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Grounding concepts for a marine lightning protection
system
Ewen M.Thomson Ph.D.
Copyright 2005
Marine Lightning Protection Inc. All
rights reserved.
Concepts
described in this document are covered by US
patent #6,708,638 and pending patents.
1.
Scope
The scope of this document is to introduce the major
concepts governing sideflash formation and
mitigation in the design of a marine grounding system. Physical principles involving potential,
electric field, potential equalization, and sideflash
formation are described. These
principles are then applied to the layout of grounding electrodes, main
conductors, and bonding conductors in a marine grounding system.
2.
Terminology
2.1.
Water terminal – a conducting fitting
that acts as a conduit for the lightning current to pass to the water
This term parallels the definition of an "air
terminal" at the top of the lightning protection system. While an air terminal is the interface
between the lightning and the lightning protection system – acting as
an initiation point for the attachment streamer – a water terminal
provides an exit point to the water.
2.2.
Grounding – the
process whereby current flows from a water terminal towards or into the
water.
When a conductor is placed in the water to act as an
exit terminal for the lightning current, it is common practice is to refer
to it as a "ground plate".
However, this is a misnomer as the voltage of any water terminal
actually that of the whole lightning protection system, which is
significantly different from zero volts. Instead, the term
"grounding" is preferable to indicate the flow of current into
the ground medium (water), rather than a point on an equipotential
at ground potential. One corollary to this is that a conductor does not
need to be immersed in the water to deliver current into the water. In
fact, a conductor in the lightning protection system can act as a water
terminal if sparks form from it, and there are cases when a down conductor,
a mast base and even a sink drain have inadvertently acted to ground the
lightning to water.
2.3.
Grounding electrode – a water terminal
connected to the lightning protection system
Rather than
defining an exit terminal that is attached to the lightning protection
system in terms of its shape, such
as a "ground plate" or "ground strip", a more
descriptive term is "electrode" to reflect its particular
function as a terminal through which current flows.
2.4.
Sideflash –
any discharge occurring during a lightning strike that involves the formation
of a spark channel from any source other than an air terminal or a
grounding electrode
Sideflashes typically involve
conductors on the boat, that may include water
tanks and crew members. We
distinguish between two types of sideflashes:
2.4.1.
Internal sideflash
– a sideflash that forms between two
conductors on the boat
2.4.2.
External sideflash – a sideflash
that forms between an on-board conductor and the water.
2.5.
Main conductor - tinned copper conductor of
at least 2AWG used in the lightning protection system wherever current flow
is expected to be generally towards the water
2.6.
Bonding conductor – tinned copper
conductor of at least 6AWG used in the lightning protection system for
potential equalization where orientation is generally parallel to the water
surface or location is inside protective zones afforded by main conductors
3.
Lightning mechanism
From a yacht's point of view, the lightning
strike begins when current flows from any part of the lightning protection
system. This is typically tens of
milliseconds after the lightning has started in the cloud. Specifically, after a column of charge
has been lowered to within a few tens of meters of ground, in a process
called the stepped leader, current flows off the
top of the lightning protection system up towards the stepped leader in a
process termed the attachment streamer.
This current either charges the lightning protection system or is
accompanied by a current flow into the water, or both. Current flows either from electronic
conduction inside conductors or in the form of propagating charged
streamers following ionization of air or water and probably totals some
hundreds of amperes. Eventually the
attachment streamer connects with the stepped leader to form a physical
attachment to the boat. At this stage the thundercloud is effectively
shorted to ground by a continuous ionized channel, and the peak current
follows, with an amplitude of several tens of kilamperes with a rise time of about 100ns during the
return stroke phase. This peak
current decays in a few tens of microseconds but may be followed by a lower
level continuing current (~few hundred amperes) for perhaps several hundred
milliseconds. While at a much lower
level, the continuing current is the process responsible for the largest
heating effects. For a more detailed
discussion of all of the processes in a lightning strike, refer to http://www.marinelightning.com/science.htm#Background
.
4.
Physical concepts
4.1.
Potential
4.1.1.
Definition
Potential is the energy per unit charge. The lightning protection system becomes
charged, usually through the air terminal, by either a direct flow of
charge from the lightning channel or by an induced flow of charge into the
surrounding air when there is no direct connection to the channel. In either event it becomes
energized. As the lightning
protection system discharges, this energy is converted into various forms
such as heat, electromagnetic, light, and sound, usually in high-power
bursts that can do considerable damage, both mechanical and
electrical. At any instant the total
charge on the lightning protection system is the difference between the
charge that has flowed into the air, usually off the air terminal, and that
which has been conducted into the water.
Whenever there is excess charge on the lightning protection system,
the system is energized, and its potential is raised above ground (see
Section 4.1.4).
Potential is the same as voltage, both being represented
by "V". Unlike a two-dimensional electric circuit where the
voltage can be defined relative to some well-defined "ground"
wire or plane, a boat consists of a complicated three-dimensional system of
conductors, some of which are connected, that is sitting on another
conductor, the water, and nothing can be regarded as being at
"ground" potential. In
this respect, a boat being struck by lightning should be regarded in the
same manner as a system with a positive ground, corresponding to the
lightning protection system, where the negative terminal is far from the
boat. The fact that ground potential
cannot be reached is actually not a problem since the major concern in
practice is the potential gradient, or rate of change of potential with distance.
4.1.3.
Equipotentials
If the potential of the lightning protection system is V0,
and we assume that the potential is zero far from the boat, then at a
particular point in between the potential has an intermediate value. A region or surface where the potential
has the same value is termed an equipotential.
This is the case inside and on the surface of a conductor. Close to a conductor, the equipotentials are surfaces that have a similar shape
to the surface of the conductor.
For example, the lightning protection system and all conductors
connected to it approximate an equipotential
region at potential V0.
If the lightning protection system consists of one long cylindrical
down conductor, then the equipotential surfaces
are also cylindrical as shown in Figure
4‑1. The
potential at any point on an equipotential
surface is at the potential of that surface. For example, the point shown in Figure 4‑1 is at the potential V1, where V0 > V1 > 0.
Figure 4‑1 Equipotential
surfaces around cylindrical
conductor
If a very thin conductor with no excess charge is now
inserted parallel to the down conductor at the point shown in Figure 4‑1, it does not change the situation so that its
potential is equal to that of the equipotential
surface that it lies on, V1, and the shapes of the
equipotential surfaces are the same as
before. However, if the uncharged
conductor is not very thin, the shapes of all of the equipotential
surfaces are changed to satisfy the condition that the conductor surface is
also an equipotential, as shown in Figure 4‑2. This
distorts the shapes of all the equipotential
surfaces. While the actual potential
of the conductor may still be close to V1, the equipotentials
between the conductor and the cylindrical conductor are compressed so that
the potential gradient is increased in this region.
Figure 4‑2
Equipotential surfaces around cylindrical
conductor in vicinity of isolated conductor
4.2.
Electric field
4.2.1.
Relation to potential
The equipotential lines on a
two-dimensional plot such as in the above figures are analogous to contours
on a topographical map. Where
contours are more closely spaced, the gradient of the land is steeper. Also, an object falling down a slope
moves across the contours at right angles.
The electric field represents the gradient of the equipotentials and also crosses each equipotential at a perpendicular. In fact, the electric field is defined as
the negative of the potential gradient.
Since in three dimensions the equipotentials
are surfaces, the electric field is parallel to the normal, where a normal
is a vector that is perpendicular to all lines drawn in the surface. In an equipotential
region, that is, a volume where the potential is constant, there is no
gradient and therefore no electric field.
For a perfect conductor the surface is an equipotential
so that any electric field is parallel to the normal. Also, the interior volume of a perfect
conductor is an equipotential region so that
there is no electric field inside.
Metallic fittings can be regarded as perfect conductors for
virtually all lightning processes.
4.2.2.
Electric field in water
When current flows from the lightning protection system
into the water through a grounding electrode, a current density field is
established in the water. The shape of
this depends on the geometry of the electrode, the hull/water boundary, and
the injected current from other electrodes.
In contrast to metallic fittings, a significant electric field
accompanies this current flow so that the surface of the water is not
necessarily an equipotential surface. A reasonable approximation for this
relationship is  where J
is the current density (in A/m2), σ is the conductivity (in
mho/m), and E the electric field
(in V/m). The magnitude of the
current density depends only on the current provided by the lightning, not
the ground impedance. Since fresh
water has about 1/100 the conductivity of salt water, electric fields, and
hence voltages, are much larger in fresh water. This electric field (or voltage gradient)
is fundamental to the problem of sideflash
initiation which is thus much more of a problem in freshwater than
salt.
At a high enough value of the electric field (about 107V/m),
the forces on individual air (or water) molecules become high enough to
separate out electrons that are then free to move in the general direction
of the electric field. That is, the
air becomes a conductor and a spark is formed, usually from the surface of
a conductor in a perpendicular direction.
Where the spark is most likely to start can hence be deduced from a
plot of the equipotential surfaces by noting
where the equipotentials are most closely
spaced. While a complete
quantitative analysis is best, much insight can be obtained from simple
sketches. For example, in the
situation shown in Figure
4‑1 and Figure
4‑2 the
introduction of the finite conductor results in a larger electric field at
its inner and outer extremities. If
either, or both, of these exceed the breakdown field, sideflash
initiation is likely.
In a more practical example, consider the case of the
water tank shown in Figure
4‑3. The tank
is near a lightning conductor and grounding electrode that are at a
potential V0 The current
density in the water (ground medium) is assumed radial so that the equipotential surfaces are hemispherical as shown. Since the water in the tank is
conducting, the equipotential surface on the tank
surface is the same shape as the tank. The corners of the tank compress the
equipotential surfaces just outside it and result
in a local enhancement of the electric field. As a consequence the inside upper corner
is likely to form a sideflash to the lightning
conductor, and the outside lower corner to the water.
Figure 4‑3
Equipotentials and probable sparking
points on water tank
One way to eliminate the risk of the sideflash
between the tank and the lightning conductor in Figure 4‑3 is to
connect the two conductors, that is, bond them together so that their
potential difference becomes zero and the local electric field is close to
zero. By equalizing the potentials of the two conductors the region between
them is thus much less hazardous to crew members in this vicinity. However, the bonding connector now
changes the potential distribution in that the tank is now at the same
potential as the down conductor, as shown in Figure 4‑4. The equipotentials become more concentrated on the outer
edge of the conductor and so increase the risk of a sideflash
from this edge, as shown in Figure
4‑4. This risk
is magnified if the conductor is close to the water.
Figure 4‑4 Equipotential surfaces near conductor bonded to down
conductor
Another technique for equalizing potentials is
shielding. This is based on the
principle that no electric field exists inside a volume surrounded by a
closed equipotential surface as long as each
conductor inside the volume is uncharged.
Since electric field represents a changing potential with distance,
a zero electric field implies a constant potential, that is, the whole
volume is an equipotential region. The most
common method to ensure that an equipotential
surrounds a region is to use a conductor surface to provide the equipotential surface and region, that is, to construct
a Faraday cage. The conductor to
be protected should be inside the shielding conductor, with the lightning
down conductor outside. The down conductor may be either bonded or not,
depending on the relative sideflash hazards
discussed above. This technique
works well for small portable instruments.
However, the increased sideflash risk from
the lower corners of the Faraday cage means that this technique cannot be
used near the water.
4.3.3.
Grounding
While it is straightforward to simulate the top three
sides of a Faraday cage with down conductors, the bottom of the cage needs
to be in the water to avoid sideflashes as noted
above. In fact, if a long grounding
electrode is immersed in the water directly below the conductor the risk of
a sideflash from the bottom of the conductor is
effectively eliminated, as shown in Figure
4‑5. Since the
vast majority of sideflashes propagate towards
the water, the shapes of grounding electrodes are more important than the
down conductors above the conductor
Figure 4‑5
Strip grounding electrode below unbonded
conductor
However, it is impractical to construct a network of
grounding strip electrodes, which is what is needed to give effective
shielding in three dimensions. An alternative
technique is to surround the conductor at risk with point electrodes that
inject current into the water in such a pattern as to reduce voltage
gradients in the vicinity of the conductor's corners. That is, the electrodes reduce the
potential difference between the corners of the conductor and the water
nearby, as shown in Figure
4‑6.
Figure 4‑6
Point electrodes below unbonded conductor
Note that in both Figure 4‑5 and Figure
4‑6 the potential of the conductor is close to that
of the lightning protection system even though the two are not bonded so
that the risk of a sideflash between the down
conductor and the conductor is virtually eliminated.
5.1.
Quasi-static field model
Consider a simple model where current i(t) is flowing into a lightning
protection system comprising an immersed grounding electrode and a single
conducting fitting that is bonded to the system. The potential of the whole system is v(t), where ground potential is an
infinite distance away. Conduction
current flows from the grounding electrode into the water and gives rise to
a current density j(t) in the water. Charge buildup on the conducting fitting
gives rise to an electric field Ec(t) which has a maximum value at same
point on the fitting of Emax(t). The situation is illustrated in Figure 5‑1.
Figure 5‑1
Model for field prediction
If we assume that the dimensions are much smaller than a
wavelength, then both the current density and electric fields are
quasi-static and electrostatic concepts can be applied. In this case the electric field at a particular
point is proportional to the voltage, and, in particular,
where the constant of
proportionality (Emax/V) is a geometrical factor. Electrical breakdown occurs if Emax(t) exceeds the critical field
strength, about 107 V/m in air.
It is useful to express this factor in terms of an equivalent
distance, deff
where
5.2.
deff
versus conductor geometry
The potential field from a charged conducting fitting raised to a potential V0 in the vicinity of a ground plane can be found by
solving La Place's equation in the region between the ground plane and the
conductor by using the method of images.
This has already been down for several simple geometries:-
(i) long cylindrical rod
perpendicular to the ground plane
(ii) sphere
(iii) long cylinder parallel to the plane
(iv) infinite plate parallel to
the ground plane.
These geometries are illustrated in Figure 5‑2.
Figure 5‑2
Conductor geometries
Once the solution for the potential field has been
found, the electric field is calculated as
and the point on the conductor
can be determined where E has a
maximum value, which is generally at the closest point to the ground
plane. If the value of the electric
field at this point is E0 then
 
Figure
5‑3 shows this factor in a dimensionless form of deff/d versus R/d on a semilog scale. The additional plot of deff =R is included to
demonstrate that the effective distance is equal to the radius for both a
sphere and perpendicular rod if d>>R, that is, the
conductor is many radii above the ground plane. Note that deff for a
perpendicular rod is about an order of magnitude smaller than that for a parallel rod of the
same size and spacing, while deff
for a plate is much larger than that for both rod and cylinder for
d>>R, approaches the rod but becomes smaller than the cylinder for
d<<R (conductor close to ground plane).
Figure 5‑3
Geometrical factors for conductor shapes
5.3.
Circuit equivalent
The equivalent circuit corresponding to Figure 5‑1 is shown in Figure
5‑4.
Figure 5‑4
Equivalent circuit
Rg is the resistance of the grounding
electrode and Cg is
its capacitance, both with respect to a ground potential at infinity. These are related by
where
is the relaxation time of the
water, ε is the permittivity of the water and σ the water's
conductivity. For salt water
is less than a nanosecond, while in fresh water, is about a microsecond. With rare exceptions (for example, a
large SSB ground plate) the capacitance of a conducting fitting is much
smaller than Cg. Since the lightning current splits
between the grounding electrode and the fitting, continuity of current
gives
where the first term in is the conduction current
and the second term the displacement current. Two situations are of interest: t>>,
when conduction current determines the voltage, and Rg=, when charge accumulation
dominates the voltage.
5.3.1.
Current dominant regime, t>>
In this case the conduction current predominates, that
is the situation is ohmic. This corresponds to the usual
interpretation for lightning grounding.
Terms such as "ground resistance" and "step
potential" imply this linear and in-phase relationship between voltage
and current. Since the relaxation
times in water are smaller than the characteristic time scales of most
lightning processes, the exception being the rise time of subsequent
strokes, it is a reasonable assumption if volume currents are flowing into
the water
In this case ground resistance can be calculated for
various geometries of grounding electrode.
Table 1 gives the ground resistance and peak voltage expected for a
30kA return stroke current.
|
Electrode type
|
Water type
|
Resistance
|
Voltage for 30kA return stroke
|
|
0.1
m2 circular plate
|
Fresh1
|
1.45 kW3
|
44 MV
|
|
Salt2
|
0.36 W3
|
11 kV
|
|
9.3 mm x 10m strip
|
Fresh1
|
235 W3
|
7 MV
|
|
Salt1
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60 mW3
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2 kV
|
1
Conductivity = 10-3 S/m 2 Conductivity = 4
S/m 3 IEEE Trans. EMC, 33,
132-138, 1991
Table 1
Resistance and peak voltage for 30kA current versus electrode shape
Rewriting as
we can determine a critical value of deff that results
in a breakdown electric field of 3x106 V/m if the potential of
the lightning protection system is V0 from
or, in terms of the current I
Table 2 gives values of this critical deff for two
lightning processes – an attachment streamer with assumed current of
500A and a return stroke with a peak current of 30kA.
|
Electrode type
|
Water type
|
Rg
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Critical deff
|
|
Attachment
I=500 A
|
Return stroke
I=30 kA
|
|
0.1
m2 circular plate
|
Fresh1
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1.45 kW
|
24 cm
|
1.5 m
|
|
Salt2
|
0.36 W
|
61 mm
|
0.4 mm
|
|
9.3mm x 10m strip
|
Fresh1
|
235 W
|
4 cm
|
23 cm
|
|
Salt2
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60 mW
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10 mm
|
60 mm
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Table 2 Critical values of effective distance for
attachment streamer and return stroke peak
Since deff can be generally interpreted as the
minimum radius of curvature for a perpendicular fitting that is not close
to the waterline, Table 2 indicates whether a fitting is likely to form a sideflash. In
the case of a boat in fresh water, even a lightning protection system with
the more effective ground strip is likely to initiate sideflashes
from almost any fitting. Fittings
that are further from the lightning grounding electrode, closer to the water, and with smaller radii of curvature are the ones
most likely to breakdown first.
5.3.2.
Charge dominant regime, Rg=∞
If a grounding electrode is not in perfect electrical
contact with the water, a rise in potential is not accompanied by ohmic conduction current flow since the conduction
current is zero. In this case the lightning current flowing in the
lightning protection system becomes displacement current out of Cg and Cc and the system
voltage, and electric field, is proportional to charge. For the maximum electric field on a
conducting fitting
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