5. Cathodic Protection  
5.10 AnodetoEarth Resistance 

Anode Earth Resistance of a Single Vertical Anode
The anode earth resistance of a single vertical anode is calculated using Dwight equation
where  R_{v} = resistance of one vertical anode to earth  
P = resistivity of backfill  
L = length of the anode (or backfill) in ft  
d = diameter of anode in ft 
The resistance of two or more vertical anodes in parallel can be calculated by Sunde equation:
where  S = spacing between the anodes in ft  
N = number of anodes 
Example:
From the data provided below, calculate the resistance of one vertical anode to earth.
Soil resistivity  100 ohmcm  
Backfill resistivity  5 ohmcm  
Backfill dimensions  8.5" x 28" (0.7083' x 2.333')  
Anode dimensions  5" x 5" x 20.5" (0.470' x 1.7081')  
Calculations:  
First determine the resistance from the anode to the outer edge of backfill columns R_{v}(i)  
Determining the resistivity of the vertical anode to backfill:  
(use the dimensions of the backfill and the resistivity of the backfill as shown above)  
R_{v,1} = R_{vi}  R_{v,backfill}
= 0.3614  0.2538 = 0.1076 ohm 

Next, calculate the resistance of the anode to soil (use backfill dimensions and resistivity of the soil)  
To get the total resistance of one anode to
earth
R_{v,total} = R_{v,1} + R_{v,2} = 0.1076 + 5.074 = 5.181 ohm 
