Reply inline....
On 11/3/2017 2:21 PM, jimlux wrote:
the speed is slower than you think.. one way is to think of it as a
wire immersed in a dielectric, for which the speed will be
sqrt(epsilon).. if you use the ham favorite of 5/13 soil, sqrt(13) is
3.6 so the propagation speed will be 27% of speed of light, or about
3.6 ns/ft
Another way is to consider it as a transmission line with a inductance
of about 1 microhenry/m, and a capacitance to ground of 10 pF/m (1cm
wire 10 cm above the soil) (not a whole lot different than RG-213,
which is, I think 13pF/meter)
My point was that stating 50 foot as the limit of an effective radial
series seems somewhat arbitrary and frankly like a significant
underestimate. I've seen lightning strikes vaporize more than 50 feet
of tree root underground exploding it into a trench.... I suspect that
the tree root has a higher resistance and inductance versus pure copper
conductor of sufficient mass and proper shape.
And the 2x rod spacing is a guide... rod spacing depends on the soil
conditions... And nothing says you can't space them closer... IN
FACT, there are conditions under where it is likely advisable to do
so...
I don't think the rod spacing depends on soil properties *if* the soil
is uniform resistivity (on a scale comparable to the rod size..
whether it's sand, 3" rocks, or 12" rocks doesn't matter). It's a
geometry thing and independent of the soil resistivity.
Table 13 in IEEE 141 gives the formulas, and rho (soil resistivity) is
a single term.
I agree with you that geometry matters re: efficient use of the
available soil volume. If you plot 3 or 6 radials out from a tower
base, and plot the rod length cylinders (circles in plan view), it
becomes readily apparent that you pretty quickly see "unused" slices of
soil in the pattern unless you change the geometry or create secondary
radials at a certain distance from the center.
But I can't quite understand how you can say that soil resistivity
doesn't impact the effective soil volume (and hence the radius of the
cylinders). It would seem to me that the effective volume of soil used
efficiently would increase as resistivity decreased. In fact, I seem to
remember some math I read somewhere that plotted it in rings where the
great majority of the "work" was accomplished in well under half the rod
length radius, and only about 10% of the work was accomplished in the
last 25% of the radius, which accounts for much more than 1/4 of the
volume..... I haven't plotted the pattern yet, but using radii < rod
length with overlapping outer 1/4 to 1/2 areas intuitively seems to be
more efficient, especially when dealing with any kind of space constraint.
Now, if you had a big insulating wall, then driving a rod on each side
might be a good idea.
Not exactly the same deal, but my 60 foot tower will be located 4 feet
from the rear edge of the foundation of my house. The ground ring
around the house and the ground ring around the foundation will be
interconnected. 2 of the radials on 60 degree pattern would pass under
the house.... The station actually becomes that "insulating wall". I'm
actually going to continue those radials from the house loop on the
other side of the house.... Essentially producing a 150 foot disc where
the station subtracts a 30x40 foot rectangle near the root, and a 50 x
150 foot rectangle is superimposed over the disc and trims away the
"excess". Additional rods are added and additional radials begun when
rods in adjacent rings exceed nominal 1.5 rod spacing. Each ring of
rods is physically connected by an actual copper "ring". My
calculations show the copper ring wire contributes almost as much as
rods of the same length.
Albeit, I am still considering alternative geometric plans.... running
numbers and cost/labor/time estimates...
73,
Clay, KY5G
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