span of 8 pages dedicated to earth conductivity there at
least 12 graphs and charts all quite distinctly displaying the
variation of measured results as a function of different specified
ground conductivities antennas and ground system combinations.

The authors were quite aware of the ground beneath their feet and duly
reported its contributions in the standard engineering fashion of
displaying first principles.

73's
Richard Clark, KB7QHC

Thanks Roy, I'm resting easy now.

Walt


On Tue, 09 Aug 2005 10:51:42 -0700, Roy Lewallen
wrote:

Rest easy, Walt. To my knowledge, no one has ever shown BL&E's
*measurements* to be invalid, or the conclusions reached from those
measurements. It's their mathematical treatment of what they expected to
happen, in the first part of their paper (Part II: Theoretical
Considerations), that wasn't correct. I don't believe I have a paper
that details the errors they made, but it was regarded my later authors
as being in error, prompting a great deal of more rigorous work. Later
authors don't generally even reference that BL&E theoretical
mathematical work. Nearly all reference their measurements, however, as
they should.

Roy Lewallen, W7EL

"Richard Clark" wrote
Both Reg and you would do well to obtain and read a copy.

===================================

Until now I have not contributed to this discussion. Neither now and
very little in the past. So please leave me out of it.

I have produced one small program (I am surprised at the attention
drawn to it) which computes radiating efficiency of a short vertical
antenna based on a novel analysis of ground loss, ie., shallow buried
radial wires which behave as lossy transmission lines.

All I have to say is that the program gives the "right" answers.
Disprove it if you can.

It is as accurate as the ground "constants" are known, that is about
plus or minus 30 percent. The answers are forthcoming within
milli-seconds. No need to go on a one month training course. And it's
free. What more do you want?

To prove it wrong you have to create a set up similar to that pruduced
by BL&E - only this time don't forget to measure ground coductivity
and permittivity!

From what Roy says, BL&E were hardly better than bungling amateurs of
their era. The only reason their report is considered to be 'The
Bible' is because it was the only one ever produced and available at
the time.

They laid down so many radials it didn't matter what ground
conductivity was.
----
Reg.

On Tue, 9 Aug 2005 19:16:45 +0000 (UTC), "Reg Edwards"
wrote:

They laid down so many radials it didn't matter what ground
conductivity was.

Hi Reg,

As usual you both lost track of the intent of the study. The whole
point was to insure it doesn't matter.

Sorry to rustle your skirts, but this falls under the heading of:
"Stating the bleeding obvious"

73's
Richard Clark, KB7QHC