Standing-Wave Current vs Traveling-Wave Current
 

On 7 Jan, 10:15, Michael Coslo wrote:
art wrote:

Probably so. But pseudo experts such as Roy and Tom and the three
Richards can't put o neck hold on the advances of science for ever,
for people like MK to follow in lockstep in the absence of knoweledge.

* * * * Crikeys, Art!

How on earth are your nemeses strangling science? Does anyone in here
take these bar room brawls seriously?

* * * * I mean just what would this strangulation achieve? Does IEEE keep an
archive of rraa? the National Science Foundation?

* * * * These arguments, For all their sound and fury, signify nothing.

I rather thought that they boys were all just feeling their oats. At any
rate, the great unwashed such as myself find it all amusing.

* * * * - 73 de Mike N3LI -

In the scientific world it is a closed community and only within that
community can members create change. So you often hear that some very
clever people did not have their ideas examined until after they were
dead which can be a hundred years.Hams are a similar closed community
with respect to what creates radiation since they only accept books
and will not or cannot debate any alternatives.When in college you are
encouraged to debate which is way to retreat to the beginings and
build up a case in opposition to the opponent.This cannot happen in
ham radio because debates cannot happen except by those that deem
themselves as experts whose mission is to protect the status quo Thus
to become an expert one must follow the written word and deride those
that deign to question the status quo.When was the last to you read of
an open debate that was thouroughly discussed to a acceptable
conclusion? Well you haven't heard one because when two heads debate
one will always use personal attack as a means of retaliation.And I
mean always.
There is one discussion on this newsgroup that has gone on for several
years
and thousands of postings about travelling waves which I for one
consider them to be ficticious
in a resonant system. Do you ever believe one side or the other will
demonstrate the concepts
so all are on a common stage.? Hell no! Personal attacks were started
years ago in an attempt to cut down the debate and all must resign
themselves that the instant experts will defend the status quo for
ever. Will we ever see a painter sell his paintings for millions while
he is still alive?
Such is life! Such is death!
Art

Standing-Wave Current vs Traveling-Wave Current
 

art wrote:
On 7 Jan, 10:15, Michael Coslo wrote:
art wrote:

Probably so. But pseudo experts such as Roy and Tom and the three
Richards can't put o neck hold on the advances of science for ever,
for people like MK to follow in lockstep in the absence of knoweledge.
Crikeys, Art!

How on earth are your nemeses strangling science? Does anyone in here
take these bar room brawls seriously?

I mean just what would this strangulation achieve? Does IEEE keep an
archive of rraa? the National Science Foundation?

These arguments, For all their sound and fury, signify nothing.

I rather thought that they boys were all just feeling their oats. At any
rate, the great unwashed such as myself find it all amusing.

- 73 de Mike N3LI -

In the scientific world it is a closed community and only within that
community can members create change.

This sounds like an indictment of the whole peer reviewed process. It's
kind of like saying that People who have driver's licenses are a closed
group.


So you often hear that some very
clever people did not have their ideas examined until after they were
dead which can be a hundred years.

Any cites here?

Hams are a similar closed community
with respect to what creates radiation since they only accept books
and will not or cannot debate any alternatives.

Here we really disagree! There is an amazing amount of antenna hokum
scattered about among amateurs.




When in college you are
encouraged to debate which is way to retreat to the beginings and
build up a case in opposition to the opponent.This cannot happen in
ham radio because debates cannot happen except by those that deem
themselves as experts whose mission is to protect the status quo Thus
to become an expert one must follow the written word and deride those
that deign to question the status quo.When was the last to you read of
an open debate that was thouroughly discussed to a acceptable
conclusion? Well you haven't heard one because when two heads debate
one will always use personal attack as a means of retaliation.And I
mean always.

Art, here is where you make a huge mistake. You are bringing personal
"feelings" into the equation. Who really gives a whoop doop dingle about
feelings?

With your Mechanical engineering background, I assume that you must
have sat in on design and other meetings. Many of the ones I have sat in
have become plenty heated.

So What? We leave the meeting and go get the job done. Then we enjoy a
beer with the people we were arguing with after work.



There is one discussion on this newsgroup that has gone on for several
years
and thousands of postings about travelling waves which I for one
consider them to be ficticious
in a resonant system. Do you ever believe one side or the other will
demonstrate the concepts so all are on a common stage.? Hell no!

Respectfully Art, there are people who will not ever hold with ideas
that are considered mainstream. If *their* alternative ideas were
accepted as fact, then there is an excellent chance that they will
abandon them and move on to something else. This is especially true if
feeling somehow come into their science. I see this fairly often.
Politics often comes to mind, in which one group is excellent at
castigation, pointing out example after example of others wrongdoing but
when in power, they seem to not be able to effectively function.

IOW, is the rebel right because they found out something new, and can
promote the idea, or are they right because they are a rebel?

Personal attacks were started
years ago in an attempt to cut down the debate and all must resign
themselves that the instant experts will defend the status quo for
ever.

I see personal attacks on both sides of the long drawn out arguments
here. All are guilty.


Will we ever see a painter sell his paintings for millions while
he is still alive?


I think there are more painters making millions than there are
scientifically respected postings on usenet.


- 73 de Mike N3LI -

Standing-Wave Current vs Traveling-Wave Current
 

On 8 Jan, 06:39, Michael Coslo wrote:
art wrote:
On 7 Jan, 10:15, Michael Coslo wrote:
art wrote:

Probably so. But pseudo experts such as Roy and Tom and the three
Richards can't put o neck hold on the advances of science for ever,
for people like MK to follow in lockstep in the absence of knoweledge.
* * * * Crikeys, Art!

How on earth are your nemeses strangling science? Does anyone in here
take these bar room brawls seriously?

* * * * I mean just what would this strangulation achieve? Does IEEE keep an
archive of rraa? the National Science Foundation?

* * * * These arguments, For all their sound and fury, signify nothing.

I rather thought that they boys were all just feeling their oats. At any
rate, the great unwashed such as myself find it all amusing.

* * * * - 73 de Mike N3LI -

In the scientific world it is a closed community and only within that
community can members create change.

* * * * This sounds like an indictment of the whole peer reviewed process. It's
kind of like saying that People who have driver's licenses are a closed
group.

So you often hear that some very
clever people did not have their ideas examined until after they were
dead which can be a hundred years.

* * * * Any cites here?

Hams are a similar closed community
with respect to what creates radiation since they only accept books
and will not or cannot debate any alternatives.

* * * * Here we really disagree! There is an amazing amount of antenna hokum
scattered about among amateurs.

When in college you are
encouraged to debate which is way to retreat to the beginings and
build up a case in opposition to the opponent.This cannot happen in
ham radio because debates cannot happen except by those that deem
themselves as experts whose mission is to protect the status quo Thus
to become an expert one must follow the written word and deride those
that deign to question the status quo.When was the last to you read of
an open debate that was thouroughly discussed to a acceptable
conclusion? Well you haven't heard one because when two heads debate
one will always use personal attack as a means of retaliation.And I
mean always.

* * * * Art, here is where you make a huge mistake. You are bringing personal
"feelings" into the equation. Who really gives a whoop doop dingle about
feelings?

* * * * With your Mechanical engineering background, I assume that you must
have sat in on design and other meetings. Many of the ones I have sat in
have become plenty heated.

* * * * So What? We leave the meeting and go get the job done. Then we enjoy a
beer with the people we were arguing with after work.

There is one discussion on this newsgroup that has gone on for several
years
and thousands of postings about travelling waves which I for one
consider them to be ficticious
in a resonant system. Do you ever believe one side or the other will
demonstrate the concepts *so all are on a common stage.? Hell no!

* * * * Respectfully Art, there are people who will not ever hold with ideas
that are considered mainstream. If *their* alternative ideas were
accepted as fact, then there is an excellent chance that they will
abandon them and move on to something else. This is especially true if
feeling somehow come into their science. I see this fairly often.
Politics often comes to mind, in which one group is excellent at
castigation, pointing out example after example of others wrongdoing but
when in power, they seem to not be able to effectively function.

IOW, is the rebel right because they found out something new, and can
promote the idea, or are they right because they are a rebel?

Personal attacks were started
years ago in an attempt to cut down the debate and all must resign
themselves that the instant experts will defend the status quo for
ever.

* * * * I see personal attacks on both sides of the long drawn out arguments
here. All are guilty.

* Will we ever see a painter sell his paintings for millions while

he is still alive?

* * * * I think there are more painters making millions than there are
scientifically respected postings on usenet.

* * * * - 73 de Mike N3LI -- Hide quoted text -

- Show quoted text -

Things changed when the influx of CBers came into the hobby. As
president of the local club it was my job to welcome them despite the
animosity that was floating around. After 5 years I quit
and watched as ham radio went down hill so I also quit getting on the
air.As Age crept up on me
I could not play around with mixers anymore so I chose antennas which
my eyes could handle.
I then got insulted when I shared what I was doing on this group as
were my patents. I got so many insults that I even dropped one I had
just applied for and left this newsgroup. I still carried on with my
work and some years ago again shared it with the group. Insults
immediately started coming thru without examining that I was
sharing.But this time it is different. I am not going away even tho
hams are not interested in new ideas and in fact push them away. True
my writing gets worse as I age which is a sorry state of affairs butI
am not willing to fade away. I WILL HANG ON AND STAY.I worked hard
during the night scouring the internet to find a link that would
explain part of the things that I talk about and which all reject and
apply insults.
I finally found a suitable site that also came with diagrams to make
it easier to understand.
It will be on another thread so please read it. If it is of interest
then you will see I am not blabbering.Never the less I am willing to
share the rest of my work with true radio amateurs that have the
manners that are required for a suitable discussion or debate.
Regards
Art Unwin KB9MZ....XG ( uk)
Art

Standing-Wave Current vs Traveling-Wave Current
 

"Gene Fuller" wrote in message
...
art wrote:

WHY? bECAUSE THE MAGNETIC FIELD LINES FROM A DIAMAGNETIC MATERIAL
SUCGH AS ALUMINUM OR COPPER IS AT RIGHT ANGLES TO THE AXIS OF CURRENT
FLOW WHICH IS NOT THE SAME AS WITH A FERRITE MAGNETIC MATERIAL



Does it matter that aluminum and copper are paramagnetic rather than
diamagnetic? Perhaps you should consider a bismuth antenna. That is the
poster child for diamagnetic metals.

73,
Gene
W4SZ

oh, don't go getting all technical on him, he's having so much fun thinking
he's pulling everyone's leg with his bafflegab... I get a good laugh out of
it every day at least.

Standing-Wave Current vs Traveling-Wave Current
 

Dave wrote:

ah, so once you have a standing wave on a line then no energy can cross the
voltage or current nodes?? thats interesting. so at the place where
current is 'always' 0 the voltage is a max right? so what happens to the
V^2/Z power at that point? is that not flowing past that point?
conversely, at the point where voltage is always zero, what happens to the
large I^2*R power at that point??? where does that go? . . .

You can see graphically exactly where the energy and power are at every
point along the line at every instant, with the program I made for the
purpose. It even separately shows the energy stored in the E and H
fields. See the recent TLVis1 thread.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:

I'd suggest that this is only if the concept of the
waves in question does not include energy. In the
limiting case of the two waves being identical no
energy crosses the nodes. In other cases, only a
portion of the energy crosses the nodes.

If the concept of the waves includes energy, some
explanation is required to account for the wave
crossing the node, but its energy does not.

Take a look at demo 4 with the TLVis1 program (described in the TLVis1
thread). Let it run to steady state, then single step. In the upper
trace, look at one of the points where the power is always zero, i.e.,
where it crosses the center line. But as you step, you can see that the
energy at that point increases and decreases with time. In fact, at some
times it's zero and at other times it's one of the points of maximum
energy density along the line. So how can this be? The power is always
zero at that point, yet the energy is increasing and decreasing with time.

The answer is that equal amounts of energy are moving to the right and
left of that point at all times; energy is flowing into and out of that
point equally from both sides. So although there are points where the
power is always zero, those aren't the points where the energy isn't moving.

There are, in fact, points along the line where the energy doesn't
change with time, but they coincide with the points where the power is
maximum. This simply means that, at those points, however much energy
flows into a point flows out at any given time, leaving the total energy
at those points constant. (Mathematically, this amounts to the existence
of a constant when you integrate power to get energy.)

So at all points along the open circuited line and at all times, energy
is either moving, increasing, or decreasing. There aren't any static
spots at all.

I find it very helpful to look at this visually -- that's why I wrote
the program. It also shows how misleading it is to mix power and energy.

Some readers like to superpose energy just as
they do voltage, but in general this is not a
valid operation so I am uncomfortable using
it as the explanation.

I agree, you can't assign energy or power to the traveling waves
separately and superpose them as you do voltage and current. TLVis1
calculates power and energy from the total voltage and current.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:

...
You can see graphically exactly where the energy and power are at every
point along the line at every instant, with the program I made for the
purpose. It even separately shows the energy stored in the E and H
fields. See the recent TLVis1 thread.

Roy Lewallen, W7EL

My sisters' son has drawn some nice pictures on his bedroom wall with
crayons--I can actually appreciate them--especially for his age--he does
show some "artistic" leanings, in my humble opinion ... of course, I
don't have to clean the crayon off the wall.

I am sure your endeavors, at least, should enjoy such
observations/considerations ... :-D

Regards,
JS

Standing-Wave Current vs Traveling-Wave Current
 

Art wrote:
"This dust is what Gauss refers to as static particles in a
gravitational field in equilibrium."

What evidence do you have that gravity is related to static particles
other than attracting their mass or that gravity affects radio waves
significantly?

Our universe may not have uniform acceleration, so are you sure about
equilibrium?

Maxwell did not need a medium for radio propagation. He was able to
calculate the velocity of radio waves and believed that because it
equaled the known speed of light his equations were correct.

Best regards, Richard Harrison, KB5WZI

Standing-Wave Current vs Traveling-Wave Current
 

Thanks for offering the two capacitor/one capacitor view of the middle
of the line. It took a bit of time to decide whether the commingling
of the charge in the single capacitor at the middle of the line would
solve my dilemma.

So I considered this one capacitor in the exact center of a perfect
transmission line. It is the perfect capacitor, absolutely
symmetrical. So as the exactly equal currents flow into it on
the exactly symmetrical leads, the charge is perfectly balanced
so that the charge coming from each side exactly occupies its
side of the conductor. As the two flows of charge flow over
the perfectly symmetrical plates, they meet in the exact
center, and flow no more. I conclude that a surface can
be found exactly in the center of this capacitor across
which no charge flows. Thus (un)happily returning me exactly
to where I was before; there is a line across which no
charge, and hence no energy, flows.

More comments below.

On Jan 2, 7:38 pm, Roy Lewallen wrote:
I'm top posting this so readers won't have to scroll down to see it, but
so I can include the original posting completely as a reference.

Keith, you've presented a very good and well thought out argument. But
I'm not willing to embrace it without a lot of further critical thought.
Some of the things I find disturbing a

1. There are no mathematics to quantitatively describe the phenomenon.
2. I don't understand the mechanism which causes waves to bounce.

I take this to imply that you are not happy with the simple "like
charge
repels"?

3. No test has been proposed which gives measurable results that will
be different if this phenomenon exists than if it doesn't. (I
acknowledge your proposed test but don't believe it fits in this category.)
4. I'm skeptical that this mechanism wouldn't cause visible
distortion when dissimilar waves collide. But without any describing
mathematics or physical basis for the phenomenon, there's no way to
predict what should or shouldn't occur.
5. Although the argument about no energy crossing the zero-current
node is compelling, I don't feel that an adequate argument has been
given to justify the wave "bouncing" theory over all other possible
explanations.

I would really appreciate seeing some other possible explanations.

One other one which I have seen and am not confortable with is the
explanation that energy in the waves pass through the point in
each direction and sum to zero. But this is indistinguishable from
superposing power which most agree is inappropriate. As well, this
explanation means that P(t) is not equal to V(t) times I(t),
something that I am quite reluctant to agree with.

The other explanation seen is that the voltage waves or the
current waves travel down the line superpose, yielding a total
voltage and current function at each point on the line which
can be used to compute the power. With this explanation, P(t)
is definitely equal to V(t) time I(t), which I do appreciate.
The weakness of this explanation is that it seems to deny
that the wave moves energy. And yet before the pulses collide
it is easy to observe the energy moving in the line, and if
a pulse was not coming in the other direction, there would
be no dispute that the energy travelled to the end of the
line and was absorbed in the load. Yet when the pulses
collide, no energy crosses the middle of the line. Yet
energy can be observed travelling in the line before
and after the pulses collide.

So...

I can give up on pulses (or waves) moving energy. I am not
happy doing that.
I can give up on P(t) = V(t) * I(t). I am not happy doing
that either.

So the (poorly developped) "charge bouncing" explanation
seems like a way out, but I certainly would appreciate
other explanations for consideration.

None of these make an argument with your logical development, although I
think I might be able to do that too. But I'm very reluctant to accept a
view of wave interaction that's apparently contrary to established and
completely successful theory and one, if true, might have profound
effects on our understanding of how things work. So frankly I'm looking
hard for a flaw in your argument. And I may have found one.

So I am not convinced that it any way goes against established theory.
I have not seen established theory attempt an explanation of how the
waves can both transport energy as well as not do so when waves of
equal energy collide.

A large part of the argument seems to revolve around a single point in a
perfect transmission line, where the current is exactly zero. This is an
infinitesimal point on a perfect line, so some anomalous things might be
expected to happen there.

Let's consider a transmission line as a huge number of series inductors
and shunt capacitors, each an ideal lumped device. In the ideal case, of
course, there would be an infinite number of each, and each would have
an infinitesimal value. However, the LC product and ratio must remain
correct even in the limiting case. Each L and C is an ideal device, so
the current into one terminal of an inductor has to equal the current
out of the other. A consequence of this is that either we have a whole
inductor with zero current, or the zero current point occurs between
inductors, at a node to which a capacitor is connected. I think we'll
get the same result using either scenario, but let's consider the second.

If we analyze this situation carefully, we'll find that the inductor on
each side of the zero-current point does have a finite current, equal in
amplitude and flowing in opposite directions. So for half of the cycle,
both are putting positive charge in the capacitor, and for the other
half of the cycle, both are removing charge. The capacitor voltage goes
up and down as a result, as we can also see by looking at the voltage at
this zero-current point. So current from both sides is contributing to
the capacitor charge, and turning off either one would change the line
conditions. Any change in the current from the inductor on one side
would change the capacitor voltage, and hence the current on the other
side. So there is an interchange of information from one side to the
other. Each inductor is conveying energy to the capacitor, which is
storing and returning it.

Ok, so let's break the capacitor into two, each being half the original
value, and constrain each inductor to deliver charge only to "its"
capacitor. The wire between the capacitors carries no current because
the capacitors always have equal voltages, and can be cut with no effect.

When there was one capacitor, it shared energy from both sides. When we
broke it into two, there was no mixing of energy from either side. Why
might one be a better description of reality than the other? It looks to
me like the argument devolves into speculation about how small the
"point" is at which the current drops to zero.

It is very, very small.

It would be instructive to see what happens as, for example, the load
resistance is increased toward infinity or decreased toward zero
arbitrarily closely, but not at the point at which it's actually there.
If the "bouncing" phenomenon is necessary only to explain the limiting
case of infinite SWR on a perfect line but no others, then an argument
can be made that it's not necessary at all. I suspect this is the case.

The same concern that arises for pulses of equal voltage also
occurs for pulses of different voltage. While the mid-point no
longer has zero current, the actual current is only the difference
of the two currents in the pulses, the charge that crosses is only
the difference in the charge between the two pulses, and the
power at the mid-point is exactly the power that is needed
to move the difference in the energy of the two pulses.

So the challenge is not so starkly obvious as it is when the
power at the mid-point is always 0, but P(t) = V(t) * I(t) can
still be computed and it will not be sufficient to allow
the energy in the two pulses to cross the mid-point (unless
one likes superposing power, in which case it will be
numerologically correct).

I agree with your argument about two sources energized in turn, and have
used that argument a number of times myself to refute the notion of
superposing powers. Once two voltage or current waves occupy the same
space, the only reality is the sum. We're free to split them up into
traveling waves or any other combination we might dream up, with the
sole requirement being that the sum of all our creations equals the
correct total. (And the behavior of waves you're describing seemingly go
beyond this.)

I sometimes think that this may actually be a debate about the
conceptual view of waves. If waves consist only of voltage and
current, then all is well, superposition works, the correct
answers are achieved. And if the power is computed after the
voltages and currents are arrived at, all is well.

But if one conceives waves as also including energy, then it
seems that the question 'where does the energy go' is valid
and the common explanations do not seem to hold up well.

The advantage to the non-interacting traveling wave model
is that it so neatly predicts transient phenomena such as TDR and run-up
to steady state. I spent a number of years designing TDR circuitry,
interfacing with customers, and on several occasions developing and
teaching classes on TDR techniques, without ever encountering any
phenomena requiring explanations beyond classical traveling wave theory.
So you can understand my reluctance to embrace it based on a problem
with energy transfer across a single infinitesimal point in an ideal line.

Yes, indeed. Though any (new) explanation would have to remain
consistent with the existing body of knowledge which works so well.

....Keith

Roy Lewallen, W7ELKeith Dysart wrote:
On Dec 30 2007, 6:18 pm, Roy Lewallen wrote:
Keith Dysart wrote:
[snip]

Standing-Wave Current vs Traveling-Wave Current
 

On 10 Jan, 10:48, (Richard Harrison) wrote:
Art wrote:

"This dust is what Gauss refers to as static particles in a
gravitational field in equilibrium."

What evidence do you have that gravity is related to static particles
other than attracting their mass or that gravity affects radio waves
significantly?
I amnot sure how they came into the earths atmosphere but Gauss has
them placed in a field in equilibrium. I do not believe and I have
not said that earths gravity has any affect on propagation.
Remember, the static particles have a very weak anti gravity
force which nullifies the earths gravitational or magnetic forces.
Thus the static particles can take a straight line velocity.






Our universe may not have uniform acceleration, so are you sure about
equilibrium?

Yes I am. That is a basic for a Pointings vector and most certainly
for Gauss.
Both of these analysis are dependent on the gravitational field being
spherical
so the calculations have to be modified slightly because out earth is
lemon shape
but it is close enough for calculations


Maxwell did not need a medium for radio propagation. He was able to
calculate the velocity of radio waves and believed that because it
equaled the known speed of light his equations were correct.

Well his equations are correct as are the laws that he condensed.
Lorenz law however was on the basis of deduction or observance
which turned out to be correct but there were no details for
Maxwell to hang on to which leaves all as a very difficult puzzle
I started the aproach of continuing Gausses work on static which
the books seem to relate as a subset of electro magnetics.
So I added a time varient to a static field which provided
a direct connection to Maxwells laws. Thus at this point I
accept the static particles at rest and inserted a radiator
in the field which ofcourse must be resonant and in equilibrium
so it didn't upset the Gaussian field. When this was done we
have a dynamic field from which we can draw the statement
that a radiator made from a diamagnetic material can be any
\hape, size elevation e.t.c as long as it is in equilibrium.
Thus this observation or deduction states that a helical
antenna is not in equilibrium unles the windings have
balancing contra windings. Thus any wound design such as EH
ntennas or Vincent antenna must have contra windings to be
in equilibrium and thus fully efficient.
Armed with the above I placed a radiator into a computor program
with an optimizer and confirmed the above i.e. it was not planar.
So why was the element tipped from parallel to the earths surface?
If you make a vector analysis of a radiator with it's many vectors
the resultant single vector is not parallel to the axis of the
radiator.
In addition I look at a helical design and not that the pitch angle is
the same
found by Kraus experimentally was the same angle as the resultant
vector of a radiator.
We then examine the radiator with a static particle at rest on it's
surface and then make a electri9cal circuit of what we see. The result
for equilibrium must be a tank circuit where
all enrgy is interchanged between the energy storage tanks( inductance
and capacitance)
Both of these expend there energy as if the terminals were shorted,
and who hasn't shorted a capacitor to generate an explosion.One can
imagine a explosive force sliding or lifting the static particles to
the inductor reciever which because the material is diamagnetic the
lines of force of the magnetic field will levitate or thrust the
particles away from the
radiator. Using Newtons law we can see that the reactionary force of
the ejected particles
will imping on the radiator itself ad make it occilated. Of course the
particles are many and the number of periods in the frequency applied
is like generating a horrendous number of samples of oscillation, much
more than the human ear does and these samplers will then apply
a mirror image of the occillationd to the recieving radiator.
So like a jigsaw puzzle the measure of difficulty in solving the given
problem is determined by the starting point. And tho I manipulated
Gauss to a Maxwell form which was the same masthematical law,as with
all things it is not only the destination that counts but everything
one observes on the way.
The bottom line is that for best efficiency for the unit volume
supplied an array must be in equilibrium. Thus distances between
radiators become smaller and elements which can be helically wound is
also shorter and by virtue of the array not being planar we have a
single feed plus the "stacked"gain.
I have not made an array but I have made many helical designs and the
like.Programs confirm
these as being legitamate. The fact that I modified the static law to
a dynamic law is the only thing that is "different". Every other
action along my travels are extensivly studied in the books tho not
relavent to radiation. I say again, the complexity depends on where
you start
and I did not view static as a subset like the books do.
Art Unwin KB9MZ...XG



Best regards, Richard Harrison, KB5WZI