Skip to contentUnited States Department of Transportation - Federal Highway Administration FHWA Home
Research Home
Report
This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-HRT-06-139
Date: October 2006

Traffic Detector Handbook:Third Edition—Volume II

APPENDIX N. GROUNDING (DESIGN GUIDELINES)

SECTION I—REASONS FOR GROUNDING

1. SAFETY GROUNDING

(1) Grounding of all metallic electrical enclosures is required for safety. If a live conductor touches the metal, a large ‘short circuit current’ flows to ground, thus tripping the circuit breaker. If the metal were not grounded, it would assume the same voltage as the touching conductor and remain so until discharged to ground. When touched, the discharge could occur through the person’s body to ground depending on the resistance of gloves, boots and the material the person is standing on.

2. SYSTEM GROUNDING

(1) A low voltage system is grounded throughout to ensure that any line-to-ground fault is cleared by the circuit breakers prior to doing any permanent power system damage such as melting of cables, etc. The system ground is usually tied to the safety ground. If the two grounds are separated, the following disadvantages occur:
(a) ‘Resistance to ground’ of both system and safety grounds is greater than would be the case if the two were connected together.
(b) High currents could still flow in the safety ground in the event of cable insulation failures in the enclosure.
(c) A high degree of coupling, through the earth, is difficult to avoid if the ground rods are in the same local area.
(d) Where decoupling is possible, voltages (often dangerous) can be possible between the nearby ‘grounded points’.

3. LIGHTNING DISCHARGE

(1) Lightning induced currents on cables must be given a fast and easy path to ground through protective devices such as lightning arresters, varistors and gas-tube arresters. If the path to ground is not provided properly, the voltage surge ‘spikes’ and resultant current and energy will damage components. Electronic components are particularly susceptible to damage since they operate at very low voltages and high speeds and are not designed to physically absorb any significant energy.

SECTION II—CALCULATION OF RESISTANCE TO GROUND

1. GENERAL

(1) A minimal resistance to ground is desirable. Older versions of the Code called for 10 ohm (Ω) maximum to ground. This requirement is now replaced with a description of the physical grounding materials, or, in the case of a substation, limiting the voltage rise due to a fault to 5000 V. The requirement for 10 Ω was difficult to design and perhaps even more difficult to obtain during installation.
(2) The resistance to ground depends on several non-exclusive factors:
(a)The number and length of ground rods
(b)The number and length of connecting ground wires in the ground grid
(c)The quality of wiring connections
(d)The resistivity of the earth
(e)The temperature of the earth
(f)The water content of the earth
(3)The last three factors are somewhat weather dependent and are therefore beyond precise design.

2. SOIL RESISTIVITY

(1) The resistivity of the soil, at the site under consideration, is a measure of the resistance to conducting electrical current and is measured in Ohm-meters (Ωm). Representative values are given Table N-1.
Table N-1. Representative values of soil resistivity.
Soil TypeResistivity ρ (Ωm)
Clay, saturated silt
100
Sandy or silty clay
250
Clayey sand or saturated sand
500
Sand
1500
Gravel
5000
Dry sand, rock
>5000
(2) The soil classification and ρ values in Table N-1 are left purposely vague since environmental effects can drastically change the resistivity of the soil. Table N-2 shows the typical variation of a nominal resistivity with different soil temperatures.
 
Table N-2. Variation of resistivity with ground temperature.
Ground Temperature (°C)Resistivity ρ (% of nominal)
20 73
10 100
0+ 139
0– (freeze) 303
– 5 798
–10 3333
(3) Resistivity varies widely with moisture content as well as temperature, with values a factor of 350% higher for soil in the ‘dry’ state than in the ‘wet’ state.
(4) In order to custom design a grounding system, the designer would need to know not only the type of soil and its resistivity, but also the condition of future measurements. For this reason, a resistivity of ρ = 100 Ωm is selected as the basis of design for grounding systems. (The system is field measured upon installation and any deficiencies can be made up by installing supplementary facilities.) It should also be noted that Ontario has little or no lightning activity during months when the ground temperature is below the freezing point.

GROUND ELECTRODE RESISTANCE TO GROUND

3.1 Ground Rods

(1) Resistance to ground for a single ground rod may be calculated from

1st equation just after 3.1 Ground Rods (1) Resistance to ground. Capital R subscript Capital G equals Capital R subscript Capital R which in turn equals the product of parenthesis lowercase rho divided by parenthesis 2 times pi times Capital L subscript Capital R parenthesis times parenthesis the summation of the natural logarithm of the quotient of 4 times Capital L subscript Capital R divided by A subscript Capital R parenthesis minus 1 parenthesis.

where

RG = Resistance to ground in Ohms (Ω)
ρ = Soil resistivity in Ohm-meters (Ωm)
LR = Rod length in meters (m)
aR = Rod radius in meters (m)
RR = Resistance to ground of one rod in Ohms (Ω).

Example 1: for 20 mm dia. x 3 m Rod

Given ρ = 100 Ωm, LR = 3 m, αR = 0.01 m

Equation 2 Just after “Example 1: for 20 mm dia. X 3 m Rod”. Given lowercase rho equals 100 ohm-meters, Capital L subscript Capital R equals 3 meters, A subscript Capital R equals 0.01 meters. Capital R subscript Capital G equals the product of parenthesis 100 divided by parenthesis 2 times pi times 3 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 4 times 3 divided by 0.01 parenthesis minus 1 parenthesis which in turn equals 32.2 ohms.

If the soil is wet and ρ decreases to ρ = 50 Ωm

Capital R subscript Capital G equals the product of parenthesis 50 divided by parenthesis 2 times pi times 3 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 4 times 3 divided by 0.01 parenthesis minus 1 parenthesis which in turn equals 16.1 ohms.

If the soil is dry and ρ increases to ρ = 300 Ωm

Capital R subscript Capital G equals the product of parenthesis 300 divided by parenthesis 2 times pi times 3 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 4 times 3 divided by 0.01 parenthesis minus 1 parenthesis which in turn equals 96.6 ohms.

It may be seen that the nominal resistance to ground of 50 Ω usually quoted for a single ground may vary substantially depending on soil type or conditions.

Example 2: for 20 mm dia. x 6 m Rod

Given ρ = 100 Ωm, LR = 6 m, αR = 0.01 m

Given lowercase rho equals 100 Ohm-meters, Capital L subscript Capital R equals 6 meters, A subscript Capital R equals 0.01 meters. Capital R subscript Capital G equals the product of parenthesis 100 divided by parenthesis 2 times pi times 6 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 4 times 3 divided by 0.01 parenthesis minus 1 parenthesis which in turn equals 18.0 ohms.

or for a 100% rod depth increase (over example 1), the resistance to ground is decreased by 44%.

Example 3: for 25 mm dia. x 3 m Rod

Given ρ = 100 Ωm, LR = 3 m, αR = 0.0125 m

Given lowercase rho equals 100 ohm-meters, Capital L subscript Capital R equals 3 meters, A subscript Capital R equals 0.0125 meters. Capital R subscript Capital G equals the product of parenthesis 100 divided by parenthesis 2 times pi times 6 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 4 times 3 divided by 0.01 parenthesis minus 1 parenthesis which in turn equals 18.0 ohms.

or for a 25% increase in rod diameter (over that of Example 1), the resistance to ground is decreased by 3%.

3.2 Pedestals

(1) Using the same formula as for a single ground rod,

Capital R subscript Capital G equals Capital R subscript Capital R which in turn equals the product of parenthesis lowercase rho divided by parenthesis 2 times pi times Capital L subscript Capital R parenthesis times parenthesis the summation of the logarithm of parenthesis 4 times Capital L subscript Capital R divided by A subscript Capital R parenthesis minus 1 parenthesis.

we have the following examples.

Example 4: for Steel Footing (220 mm dia. x 2300 mm)

Given ρ = 100 Ωm, LR = 2.30 m, αR = 0.110 m

Given lowercase rho equals 100 ohm-meters, Capital L subscript Capital R equals 2.30 meters, A subscript Capital R equals 0.110 meters. Capital R subscript Capital G equals the product of parenthesis 100 divided by parenthesis 2 times pi times 2.30 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 4 times 2.30 divided by 0.0110 parenthesis minus 1 parenthesis which in turn equals 23.7 ohms.

or 26 % "better" than a single rod.

Example 5: for Steel Footing (85 mm dia. x 1830 mm)

Given ρ = 100 Ωm, LR = 1.830 m, αR = 0.043 m

Given lowercase rho equals 100 ohm-meters, Capital L subscript Capital R equals 1.830 meters, A subscript Capital R equals 0.043 meters. Capital R subscript Capital G equals the product of parenthesis 100 divided by parenthesis 2 times pi times 1.830 parenthesis times parenthesis the summation of natural logarithm of parenthesis 4 times 1.830 divided by 0.043 parenthesis minus 1 parenthesis which in turn equals 36.0 ohms.

or 12 % "worse" than a single ground rod.

3.3 Plate Electrodes

General

(1) For a single plate,

Capital R subscript Capital G equals Capital R subscript Capital P which in turn equals the product of parenthesis lowercase rho divided by parenthesis 2 times pi times Capital L subscript Capital R parenthesis times parenthesis the summation of the natural logarithm of parenthesis 8 times Capital W subscript Capital P divided by parenthesis 0.5 times Capital W subscript Capital P plus Capital T subscript Capital P parenthesis parenthesis minus 1 parenthesis.

where

RP  = Resistance of plate to ground in Ohms
LP  = Length in meters
WP = Width in meters
TP  = Thickness in meters.

Example 6: for 610 x 610 x 6 mm Plate

Given ρ = 100 Ohm, LP = 0.61 m, WP = O.61 m, TP = O.OO6 m

Given lowercase rho equals 100 ohms, Capital L subscript Capital P equals 0.61 meters, Capital W subscript Capital P equals 0.61 meters, Capital T subscript Capital P equals 0.005 meters. Capital R subscript Capital G equals the product of parenthesis 100 divided by parenthesis 2 times pi times 0.61 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 8 times 0.61 divided by parenthesis 0.305 plus 0.006 parenthesis parenthesis minus 1 parenthesis which in turn equals 45.8 ohms.
3.4 Wire Grids

General

(1) For the case of a grounding system consisting of a wire grid only, the wire shape forms a ground plane (similar to antenna design), which if buried deep enough, can constitute the most effective part of the grounding system. (Ground rods are normally driven, in any event, in order to penetrate below the frost line.)

The resistance to ground for a grid system is approximated by

Capital R subscript Capital G equals Capital R subscript Capital W which in turn equals the product of parenthesis lowercase rho divided by parenthesis pi times Capital L subscript Capital W parenthesis times parenthesis the summation of the natural logarithm of the quotient of 2 times Capital L subscript divided by the square-root of the product of D subscript Capital W times Capital Z subscript Capital W parenthesis plus parenthesis the quotient of 1.4 times Capital L subscript W divided by the square-root of Capital A subscript Capital W parenthesis minus 5.6 parenthesis.
RW  = Resistance of wire grid in Ohms
LW  = Total Length of grid wires in meters
dW = Diameter of wire in meters
ZW  = Burial depth of grid in meters
AW  = Plan area covered by grid in square meters.

Example 7: Using 3 x 3 m grid with cross-tie

This shows a 9.84-foot by 9.84-foot (3-meter by 3-meter) square grid bisected horizontally by a straight line. Given ρ = 100 Ωm, LW = 5 x 3 = 15 m, ZW = 0.3 m
AW = 3 x 3 = 9 sq m, dW = 0.0105 m (#2/0)
Given lowercase rho equals 100 ohm-meters, Capital L subscript Capital W equals 5 times 3 which in turn equals 15 meters, Capital Z subscript Capital W equals 0.3 meters, Capital A subscript Capital W equals 3 times 3 which in turn equals 9 square meters, D subscript Capital W equals 0.0105 meters. Capital R subscript Capital G equals Capital R subscript Capital W which in turn equals the product of parenthesis lowercase 100 divided by parenthesis pi times 15 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 2 times 15 divided by the square-root of the product of 0.0105 times 0.3 parenthesis plus parenthesis 1.4 times 15 divided by the square-root of 9 parenthesis minus 5.6 parenthesis which in turn equals 16.4 ohms.

Example 8: Using 3 x 3 m triangular grid

This shows a 9.84-foot by 9.84-foot by 9.84-foot (3-meter by 3-meter by 3-meter) equilateral triangle grid. Given ρ = 100 Ωm, LW = 3 + 3 + 3 = 9 m, ZW = 0.3 m
AW = 0.5 x 3 x 3 sin(60o) = 3.90 sq m, dW = 0.0105 m (#2/0)
Given lowercase rho equals 100 ohm-meters, Capital L subscript Capital W equals 3 plus 3 plus 3 which in turn equals 9 meters, Capital Z subscript Capital W equals 0.3 meters, Capital A subscript Capital W equals 0.5 times 3 times 3 sin of 60 degrees which in turn equals 3.90 square meters, D subscript Capital W equals 0.0105 meters. Capital R subscript Capital G equals Capital R subscript Capital W which in turn equals the product of parenthesis lowercase 100 divided by parenthesis pi times 9 parenthesis times parenthesis the summation of natural logarithm of the quotient of 2 times 9 divided by the square-root of the product of 0.0105 times 0.3 parenthesis plus parenthesis the quotient of 1.4 times 9 divided by the square-root of 3.9 parenthesis minus 5.6 parenthesis which in turn equals 23.3 ohms.
3.5 Multiple Rods

General

(1) The combined effect of several rods is similar to the rod resistance acting in parallel and is given by

Capital R subscript Capital G equals Capital R subscript Capital M Capital R which in turn equals the product of parenthesis the quotient of lowercase rho times 2 times pi times N times Capital L subscript Capital R parenthesis times parenthesis the summation of the natural logarithm of parenthesis the quotient 4 times Capital L subscript Capital R divided by A subscript Capital R parenthesis minus 1 plus parenthesis the quotient of 2.8 times Capital L subscript Capital R times parenthesis the square-root of parenthesis N parenthesis minus 1 parenthesis squared divided by the square-root of Capital A subscript Capital R parenthesis.

where

RMR = Combined resistance of multiple rods to ground in Ohms
LR = Rod length in meters
n = Number of rods
AR = Area covered by the n rods in square meters.

For 20 mm x 3 m rods,

Capital R subscript Capital M R equals the product of parenthesis the quotient of lowercase rho divided by the product of pi times N parenthesis times parenthesis 1 plus the quotient of 1.4 times parenthesis the square-root of parenthesis N parenthesis minus 1 parenthesis squared divided by the square-root of Capital A subscript Capital R parenthesis.

Example 9: Using four rods on 3 m square

Given ρ = 100 Ωm, αR = 0.01 m, LR = 3 m, n = 4, AR = 3 x 3 = 9 sq m

Given lowercase rho equals 100 ohm-meters, A subscript Capital R equals 3 meters, N equals 4, A subscript Capital R equals 3 times 3 which in turn equals 9 square meters. Capital R subscript Capital M R equals the product of parenthesis the quotient of 100 divided by the product of pi times 4 parenthesis times parenthesis 1 plus the quotient of 1.4 times the square of parenthesis the square-root of parenthesis 4 parenthesis minus 1 parenthesis divided by the square-root of 9 parenthesis which in turn equals 11.7 ohms.

(Note: rods not connected by wire)

3.6 Combination Rod and Wire Grids

General

(1) It is may be necessary to include both rod and wire grids for service grounds, substations, etc.

The resistance to ground of the combined system is given by

Capital R subscript Capital G equals the quotient of parenthesis Capital R subscript Capital W times Capital R subscript Capital MR minus Capital R subscript Capital W R squared parenthesis divided by parenthesis Capital R subscript Capital W plus Capital R subscript Capital M R minus parenthesis 2 times Capital R subscript Capital W R parenthesis parenthesis.
RG = Total system resistance to ground in Ohms
RW = Resistance of wire grid in Ohms (Subsection 3.4)
RMR = Resistance of multiple rods in Ohms (Subsection 3.5)
RWR = Mutual resistance factor of the wires to the rods
Which in turn equals Capital R subscript Capital W R which in turn equals parenthesis lowercase rho divided by the product of pi times Capital L subscript Capital W parenthesis times parenthesis the natural logarithm of parenthesis the quotient 2 times Capital L subscript Capital W divided by Capital L subscript Capital R parenthesis plus the quotient of 1.4 Capital L subscript Capital W divided by the square-root of parenthesis Capital A subscript Capital W parenthesis minus 4.6 parenthesis.

For 20 mm x 3 m rods,

Which in turn equals Capital R subscript Capital W R which in turn equals parenthesis lowercase rho divided by the product of pi times Capital L subscript Capital W parenthesis times parenthesis the natural logarithm of parenthesis 0.67 parenthesis plus the quotient of 1.4 times Capital L subscript Capital W divided by the square-root of parenthesis Capital A subscript Capital W parenthesis minus 4.6 parenthesis.

Example 10: Using 3 x 3 m grid with cross-tie and rods

This shows a 9.84-foot by 9.84-foot (3-meter by 3-meter) square grid bisected horizontally by a straight line. Given ρ = 100 Ωm, LR = 3 m, αR = 0.01 m,
AW = AR = 3 x 3 = 9 sq m, n = 4, ZW = 0.3 m, dW = 0.0105 m (#2/0), LW = 5 x 3 = 15 m,
Given lowercase rho equals 100 Ohm-meters, Capital L subscript Capital R equals 3 meters, lowercase A subscript Capital R equals 0.01 meters, Capital A subscript Capital W equals Capital A subscript Capital R which in turn equals 3 times 3 which in turn equals 9 square meters, N equals 4, Capital Z subscript Capital W equals 0.3 meters, D subscript Capital W equals 0.0105 meters, Capital L subscript Capital W equals 5 times 3 which in turn equals 15 meters. Capital R subscript Capital W R equals parenthesis lowercase rho divided by the product of pi times Capital L subscript Capital W parenthesis times parenthesis the natural logarithm of parenthesis 0.67 parenthesis plus the quotient of 1.4 times Capital L subscript Capital W divided by the square-root of parenthesis Capital A subscript Capital W parenthesis minus 4.6 parenthesis.
Substituting the given data in the formula, we have
Capital R subscript Capital W R equals parenthesis 100 divided by the product of pi 15 parenthesis times parenthesis the natural logarithm of parenthesis 0.67 times 15 parenthesis plus the quotient of 1.4 times 15 divided by the square-root of parenthesis 9 parenthesis minus 4.6 parenthesis which in turn equals 10.0 ohms.
Capital R subscript Capital M R equals parenthesis 100 divided by the product of pi times 4 parenthesis times parenthesis 1 plus the quotient of 1.4 times parenthesis square-root of parenthesis 4 parenthesis divided by the the square-root of parenthesis 9 parenthesis parenthesis which in turn equals 11.7 ohms.
(from Example 9).
Capital R subscript Capital W equals parenthesis 100 divided by the product of pi times 15 parenthesis times parenthesis the natural logarithm of parenthesis the quotient of 2 times 15 divided by the square-root of parenthesis 0.0105 times 0.3 parenthesis plus the quotient of 1.4 times 15 divided by the square-root of parenthesis 9 parenthesis minus 4.6 parenthesis which in turn equals 16.4 ohms.
(from Example 7).
Capital R subscript Capital G equals the quotient of parenthesis Capital R subscript Capital W times Capital R subscript Capital M R minus the square of Capital R subscript Capital W R parenthesis divided by parenthesis Capital R subscript Capital W plus Capital R subscript Capital M R minus the product of 2 times Capital R subscript Capital W R parenthesis.
Substituting the above results in the formula for RG, we have
Capital R subscript Capital G equals the quotient of parenthesis16.4 times 11.7 minus 100 parenthesis divided by parenthesis16.4 plus 11.7 minus 20 parenthesis which in turn equals 11.3 ohms.
If the site soil was clayey sand instead of clay, ρ would be 500 Ωm instead of 100 Ωm (Table 1) and the resistance to ground would be
Capital R subscript Capital G equals 11.3 times 500 divided by 100 which in turn equals 56.5 ohms.
3.7 Single Wire

General

(1) A single wire or counterpoise directly buried in earth has a resistance to ground of

Capital R subscript Capital G equals Capital R subscript Capital C which in turn equals the product of parenthesis lowercase rho divided by parenthesis 2 times pi times Capital L subscript Capital R parenthesis times parenthesis the summation of the natural logarithm of parenthesis Capital L subscript Capital W divided by A subscript Capital W parenthesis plus the natural logarithm parenthesis Capital L subscript Capital W divided by Capital Z subscript Capital W parenthesis minus 2 plus parenthesis 2 times Capital Z subscript Capital W divided by Capital L subscript W parenthesis minus parenthesis the square of Capital Z subscript Capital W divided by the square of Capital L subscript Capital W parenthesis parenthesis.

where RC = Resistance to ground of buried conductor in Ohms.

Example 11: Using #6 AWG wire

Given ρ = 100 Ωm, ZW = 0.6 m, LW = 50 m, αW = 0.00252 m,

Given lowercase rho equals 100 ohm-meters, Capital Z subscript Capital W equals 0.6 meters, Capital L subscript Capital W equals 50 meters, A subscript Capital W equals 0.00252 meters. Capital R subscript Capital G equals the product of parenthesis 100 divided by parenthesis 2 times pi times 50 parenthesis times parenthesis the summation of the natural logarithm of parenthesis 50 divided by 0.00252 parenthesis plus the natural logarithm parenthesis 50 divided by 0.6 parenthesis minus 2 plus parenthesis 2 times 0.6 divided by 50 parenthesis minus parenthesis the square of 0.6 divided by the square of 50 parenthesis parenthesis which in turn equals 3.93 ohms.
3.8 Summary of Calculations

General Formulae

Single Rod Only:Capital R subscript Capital G equals Capital R subscript Capital R which in turn equals the product of parenthesis lowercase rho divided by parenthesis 2 times pi times Capital L subscript Capital R parenthesis times parenthesis summation of the natural logarithm of parenthesis 4 times Capital L subscript Capital R divided by A subscript Capital R parenthesis minus 1 parenthesis.
Single Plate Only:Capital R subscript Capital G equals Capital R subscript Capital P which in turn equals the product of parenthesis lowercase rho divided by parenthesis 2 times pi times Capital L subscript Capital P parenthesis times parenthesis summation of the natural logarithm of parenthesis 8 times Capital W subscript Capital P divided by parenthesis 0.5 times Capital W subscript Capital P plus Capital T subscript Capital P parenthesis minus 1 parenthesis.
Wire Grid Only:Capital R subscript Capital G equals Capital R subscript Capital W which in turn equals the product of parenthesis lowercase rho divided by the product of pi times Capital L subscript Capital W parenthesis times parenthesis the summation of the natural logarithm of parenthesis 2 times Capital L subscript Capital W divided by the square-root of the product of subscript Capital W times Capital Z subscript Capital W parenthesis plus parenthesis 1.4 times Capital L subscript Capital W divided by the square-root of Capital A subscript Capital W parenthesis minus 5.6 parenthesis.

Multiple Rods Only:

Capital R subscript Capital G equals Capital R subscript Capital M R which in turn equals the product of parenthesis lowercase rho divided by the product of 2 times pi times N times Capital L subscript Capital R parenthesis times parenthesis the summation of the natural logarithm of parenthesis 4 times Capital L subscript Capital R divided by the A subscript Capital R parenthesis minus 1 plus parenthesis the product of 2.8 times Capital L subscript Capital R times the square of parenthesis the difference of the square-root of n and 1 parenthesis divided by the square-root of capital A subscript Capital R parenthesis.
Multiple Rods and Wire Grid:Capital R subscript Capital W R equals the quotient of parenthesis Capital R subscript Capital W times Capital R subscript Capital M R minus the square of Capital R subscript capital W R parenthesis divided by parenthesis Capital R subscript Capital W plus Capital R subscript Capital M R minus the product of 2 times Capital R subscript Capital WR parenthesis.

where

Capital R subscript Capital W R equals the quotient of parenthesis Capital R subscript Capital W times Capital R subscript Capital M R minus the square of Capital R subscript capital W R parenthesis divided by parenthesis Capital R subscript Capital W plus Capital R subscript Capital M R minus the product of 2 times Capital R subscript Capital WR parenthesis.

Single Wire Only:

Capital R subscript Capital G equals Capital R subscript C which in turn equals the product of parenthesis lowercase rho divided by the product of 2 times pi times Capital L subscript Capital W parenthesis times parenthesis the summation of the natural logarithm of the quotient of Capital L subscript Capital W divided by A subscript Capital W plus the natural logarithm of the quotient of Capital L subscript Capital W divided by Capital Z subscript Capital W minus 2 plus parenthesis 2 times capital Z subscript Capital W divided by Capital L subscript W parenthesis minus the quotient of the square of Capital Z subscript Capital W divided by the square of Capital L subscript Capital W parenthesis.

The symbols that appear in the above formulae are defined as:

RG = Total resistance to ground of the system in Ohms
RR = Resistance to ground of a single ground rod in Ohms
RP = Resistance to ground of a single ground plate in Ohms
RW = Resistance to ground of a single ground wire in Ohms
RMR = Resistance to ground of multiple ground rods in Ohms
RWR = Mutual resistance factor of wires to rods in Ohms
RC = Resistance to ground of a single buried wire in Ohms
LR = Length of ground rod in meters
LW = Length of wire in meters
LP = Width of plate in meters
TP = Thickness of plate in meters
AW = Area of wire grid in square meters
AR = Area covered by several ground rods in square meters
aR = Radius of ground rod in meters
aW = Radius of wire in meters
dW = Diameter of wire in meters
ZW = Burial depth of wire in meters
n = Number of ground rods
ρ = Soil resistivity in Ohm-meters.

Useful Formulae

(1) Since the Ministry’s grounding system uses common components of

then the general formulae can be reduced to reflect the physical parameters of the common items as follows:

The foregoing formulae are approximate and may be used where special conditions apply.

3.9 Application

(1) The Ministry’s designs for grounding systems are based on the following premises:

(a) A resistance to ground of 10 Ω should be obtained in accordance with good practice.
(b) In cases where 10 Ω to ground is impossible to obtain using practical methods, 25 Ω to ground is the minimum requirement provided that adequate steps are taken to ensure that step and touch voltages do not present a safety problem to workers or the public.
(c) Every effort is to be made to meet the 10 Ω to ground requirement, where practical, by addition of ground electrodes and wire in the field.
(d) Since soils and their resistivity vary widely with location and environment respectively, the Ministry’s standard criteria for design is ρ = 100 Ωm. The resistance to ground of the designed system is field checked and any required alterations are made at that time. Where it is obvious to the designer that increased grounding facilities will be required (sand, gravel, rock, etc.), the required facilities can be estimated from Table N-3 and included in the design.
(e) Table N-3 is derived from the general formulae of Subsection 3.8.
(f) The following notes apply to Table N-3:
(i) Configuration No.9 may be used with continuous #6 ground wire commonly used for lighting. Grounding at every 5th pole applies.
(ii) Configurations No. 11 or 12 may be used for grounding in clay or areas that remain damp. Configuration No. 13 should be used as the ‘standard’ design.
(iii) Configurations No. 15 to 18 indicate the results of adding more wire and rods to the grid. If dry sand, gravel, or rocky areas are unavoidable, the principles illustrated may be extended by manual calculation using the formulae given.
(iv) Values shown in brackets are for information as a simpler grid would normally be required.
(v) Values shown are ‘stand alone’ values (isolated ground). An approximation of resistance to ground for any number of the systems, which are tied together with ground wire, may be made by considering the values to be in parallel.
3.10 Problem Areas

Problem areas are identified as:

(1) Bedrock or shallow overburden of less than 1 m depth over bedrock:

(a) It will be necessary to drill 150 mm (min) holes in the bedrock and backfill these with a cementous iron slag slurry mixture (trade name: ‘Embico’). Note that previously used methods used rock salt as the chief conductor and that this method is no longer recommended due to corrosion. Difficulty in obtaining (and measuring) proper resistance to ground will be encountered as the ground depends, to some extent, on the number of seams between rock layers that are encountered. In this situation, the first design choice would be to locate the object to be grounded away from the rock area. If this is unavoidable, configuration No. 18 in Table N-3 should be used for design and added to during construction if necessary.

(2) Soil overburden of 1 m to 2 m depth over bedrock:

(a) Plates may be used as ground electrodes with the same configurations shown in Table N-3 for rods (depending on type of soil overburden). A minimum of 300 mm of soil should be left between the rock and plate and the #2/0 wire grid.

(3) Rock Fill

(a) Areas of rock fill can be assumed to have a resistivity in excess of 10,000 Wm. A previously used method was to run two parallel runs of #2/0 wire through the voids in the rock fill to a location suitable for use of normal grounding methods. The method causes large voltages to appear at the cabinet due to the high inductance of the leads to ground and should be avoided by placing at least 2.0 m of earth fill over the rock fill.
Table N-3. Resistance to ground for various ground system configurations and soils.
Ground System ConfigurationDescriptionNormal UseResistance to Ground (Ω)in Clay (ρ=100Ωm)Resistance to Ground (Ω)in Sandy Clay (ρ=200Ωm)Resistance to Ground (Ω)in Clayey Sand (ρ=500Ωm)Resistance to Ground (Ω)in Sand (ρ=1500Ωm)Resistance to Ground (Ω)in Sand, Gravel (ρ=5000Ωm)
Row 2—Very small black circle representing a single 20-millimeter (0.8-inch) by 3-meter (9.8-foot) rod. 1.Single 20 mm x 3 m rodAdditionto system32801604801610
Row 3—Small black circle representing a single 220-millimeter (8.7-inch) diameter by 2300-millimeter (90.6-inch) steel footing. 2.Single 220 mm dia. x 2300 mm steel footingPoles(requires additional system)28701404201400
Row 4—Very small black circle representing a single 85-millimeter (3.3-inch) diameter by 1830-millimeter (72.0-inch) steel footing. 3.Single 85 mm dia. x 1830 mm steel footingPoles,cabinets (requires additional system)401002006002000
Row 5—Very small black square representing a 610- by 610- by 6-millimeter (24.0- by 24.0- by 0.2-inch) plate. 4.610 x 610 x 6 mm plateRockoverburden 0.6 to 2.0 m461152306902300
Row 6—The number 3 above a short black horizontal line representing a single number 6 wire, bare, 3 meters long. 5.Single #6 wire, bare, 3 m longAdditionto system411032056152050
Row 7—The number 3 above a short black horizontal line representing a single number 2/0 wire, bare, 3 meters long. 6.Single #2/0 wire, bare, 3 m longAdditionto system38951905701900
Row 8—The number 3 above a short black horizontal line representing a single number 6 wire, 2 rods. 7.Single #6 wire, 2 rodsService193895290950
Row 9—The number 3 above a short black horizontal line connected on the left side to a small black square, all of which represents a single number 2/0 wire, 2 plates. 8.Single #2/0 wire, 2 platesServicein overburden27541404101400
Row 10—The number 1 above a short black horizontal line connected on the left side to a small black circle and on the right side to a very small black circle, all of which represents a 220-millimeter (8.7-inch) diameter by 2300-millimeter (90.6-inch) steel footing, number 6 wire, 1 rod. 9.220 mm dia. x 2300 mm steel footing, #6 wire, 1 rodPoles193895285950
Row 11—The number 1 above a short black horizontal line connected on the left side to a moderately small black circle and on the right side to a very small black circle, all of which represents an 85-millimeter (3.3-inch) diameter X 1830-millimeter (72.0-inch) steel footing, number 6 wire, 1 rod. 10.85 mm dia. X 1830 mm steel footing, #6 wire, 1 rodPoles163480240800
Row 12—Equilateral triangle with small black circle at the top vertex and very small black circles at the two base vertices, with the numeral 3 printed on each side, all of which represents item 11, with 85 millimeter diameter (3.3-inch) by 1830-millimeter (72.0-inch) steel footing, number 2/0 wire, 2 rods. 11.85 mm dia. x 1830 mm steel footing, #2/0 wire, 2 rodsCabinets142870210700
Row 13 —Equilateral triangle with small black circle at the top vertex and very small black circles at the two base vertices; straight lines connect the center of each side of the triangle to the center of the triangle; the numeral 3 is printed at each side. All of this represents item 12, with 85-millimeter (3.3-inch) diameter by 1830-millimeter (72.0-inch) steel footing, number 2/0 wire, 3 rods. 12.85 mm dia. x 1830 mm steel footing, #2/0 wire, 3 rodsCabinets132665195650
Row 14 —Square with very small black circles at each corner. A horizontal line across the upper two-thirds has a small black circle hanging from it by a short black line. The numeral 3 is printed below the bottom of the square. All of this represents item 13, with 85-millimeter (3.3-inch) diameter by 1830-millimeter (72.0-inch) steel footing, number 2/0 wire, 4 rods. 13.85 mm dia. x 1830 mm steel footing, #2/0 wire, 4 rodsCabinets102050150250
Row 15 —Square with very small black circles at each corner. The numeral 3 is printed just above the bottom line of the square. All of this represents item 14, with number 2/0 wire, 4 rods. 14.#2/0 wire, 4 rodsService Anyfor ρ < 125 Ωm 112255165550
Row 16 —Square with very small black circles at each corner. Straight lines connect the center of each side of the square to the center of the square. The numeral 3 is printed just below the bottom side of the square. All of this represents item 15, with number 2/0 wire, 4 rods, 2 ties. 15.#2/0 wire, 4 rods, 2 tiesAnyfor ρ < 125 Ωm112255165550
Row 17 —Square with very small black circles at each corner. Straight lines connect the center of each side of the square to the center of the square. Horizontal lines shoot off to the right and left of the top and bottom of the square. The numeral 3 is printed on the lower left and lower right shooting lines and the bottom line of the square. All of this represents item 16, with number 2/0 wire, 4 rods, 2 ties, 4 tails. 16.#2/0 wire, 4 rods, 2 ties, 4 tailsAnyfor 125 < ρ < 150 Ωm(9)1845135450
Row 18 —Square with very small black circles at each corner. Straight lines connect the center of each side of the square to the center of the square. Horizontal lines shoot off to the right and left of the top and bottom of the square. Vertical lines shoot off to the top and bottom of the page from the right and left sides of the square. The numeral 3 is printed on the lower left and lower right shooting lines and the bottom lines of the square. The numeral 3 is also printed on the upper right vertical shooting line and the lower left vertical shooting line. All of this represents item 17, with number 2/0 wire, 4 rods, 2 ties, 8 tails. 17.#2/0 wire, 4 rods, 2 ties, 8 tailsAnyfor 150 < ρ < 200 Ωm(6)123090300
Row 19 —Square with very small black circles at each corner. Straight lines connect the center of each side of the square to the center of the square. Horizontal lines shoot off to the right and left of the top and bottom of the square. Vertical lines shoot off to the top and bottom of the page from the right and left sides of the square. The numeral 3 is printed on the lower left and lower right shooting lines and the bottom lines of the square. The numeral 3 is also printed on the upper right vertical shooting line and the lower left vertical shooting line. All of this is bounded by an outer square with 4 small black circles at its vertices. All of this represents item 18, with number 2/0 wire, 8 rods, 6 ties. 18.#2/0 wire, 8 rods, 6 tiesAnyfor 200 < ρ < 350 Ωm(5)102575250
3.11 Application Guidelines
(1) From the examples in the foregoing sections, it is immediately obvious that obtaining a 10 Ω resistance to ground is difficult in soils with high resistivity.
(2)  The effect of ground rod diameter is small. About 8% less resistance to ground is obtained by using a 25 mm diameter rod instead of a 20 mm rod. Much better results are obtained by making ground rods longer rather than thicker.
(3) The effect of electrode material (copper or steel) has negligible effect on results since the resistivity of all metals is much less than that of all soils.
(4) Ground rod spacing should be kept within one rod length spacing of each other.
(5) The effect of the size and type of wire interconnecting the ground rods has little effect on results. The #2/0 AWG cable usually used is sized to withstand a 50,000 ampere lightning discharge without complete melting.
(6) The upper 1.0 m of ground rod does not have much effect, even in wet soil. A minimum depth of 2.0 m gives about 25% more resistance to ground than the 3.0 m standard depth rod.
(7) In order to design proper grounding, a soils classification at the intended location should be obtained from the Regional Geotechnical Office (if not on the ‘Soils Profile’ or indicated on borehole logs included with contract drawings) and District personnel should be consulted.
(8) If the equipment to be grounded will be in a new fill location, the fill should not be composed of sand, gravel, rock and the like (if practical). A note on the grading drawings should be added where necessary: ‘Fill in the area of (equipment) to be cohesive material only or similar.’
(9) Table N-3 gives the number of ground rods (20 mm x 3.0 m) and grid configurations required for various classes of soil. Where there is not an apparent site problem, ground designs corresponding to ρ = 100 Ωm should be used by the designer. Where necessary after testing, the design may be adjusted during construction. Where it is not practically possible to obtain 10 Ω to ground, an absolute minimum of 25 Ω may be used.

SECTION III—EFFECTS OF LIGHTNING

1. GENERAL

The effects of lightning on outdoor electrical and electronic equipment can be costly. Damage from lightning may result from:

Since it is not practical to protect outdoor equipment against direct strokes, protective systems apply to the prevention or handling of surges and transients. The protective systems consist of the application of proper ground, suppression, and shunting devices.

Since weather is somewhat unpredictable, protection design is based on the following probabilities:

2. DESIGN CRITERIA

The design criteria adopted for protection of the Ministry’s electronic equipment are:

Figure N-1 indicates waveforms and timing of lightning protection devices.

FIGURE N-1. VOLTAGE AND CURRENT WAVEFORMS. A curve representing percent of maximum voltage or current declines slowly from 100 percent at approximately 0.9 volts to approximately 50 percent at 50 microseconds to approximately 40 percent at 80 microseconds. A lightning arrestor is shown as firing at 20 microseconds to 400 microseconds. A second curve shows that an MOV fires at 0.007 microseconds and a gas tube at 0.15 microseconds, resulting in a much slower rise in maximum discharge current and a much sharper decline. The maximum discharge percent is only 15 at 50 microseconds and only 3 percent at 80 microseconds.
Figure N-1. Voltage and current waveforms.

Note that the times needed for protection are much too fast to allow power circuit protection devices such as breakers, fuse, lightning arresters etc. to operate effectively. However, devices such as gas tubes and metal oxide varistors (MOVs) will initiate protection at about 0.15 μs and 0.007 μs, respectively.

3. POWER SURGES

Surges in any equipment including cables, poles, etc. can be induced by lightning strikes as far as 6 km away. Surges on overhead high voltage lines are grounded through lightning arresters at transformer locations.

Figure N-2 shows the voltage and current distribution through the earth near the bottom of the utility pole. For the design value of resistivity ρ = 100 Ωm, a voltage of 15,000 volts would be transferred through the earth for a distance of 5.3 m. It is therefore necessary to keep the service ground a minimum distance from the Hydro ground as indicated in Figure N-3. Since the designer seldom knows where the Hydro ground line is located, the convention of 5.5 m to the center of the pole is used as a design practice. Note that a large voltage will appear at the service ‘SN’ due to the Ldi/dt voltage on the grounding cable.

Figure N-2 shows the voltage and current distribution in the earth near the bottom of a utility pole. The voltage intensity declines in proportion as the area of a sphere surrounding the base of the pole expands.
Figure N-2 shows the voltage and current distribution in the earth near the bottom of a utility pole. The voltage intensity declines in proportion as the area of a sphere surrounding the base of the pole expands.
Figure N-2 shows the voltage and current distribution in the earth near the bottom of a utility pole. The voltage intensity declines in proportion as the area of a sphere surrounding the base of the pole expands.


Figure N-2. Voltage in earth due to discharging lightning current at service pole.

 

Recommended improvement to system ground connections.
Figure N-3. Recommended improvement to system ground connections.

4. OTHER SOURCES OF POSSIBLE DAMAGE

Traffic signal systems contain many other sources of transient voltages and currents within the controller cabinet. These sources are not considered as severe as the energy surge through the service neutral and all have protection devices installed within the cabinet. Some sources are:

(a) Detector Loops—inductive loop detector electronics units are protected internally with their own lightning arrester and are also provided with external MOVs at the input file. Failure rate due to lightning damage is very low as the voltage impressed on a loop is caused by capacitive effects.
(b) Detector Cable—the possibility of induced currents caused by transient voltages in the earth is minimized by shielding the detector cable and leaving both ends of the shield cut off.
(c) 

Signal Cable—signal cable is shielded by metal poles (above ground), but is subject to induced currents caused by transient voltages in the earth. The load switches and the AC-terminals of the cabinet are protected by MOVs and the failure rate is low.

(d) Direct Hits on Cabinet—although nothing can be done to ensure a complete lack of damage, the controller cabinet may be considered to be protected by an umbrella cone of 30o from an overhead line and somewhat protected by a 45o cone. It is not desirable, however, to install the cabinet directly under the lines due to possible electromagnetic interference. The cabinet location (Figure N-4) should be:
  • 11 m minimum from the supply pole
  • 3 m minimum (horizontally) clear of overhead lines
  • Within the 30° to 45° cone of protection (within 15 m for normal height lines) of the overhead lines.
If the controller is to be situated across the road from the hydro lines, then the #6 AWG (green) ground wire and the" feeder wires should be run in rigid steel duct, to the nearest electrical chamber. These conductors should then be run to the next chamber across the road via the under-pavement crossing, and from this chamber to the controller in any approved electrical duct, not necessarily of metal.
(e) Direct Hits on Poles or Equipment—this condition would cause severe damage. The method of mitigating possible damage effects consists of installing a #6 AWG RWU 90 (green) system ground wire connecting all poles and intersection equipment and installing a ground rod on each corner. Connection of the system ground around the intersection should be made at one point only (the service ground bus) as indicated in Figure N-5.
Controller cabinet location for best lightning protection.
Controller cabinet location for best lightning protection.

Figure N-4. Controller cabinet location for best lightning protection.

Figure N-4 shows that the controller cabinet is located at least 5.5 meters from the first grounding rod. The grounding rods are separated at least 3 meters apart and at least 5.5 meters from the electrical supply pole. Wires to the grounding rods are in rigid steel duct located underground.
Figure N-5 shows that the signal grounding system includes no ground electrodes at the cabinet and includes lightning arrestors and hybrid suppressors between the service cabinet and the ground. It also shows that the control equipment in the cabinet is additionally protected by lightning suppressors in the cabinet.

Figure N-5. Signal grounding system (with or without lighting). No ground electrodes at cabinet.

SECTION IV—SUMMARY OF DESIGN GUIDELINES

1. TRAFFIC SIGNAL SYSTEMS

(1) Design standard grounding system under normal circumstances (Figures N-3 and N-5):

(2) Use improved design as per Table N-3 for grounds in sand, gravel, or rock. Consult Geotechnical Information and District Maintenance.

(3) Both ends of the detector cable shield should be cut off and left unconnected.

(4) Locate controller at least 11 m from a hydro pole and at least 3 m horizontally from overhead lines. Locate controller 1.5 m clear minimum from metal objects such as poles, fences, and guide rails.

SECTION V—REFERENCES

(1) Biddle Instruments, Getting Down to Earth: A Manual on Earth Resistance Testing for Practical Man, 4th ed., 1981.
(2) Bodle, D., Electrical Protection Guide for Land-Based Radio Facilities, Joslyn Electronic Systems, 1971.
(3) Burns, G.A, “Lightning Damage to Tank-Gauging Equipment Solved by Modification Instead of Replacement,” Oil and Gas Journal, pg. 93, September 14, 1981.
(4) Canadian Standards Association, Canadian Electrical Code Part I, Section 10, Grounding and Bonding, 1987.
(5) Carpenter, R.B., “Total Isolation from Lightning Influences,” IEEE Transactions on Industry Applications, Vol. 1A-17, No. 3, pg. 334, May/June 1981.
(6) Cunagin, W.D. and Avoub, N.A., Lightning Protection Hardware and Techniques for Electronic Traffic Control Equipment, Federal Highway Administration, February, 1986.
(7) Dasen, M., Insulation Tester – Megger, Algonquin College.
(8) Dasen, M., Meg-Earth Tester, A1gonquin College.
(9) Denny, H.W. and Rohrbaugh, J.P., “Transient Protection, Grounding, and Shielding of Electronic Traffic Control Equipment,” NCH RP Report 317, Transportation Research Board, June, 1988.
(10) Edco, Inc., Lightning Protection for Traffic Control, Edco Technical Bulletin No. 200-01, May, 1978.
(11) Edco Inc. of Florida, Installation Technical Bulletin # 100484, 1984.
(12) Epstein. B.M., “For Best Results, Treat Power and Computer Requirements as One System,” EC&M, pg. 130, August 1986.
(13) Fink, D.G and Beaty, H.W., Standard Handbook for Electrical Engineers, 11th Edition, 1978.
(14) Freund, A, “Protecting Computers from Transients,” EC&M, pg. 65, April 1987.
(15) General Electric, Transient Voltage Suppression, 3rd Edition.
(16) Gunn, R., “Facility Noise Control from the Ground Up,” EC&M, pg. 56, April 1987.
(17) Harder, J.E., Hughes, A.E., and Vosicky, J., “Analytical Method for Coordination of Surge Arresters with Current-Limiting Fuses,” IEEE Transactions on Industry Applications, Vol. lA-17, No. 5, pg. 445, September/October 1981.
(18) Institute of Electrical and Electronic Engineers, Inc., IEEE Guide for Radio Methods of Measuring Earth Conductivity, IEEE Standard 356-1974.
(19) Institute of Electrical and Electronic Engineers, Inc., IEEE Guide for Safety in Substation Grounding. IEEE Standard 80-1976.
(20) Institute of Electrical and Electronic Engineers, Inc., IEEE Guide for the Installation of Electrical Equipment to Minimize Electrical Noise Inputs to Controllers from External Sources, IEEE Standard 518-1982.
(21) Institute of Electrical and Electronic Engineers, Inc., ”IEEE Standard Procedures for the Measurement of Radio Noise from Overhead Power Lines,” IEEE Transactions on Power Apparatus and Systems, Vol. Pas -100, No. 8, August 1981.
(22) Institute of Electrical and Electronic Engineers, Inc., “Modeling Current-Limiting Surge Arresters,” IEEE Transactions on Power Apparatus and Systems, Vol. Pas -100, No.8, August 1981.
(23) Lee, W.R., “The Dangers of Lightning,” ETI Canada, pg. 27, November 1978.
(24) Michaels, E.C., “Principles and Techniques for Grounding and Bonding in Hazardous( Classified )Locations,” Plant Engineering, pg. 133, September 17, 1981.
(25) Mims, F.M., “Introducing the Varistor,” Computers and Electronics, pg. 88, May 1983.
(26) Ontario Hydro Inspection Department, “Electrical Inspection, Provincial Government,” Electrical Inspection Guide 26-4, December 1975.
(27) Ontario Hydro Inspection Department, “Pub1ic Roads - Electrical Devices,” Electrical Inspection Guide 11-3, August 1984.
(28) Ontario Hydro Inspection Department, “Rule 10-208: Grounding Connections for Two or More Buildings or Structures,” Bulletin 10-6-0, April 1987.
(29) Plumber, J.A. and Crouch, K.E., Lightning Protection for Traffic Control Systems, National Aeronautics and Space Administration, 1978.
(30) Schwarz, S.J., “Analytical Expressions for the Resistance of Grounding Systems,” presented at the AIEE Summer and Pacific General Meeting, Los Angeles, June 1954.
(31) Stifter, F.J., “Power-Line Disturbances,” Computers and Electronics, pg. 35, October, 1983.
(32) Thomas, P., Investigative Report - Lightning Problems on 170/332 Traffic Control Systems, Ministry of Transportation of Ontario, June 1985.
(33) Waterson, A. and Maher, P., “Computer Power - Problems and Solutions,” EC&M, pg. 67, December 1982.
(34) Westinghouse Electric Corporation, Electrical Transmission and Distribution Reference Book, 1950.
(35) “Equipment, Manuals and Procedures Evaluation for the Design and Maintenance of Traffic Signal Systems,” Report No. 2, Grounding, Ministry of Transportation of Ontario, May 1988.

Previous | Table of Contents | Next

 
FHWA-HRT-06-139
ResearchFHWA
FHWA
United States Department of Transportation - Federal Highway Administration