1. NACE
Companion to the Peabody Book
October 26, 2000
Revision 1.1M
Dwight's Equation for Single Vertical Anode Resistance to Earth - millimeters
Soil resistivity in ohm-cm 10,000 ohm-cm
Rod length in mm 2134 mm
Rod diameter in mm 203 mm
Resistance of vertical rod in ohms 25.6 ohms
Dwight's Equation for Single Vertical Anode Resistance to Earth - meters
Resistivity of backfill material (or earth) in ohm-cm 10,000 ohm-cm
Length of anode in meters 2.13 m
Diameter of anode in meters 0.203 m
Resistance of one vertical anode to earth in ohms 25.6 ohms
Dwight's Equation for Multiple Vertical Anodes in Parallel - meters
Soil resistivity in ohm-cm 10,000 ohm-cm
Number of anodes in parallel 10 each
Length of anode in meters 2.13 m
Diameter of anode in meters 0.203 m
Anode spacing in meters 3.0 m
Resistance of vertical anodes in parallel to earth in ohms 4.52 ohms
NOTICE
For these equations to be valid the soil must be homogeneous and L >> d. With low resistance backfill,
as coke, d is taken as the diameter of the coke and L as the length of the backfill provided it does not
extend too much greater than the length of the anode (about 1.5 times the coke diameter).

2. NACE
Companion to the Peabody Book
October 26, 2000
Revision 1.1M
Modified Dwight's Equation for Multiple Anodes Installed Horizontally
Resistance, in ohms, of horizontal anode to earth
Resistivity, in ohm-cm, of backfill material (or earth)
Length of anode in meters
Twice depth of anode in meters
Diameter of anode in meters
10,000 ohm-cm
2.13 m
3.7 m
0.203 m
22.52 ohms
NOTICE
For these equations to be valid the soil must be homogeneous and L >> d. With low resistance backfill,
as coke, d is taken as the diameter of the coke and L as the length of the backfill provided it does not
extend too much greater than the length of the anode (about 1.5 times the coke diameter).

3. NACE
Companion to the Peabody Book
October 26, 2000
Revision 1.1M
Galvanic Anode Life
Mag Anode Zinc Anode
Weight = 109 kg Weight = 30 kg
Efficiency = 0.50 Efficiency = 0.90
Utilization Factor = 0.85 Utilization Factor = 0.85
Current = 2.0 A Current = 2.0 A
Mg Life = 5.9 yrs Zn Life = 1.1 yrs
Consumption Solution
Output² Rate² Potential³
Anode¹ (amp-hr/kg) (kg/amp-hr) Efficiency² (Cu-CuSO4)
Zinc 815 10.8 90% -1.1 V
Std. Mg 1100 7.9 50% -1.4 to -1.6 V
Hi-Pot Mg 1100 7.9 50% -1.7 to -1.8 V
1. Anodes installed in suitable chemical backfill.
2. Current efficiency with current density. The shown efficiency, and the resulting consumption rate, are
at approximately 30 milliamps/ft² of anode surface. Efficiencies are higher at higher current densities and
lower at lower current densities.
3. The potentials are solution potentials. When calculating driving potentials, the difference between the
protected structure and the anode, allow for anode polarization. Anode polarization is also influenced by
current density at the anode surface. For magnesium polarization allow for 0.1 V anodic polarization.
Zinc in a proper backfill is not usually subject to significant anodic polarization and the solution potential
may be used.

4. NACE
Companion to the Peabody Book
October 26, 2000
Revision 1.1M
Rectifier Total Circuit Resistance
Ground bed resistance (ohms) 3.08 ohms
Cable resistance (ohms) 0.097 ohms
Pipeline/structure to earth resistance (ohms) 7.53 ohms
Total circuit resistance (ohms) 10.71 ohms
Deep Anode Ground Bed Resistance - meters
Effective soil resistivity (ohm-cm) 10,000 ohm-cm
Anode length (meters) 12 m
Anode diameter (meters) 0.203 m
Resistance to earth of a vertical single anode (ohms) 6.74 ohms
Rectifier Efficiency
K = Meter constant DC Amps = 1.00 A
N = # of revolutions of disk DC Volts = 2.00 V
T = Time in seconds K= 0.01
N= 4
T= 10 sec
Efficiency = 27.78%

5. NACE
Companion to the Peabody Book
October 26, 2000
Revision 1.1M
Impressed Current - # of Anodes Required
Wt = Weight per anode (kg) Wt = 27.2 kg
CR = Consumption rate (kg/amp-year) CR = 0.34 kg/A-yr
DL = Desired life (years) DL = 20 yrs
Current = Current required (amps) Current = 15.00 A
UF = Utilization factor UF = 0.60
# anodes = 7 each
# of Anodes Required Based on Current Discharge
* from anode manufacturer data
MD = Maximum discharge per anode (amps) MD = 2.50 A
Current = Current required (amps) Current = 15.00 A
# anodes = 6 each
Cable Resistance
Resistance per km 0.833 ohms/km
Length in meters (sum of positive and negative cables) 117 m
Cable resistance 0.097 ohms