1. 2015 International Conference on Lightning and Static Electricity (Toulouse, France)
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ELECTROMAGNETIC MODELING OF RETURN
CONDUCTOR CONFIGURATIONS USING THE FINITE
ELEMENT METHOD
Justin P. McKennon*
*Lightning Technologies, an NTS Company,USA. jmckennon@nts.com
Keywords: Finite Element Analysis, Boundary Conditions,
COMSOL Multiphysics, Return Conductor
1 Abstract
Return conductor networks are typically used to provide a
low inductance return path back to the generator during most
full vehicle tests and tests of other large objects. There are
several commonly used methods of return networks, the most
popular of which are coaxial return arrays and ground planes.
During the construction of these arrays, practical
considerations often take precedence over the intended design
due to facility constraints, time, materials, and accessibility
issues. While conducting tests, it is not uncommon for wires
to be moved, droop, or fall, and the impact of these changes
on measurements and current flow is not well understood.
Utilizing the finite element method in COMSOL
Multiphysics, these effects can be accurately calculated. In
this work, a sample wing box is constructed in COMSOL
with several ribs and spars. A coaxial return array and ground
plane return network are modelled, with common routing and
configuration defects analyzed.
2 Introduction
The rationale for making use of a coaxial return array
configuration can be explained by examining the magnetic
fields within hollow conductors. If there are two conductors
carrying equal current in the same direction, the fields
produced by the two conductors cancel along a long
equidistant from the two conductors. The fields at other points
do not cancel, but their sum is lower than in the space outside
the conductors [1]. If there are three equally spaced parallel
conductors carrying equal currents, the fields are further
reduced in the intervening space between the conductors [1]
[2]. The more conductors carrying identical currents that are
arranged in a cylindrical configuration, the more magnetic
field cancellation occurs within the cylinder. If an infinite
number of parallel conductors are arranged in this
configuration so that they merge, forming a near solid tube,
the magnetic field due to currents on the tube becomes zero
everywhere inside the tube [1] [2]. Thus, by making use of
these principles, the impact of the return path on the test
object and measurements can be greatly reduced with the
aircraft or test object acting as the center conductor and the
return path as the outer conductor.
The further the return conductor array is from the surface of
the aircraft, the less the fields created by current travelling in
the conductor interact with the aircraft or test object inside the
array. However, due to practical limitations, the separation of
the wires is generally limited to 1-2 meters, which is a
common height that landing gear and test support objects are
able to raise the object above the ground. Wires are generally
held in place by return array stanchions such as those shown
below in Figure 1 [2].
Figure 1- Typical Stanchion Support of Return Conductors
Due to the randomness associated with taking measurements
(changes in applied current between injections, facility noise,
etc.) it is very difficult to characterize the influence of the
wires on the test object. Thus, in order to accurately
determine the influence of the return wires on the test object,
a geometrically accurate representation of the test setup must
be developed, including the array, and the fields and current
densities must be calculated.
Another common return network configuration involves the
use of a ground plane. Current is returned from the root of the
test object along a ground plane under the test object, which
connects to the generator to complete the circuit. Large test
objects often make use of this technique due to it being much
easier to implement than the return array. The intent of this
configuration is to minimize the influence of the return
current on the test object, due to the current density anywhere
in the ground plane being small [2].

2. 2015 International Conference on Lightning and Static Electricity (Toulouse, France)
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Using software packages such as COMSOL Multiphysics,
highly accurate models of test objects (often derived directly
from Computer-Aided-Design (CAD) files) can be solved
analytically determining the field levels and current densities
associated with a test, without any of the issues associated
with noise or measurement challenges. COMSOL in
particular employs the Finite Element Method to solve
systems of partial differential equations that represent the
entirety of the physics interactions occurring in the model.
This paper focuses on the simulation and analysis of a
representative wing section in various return array
configurations through the use of the Finite Element Method
in COMSOL.
3 Model Development
3.1 Model Geometry
The model used in this work is that of a representative
aluminium wing section. The upper and lower wing skins are
both 0.2” thick, as are the forward and aft spars. Two
representative conductors are routed through the structure and
there are two apertures; one corresponding to an access panel
that may not be installed fully, and the second corresponding
to a NACA scoop as shown in Figure 2.
Figure 2 - Apertures in Geometry
200kA of the quad exponential analytical waveform for
Current Component A, defined in [3], is injected at 8 discrete
points intended to represent the redistribution of current that
occurs during an outboard wing tip strike. The injection
points are shown in Figure 3.
Figure 3 - Injection Points
Current flows through the wing structure and is removed at
the opposite end with connections to the return conductor
array. The ideal setup for the return array, in a pure coaxial
configuration – essentially an infinite number of infinitely
close return conductors, is shown in Figure 4.
Figure 4 - Ideal Return Array Setup
This configuration serves as the control for this research. The
effects of the return network on the test article are negated in
this configuration, allowing for the “True” values associated
with measurements to be obtained in this model.
3.2 Model Boundary Conditions
In order for the current density, electric fields, and magnetic
fields to be determined in an analytical model, proper
boundary conditions must be applied in order for the
governing mathematical equations to be solvable. This work
makes use of the Radio Frequency (RF) module in COMSOL
to do so. This work uses a 3D formulation of Maxwell’s
Equations to calculate the electromagnetic fields and current
densities, shown in Equation 1.
(1)
In (1), the magnetic vector potential, A, is solved for, and the
associated current densities and fields are determined. The
constitutive relations, and specific material parameters
(conductivity (σ), permittivity (ɛ), permeability (μ)), are
specified for each domain in the model. This allows for
different material types – aluminium, air, copper – to be
applied on various domains throughout the model to influence
the electromagnetic fields and flow of current accordingly.
One additional boundary condition is specifically used in this
model and warrants discussion. The Perfect Electrical
Conductor (PEC) boundary condition is applied
on all exterior surfaces to limit the solution to the model to a
finite size. This boundary condition sets the tangential
components of the electric potential to zero. It imposes
symmetry for electric and magnetic fields, and any current
flowing into a boundary with the PEC condition applied is
perfectly balanced by induced surface currents. This allows
for the PEC boundary condition to function as a way to

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“Ground” the model and provide a way for any displacement,
conducted, and induced surface currents to be grounded. The
PEC boundary condition, in this work, is applied on all
exterior surfaces in the air domain of the model, as well as on
the connections to the return array conductors.
3.3 Mesh
The Finite Element Method is a numerical technique for
finding approximate solutions to systems of differential or
partial differential equations that are governed by boundary
conditions. At its core, the finite element method divides the
generated model geometry into smaller pieces – finite
elements – and uses variational methods to solve the problem
by minimizing the associated error function and achieve
convergence.
Once the geometry has been developed and the boundary
conditions have been applied, the model needs to be meshed.
COMSOL provides a robust, automatic meshing algorithm
that performs much of the meshing without need for user
input. Care must be taken to analyze the generated mesh and
ensure that sufficient mesh density exists in the regions of
interest in the model. The determination of the proper mesh
density falls outside the scope of this work. Using the
automatic meshing algorithm in COMSOL, Figure 5 is
produced.
Figure 5 - Meshed Model
4 Results
4.1 Nominal Coaxial Configuration
The wing model was first simulated in an ideal array
configuration, with no defects present in the geometry of the
return array to serve as a control for this work and provide a
basis for comparison. This configuration is a pure coaxial
geometry, with all of the current being returned along the
model boundaries to the current source. This is equivalent to
an infinite number of infinitely close return conductors.
Figure 6 shows the nominal configuration.
Figure 6 - Ideal Return Array
This configuration serves to demonstrate the current density
in the various components in the model, without the exterior
influence of any individual return conductors contributing to
the measurements. A plot of the current density, at 6.4 μS in
log base 10 scale, is shown in Figure 7.
Figure 7 - Current Density in Wing Box with Ideal Array
Configuration
As shown, the current density is concentrated at the edges of
the model. The skin effect, caused by the presence of eddy
currents in the Ribs, can also be seen in Figure 7.
Surface current density measurements in the upper wing skin,
FWD and AFT Spars, and on the lower wing skin near each
aperture were taken. The location of these measurements is
shown in blue in Figure 8. Figure 9 shows the measured
surface current densities at each location under the Ideal
Array Configuration.
Figure 8 - Surface Current Density Measurement Locations
on Exterior Surfaces

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Figure 9 - Ideal Return Array Surface Current Density
Measurements
4.2 Array Configuration With Uniform Spacing
Since physical limitations (size, space, inductance, and
accessibility) prevent the use of the nominal configuration
shown in section 4.1, actual tests are run with a finite number
of conductors in the return array. The number of conductors
varies between individual tests and test articles; however the
most common array configuration involves several wires
encompassing the wing circumferentially. The configuration
used in this work has uniformly spaced conductors (in
relation to both the test object and one another). Each wire is
12 inches from the test article, and 18 inches from adjacent
wires. This spacing remains constant throughout the length of
the article, and is shown in Figure 10.
Figure 10 - Uniform Return Conductor Array Geometry
The same measurements described in section 4.1 were taken
with the uniformly spaced array conductors, and are shown in
Figure 11.
Figure 11 - Uniform Return Array Surface Current Density
Measurements
4.3 Array Configuration without Uniform Spacing
In order to take measurements during actual testing, parts of
the test article need to be opened, closed, moved, or altered. It
is not uncommon for the wires of the array to be moved
accidentally, or repositioned to accommodate personnel or
test equipment. Additionally, due to laboratory space and
inductance constraints, it may not be possible to uniformly
space the conductors. In Figure 12, a random, 10% variation
in conductor-to-conductor and conductor-to-test-object
spacing is introduced. This randomly displaces each of the
wires in the array from their uniform locations.
Figure 12 - Random Spaced Conductor Geometry
Figure 13 shows the surface current waveforms in this
configuration.
Figure 13 - Non-Uniform Return Array Surface Current
Density Measurements

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4.4 Array Configuration with Uniform Spacing and
Sagging Wires
During some tests, it is not uncommon for individual wires in
the array to sag or droop. When this happens, the rest of the
array can stay intact (with the intended spacing), but one or
multiple wires can hang closer to, or further away from, the
test article. This is most common on wires routed along the
upper wing skin (wire sags closer to the surface) and lower
wing skin (wire sags further away from surface). Figures 14
and 15 show the sagging wires in this configuration. In each
case, the wire is sagging 4 inches from the uniform
configuration. Figures 16 and 17 show the surface current
density measurements in each configuration.
Figure 14 - Wire Sagging Away from Lower Wing Skin
Figure 15 - Wire Sagging Towards Upper Wing Skin
Figure 16 - Wire Sagging Away from Lower Wing Skin
Surface Current Density Measurements
Figure 17 - Sagging Wire Towards Upper Wing Skin Surface
Current Density Measurements
4.5 Ground Plane Configuration
In situations where it is not possible to suspend wires above
the test article, a common approach is to make use of a large
ground plane. This technique is commonly used by
manufacturers of large transport aircraft. Figure 18 illustrates
this test setup. Figure 19 shows the measured current densities
in this configuration.
Figure 18 - Ground Plane Configuration
Figure 19 - Ground Plane Surface Current Density
Measurements
4.6 Magnetic Field Intensity Seen by Conductors
Through Apertures
The simple deviations from the nominal configuration
described in 4.1 - 4.5 all produce changes in the surface
current density measurements throughout the test article.
Since the goal of the coaxial configuration is to reduce the
magnetic fields seen by the center conductor, these deviations
from the ideal design all cause changes in the magnetic fields
that penetrate apertures in the test article. The test article in
this work has both a NACA Scoop, and an access panel that

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serve as electromagnetic apertures. These apertures allow
time-varying magnetic flux to pass through them, and interact
with conductors inside the test object. In most cases, the
magnetic flux coupling from exterior sources that occur here
is not representative of the actual in-flight aircraft
environment. During flight, all access panels are securely
closed, providing electromagnetic shielding for the
conductors inside the wing. For example, if during testing, an
access panel is left un-installed or poorly installed (missing
fasteners), the magnetic fields generated by the test setup are
allowed to interact with the conductors, potentially skewing
measurement data. Each of the simple defects described in 4.2
– 4.5, all cause variations in the intensity of the magnetic field
seen by conductors passing near these apertures. Figure 20
shows the magnetic field intensity throughout the test article
in log base 10 scale and the magnetic flux coupling with
interior conductors occurring through apertures in the test
article (NACA Scoop, Access Panel). Figures 21 and 22 show
the measured magnetic field intensities seen by the lower
conductor in the NACA Scoop Bay (Figure 21) and the
Access Panel Bay (Figure 22) for the configurations described
in 4.1 - 4.5.
Figure 20 - Magnetic Flux Coupling with Interior Conductors
Figure 21 - Magnetic Field Intensity Seen by Lower
Conductor in NACA Scoop Bay
Figure 22 - Magnetic Field Intensity Seen by Lower
Conductor in Access Panel Bay
5 Results
As shown in 4.1-4.6, each return array configuration produces
varying results. Table 1, shown below, compares the peak
surface current density measurements for each of the
configurations to the ideal configuration for the FWD Spar,
Aft Spar, Upper Wing Skin, and Lower Wing Skin
Measurements near the NACA Scoop and Access Panel.
Table 2 summarizes the magnetic field intensity data seen by
the lower conductor in the NACA Scoop and Access Panel
bays.
Table 1 - Surface Current Density Comparison Data
Configuration FWD
Spar
(A/m)
AFT
Spar
(A/m)
Upper
Wing
Skin
(A/m
Lower
Wing Skin
NACA
(A/m)
Lower Wing
Skin Access
Panel (A/m)
Ideal 8,100 8,300 33,600 33,800 33,200
Uniform 8,900 9,400 34,100 31,900 32,000
Random 9,000 10,000 34,400 31,000 30,900
Upper
Wire Sag
8,200 9,500 35,800 31,800 31,000
Lower
Wire Sag
8,500 9,800 35,000 31,500 31,450
Ground
Plane
8,500 8,000 27,000 38,500 40,100
Table 2 - Lower Conductor Magnetic Field Intensity
Comparison Data
Configuration Magnetic Field Intensity
Lower Conductor in
NACA Scoop Bay (A/m)
Magnetic Field Intensity
Lower Conductor in
Access Panel Bay (A/m)
Ideal 1,600 3,300
Uniform 1,400 3,600
Random 1,340 3,700
Lower Sag 1,300 3,350
Ground Plane 1,300 5,100

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6 Conclusion
In this work, several common return array configurations
were examined. An ideal coaxial return arrangement, in
which the magnetic fields generated by the return conductors
are very low, serves as the control for this research. Since the
ideal array is not attainable, the currently accepted best
practice is to uniformly space several conductors
circumferentially around the wing. Comparing the surface
current density measurements between the ideal and realistic
return arrays shows that the uniform configuration can serve
as an appropriate return configuration. With variations in the
surface current density measurements being less than 2,000
A/m between the two, in addition to comparable magnetic
field intensity measurements, it is reasonable to state that
measurements taken within a uniform return configuration are
acceptable. The ground plane return configuration produces a
significantly different current distribution, skewed towards
the lower wing skin area. Since the return is below the test
object, the path of least resistance is through the lower skin,
which explains the increased current density and magnetic
field readings.
However, as defects are introduced into the uniform array, be
it through improper spacing or sagging wires, the surface
current density also changes. With a variability in spacing
(conductor to conductor /conductor to test object) of 10% (or
less than 2 inches), the current density measurements change
by several hundred A/m (for a 200kA test current). During
actual testing, these distances can certainly be larger than 2
inches (from the uniform location), and the impacts of these
non-uniformities will continue to increase, especially near
apertures.
To summarize, the currently accepted method of a coaxial
return array provides a suitable return path for the current,
with minimal impact on the test object and measurements.
Deviations from this uniform array do have an impact
proportional to the distance the wire is located away from its
uniform (intended) location.
Poorly constructed arrays, or arrays that have been
unintentionally modified during testing, can skew data and
yield potentially misleading data as a result. Care must be
taken to ensure that the array stays in the uniform
configuration as much as possible, as deviations in return
conductor routing locations will alter current flow and impact
measurement data, providing an unrealistic aircraft
environment.
7 References
[1] Wieting, T, et al.: ‘Electromagnetic Field
Investigations Inside a Hollow Cylinder’,
International Journal for Computation and
Mathematics in Electrical and Electronic
Engineering, April 1995, pp. 223-227
[2] Fisher, F., Perala R., and Plumer, J.A.: ‘Lightning
Protection of Aircraft’ (Lightning Technologies,
2004, 2nd
edn)
[3] SAE ARP 5412B: ‘ Aircraft Lightning Environment
and Related Test Waveforms’, 2013