Fwd: Re: [TowerTalk] Wire for Radials

[Jim Lux]

>Date: Wed, 12 May 2004 18:31:47 -0700
>To: "Jerry Keller" <k3bz at arrl.net>
>From: Jim Lux <jimlux at earthlink.net>
>Subject: Re: [TowerTalk] Wire for Radials
>
>At 07:31 PM 5/12/2004 -0400, you wrote:
>>Well, ON the ground, actually. I picked up a 33-foot aluminum mast and was
>>thinking to put it up for 40M. Also, I'm putting a 160M inverted ell. Both
>>will need a radial system. I was thinking of taking a turn around a common
>>nail every 30 feet or so, and pressing the nail into the turf to keep the
>>wires down and tight.... then letting the lawn grow over them in time. But I
>>was concerned about the wire size (it seemed small) and that it's bare
>>copper. I occasionally fire up the kilowatt and wasn't sure bare copper was
>>a good idea, as I've heard that there might be high voltages at the ends of
>>the radials.
>>
>>The next question I have is: should I tie the two radial systems together
>>wherever they cross?  And should I tie the radials to the tower ground
>>system wherever they cross it?
>
>
>A follow up..
>You're basically trying to increase the conductivity of the earth with 
>this sort of thing.  It's not a resonant system, so things like high 
>voltages, ground loops, etc., aren't really relevant. There's so much 
>coupling between radials or ground grid and the earth that the earth will 
>dominate.  One could probably do a criss/cross pattern and it would work 
>almost as well, although, in theory, if you had enough wires, and they are 
>arranged in the direction of the current flow, it would help.
>
>However, consider this... Let's say we've got a cube of dirt in a big test 
>cell and we want to put wires into it to reduce the (RF) resistance.
>
>Say you have soil thats 0.005 Siemens/meter conductivity.  That means that 
>if you took a 1x1x1 meter cube of the soil and hooked up a big metal plate 
>on each end, and measured the DC resistance, it would be 200 ohms.  If the 
>epsilon were 13 (as widely used for modeling), the capacitance in your two 
>plate apparatus with the dirt in the middle would be about 115 pF.  You're 
>working at 7MHz, so the impedance of that cubic meter of dirt is about 197 
>ohms (it just came out that way...) (If you're looking in a table of 
>dielectric properties, this would mean that the dissipation factor (tan d) 
>is about 1, which it is: http://home.earthlink.net/~w6rmk/soildiel.htm )
>
>Now stick some wires in the dirt to "help" the process along AWG 24 is 
>about 0.1 ohm/ft and you've got 3 feet or so of it, so it's a LOT more 
>conductive (at least as far as DC goes).  To a first order, you've got a 
>0.3 ohm resistor in parallel with a 200 ohm resistor and a 200 ohm 
>capacitor. However, that wire also has some inductance.  A good working 
>number for thin wires is 1 uH/meter, so you've got a 1 uH inductor.  That 
>1uH has an impedance of about 44 ohms at 7MHz, so it's not quite so good 
>as you originally thought, but still, if you have 1 wire per square meter 
>of cross sectional area, you've dropped the ground impedance from about 
>280 ohms to about 15-20% of that.
>
>I've ignored a lot of aspects in this quick analysis (like the fact that 
>the current flows sideways as well as along, and it flows into and out of 
>the wire from the soil (because the soil is a lossy capacitor and the wire 
>is a lossy inductor, and they are in parallel).  I've also egregiously 
>simplified the inductance calculation.
>
>Finally, what you're really worried about is overall total RF losses, and 
>the current density is higher near the base, so all things being equal, 
>you'd prefer to have lower resistance there than farther out.
>
>Some other interesting observations...
>
>If the epsilon is much higher, that makes the capacitance larger, which 
>reduces the loss.  if the water content increases, that helps two ways: it 
>increases the conductivity AND it increases epsilon..
>
>By the way, 13 for epsilon is probably optimistic at 10 MHz kinds of 
>frequencies... The charts I have(taken from Von Hippel, which is sort of 
>the dielectric bible) show that dielectric constant varies with frequency 
>and it tends to be lower at higher frequencies.  Those charts you see 
>everywhere were generally created for the AM broadcast industry, and are 
>at 1 MHz.
>
>
>Jim, W6RMK