p = resistivity of electrolyte in ohm- centimeters 



N = number of anodes in parallel 



L = length of anode (or backfill column) in meters 



D = diameter of anode (or backfill column) in 

 meters 



S = anode spacing in meters 



The resistance of the anode group is the sum of Rv and the internal re- 

 sistance of the group, that is, the internal resistance of a single anode 

 divided by the number of anodes in the group. 



Equation (3) may be used to construct a chart for use with the anode 

 size and backfill size to be used for a particular project. Such a chart, 

 based on impressed current anodes 0.05 meter (2 inches) in diameter and 1.5 

 meters long in 0.2-meter (8 inch) by 2.1-meter (7 foot) backfill columns of 

 50 ohm-centimeters resistivity, is shown in Figure 102. A similar typical 

 design chart for galvanic anodes is shown in Figure 103. Note that both 

 charts are based on electrolyte resistivity of 1 000 ohm- centimeters. Anode 

 (or backfill column) resistance to electrolyte is directly proportional to 

 electrolyte resistivity. For example, consider 15 anodes in parallel at 7.6 

 meters (25 feet) spacing in 2 200 ohm-centimeter soil. Anode (in backfill) 

 resistance in 1 000 ohm-centimeter soil, shown on the chart in Figure 103, 

 is 0.233 ohm. Resistance in 2 200 ohm-centimeter soil = 0.233 x 2 200/1 000 

 = 0.513 ohm. To this add the internal resistance of the group. From use of 

 equation (2) the internal resistance of one electrode is 0.106 ohm, making 

 the internal resistance of the group (0.106/15) = 0.007 ohm, a negligible 

 amount. The total resistance is 0.520 ohm, but 0.513 ohm could be used 

 safely. 



(5) Calculating Resistance in Cables . Cathodic protection design 

 also requires a knowledge of the resistance of various sizes of copper wire 

 or cable most often used in anode installations. Resistance data and common 

 use of some of the most commonly used sizes are shown in Table 57. 



(6) Calculating Anode Lifespan . If current output of a galvanic 

 anode of any given weight is known, its approximate useful life can be 

 calculated. The calculation is based on the theoretical ampere hours per 

 newton of the anode material, and its current efficiency (see Table 52). 

 Also involved is a utilization factor, which may be taken as 85 percent. 

 This means that when the anode is 85 percent consumed it will require 

 replacement. This is because there is insufficient anode material remaining 

 to maintain a reasonable percentage of its original current output. 



Expressions for determining individual anode life for different materials 

 are presented below with efficiency and utilization factors expressed as 

 decimals: 



(a) For magnesium: 



anode weight 



, . _ . ., 0.026 ' in newtons • efficiency * utilization factor 



Life in Years = ■ — t — = - ■ 



anode current in amperes ' 



365 



