(29C) Lightning Performance of Vertical Antenna Ground Systems

[SlideRule]

from Lightning Performance of Vertical Antenna Ground Systems, IEEE TRANSACTIONS ON BROADCASTING,f VOL. BC-25, NO. 1, MARCH 1979
…
ABSTRACT
Most vertical antennas used in the AM standard broadcast band in the United States have extensive radial ground systems beneath them which serve as image planes. These same image planes can function as excellent ground systems for dissipating lightning discharges. When subjected to a lightning stroke, the "surge impedance" of a ground system is almost always lower than its measured resistance since the soil adjacent to the electrode may break down under the stress caused by intense electric fields. An equation is given for calculating the resistance of a counterpoise, and an HP-29C calculator program is included. Methods and instrumentation for measuring soil resistivity and ground-system resistance are also described.
…
Resistance Measurement
The usual technique is called the "Fall of Potential Method" … Another measurement technique … only one measurement need be taken to determine the ground bed resistance … For certain electrode configurations, equations exist which may be used to predict ground bed resistance if the physical dimensions of the bed and the soil resistivity are known. The formula for a radial-wire counterpoise is:
[attachment=7184]
for
n = number of counterpoise wires
p = soil resistivity (ohm-meters)
L = length of one counterpoise wire (meters)
a = radius of one counterpoise wire (meters), and
R = total resistance of radial ground system (ohms)
…
the listing of an HP-29C calculator program which will calculate R when the parameters n,p, L, and a are supplied as data inputs.
…
Listing of HP-29C Program Which Will Calculate Resistance of Counterpoise.
Keystrokes
g LBL 0
g DEG
ST0 4
R↓
ST0 3
R↓
ST0 2
R↓
ST0 1
1
-
ST0 0
0
g LBL 1
1
RCL 0
RCL 1
÷
1
8
0
×
f sin
+
f LST x
÷
f LN
+
g DSZ
GTO 1
RCL 4
RCL 3
÷
STO 6
g x²
1
+
√x
STO 5
1
+
RCL 6
÷
f LN
RCL 6
+
RCL 5
-
+
RCL 2
x
RCL 3
÷
RCL 1
÷
2
÷
g π
÷
g RTN

To run program:
Data Input
Number of radials, n Enter↑
Soil resistivity, p Enter↑
Radial length, L Enter↑
Radial radius, a GSB 0

Program output: Resistance of radial ground system, ohms

I'm still searching for a 'open-source' document; the aforementioned 'pay-source' url has a thorough exegesis.

BEST!
SlideRule

[SlideRule]

The 'omitted' equation(s) added as a JPG.

[StephenG1CMZ]

Interesting. I wonder how switching from AM to FM might affect those formulae?