Here it is in Octave/Matlab form..
(untested so far..)
probably need to check for line wraps
% formulas for grounding electrode resistance
% approximate formulas from IEEE Std 142-1999, Table 13
% see also MIL-HDBK-419A
% http://www.uscg.mil/Petaluma/TPF/ET_SMS/Mil-STDs/MILHDBK419.pdf
% dimensions in cm
% resistivity in ohm-cm
% typical values 0.1 to 10
%pi = 3.14159265358979;
rho = 1; % ground resistivity (inverse of sigma, conductivity)
% hemisphere
a = 1; %radius of hemisphere
R = rho / (2 *pi * a);
% Ground rod length L, radius a
L = 1;
R = rho / (2 *pi*L) * (ln(4*L/a)-1);
% two ground rods, spacing s, s>L
Ls = L/s;
R = rho/(4*pi*L)*(ln(4*L/a)-1) + rho/(4*pi*s)*(1-1/3*Ls^2+ 2/5 * Ls^4);
% two ground rods, spacing s, s<L
Ls = L/s;
sL = s/L;
R = rho/(4*pi*L)*(ln(4*L/a)+ln(4*Ls) -2 + sL /2 -sL^2 /16 + sL^4 /512 );
% can continue series
%horizontal wire length 2L, depth s/2
Ls = L/s;
sL = s/L;
R = rho/(4*pi*L) * (ln(4*L/a)+ln(4*Ls) -2 + sL /2 -sL^2 /16 + sL^4 /512 );
% yes, exactly the same as the previous equaltion
% right angle bend of wire, arm length L, depth s/2
Ls = L/s;
sL = s/L;
R = rho/(4*pi*L) * (ln(4*L/a)+ln(4*Ls) - 0.2373 ...
+
0.2146 * sL ...
+
0.1035 * sL^2 ...
+
0.0424 * sL^4 );
% three point star
Ls = L/s;
sL = s/L;
R = rho/(6*pi*L) * (ln(4*L/a)+ln(4*Ls) + 1.071 ...
-
0.209 * sL ...
+
0.238 * sL^2 ...
- 0.054 *
sL^4 );
% four point star
Ls = L/s;
sL = s/L;
R = rho/(8*pi*L) * (ln(4*L/a)+ln(4*Ls) + 2.912 ...
-
1.071 * sL ...
+
0.645 * sL^2 ...
- 0.145 *
sL^4 );
% six point star
Ls = L/s;
sL = s/L;
R = rho/(12*pi*L) * (ln(4*L/a)+ln(4*Ls) + 6.851 ...
-
3.128 * sL ...
+
1.758 * sL^2 ...
- 0.490 *
sL^4 );
% eight point star
Ls = L/s;
sL = s/L;
R = rho/(16*pi*L) * (ln(4*L/a)+ln(4*Ls) + 10.98 ...
- 5.51
* sL ...
+ 3.26
* sL^2 ...
- 1.17 *
sL^4 );
% ring of wire, ring Diameter D, wire diameter 2*a, depth s/2
R = rho/(2*pi^2*D)*(ln(4*D/a)+ln(4*D/s));
% buried horizontal strip. Length 2L, section a by b
% depth s/2, b<a/8
sL = s/L;
R = rho/(4*pi*L)*( ln(4*L/a)+(a^2-pi*a*b)/(2*(a+b)^2) + ln(4*L/s) - 1 ...
+ sL/2 + sL^2 / 16 + sL^4 / 512);
%buried horizontal round plate, radius a, depth s/2
as = a/s;
R = rho/(8*a) + rho/(4*pi*s)*(1 - 7/12 *as^2 + 33/40 *as^4 );
% series continues
%buried vertical round plate, radius a, depth s/2 (to center of plate)
as = a/s;
R = rho/(8*a)+rho(4*pi*s)*(1 + 7/24 *as^2 + 99/320 *as^4);
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