Re: [TowerTalk] Re: radials for shunt fed tower

[Jim Lux <jimlux@earthlink.net>]

At 09:31 AM 12/15/2004, W2RU - Bud Hippisley wrote:
> At 17:57 2004-12-05, w7kxb@comcast.net wrote:
> >Thanks for the Heads Up. Found it 
> at:http://www.ncjweb.com/k3lcmaxgainradials.pdf
>
> In a cursory reading of K3LC's radial article, I found two data points 
> that seem counter-intuitive to me.

As you're probably aware, modeling of ground systems is a pretty dicey 
operation, even using the NEC4 modeling engine. NEC4 has been validated 
pretty extensively and  does model a system quite accurately, provided 
you've described what you're modeling sufficiently accurately.

So, why do you get seemingly weird effects?  A couple things spring to mind 
(although I haven't rigorously looked into it, for reasons described below):

1) Al modeled the vertical as a AWG12 copper wire, which is probably more 
lossy than the usual large diameter aluminum tube or large diameter tower. 
(Anyone got some good modeling parameters for towers?)  The increased loss 
changes the current distribution a bit along the antenna, which changes the 
induced current distribution in the ground system.

2) The ground system losses are a combination of two things: the radial 
current flow to form the "image" of the monopole; and the dissipative loss 
of the E and H fields in the earth surface.  The former is essentially a 
resistive kind of thing, and the copper ground wires reduce the sheet 
resistance (this is what all those other models of ground systems 
(including George Brown's) analyze to death at around 1 MHz).  The latter 
is strongly influenced by the skin depth of the earth and it's 
lossiness.  Looking over some charts derived from George Hagn's work at 
SRI, skin depth varies from a meter or so in "Very Good" soil to 10-15 
meters in Very Poor.  However, skin depth needs to be combined with the 
resistivity to determine loss. So what if skin depth is 1/2, if the 
conductivity is 5 times greater.  There's also whether the conductivity is 
greater because of the water content, which changes the epsilon (which also 
changes the skin depth).

3) The same wire size was used in all ground screens, and a real tradeoff 
shouldn't be with a fixed length of fixed size wire, but on the cost of the 
wire (which pretty much scales with mass).  Are you better off with 1000 
feet of AWG 16 or 250 feet of AWG 10 or 10,000 feet of AWG 26?  The labor 
cost is another aspect.


In the case of the models, one has to be very careful about things like 
skin effect, when the skin depth is a fraction of the wire diameter. In 
air, skin depth at 1MHz in copper is about 0.003 inches. Compare to AWG 16 
wire, which is 0.05 inches in diameter, approximately. The skin depth might 
be different if the conductor is immersed in a medium other than air (I 
assume NEC4 takes this into account, though).  However, the change in skin 
depth means that the resistivity of the ground wires (and their loss) 
changes with frequency: to a first order, as 1/sqrt(frequency), so the same 
ground wire will have twice the loss on 40m as it does on 160m.  Depending 
on the relative ratio of the grounding network resistivity and the soil 
resistivity, this might change the optimizing tradeoff.

Now to the practical aspects... real soil is generally not particularly 
homogeneous or consistent.  You could easily have variations of an order of 
magnitude over distances of a few feet (in my own case, it depends on how 
close the rocks are to the surface and how recently and where the watering 
happened).  These variations can account for performance variations on the 
order of a dB or so, which is the same magnitude as the variations for the 
different ground radial lengths, etc.




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