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I'm in the mountains doing installation of a substation grounding in Thailand, after 15 years of labor suprvision on construction works and rote following of plans has really blunted my engineering/math analysis skills,forgotten most of my college elect. theories, dont have university access now so pls bear with me coz im not planning to be a design engineer but only want to understand.

I was wondering why in most calculations does the nat.logarithm terms always appears, for example :

(1)Basic Resistance Formula : R = rho*Lenght/Area

(2)Resistance of ground rod bed R2= (rho/(2pi*N*L))*(ln(4L/a)-1+((2kL/A^0.5)*(N^0.5-1)^2

(3)Resistance of grid R1= (rho/pi*Lc)*(ln(2Lc/(b*2h)^0.5)+(k*Lc/A^0.5)-k')

(4)Mutual Resistance Rm = (rho/pi*Lc)*(ln(2Lc/L)+(k*Lc/A^0.5)-k'+1)

(5)Final ground reisitance Rg = R1*R2-Rm^2/ (R1+R2-2Rm)

whre :

rho = soil resistivity in ohm*m , linear units in meters

a = diameter of ground rod

b = diametrer of ground grid or mesh & connecting conductor

L = lenght of rod

Lc = total lenght of grid conductors

A = land area occupied by ground grid with rod

k,k' are experimental constants to be sourced from IEEE table

Lt = Lc + L

Also why is the above are different from recommended formula :

(5) Rg = (rho/4)*(pi/A)^0.5 + rho/ Lt

which is taken basically from

(6) Rg = (rho/4)*(pi/A)^0.5

Can remove the terms with "A" on formulas (2) to (4) coz the result will give me lower resistance result as compared to (5)

all formulas are taken from IEEEstd 80 except for (1), that my friend lend to me but would lessen my professional leverage if I further ask.

thanks for any expalination on this matters, laymans terms are also welcome.

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# Grounding(Earthing)Resistance Calc.

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