Memoria Investigaciones en Ingeniería, núm. 29 (2025). pp. 190-204
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Computational study of the direct impact of a 200 kA lightning strike on
external floating roof tanks
Estudio computacional del impacto directo de un rayo de 200 kA sobre tanques
externos de techo flotante
Estudo computacional do impacto direto de uma descarga atmosférica de 200 kA
em tanques externos de teto flutuante
Juan David Losada Losada
1
(*), Darwin Marín Yépez
2
, Camilo Younes Velosa
3
Recibido: 09/08/2025 Aceptado: 14/10/2025
Summary. - This study investigates the electromagnetic behavior of external floating roof tanks subjected to a direct
200 kA lightning strike. Using computational electromagnetics, electric and magnetic fields were calculated for two
scenarios: with and without the use of bypass conductors, as recommended by API RP-545. Simulation results revealed
that electric field values at the junction between the tank wall and the floating roof exceed 200 kV/m in the absence of
bypass conductors, increasing the risk of ignition. The implementation of bypass conductors significantly reduced the
field intensity, indicating their effectiveness in mitigating fire hazards in flammable storage environments.
Keywords: Lightning; floating roof tank; computational electromagnetism.
1
Docente. Facultad de Ciencias e Ingeniería de la Universidad de Manizales (Colombia),
jlosada@umanizales.edu.co, ORCID iD: https://orcid.org/0000-0001-9935-9977
2
Docente. Facultad de Ciencias e Ingeniería de la Universidad de Manizales (Colombia),
dmariny@unal.edu.co, ORCID iD: https://orcid.org/0000-0002-2709-361X
3
Docente. Facultad de Ingeniería y Arquitectura de la Universidad Nacional de Colombia (Colombia),
cyounesv@unal.edu.co, ORCID iD: https://orcid.org/0000-0002-9685-8196
J. D. Losada Losada, D. Marín Yépez, C. Younes Velosa
Memoria Investigaciones en Ingeniería, núm. 29 (2025). pp. 190-204
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Resumen. - Este estudio investiga el comportamiento electromagnético de tanques externos con techo flotante
sometidos a la descarga directa de un rayo de 200 kA. Mediante electromagnetismo computacional, se calcularon los
campos eléctricos y magnéticos para dos escenarios: con y sin el uso de conductores de derivación, según lo
recomendado por API RP-545. Los resultados de la simulación revelaron que los valores del campo eléctrico en la
unión entre la pared del tanque y el techo flotante superan los 200 kV/m en ausencia de conductores de derivación, lo
que aumenta el riesgo de ignición. La implementación de conductores de derivación redujo significativamente la
intensidad del campo, lo que indica su eficacia para mitigar los riesgos de incendio en entornos de almacenamiento
inflamables.
Palabras clave: Descarga atmosférica; tanque externo con techo flotante; electromagnetismo computacional.
Resumo. - Este estudo investiga o comportamento eletromagnético de tanques de teto flutuante externo submetidos a
uma descarga direta de raio de 200 kA. Utilizando eletromagnetismo computacional, calcularam-se os campos
elétricos e magnéticos para dois cenários: com e sem o uso de condutores de bypass, conforme recomendado pela API
RP-545. Os resultados das simulações revelaram que, na ausência de condutores de bypass, os valores do campo
elétrico na junção entre a parede do tanque e o teto flutuante ultrapassam 200 kV/m, aumentando o risco de ignição.
A implementação dos condutores de bypass reduziu significativamente a intensidade do campo, demonstrando sua
eficácia na mitigação de riscos de incêndio em ambientes de armazenamento de líquidos inflamáveis.
Palavras-chave: Descargas atmosféricas; tanque de teto flutuante; eletromagnetismo computacional.
J. D. Losada Losada, D. Marín Yépez, C. Younes Velosa
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1. Introduction. - Colombia is a tropical country characterized by distinctive atmospheric conditions and high
lightning density. The nation possesses abundant oil resources and continues to expand its exploration, production,
transportation, and refining sectors. The most commonly used oil storage tanks include fixed roof tanks, external
floating roof tanks, and internal floating roof tanks.
This study focuses on external floating roof tanks, analyzing the effects of direct lightning strikes and reviewing the
applicability of the API RP-545 (2009) standard within the context of Colombia’s atmospheric activity [1]. Previous
research on hydrocarbon storage tank fires has demonstrated a significant probability of ignition resulting from direct
lightning strikes, with external floating roof tanks presenting the highest associated risk [2]–[5].
The objective of this research is to assess the effectiveness of bypass conductors in mitigating the risk of ignition
caused by direct lightning strikes on external floating roof tanks through electromagnetic field simulations. Electric
and magnetic fields were computed using FEKO simulation software for two configurations: one without bypass
conductors (Case I) and another incorporating bypass conductors as recommended by API RP-545 (Case II).
2. Methodology. – This study employed computational electromagnetics to evaluate the transient electromagnetic
fields generated by a direct 200 kA lightning strike on an external floating-roof (EFR) tank. The analysis focused on
the critical roof–wall junction region, where high electric-field gradients can cause ignition in flammable vapor zones.
Ignition Criteria: Physical and Operational Justification
Two complementary criteria were employed to evaluate the ignition risk in the seal (rim) region:
(i) Field Criterion (screening): The operational threshold kV/m was adopted as a conservative indicator
of pre-breakdown conditions in non-uniform seal geometries. This threshold, widely referenced in EFR/TTE studies,
identifies regions exhibiting high electric-field gradients along roof–wall edges. It does not represent the planar air
breakdown field (~3 MV/m at 1 atm) but rather serves as an indicator of streamer or leader inception in configurations
with sharp edges, corners, and micro-asperities [6]-[9].
(ii) Energy criterion(decisive): The energy available within the seal gap is expressed as:
or, in the absence of prior conduction,
This is compared with the minimum ignition energy (MIE) of hydrocarbon-air mixtures, typically mJ
(for methane/propane/light gasoline vapors), with slight enhancement due to humidity and reduction near
stoichiometric conditions [1],[6].
Real Vapor Parameters
For light combustible vapors (e.g., gasoline), reported MIE values lie in the range of 0.15–0.30 mJ; for jet
fuel/kerosene, they are typically higher. The relevant gap length is approximately 10 mm (seal section), under ambient
pressure and relative humidity of 40–80 %. This analysis considers the following aspects:
• Composition: Concentration ranges between the LEL–UEL limits are evaluated; the representative case is near
stoichiometric conditions.
• Seal Geometry: Sharp edges and corners reduce the streamer inception field; therefore, is
considered conservative for this geometry.
• Leader Criterion (Rizk/ELI): The integral condition for leader inception in short gaps with small curvature radii
is discussed in the appendix (not included here for brevity) [9],[10].
Mechanism Distinction
• Direct Spark in the Gap: Characterized by high local electric fields within the seal region; governed by and
.
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• Induced Spark: Caused by non-uniform equipotential distributions around the rim; associated with
and transient currents induced in nearby metallic components.
• Potential Equalization (post-impulse): After the current front, residual currents may bridge weak gaps; is
evaluated over longer time windows together with .
2.1 Model of lightning current and calculation of electromagnetic field. - The lightning return channel was modeled
using a base current with a double-exponential waveform equivalent to the 10/350 µs impulse specified in IEC 62305,
adjusted to a peak current (representing the conservative level for the first stroke). The excitation is
injected at the channel base and coupled to the FDTD subdomain (rim box).
Temporal waveform and intensity
The following expression was adopted:
(1)
Where u(t) is the step function. To obtain a peak current with a front time of approximately
and a tail of 350 , the following reproducible parameters were set:
This produces and a maximum rate of current rise of approximately
, consistent with
IEC 62305. The Heidler model was parameterized in an appendix (not shown here) for cross-verification purposes
[11],[12],[13],[14].
Figure I. Double exponential model f lightning current for 200kA
The lightning channel was represented as a vertical thin wire of length L=2 km above the impact point (angular
perturbations of ±10° were included in the sensitivity analysis). The MTLE model (Modified Transmission Line with
Exponential Decay) was adopted for the spatial current distribution:
(2)
With a return velocity
and a characteristic length km. The coupling with the tank was solved
using a hybrid approach (thin-wire + FDTD).
Impact Point and Impedances
Two critical scenarios were considered: (i) impact at the rim (roof–wall junction), and (ii) impact at the roof center.
J. D. Losada Losada, D. Marín Yépez, C. Younes Velosa
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The effective grounding impedance of the tank–ring–down conductor–ground assembly was evaluated as:
(3)
for μs. Both peak and average values were reported over the front duration.
Sensitivity to and front time
Parametric sweeps were performed for and front times (by
adjusting a and b in Eq, (1)). The key metrics exhibited the following approximate dependencies:
With The 95% confidence interval (CI) band are included in figure II-IV.
Figure II. Design curve: at the rim versus N with 95% confidence interval (CI) band.
Figure III. Design curve: versus Contact resistance (logarithmic scale)
Figure III. Design curve: W in Gap versus immersion depth . Dashed line: MIE ≈ 0.2 mJ.
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Current and Voltage Paths
The current and voltage distributions were analyzed to characterize the transient coupling mechanisms at the roof–wall
interface. The induced roof–wall potential was obtained along the shortest path across the 10-mm seal gap, where the
highest electric field gradients occur, according to:
(4)
Bypass and down-conductor currents were calculated for each conductor as:
(5)
And the total current to ground through the down-conductors and peripheral ring was determined accordingly.
The available energy within the seal gap was evaluated using a dynamic resistive model valid prior to breakdown,
given by:
(6)
Which, in the absence of pre-breakdown conduction, can be approximated as:
(7)
The computed energy values were subsequently compared with the minimum ignition energy (MIE) of hydrocarbon–
air mixtures to assess the ignition risk at the seal region.
2.2 Numerical Modeling Using the Finite-Difference Time-Domain Method (FDTD). - To analyze the transient
electromagnetic coupling of a direct lightning strike on an external floating-roof tank (EFR), a three-dimensional
explicit FDTD model based on a Yee grid was employed, solving Maxwell’s equations in the time domain with a stable
and controlled space–time discretization. The approach was configured as a hybridization scheme, consisting of an
FDTD subdomain that encloses the roof–wall boundary region (the seal area)—where the highest field gradients
occur—and the macro-structure of the tank, the grounding system, and the return path, which were modeled using
impedance surfaces and thin-wire models. These were coupled through Huygens/equivalent field surfaces. This scheme
significantly reduces computational cost by several orders of magnitude without sacrificing accuracy in the critical
region.
Model Geometry
The tank was represented as a conductive cylinder with an external floating roof. The following geometric
parameters were defined for reproducibility:
• Roof type: External floating roof (EFR) of annular pontoon type; modeled as a conducting sheet with surface
impedance (equivalent to carbon steel).
• Main dimensions: Diameter D=16 m, shell height H=12 m; nominal thicknesses and
mm.
• Roof–wall clearance: Uniform gap mm (1 cm).
• Edge seal: Mechanical seal of brush/metallic type; an explicit air gap of (height) and mm
(width) was modeled within the roof–wall clearance. This gap defines the region of highest risk for dielectric
breakdown.
• FDTD subdomain (rim box): Rectangular prism following the roof perimeter.
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• Dimensions: axial length (full circumference), radial thickness (0.6 m inward + 0.6 m
outward from the tank wall), and height (centered at the seal elevation). This subdomain captures the
intense electromagnetic fields in the rim region; the remainder of the structure is treated through hybridization.
Grounding system and conductor modeling
Grounding system: A peripheral copper ring (cross-section 70 ) was buried at a depth of 0.5 m, connected to
four down conductors at 90° intervals, within a lossy soil medium. The effective grounding impedance of the
tank was measured during the first microseconds as , using potential and current probes.
Shunts: Copper conductors (50 ) were used to connect the roof and wall, with a submersion depth of 30 cm in
the liquid (following API practice). The contact resistance at mechanical joints was set to
Bypass conductors: For the mitigated configuration, copper bypass conductors (120 ) were added between the
upper edge of the wall and the roof, following the shortest possible length criterion, with a contact resistance of
Their distribution was uniform along the tank perimeter (sensitivity section not shown) for parametric analysis
purposes.
Computational domain and boundary conditions
FDTD subdomain (rim box): , centered at the seal. This local enclosure captures
the maximum values of and the transients
PML boundaries: Convolutional perfectly matched layers (CPML) were implemented on the six faces of the
subdomain, with a thickness of cells and a third-order polynomial conductivity profile (m=3):
(8)
Where is the normal coordinate to the PML, d= its thickness, the impedance of free space and
the target reflectivity.
This configuration ensures numerical reflections below -60 dB within the frequency band of interest.
Coupling with macro-structure: Huygens/equivalent field surfaces were used on the inner faces of the rim box to
exchange fields with the tank enclosure and the lightning channel (modeled using thin-wire/SIBC elements).
Spatial and temporal discretization
Meshing criteria. Two main restrictions were imposed: (i) Skin depth resolution in metallic materials, and (ii) geometric
resolution of the seal gap.
,
(9)
For MHz (a conservative value for a 10/350 µs waveform), mm and mm so the
SIBC/PEC assumption remains valid (t >> δ). The dominant restriction is geometric, due to the 10 mm seal gap. A
grid size of cm was adopted within the rim box, with a conformal/effective subcell for the gap an accepted
practice that reproduces local field gradients without sub-millimeter meshing.
Alignment with Recommended Practices (API RP-545, NFPA 30, API 2003)
Summary of Relevant Requirements (Implemented in the Model):
• Submerged Shunts: Immersion depth ≥ 0.3 m, spacing ≤ 3 m, sufficient metallic cross-section, and electrical
continuity. Implementation: copper shunts of 50 mm² cross-section, with immersion depth parameterized as
m.
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• Bypass Conductors: At least two, spaced ≤ 30 m (for , ; here ), with minimum
length and low contact resistance .
Implementation: copper conductors , with
• Seal and instrumentation insulation: Electrical isolation of seal components and guide/measurement devices (to
prevent spark trajectories).
Implementation: dielectric materials in the seal and joint treatment explicitly modeled.
NFPA 30 provides the operational safety context (ventilation, handling during storms), while API 2003 addresses
hazards associated with static electricity, lightning, and stray currents. The numerical model reproduces the mitigating
effect of these practices on , , and .
3. Results. - The storage tanks of hydrocarbons of external floating roof are those that present the highest probability
of a fire by atmospheric electric discharges [15], API-RP-545 standard presents a particular development in analysis
and approach to protection for this type of tanks [16],[17]. Before 2009, the tank's own protection systems were
developed in the shunt systems as an equipotential element between the tank roof and the tank wall, these equipotential
elements were built above the floating roof. The following table I summarizes the protection elements used in floating
roof tanks before 2009 and after 2009.
External floating roof tank
Analysis API-RP-545 standard
Before 2009
After 2009
Use of the norm API-2003
Use of the norm API-545
Use of Shunt above the floating
roof. Equipotential elements
Shunt immersed in the liquid at least 30 cm.
Equipotential elements canceling the oxygen
component before a possible spark produced by
lightning.
External protection with the
rolling sphere method.
Bypass conductors connected between the top of
the tank and the roof of the tank.
Electrical insulation of more than 1kV between
the elements of the roof of the tank and the wall
of the tank (seals, springs, scrapers.)
Table I. Tank protection elements based on API-545 standard.
A simulation was carried out to analyze the behavior of the electromagnetic fields in the external floating roof tanks,
analyzing two particular cases: case 1 with equipotential elements shunt between the roof of the tank and the wall without
making differentiation if it is immersed in the liquid or not.
The second case with equipotential elements shunt between the roof of the tank and the wall and adding bypass conductors
between the top of the wall of the tank and the floating roof according to API-RP-545.
A. Case I:
For the effects of the simulation, the equipotential bonding of the roof and the wall was carried out with the entire structure
of the tank with a direct impact of 200 kA. For simulation purposes, the entire surface of the tank roof was modeled to
electrical contact with the section of the wall surface.
A comparison is made between the magnitudes of the electromagnetic fields that are obtained when lightning directly
impacts the roof of the tank that is considered the most critical scenario.
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Figure III shows the behavior of the intensity of the electromagnetic fields at the point of impact and in the equipotential
bonding between the roof of the tank and the wall. The highest intensities occur in the wall of the tank at the high point and
in the equipotential bonding between the wall and the tank at the bottom point where the beam is impacting. According to
the reference of 200 kV/m as maximum potential in which sparks can be presented at points at different potentials [18], the
following results obtained in the simulation are analyzed. At the junction between the roof and the wall, there is the highest
probability that flammable gases and vapors are present and that is where the potentials of 240 kV/m maximum and 210
kV/m minimum occur.
Figure III. Electric field strength [kV/m] with equipotential shunt, isometric view
According to these results it has that for equipotential shunt elements both immersed in the liquid and located above the
tank before a discharge of 200kA there are values above 200kV/m, values that represent a high probability of ignition due
to atmospheric electrical discharges and in the presence of flammable vapors. Table II.
Results (E, B) for direct impact of 200kA.
On the roof of the external floating tank.
At the junction between the roof and the wall.
Electric field (kV/m)
Magnetic field
(kA/m)
Electric field
(kV/m)
Magnetic field
(kA/m)
Max. Value
300
12.5
240
5.4
Min. Value
30
1.5
210
4.8
Table II. Electric and magnetic field case I.
B. Case II:
For the effects of the simulation, the equipotential bonding of the entire roof with the rest of the tank structure of the tank
was performed and a direct impact of the first return discharge of 200kA of magnitude was made. Bypass conductors were
added between the top of the tank wall and the floating roof. The selected conductor is equivalent to a 120 mm2 copper
cable, to simulate the bypass conductor. For the simulated tank of 16 meters in diameter and 12 meters in height, 4 bypass
conductors were located.
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Figure IV. Electric field strength [kV/m] with equipotential shunt+ bypass, isometric view.
At the junction between the roof and the wall is where there is the highest probability that flammable gases and vapors
are present and that is where potentials of 150 kV/m maximum and 90 kV/m minimum occur. According to these
results, for equipotential shunt elements, adding a bypass conductor to a discharge of 200 kA has values below 200
kV/m, values that represent a considerable decrease in the probability of starting a fire in the face of an atmospheric
electrical discharge. And in the presence of flammable vapors.
Results (E, B) for direct impact of 200kA.
On the roof of the external floating tank.
At the junction between the roof and the wall.
Electric field (kV/m)
Magnetic field
(kA/m)
Electric field
(kV/m)
Magnetic field
(kA/m)
Max. Value
40
3.3
150
4.5
Min. Value
15
2.7
90
3.9
Table III. Electric and magnetic field case II.
The simulation results indicate that using only shunt equipotential is not sufficient in terms of protection because they
have values of more than 200 kV/m, which represents a high probability of starting a fire. By adding bypass conductors,
the values of electric field are in values lower than 200 kV/m, which decrease the probability of sparks in elements
that are not at the same potential.
4. Conclusions. - Numerical simulations of direct 200 kA lightning strikes on external floating-roof tanks reveal a
strong dependence of electric field intensity on the tank’s equipotential configuration. When only shunt conductors are
present—either immersed in the liquid or located above the floating roof—the maximum electric field at the roof–wall
junction exceeds 200 kV/m, reaching values between 210 kV/m and 240 kV/m. Such magnitudes correspond to pre-
breakdown conditions and a high probability of vapor ignition.
In contrast, the inclusion of bypass conductors as recommended by API RP-545 reduces the electric field in the critical
rim region to approximately 90–150 kV/m, well below the ignition threshold. This significant reduction confirms that
bypass conductors enhance potential equalization and effectively mitigate lightning-induced ignition hazards in
flammable storage environments.
The results support the adoption of API RP-545 mitigation practices in petroleum facilities, particularly in tropical
regions with high lightning density. Future work should integrate thermodynamic and gas-diffusion models to assess
the combined electromagnetic and chemical ignition mechanisms and validate the numerical findings through
experimental or field measurements.
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[18] Liu, Y.; Yakun, Z. F.; Analysis of the effect on the large floating roof oil tanks struck by indirect lightning based
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Appendix A.
Detailed Electromagnetic Formulation and Parameters
A.1 Electromagnetic Field Formulation
The radiated electromagnetic fields due to a time-varying current source were computed using the classical electric
dipole formulation, given by
where A is the magnetic vector potential, the current vector, the distance between the source and observation
point, and the wavenumber.
Assuming a thin dipole aligned along the z-axis, the potential reduces to
and the corresponding fields are obtained from
subject to the Lorentz condition.
A.2 Governing Maxwell equations
For time-domain simulation, Maxwell’s equations were expressed as
With constitutive relations and .
The discrete forms of Ampère’s and Faraday’s laws were implemented using the Yee cell scheme to ensure second-
order accuracy in both space and time.
A.3 Discretization and Stability (CFL Condition)
The Courant–Friedrichs–Lewy (CFL) condition for a 3D uniform grid is
where ensures numerical stability.
A grid step of cm and a maximum time step of 0.037 ns were used in all simulations, which yielded convergence
errors below 1.5 %.
A.4 Material parameters
Material
]
Model/Justification
Steel (roof/wall)
1.0
1.0
IBC; for f ≤ 1 MHz,
Copper
(bypass/shunts/rings)
1.0
1.0
Thin wires and bars modeled using SIBC or thin-wire
elements;
Hydrocarbon vapor
1.9
1.0
Typical range for light vapors; negligible transient losses.
Air (seal gap)
0
1.0006
1.0
10 mm x 10 mm air gap; conformal/effective subcell used
to capture the field gradient.
Soil (ground)
0.01
10.0
1.0
; equivalent half-space medium for
grounding.
J. D. Losada Losada, D. Marín Yépez, C. Younes Velosa
Memoria Investigaciones en Ingeniería, núm. 29 (2025). pp. 190-204
https://doi.org/10.36561/ING.29.12
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
203
A.5 Perfectly Matched Layers (CPML) and Mesh Independence
A convolutional perfectly matched layer PML with 10–12 layers and third-order conductivity profile (m=3) were
implemented on all domain boundaries to prevent spurious reflections. This configuration ensured numerical reflection
levels below −60 dB across the frequency range of interest, providing a stable and fully absorbing boundary condition.
To evaluate the spatial resolution required for numerical accuracy, a mesh-independence study was conducted using
the most demanding performance metric—the maximum electric field () within the seal gap under rim-impact
excitation (unmitigated case). Three nested meshes were tested while maintaining identical excitation conditions and
PML boundary parameters.
Mesh independence in the FDTD subdomain (rim box).
Cell size (cm)
in the seal (kV/m)
Relative error vs. 1 cm
4.0
18,500
12.3%
2.0
20,800
1.4%
1.0
21,100
---------
The results demonstrate monotonic convergence with mesh refinement. A spatial cell size of Δ=2 cm yields an error
below 1.5 % relative to the finest grid (Δ=1 cm), representing an optimal balance between numerical accuracy and
computational efficiency. For consistency, the PML thickness, conductivity profile, and Courant–Friedrichs–Lewy
(CFL) ratio were kept constant throughout all simulations.
A.6 Extended Validation and Uncertainty Analysis
A Latin Hypercube Sampling (LHS) analysis with N=200 simulations was performed by varying the soil resistivity
(100–1000 Ω·m), contact resistance ( Ω), and lightning impact position (±0.5 m).
The resulting median, interquartile range, and 95 % confidence intervals for , , and total bypass current
were consistent with analytical predictions, confirming model robustness.
A.7 Statistics, Sensitivity, and Uncertainty
Median values and 95% confidence intervals (CI 95%) were obtained for three key metrics under a 200 kA, 10/350 µs
lightning current waveform, considering variations in the number of bypass conductors (N), contact resistance (Rₐ),
and immersion depth (d₍ᵢₘₘ₎).
Representative values consistent with the parameter sweeps described in section 2 (Methodology) were adopted.
Configuration
Without bypass
(N=0)
20,800 [18,300, 23,300]
210 [180, 240]
0.45 [0.36, 0.54]
N = 4, S = 120 mm²
12,900 [11,600, 14,200]
120 [105, 135]
0.12 [0.10, 0.15]
N = 6, S = 95 mm²
10,700 [9,700, 11,800]
108 [95, 122]
0.10 [0.08, 0.12]
d₍ᵢₘₘ₎ = 0.5 m
----------
----------
0.06 [0.05, 0.07]
Rₐ = 1 × 10⁻² Ω
----------
158 [142, 174]
---------
J. D. Losada Losada, D. Marín Yépez, C. Younes Velosa
Memoria Investigaciones en Ingeniería, núm. 29 (2025). pp. 190-204
https://doi.org/10.36561/ING.29.12
ISSN 2301-1092 • ISSN (en línea) 2301-1106 – Universidad de Montevideo, Uruguay
204
Author contribution:
1. Conception and design of the study
2. Data acquisition
3. Data analysis
4. Discussion of the results
5. Writing of the manuscript
6. Approval of the last version of the manuscript
JDLL has contributed to: 1, 2, 3 4, 5 and 6.
DMY has contributed to: 1, 2, 3 4, 5 and 6.
CYV has contributed to: 1, 2, 3 4, 5 and 6.
Acceptance Note: This article was approved by the journal editors Dr. Rafael Sotelo and Mag. Ing. Fernando A.
Hernández Gobertti.
