Topband: Anyone purchased the ARRL book on Short Antennas for160???

Guy Olinger K2AV olinger at
Thu Jan 23 14:17:00 EST 2014

On Thu, Jan 23, 2014 at 10:12 AM, Richard Fry <rfry at> wrote:

> Guy Olinger wrote:
>> Careful here  ... The presence of 0.4 wavelength buried radials turns the
>> ground underneath from the typically inferior Carolina medium into a
>> superior composite medium. Use of four elevated radials **over that
>> composite medium** is far superior to four elevated over 2-3-4 mS/m.
> The NEC4.2 analysis linked below does not support the statements in the
> above quote.

It does not. That is a fact. But, again, be careful. It's not because NEC
x.x produces the right numbers in all circumstances.

NEC x.x has no means of literally calculating ground specifics as if ground
were a conductor. Norton Sommerfeld ("high accuracy" ground) is an
**approximation method**. Like any approximation method, it is selected to
serve a particular paradigm of circumstances, and will be blind and weak to
others. NEC 4.x ground calculation is *tuned* for the *money* paradigm, the
commercial MF BC paradigm. It underestimates ground loss where radials
would not be accepted as kosher by the FCC.

The particular blind spot that applies to extrapolations of commercial BC
experience is actual loss in earth, where vertical principal radiators are
involved, and sparse and/or irregular and/or short radials/counterpoise are

The demonstration of this weakness is to spend time trying to get NEC 4.x
to predict current carefully MEASURED in radials in the watershed 1937
Brown, Lewis & Epstein study, figure 42. NEC x.x can't do it because it is
using an **approximation** method for those calculations. You will never
generate those dips in the radial current. That requires treating ground as
a finite network of "small" conductors, and running the calculations as if
everything was wire, where the ground characteristics defined wire
resistance and lossy wire insulation of the "stand-in" wires.

This results in a computational density which is the side of the square
divided by the spacing of data points raised to the FOURTH power. Squared
because 5 on a side is 25 points overall, 10 on a side is 100 points, 100
on a side is 10,000 points, etc.

NEC literal calculations generate a square law number of operations on data
points required for a literal calculation. Every data point must be related
to every other data point and the results of that calculation book-kept, a
book of comparison points.

A 100 meter square with data points every meter generates 10,000 data
points (one for each unique square meter). This results in 100,000,000
comparison points. A 500 meter square with the same granularity generates
250,000 data points, and 62,500,000,000 comparison points.

If each comparison calculation in the 500 meter model took 2 microseconds
and occupied 16 bytes of storage, the literal calculations of a 500 meter
square would take 125,000 seconds and a terabyte of active processing
memory with an working set pretty close to the entirety, making the process
highly storage-bound, Accounting for that and using a highly optimistic 10
microsecond storage bound processing time, the run time balloons to 174
hours or a little over a week.

So both the storage required and the run time are multiplied by quite worse
than a square law, and even with modern fast PC's can generate week and
month-long run times.  Going back to the time of origin of the Sommerfeld,
the state of computation back then meant literal method programs NEVER
completed. You did an *approximation* method or you did nothing at all.

And that bordering-on-impossible task *assumes* that ground has a
*monolithic* quality. This is not at all to minimize the approximation
method. Those guys were rightfully heroes for coming up with something that
could run to completion at all, and be tunable to attain decently accurate
results in the *money* paradigm of commercial MF BC radio.

Just don't equate NEC to natural law. There are scattered places where the
limitations bung the results, like 160m ham radio and small lots. We have
got to get away from this idea that in all the problems presented to NEC
that all the issues are being calculated directly from basic radio math
equations in EE courses.

When NEC x.x can generate the BL&E *measured* curves from real ground data,
I'll be riveted to the process, God permitting I live so long.

73, Guy K2AV

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