Richard Fry wrote:

The FCC approach for AM broadcast stations is to use the pattern/gain
of the radiator over a perfect ground as a basis for the groundwave
field intensity at a given distance over real ground, as determined by
the FCC's MW propagation curves -- which curves are based on real-
world, measured performance.

With the advent of NEC and NEC-2, some have been misled by the
elevation pattern shown for a vertical radiator at an infinite
distance over real ground as being that of the radiation launched by
that vertical radiator. But it is not, it is only the amount of that
original radiation that survives at an infinite distance, for those
ground conditions (and for flat earth, at that).

That is correct, except only the people who misunderstand surface wave
propagation are being misled.

This has led to the concept of a "take-off angle" from a ground-
mounted vertical where peak radiation occurs, and that little to no
radiation occurs from the monopole in and near the horizontal plane.
But that isn't the case -- the relative field over real ground at low
elevation angles close to the vertical radiator can be very high, and
will continue onward to produce a long-range skywave. Even radiation
at an elevation angle of one degree will reach the ionosphere, due to
earth curvature.

Radiation at one degree will indeed reach the ionosphere. But not the
radiation propagating as a surface wave, as I'll show.

The field launched at very low angles contacts the ground and in doing
so, induces a current into it. This extracts power from the wave as it
propagates. The result is that the surface wave field is attenuated
quite rapidly with distance. At AM broadcast frequencies, it propagates
far enough to be useful for local broadcasting, but it doesn't reach the
ionosphere. If it did, fading (due to surface and sky wave interference
at distant points) would be a much more serious problem for broadcasters
than it is. As you go higher in frequency, the attenuation becomes
greater, so the surface wave propagates even less distance before
dropping below the noise level. No measurable fraction of it ever goes
anywhere near far enough to reach the ionosphere.

The theoretical elevation patterns shown in my plots don't exist very
far from the antenna, but they are a closer to reality over real
ground than those shown by NEC and NEC-2 for an infinite distance over
the same ground, and assumed also to exist close to the radiator.

NEC (NEC-2 and NEC-4) does a very good job of showing surface wave
("ground wave") field strength. It uses the same calculation method as
used by the FCC and, I understand that NEC modeling results are now
being accepted by the FCC in lieu of measurement for AM broadcast proof
of performance.

The results obtained using NEC-4 to calculate the groundwave field
intensity within the useful daytime coverage areas of AM broadcast
stations give much better correlation to the measured fields, and to
the methodology of using the theoretical pattern with the FCC's MW
propagation curves.

NEC-2 and NEC-4 give virtually identical results for both ground and sky
wave propagated fields. The results below were done using EZNEC Pro with
the double precision NEC-4 calculating engine. Results using the double
precision NEC-2 engine were different by less than 0.1 dB.

Here are some numerical values to illustrate what happens to the ground
wave field(*). Two antennas are analyzed, one at 1 MHz and the other at
7 MHz. Each is 1/4 wavelength high with effectively a zero loss ground
system. The 1 MHz antenna is 7 inches in diameter, the 7 MHz antenna one
inch diameter. (Diameter in this range makes no significant difference.)
Ground is "average" -- 5 mS/m conductivity, dielectric constant of 13.
Data are for elevation angles of zero, one, and two degrees, to
distances of 50 miles. In that distance range, the difference between
flat and curved Earth is negligible. The reported field strengths are in
dBi for easy comparison; to convert to mV/m, use

mV/m = 1000 / Distance(m) * Sqrt(30 * Power(w)) * 10 ^ (dBi / 20)

dBi is a comparison to the field from an isotropic antenna with the same
input power, measured at the same distance. So if the attenuation of all
parts of the field is the same with distance (in other words, if the
pattern is the same shape at all distances), the dBi field strength will
be the same at all distances.

First, the results. Field intensities are shown at various distances
from the antenna. These are the entire field, including surface wave.
View with a fixed-width font.

Field strengths, dBi, are under each elevation angle:

-- Elev angle --
Freq(MHz) Dist(mi) 0 deg 1 deg 2 deg
1 inf -inf -11.8 -6.8
1 1 4.0 3.6 3.4
1 10 -2.8 -5.0 -4.6
1 50 -18.7 -12.6 -7.0
7 inf -inf -18.1 -12.7
7 1 -15.8 -15.4 -12.2
7 10 -36.7 -18.3 -12.8
7 50 -50.8 -18.1 -12.7

The two lines with "inf" distance are sky wave only, that is, the field
is evaluated at a great enough distance that the ground wave has decayed
to effectively zero. This is what you'll see with EZNEC's Far Field
analysis, or with NEC if you don't include the ground wave. The
difference between these and the entries at other distances represents
the contribution of the ground wave at those distances.

As Richard has observed, the field strength is zero at zero elevation
angle and long distances. At the AM broadcast frequency of 1 MHz,
there's still the useful field strength of -18.7 dBi at the surface at
50 miles (even though the field strength is 20 dB greater -- not shown
-- at an elevation angle of 20 degrees). Notice, though, how the zero
degree field relative field strength continues getting smaller with
distance. Fortunately for the broadcasters, the surface wave component
doesn't detach itself from the Earth and head for the ionosphere as the
Earth curves away, but follows the curvature of the Earth. This allows
broadcasting beyond the horizon without ionospheric skip, and prevents
fading from the ground wave alone. It doesn't reach the ionosphere as
Richard has claimed.

The ground wave contribution is noticeable at one and two degrees also.
But look at what happens with distance (at 1 MHz). At 50 miles, the
ground wave contribution at those angles is hardly noticeable, as you
can see by comparing the dBi field strength at that distance with the
dBi field strength at an infinite distance. Interestingly, the dBi field
strength is shown to be very slightly lower at 50 miles than at an
infinite distance. This might be due to some of the power in the surface
wave at 50 miles being transferred to the sky wave at greater distances,
or it might be due to small calculation errors. But the differences are
slight, indicating that no significant ground wave energy remains at 50
miles at elevation angles of 1 and 2 degrees. There's no noticeable
ground wave energy at higher angles at or beyond 50 miles, and very
little at closer distances.

An analysis of the 7 MHz antenna shows the same thing, except that the
ground wave decays faster as expected. At that frequency, the one and
two degree field strengths have reached their sky wave-only values at 10
miles -- indicating essentially full decay of the ground wave -- , and
the zero degree field strength is less than -50 dBi at 50 miles.

The _ARRL Antenna Book_ propagation chapter devotes only one paragraph
to surface wave propagation(*). It summarizes that "The surface wave is
of little value in amateur communication, except possibly at 1.8 MHz."
Analysis which concludes that the surface wave plays a role in
ionospheric skip is erroneous and leads to conclusions which are simply
and demonstrably not true. Ground wave field strength is of interest at
HF only for communicating with stations within a few miles, and at MF
with stations within a few tens of miles.

(*) Technically, the surface wave is only one kind or component of a
ground wave, as explained in the _ARRL Antenna Book_. However, NEC uses
"ground wave" to mean the wave in contact with the ground, which some
others call the surface wave. This discussion is about the wave in
contact with the ground, for which I've used "ground wave" and "surface
wave" pretty much interchangeably. There's a good discussion of surface
wave propagation in Terman's _Radio Engineering_ as well as other
references.

Roy Lewallen, W7EL