Richard,

I disagree with your conclusion that currents flow circumferentially. It
does not say so in the paper, and I don't believe it can be inferred
from what is said in the paper. If you were to draw a diagram showing
the currents produced by the phase shift between earth and radial
currents, you'd find that the net current resulting from this phase
shift is purely radial, not circumferential.

If the currents flow circumferentially, do they flow clockwise or
counterclockwise, and at what magnitude relative to the radial currents?
Surely there's some reference which shows this calculation which you
could direct me to or, if not, you could show how the calculation is
done and what the result is.

Roy Lewallen, W7EL

Richard Clark wrote:
On Mon, 09 Apr 2007 09:08:09 -0700, Roy Lewallen
wrote:

Richard Clark wrote:
On Sun, 08 Apr 2007 23:56:37 -0700, Roy Lewallen
wrote:

Indeed it is. Can you point me to a reference where I can get a more
detailed explanation of this circumferential current and its cause?
Hi Roy,

Brown, Lewis and Epstein.

Which page?

Hi Roy,

It is distributed through the discussion.

Pg. 757 (at the top of the page introduces):
"These losses are due to conduction of earth
currents through a high resistance earth..."

"Where there are radial ground wires present,
the earth current consists of two components,
part of which flows in the earth itself and
the remainder of which flows in the buried wires."

"...all the various components differ in phase."

This establishes the relationship and distinction in the various
currents. It is the current in the earth that is the topic of
discussion here. That current is out of phase with respect to the
currents (at the same radial distance) found in the buried wires. No
wires, no phase issue. No phase issue, and earth currents would be
radial. Now, to distinguish this from circumferential is not to say
this is absolute (it does not follow an arc of constant radius).

This is extended to coverage at the bottom of page 758:
"The actual earth current and the current flowing in the
radial wires are given...." [formula shown in the original]

"From (8) [that formula] we see that the earth
current proper leads the current in the wires
by 90 electrical degrees."

At a radius, the earth phase and the wire phase exhibit a potential
difference which results in conduction that is not strictly radial
(the term circumferential through the combination of vectors might be
replaced with spiral, or diagonal). The earth's resistance comes into
play at page 760:
"When the earth is of good conductivity [a paradox ensues],
the current leaves the wires and enters the earth closer to
the antenna than it does when the earth is a poor conductor."
and hence the advice for replacing dirt with sand OR providing more
closely spaced radials, closer in.

"Thus the regions of high current density are subjected
to still more current with higher losses in these regions."

73's
Richard Clark, KB7QHC

On Mon, 09 Apr 2007 12:12:32 -0700, Roy Lewallen
wrote:

I disagree with your conclusion that currents flow circumferentially. It
does not say so in the paper, and I don't believe it can be inferred
from what is said in the paper.

Hi Roy,

To insist that the paper be complete where the reader has the
competence to understand what is implied; well, that goes beyond
standard practice. Further, the implication is hardly momentous when
the force of the writing is in demonstrating (not finding) a solution
to loss. Their style is clearly descriptive, not pedantic.

One very simple observation drawn directly from the text
at page 760:
"When the earth is of good conductivity,
the current leaves the wires and enters the earth closer to
the antenna than it does when the earth is a poor conductor."

How is it THIS current is traveling radially, the same direction as
the wires, both leaving the wire (an orthogonal aspect) and yet moving
in the same direction. This is a contradiction to the geometry of the
description if we are to abide by your rejection of my
"interpretation."

Their (not my) statement, supported by their other text, hardly makes
sense otherwise. Current only flows along a potential gradient and
the phase shift between (by their own distinctions) wire and ground
constitutes such a gradient.

It is a vastly more speculative "interpretation" to suggest the
current leaves the wire to travel in the same direction and the
authors definitely don't say that, do they? Common sense would
dictate a fairer interpretation that conforms to phases and the
distinctions (separation of currents) they drew from them.

73's
Richard Clark, KB7QHC

So, does the current go clockwise or counterclockwise? How much goes
that way compared to the radial component? Where can I find a
quantitative or explicit statement of your interpretation?

Roy Lewallen, W7EL

Richard Clark wrote:
On Mon, 09 Apr 2007 12:12:32 -0700, Roy Lewallen
wrote:

I disagree with your conclusion that currents flow circumferentially. It
does not say so in the paper, and I don't believe it can be inferred
from what is said in the paper.

Hi Roy,

To insist that the paper be complete where the reader has the
competence to understand what is implied; well, that goes beyond
standard practice. Further, the implication is hardly momentous when
the force of the writing is in demonstrating (not finding) a solution
to loss. Their style is clearly descriptive, not pedantic.

One very simple observation drawn directly from the text
at page 760:
"When the earth is of good conductivity,
the current leaves the wires and enters the earth closer to
the antenna than it does when the earth is a poor conductor."

How is it THIS current is traveling radially, the same direction as
the wires, both leaving the wire (an orthogonal aspect) and yet moving
in the same direction. This is a contradiction to the geometry of the
description if we are to abide by your rejection of my
"interpretation."

Their (not my) statement, supported by their other text, hardly makes
sense otherwise. Current only flows along a potential gradient and
the phase shift between (by their own distinctions) wire and ground
constitutes such a gradient.

It is a vastly more speculative "interpretation" to suggest the
current leaves the wire to travel in the same direction and the
authors definitely don't say that, do they? Common sense would
dictate a fairer interpretation that conforms to phases and the
distinctions (separation of currents) they drew from them.

73's
Richard Clark, KB7QHC

On Mon, 09 Apr 2007 13:27:21 -0700, Roy Lewallen
wrote:

So, does the current go clockwise or counterclockwise? How much goes
that way compared to the radial component? Where can I find a
quantitative or explicit statement of your interpretation?

Hi Roy,

Probably in a library. Field work seems to resolve issues too. It
may even prove your speculation in contradiction to mine. Outside of
these authors, we both seem to be shy of "authoritative references" to
parse that Byzantine statement of theirs.

I can only further speculate that BL&H were remiss in specifically
quantifying loss (you aren't asking me for numbers you are already
aware of, are you?), while offering numerous formulaic relationships
of loss against many factors. If we look at their data and observe
that adding radials lowers loss, but not by any precise relationship,
are we left without quantifiable proof, or the obvious implication of
strong correlation? Was there deceit in their arriving at some
conclusions through inference? As Reggie would note, they didn't
actually measure earth at all! Such a retort was met with indignity
in the past, is it now their impeachment?

However, as to counter/anti/clockwise, What impels current to follow
any such presumption? There are two sides to every wire laying in a
plane and phase mappings for earth currents that are symmetrical about
them. To anticipate your challenging me on that statement (clearly
BL&H never, explicitly say this), I can only offer a modest sense of
observing the bleeding obvious. Myself, I don't find BL&H so obscure
to impose this remarkable characteristic that current leaves the wire
on only one side.

Brown, Lewis and Epstein were REPORTING, not inventing, nor offering
pedant readings of scripture. Scribes, such as we are, are free to
interpret within the bounds of their own data, assumptions, and
conclusions. I've offered mine that conforms to many of their points.
If you have your own, you must survive by the same strictures. Given
the specific contention, I am especially intrigued in how you would
answer why the current departed the wire, and where it goes in light
of a potential map created by the phase shifts.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
On Mon, 09 Apr 2007 13:27:21 -0700, Roy Lewallen
wrote:

So, does the current go clockwise or counterclockwise? How much goes
that way compared to the radial component? Where can I find a
quantitative or explicit statement of your interpretation?

Hi Roy,

Probably in a library. Field work seems to resolve issues too. It
may even prove your speculation in contradiction to mine. Outside of
these authors, we both seem to be shy of "authoritative references" to
parse that Byzantine statement of theirs.

I can only further speculate that BL&H were remiss in specifically
quantifying loss (you aren't asking me for numbers you are already
aware of, are you?), while offering numerous formulaic relationships
of loss against many factors. If we look at their data and observe
that adding radials lowers loss, but not by any precise relationship,
are we left without quantifiable proof, or the obvious implication of
strong correlation? Was there deceit in their arriving at some
conclusions through inference? As Reggie would note, they didn't
actually measure earth at all! Such a retort was met with indignity
in the past, is it now their impeachment?

However, as to counter/anti/clockwise, What impels current to follow
any such presumption? There are two sides to every wire laying in a
plane and phase mappings for earth currents that are symmetrical about
them. To anticipate your challenging me on that statement (clearly
BL&H never, explicitly say this), I can only offer a modest sense of
observing the bleeding obvious. Myself, I don't find BL&H so obscure
to impose this remarkable characteristic that current leaves the wire
on only one side.

Brown, Lewis and Epstein were REPORTING, not inventing, nor offering
pedant readings of scripture. Scribes, such as we are, are free to
interpret within the bounds of their own data, assumptions, and
conclusions. I've offered mine that conforms to many of their points.
If you have your own, you must survive by the same strictures. Given
the specific contention, I am especially intrigued in how you would
answer why the current departed the wire, and where it goes in light
of a potential map created by the phase shifts.

73's
Richard Clark, KB7QHC

Ok, I understand that. Your answers to the two questions I asked are
that you don't know and you don't know. In the absence of any evidence,
I'll continue to disbelieve there's a circumferential component of the
current.

Roy Lewallen, W7EL

On Mon, 09 Apr 2007 16:42:10 -0700, Roy Lewallen wrote:


Brown, Lewis and Epstein were REPORTING, not inventing, nor offering
pedant readings of scripture. Scribes, such as we are, are free to
interpret within the bounds of their own data, assumptions, and
conclusions. I've offered mine that conforms to many of their points.
If you have your own, you must survive by the same strictures. Given
the specific contention, I am especially intrigued in how you would
answer why the current departed the wire, and where it goes in light
of a potential map created by the phase shifts.

73's
Richard Clark, KB7QHC

Ok, I understand that. Your answers to the two questions I asked are
that you don't know and you don't know. In the absence of any evidence,
I'll continue to disbelieve there's a circumferential component of the
current.

Roy Lewallen, W7EL

Roy, it seems to me everyone has missed an important point concerning a circumferential component of the
current.

We know that the current flowing on the radial wires is radial in direction. What seems to be missed is the
current that returns to earth between the wire radials. That current is going to flow in the direction of the
lowest resistance. As such it's not going to flow radially alongside the currents flowing on the wire, because
the radial resistance of earth between the radial wires is much greater than the resistance of the wires.
Consequently, currents reaching earth between the wires will find a lower resistance by traveling toward the
nearest radial wire instead of continuing in a perfectly radial direction. This new direction of current flow
will not necessarily perfectly circumferential, but will certainly be somewhere between radial and
circumferential.

Walt, W2DU

On Thu, 12 Apr 2007 18:55:30 GMT, Walter Maxwell
wrote:

This new direction of current flow
will not necessarily perfectly circumferential, but will certainly be somewhere between radial and
circumferential.

Hi Walt,

So as BL&H report without too much pain:
at page 760:
"When the earth is of good conductivity,
the current leaves the wires and enters the earth closer to
the antenna than it does when the earth is a poor conductor."

Now, as to your comment
That current is going to flow in the direction of the
lowest resistance.

It is awfully damned hard to beat the least resistance path of copper
over earth. And yet BL&H offer us this observation I requote above.

What will trump a higher resistance path is greater potential
difference and proximity. Note that BL&H are quite specific about
proximity to the antenna, and hence it follows that the separation
between radials is closer there, than further out from the antenna.
Certainly I can find no where to quote this observation of growing
closeness from BL&H for Roy's consideration, but I trust my common
sense of geometry here too, and I will proceed.

BL&H report (without going into the how, or how much):
"From (8) [that formula] we see that the earth
current proper leads the current in the wires
by 90 electrical degrees."
such that at "that" radial distance, there must exist the greatest
circumferential potential difference between the wire and the earth
currents which is clearly mandated by phase. If a potential gradient
along the circumference is greater than that along the radial, and the
distance along the circumference is smaller than the distance along
the radial; then it stands to reason why BL&H even offer to comment
"current leaves the wire."

Current through earth is largely lost to heat although I do have a
fractal antenna that uses earth current to optimize its low angle
launch characteristics.

Ultimately this reduces to the rather pedestrian observation that more
radials closer in serve efficiency - observed and reported by BL&H.

73's
Richard Clark, KB7QHC

Walter Maxwell wrote:

Roy, it seems to me everyone has missed an important point concerning a circumferential component of the
current.

We know that the current flowing on the radial wires is radial in direction. What seems to be missed is the
current that returns to earth between the wire radials. That current is going to flow in the direction of the
lowest resistance. As such it's not going to flow radially alongside the currents flowing on the wire, because
the radial resistance of earth between the radial wires is much greater than the resistance of the wires.
Consequently, currents reaching earth between the wires will find a lower resistance by traveling toward the
nearest radial wire instead of continuing in a perfectly radial direction. This new direction of current flow
will not necessarily perfectly circumferential, but will certainly be somewhere between radial and
circumferential.

Walt,

I hadn't missed that phenomenon, but didn't mention it because it
doesn't produce a circumferential current. If you look at the current
flowing from the earth to each radial wire, you'll see that the sum of
these currents will be purely radial, assuming that the system is
symmetrical, i.e., radials are equally spaced and equal length, the
ground is homogeneous, and the radiator is vertical. Consider a bit of
current returning between two radials, which is a little closer to the
radial on the right. It'll detour to the right, giving it a rightward
component as well as an inward radial component. But for every such bit
of current, there's another one the same distance from the radial to the
left which will have leftward and inward radial components. The radial
components are in the same direction (inward) so will add but the
circumferential ones (leftward and rightward) cancel, leaving a net
radial current flow. You can say that the returning currents bend to the
right or left as they propagate toward the antenna base, but not that
there's a systematic circumferential current flow -- no current crosses
from radial to radial in a clockwise or counterclockwise circular
pattern like Richard implied.

I recall reading a paper which showed that connecting radials with
circumferential wires actually degrades a ground system's effectiveness,
but I wasn't able to lay my hand on it when I looked.

Roy Lewallen, W7EL

Roy Lewallen wrote:
So, does the current go clockwise or counterclockwise? How much goes
that way compared to the radial component? Where can I find a
quantitative or explicit statement of your interpretation?

I think, based on the excerpt Richard has provided, it does both.
Imagine a leaky hose with water diffusing into the surroundings. So, if
you were to integrate over the entire width,or over any region which is
symmetric over the wire, the *net* is entirely radial, but if you look
at a small region, directly adjacent to the wire, there will be current
diverging from the wire as you move outward (assuming current flow is
outward... obviously, on the opposite half cycle, it converges toward
the wire, as it moves generally inward)...

I suspect one could also analyze it as a wave propagating away from teh
wire in the lossy surrounding medium, where the medium has a lower
propagation velocity than in the wire. (e.g. imagine a waveguide made
with the walls being soil)

Another sort of "hydraulic" model would be if you represented the
radials as below grade drainage ditches which have a lot more pitch than
the surrounding soil, so the water tends to flow diagonally down the
ditch walls.

The interesting question would be whether this is important at all..

One might go through lots and lots of analysis, worrying about the small
incremental effects of non-radial current, and find that the inherent
variations in soil properties are orders of magnitude larger.

Sounds like a good exercise for a graduate level E&M or calculus class..
you could cast it as a similar exercise in heat flow.. both temperature
and electrostatic fields satisfy Laplace's equation.

On Mon, 09 Apr 2007 17:04:35 -0700, Jim Lux
wrote:

The interesting question would be whether this is important at all..

Hi Jim,

Additional current through earth brings no net positive result and the
question asked where the source of loss resides.

Being unable to quantify temperature is no reason to keep picking up
the wrong end of a soldering iron. "I don't believe it's hot" has
rarely offered salve for burns. ;-)

73's
Richard Clark, KB7QHC