On 12/28/11 4:54 PM, Jim Brown wrote:
> On 12/28/2011 2:42 PM, Jim Lux wrote:
>> At some point, though, if you have enough wires, the cage will be
>> identical to the tube.
>>
>> I'd say off the cuff that when the spacing between wires is smaller than
>> the distance to the tree (or broomstick) inside the cylinder, you can
>> start to ignore what's in the middle.
>
> Jim  one of the variables in this antenna is the current distribution
> within the live tree, which will depend on the distribution of moisture
> within the tree. The significance of this is the relationship between
> the effective electrical diameter of the tree and this wire cage (that
> is, the spacing between the wires and the "tree" as an electrical
> element). The next question, of course, is what's that distribution and
> what's the effective diameter?
>
That's an interesting question. The paper from the Italians actually
was using electric resistance tomography (and radar) to look at exactly
that: the distribution of water content within the tree.
I think, from an "antenna next to the tree", it doesn't make much
difference: that is, the tree is a tiny fraction of a wavelength in
diameter, so you could take the entire tree as being homogeneous.
So, if a 1 ft diameter tree is about 3kohms/meter length (based on the
conductivity data in the various articles), the worst case for mutual
coupling would be if the tree and the antenna were colocated (i.e. on
top of each other). that is, it's like the tree and the antenna are in
parallel.
Let's further worst case it by assuming the current distribution on the
antenna is uniform (and not decreasing towards the end of the tree) (so
I don't have to go run the integrals in my head or get a piece of paper
out)..
What we effectively have (for 40 meter vertical) is a 10 meter wire with
resistance, say, 1 ohm in parallel with a 10 meter 30kOhm resistor.
This is in series with the radiation resistance of roughly 30 ohms.
For a given voltage at the feedpoint, the current in the tree will be
1/30,000th that in wire. The power dissipated is that squared.. or, in
other words, negligible.
This is a fascinating observation...
IN other places, we've discovered that trees are like soil (similar
conductivity and epsilon), and we know that laying an antenna on the
ground doesn't work all that well. However, that's the difference
between half of the space being occupied by the lossy medium and just a
tree's worth.
To compare.. if I put two 8 foot rods into the soil 10 meters apart, the
resistance would be a LOT less than 30 kohms. (more like 2030 ohms).
ANyway, I think this is right... I could easily have screwed up
somewhere along the way.
What's more interesting is the idea of propagation losses through the
"forest medium".. Consider forest as a nottoolossy dielectric (i.e.
conductivity is, say, .05 mS/m) but because you go through many meters,
even something like 0.01 dB/m will add up.
That model is the one used by Tamir in his papers from 1967 and 1977
It's described in this
http://kom.aau.dk/antprop/pub/phdth/izk2002/vtc99izk.pdf
which I just found, and which is useful because they give some actual
statistics for tree size distribution and spacing in real forest (in
Denmark, as it happens).
They did measurements at 146, 390, 961, and 1900 MHz, which is a bit
high for our HF, but we can probably look at the 146 MHz data as a bound..
They model the forest loss (over the spreading 1/r^2) loss as 1/r^d*
exp(alpha*r), where d and alpha are the relevant parameters. I'll have
to run the numbers in their equation to figure out what it would work
out to for our frequencies.
Their summary seems to say, something around 0.02dB/meter for HF
frequencies. (this is for vpol)
And, there's Longley (as in LongleyRice propagation model) who talks a
bit about forest attenuation in the NBS report OT78144...
http://www.its.bldrdoc.gov/pub/ot/ot78144/ot78144.pdf
He mentions that loss with Vpol is 15dB more than Hpol for VHF at 1
mile. (so putting up that vertical in the forest may not be as good an
idea as stringing up even a lame dipole... 15dB is huge) Longley cites
a 1969 paper by Vincent (which I don't have, but I'll have to get) with
data from 7100 MHz (finally, our frequencies of interest) His numbers
were epsilon of 15 (at 7MHz) and conductivity of 3 mS/m.
Everyone seems to say that scattering effects and diffraction are
important, and propagation just above the top of the forest is
important, more than propagation through the forest, especially for VHF
and up.
What this means for HF? I don't know.. Say you had a Hpol yagi that was
50 feet off the ground in the middle of a 100 ft tall forest.
If that antenna from a long distance away (and without the forest) looks
sort of like a wide beam flashlight with a reflection off the surface
helping or hurting, depending on the phase.. then the same thing in the
forest might look like the same flashlight, except in a tub of slightly
muddy water.
You could do a fascinating science fair project or thesis experiment
with a scale model using something like a 10GHz gunnplexer.
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