# Grounding(Earthing)Resistance Calc.

1. Feb 20, 2006

### dsky

Dear Experts,
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.

2. Mar 1, 2006

### Astronuc

Staff Emeritus
The natural log often is involved because there is an integral of dr/r for which the solution is ln r, and with limits, b -> a, one would get ln b - ln a - ln b/a.

3. Jun 29, 2010

### iyaz_caem55

Hello. i want to ask you. can you help me??
1. can you give me an equation of single rod resistance of earhing??
2. i can't find coefficient of k dan k' in IEEE. in single rod, can k dan k' neglect or avoid (equal zero)???
the data of single rod on my schoolproject:
1. there is no area (A) because just one rod.
2. N = 1 , because just one rod.

thank you for answering my question.

4. Jul 1, 2010

### m.s.j

Rrod=ρ/2πLr .[ln(8Lr ⁄ d)– 1]

ρ: is the resistivity of the soil in Ω•m
Lr: is the length of the ground rod in m
D: is the diameter of the ground rod in m

5. Jul 1, 2010

### iyaz_caem55

wow thank you m.s.j.
1. why can the "ln(8Lr ⁄ d)" change "ln(4Lr ⁄ d)" ?
2. can you give me the equation of "Resistance of grid R1" and "Mutual Resistance Rm" of single rod?
will be Resistance of grid R1= (rho/pi*Lc)*(ln(2Lc/(b*2h)^0.5)-k') ?
wiil be Mutual Resistance Rm = (rho/pi*Lc)*(ln(2Lc/L)-k'+1) ? is it right? may the "Rm" be negative value because of the large k' ?
i m sorry. i m very confusing. thank you again.

6. Jul 1, 2010

### m.s.j

1-In mentioned formula "2a" is the diameter of ground rod not "a" (please refer to IEEE 80, page 66 and BS 7430)
R2= (rho/(2pi*N*L))*(ln(4L/a)-1+((2kL/A^0.5)*(N^0.5-1)^2

2- Grounding grid and mutual resistance for single rod is meaningless.

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