Re: Explanation of "Optimum" Buried Radial Length Calculations (still long)


From: Bill Coleman (
Date: Tue Mar 27 2001 - 09:12:19 CST

On 3/26/01 8:41 PM, James R. Duffey at wrote:

>Bill - Thanks for your comments on my optimum radial length calculations. I
>am sorry I didn't take time to detail all my calculations, but the post was
>getting too long. I thought I had put in enough detail for someone to
>reproduce the calculations, at least roughly, but I guess I was wrong.
>Sorry. You made the comment:
>"I don't know how you arrived at the numbers for this chart."

I suppose my comment was directed at the 3.9 foot radials for 20m. I
don't see the utility of radials of less than about .15 wl. They're just
not effective.

>I did include a comment:
>"I did the above calculations based on the 0.02 wavelength separation
>between radial ends."

Seems a bit on the tight side. It only means you'll put down a bit more
wire than you probably need to.

>If I take your suggestion;
>"So, if you run a computation, you'll find that for a .2 wl radial length,
>you have a .4pi wl circumference, which you then divide by .025 or .05 to
>get 25-50 radials."
>If I divide 0.4*pi*wl* by 0.2 wavelengths(wl), then I get 63.8 radials. I
>didn't do this, so I got 62, which I will explain below.

By my calculations, .2 wl * 2pi / 0.02 wl = about 62.8 radials.

>I used 0.02 wavelengths for the radial separation for several reasons. I
>think it is a representative value for below average soils, and I chose this
>as a conservative approach. I respect and value Tom, W8JI's opinions, and he
>is a valuable resource. Although he usually suggests the 0.25 to 0.5
>wavelength radial separation he also has, on occasion suggested that a range
>of 0.01 to 0.05 wavelengths is also applicable, with the lower numbers being
>more applicable to poorer soils.

Much of this information is detailed in the ARRL handbook. You can
actually look at the curves and see how much improvement you get with
each set of radials.

>I initially approached the problem like you did, assuming that the perimeter
>of the radial system was a circle.

This works. One thing I noticed was that closer to the center, the wires
are closer together than the required 0.025 wl. This lead to the idea of
splitting or forking radials to maintain the required spacing. This ends
up using a lot less wire, but has the complication of requiring lots of
connections that are in contact with the ground or buried. That's why
most opt for full-length radials.

>The total length of wire required, L, is given by L = nr, where r is the
>radial length.
>Adjacent radials form an isosceles triangle with sides L and a base equal to
>the radial separation.

Got it.

>I would like to expand on your comment:
>"You get little benefit from radials substantially shorter than .2 wl, and
>there's little reason to go beyond .25 wl."
>I basically agree with this. However, I think that the biggest advantage is
>obtained by going from no radials to a radial based ground system. However
>good data for no radials is hard to come by. I will work on that next.

If your antenna system needs radials, you need to install them. It won't
work well without them.

One other factor for short radials -- if you install a 1/4 wave vertical,
you actually need MORE radials close to the driven element, since that is
where the current is. In a typical installation, you usually get this,
since the widest spacing occurs far from the element. So, at some point,
you get a diminishing return for making the radials shorter -- because
you can't decrease the number of radials as you get close to the radiator
without incurring more loss.

>None the less, 0.2 wavelength radials are probably the best length to use
>for the typical amateur. The exact number should be determined by the
>quality of the soil where you are erecting the antenna.
>I suspect that your 48 radial 0.22 wwavelength radial ground system will
>perform great without a significant cost impact. Let us know how it turns

I suppose it's time to start digging the whole to place the tower....

Bill Coleman, AA4LR, PP-ASEL Mail:
Quote: "Not within a thousand years will man ever fly!"
            -- Wilbur Wright, 1901

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