**Help Information**

**For**

**Loresco Grid Resistance
Calculator**

Note: Do not use commas in the input values. If the decimal is not entered, it is

assumed to be just to the right of the right-most digit entered.

**English Units or Metric Units:**
You may choose Metric or English input units by use of the input unit
select button prior to entering variables. For example, if you wish
to enter variables in English units and English units (ft & in)
appear next to the input variable entry slots, simply enter the
proper numbers and continue. However, if you wish to enter the
variables in English units and Metric units (m & cm) appear next
to the input variable entry slots, left click the mouse on the
"English Units" button. Note: the required units for
Resistivity are ohm-cm regardless of the input units selection.

**Total Length of Grid Conductors, (m
or ft):** Enter the total length of the grid conductors in meters
or feet.

**Avg. Length of Ground Rods, (m or
ft):** Enter the average length of the ground rods or the grounding
backfill columns, if used, in meters or feet. If a grounding backfill
column is used, you should enter the total length of the backfill
regardless of the length of the ground rod or contacting electrode
within the backfill.

**Soil Resistivity of Upper Layer,
(ohm-cm):** Enter the average resistivity of the upper layer of
soil around the grounding grid in ohm-cm. This is the value of soil
resistivity from the surface to a depth of H as determined though
field-testing. Soil resistivities may vary from a low of 100 to a
high of 1,000,000 ohm-cm or more. Regardless of the input units
selected, the units for resistivity must be in ohm-cm.

**Soil Resistivity of Deeper Layer,
(ohm-cm):** Enter the average resistivity of the deeper layer of
soil around the grounding electrode in ohm-cm. This is the value of
soil resistivity from the depth of H downward as determined though
field-testing. Soil resistivities may vary from a low of 100 to a
high of 1,000,000 ohm-cm or more. Regardless of the input units
selected, the units for resistivity must be in ohm-cm.

If the soil is uniform resistivity to a depth greater than or equal to the average rod depth, a single soil resistivity layer model is used. In this case, enter the same resistivity for both the upper and deeper layers, and enter any value for the Thickness of the Upper Layer, H.

In order for this approximate model to be valid, the resistivity of the deeper layer must be equal to or less than the resistivity for the upper layer. If the deep layer resistivity is less than the resistivity of the upper layer, it must not be less than 20% of the resistivity of the upper layer.

**Diameter of Grid Conductors, (cm or
in):** Enter the diameter of the grid conductors in centimeters or
inches. If Loresco grounding enhancement backfills are used around
the grid conductors, enter the equivalent diameter of the backfill.

**Diameter of Ground Rod or Backfill
Columns, (cm or in):** Enter the diameter of a single ground rod or
of a backfill column, if used, in centimeters or inches. Again, this
is the diameter the LORESCO grounding backfill, if used, or the
actual electrode diameter, if no backfill is used.

**Number of ground rods:** Enter the
total number of ground rods installed. If Loresco grounding backfill
columns are used, enter the number of backfill columns. Regardless of
the number or type of electrodes installed in a single hole or
grounding backfill column, this is considered one rod.

If neither ground rods nor grounding backfill columns are to be installed, enter zero for this value. The calculator will then estimate the resistance of the grid without ground rods.

**Depth of Grid Burial (m or ft):
**Enter the depth of burial of the grid in meters or feet. If the
grid is laying on the surface of the earth, you may enter zero.

**Thickness of Upper Soil Layer, (m or
ft):** Enter the thickness of the upper soil layer in meters or
feet. If the soil resistivity is uniform to a depth equal to or
greater than the average rod length, a single soil resistivity layer
model is used. In this case, you must enter the value of the upper
soil resistivity for both the upper and lower resistivity values
required and enter any number for the Thickness of the Upper Layer,
H. In order for the two layer model to be valid, the thickness of the
upper layer should be at least 10% of the long-side grid length.

**Short-Side Grid Length, (m or ft):**
Enter the length of the short side of the rectangular area covered by
the grid.

**Long-Side Grid Length, (m or ft):
**Enter the length of the long side of the rectangular area covered
by the grid.

**Result:** This is the
resistance-to-earth in ohms of the electrode system described by the
input data. If the estimated resistance is higher than the required
value, one or more of the design variables may be changed in order to
determine its effect on the expected resistance.

The most recent result along with the input data is displayed in output column 1. You may recalculate by reentering the required variables while changing any one or all of the input data values for the next calculation. As additional calculations are undertaken, the output results automatically scroll to the right. In other words, at any time you may compare the two most recent calculation results.

**General Information:**

This calculator employs the techniques
of estimating the resistance to earth of a grounding grid either with
or without the attachment of vertical ground rods as described in
ANSI / IEEE Standard 80. The specific equations used were developed
for uniform soil resistivity by S. J. Schwarz and published in his
paper titled, "Analytical Expressions for Resistance of
Grounding Systems", *AIEE transactions,* vol 73, part
III-B, 1954, pp 1011-1016. The resistances of the grid and vertical
rods are combined using resistance equations developed by R.
Rudenberg ("Grounding Principles and Practices – 1,
Fundamental Considerations on Grounding Currents." *Electrical
*Engineering, vol 64, no 1, Jan 1945, pp 1 – 13.) and E. D.
Sunde (*Earth Conduction Effects in Transmission Systems*. New
York: McMillan, 1968.). The two layer model used is based on work by
C. J. Blattner in his paper "Study of Driven Ground Rods and
Four Point Soil Resistivity Tests." *IEEE Transactions on
Power Apparatus and Systems*, vol PAS-101, no 8, Aug 1982, pp 2837
– 2850. Finally, the constants related to the geometry of the
system are determined by expressions developed by S. W. Kercel in his
paper "Design of Switchyard Grounding Systems Using Multiple
Grids." *IEEE Transactions on Power Apparatus and Systems*,
vol PAS-100, no 3, Mar 1981, pp 1341 – 1350.

The two-layer resistivity model is based on the premise that the ground rods or backfill columns are installed in deeper, lower resistivity soil, as compared to the surface soils where the grid is buried. This calculator model assumes that the rods are driven to a depth such that the top of the rod is at the depth of the grid burial, which is normal for most installations.

For the two-layer resistivity model to provide reasonably accurate results, the resistivity of the upper layer must be greater than or equal to the resistivity of the deeper layer. In addition, the resistivity of the deeper layer cannot be less than 20% of the resistivity of the upper layer. The thickness of the upper layer, H, must also be greater than or equal to 10% of the long-side grid length. Finally, the thickness of the upper layer, H, must be greater than or equal to the grid depth and less than or equal to the average ground rod length.

If the soil is relatively uniform from the surface to a depth equal to or greater than the average length of the ground rods, a single layer resistivity model can be used by entering the same value of soil resistivity for both the upper and lower soil resistivity values. In this case, any value can be entered for the depth of the upper layer, H.

Revised: March 9, 2000