Frank, don't forget to use a 1/4-wave vertical when calculating
efficiency.

I assume you always include the power in the ground wave in the total
power radiated when calculating efficiency.

I think radial length intervals of 0.5 metres will be OK for 100 or
more radials.

Reg,

I have always used the 1/4 wave vertical to calculate efficiency.
Most of my calculations do not include the surface wave. The problem
with including the surface wave is that it is computed over a cylindrical
surface at x meters from the antenna. Technically not a surface, but
rather a vertical line in cylindrical coordinates. The surface is implied
due to the expected symmetry of radiation. In my calculations I have
taken "x" as 200 m, so as to ensure the result is in the far-field at 8 MHz
(nominal 5 wavelengths). I compute the field at 1 m intervals, in the "z"
direction to 200 m. To include the total field I would have to allow z
to approach infinity. Taking these data from the NEC output text file, I
import it to Excel. In Excel I compute the radial distance and elevation
angle to the source. Since my increments are in steps of one meter
I can only approximate integral degree points; removing those points
far from integral degrees. I could employ
linear interpolation, but the field intensity variation is relatively
smooth,
and adds no discernable ripple to the radiation pattern. I then
normalize these data to 1 m to match the spherical data for the
sky wave pattern. At 45 degrees elevation there is very little
ground wave effects, I can then combine the two normalized
sets of data, and numerically integrate over a hemispherical surface.

Sorry to bore you with these details, but just to give an idea of
the tedious steps involved in including the surface wave. To compute
the total radiated sky wave involves a simple command in NEC.
Just the same I can compute the total radiated power at 0.5 m
and 10 m radial lengths as a comparison. At every 0.5 m it would
drive me nuts.

Attempting to model a 100 radial system I continually run into
road blocks. At one point I had a complex matrix with 3.6
million entries. Still I think I have a viable model that needs
just a little refinement. Due to the rotational symmetry of the
structure I can employ methods that greatly reduce run time. The
model that should work will consist of thirty-three 10 cm
radials. At the end of these short radials I connect three 9.9 m
radials for a total of 99 radials. If I run into problems I may
have to reduce the segmentation to 25 cm. What is interesting,
in my preliminary results, is that there is only a 2% improvement
in sky wave total radiated power with 120 radials over 36 radials.

Frank