Vortex Lattice CFD Application and Modeling Validation for
Ground Effect Aircraft
KARL ZAMMIT, HOWARD SMITH, NOEL SIERRA LOBO, IOANNIS K. GIANNOPOULOS
Centre of Excellence for Aeronautics,
School of Aerospace, Transport and Manufacturing,
Cranfield University,
Cranfield, MK43 0AL
UNITED KINGDOM
Abstract: - This paper explores the application of vortex lattice computational fluid dynamics method capability
to model aircraft flight near to ground, utilizing the ground effect. Computational results were correlated with
existing analytic formulations and benchmarked against experimental data from the public domain. A case
aerodynamics design study was formed, based on the Russian A-90 Orlyonok Ekranoplan wing. The study
provided a verification and a validation step towards advancing ground effect aircraft turnaround conceptual
and preliminary design time, using the rapid aerodynamics results generation vortex lattice CFD method.
Key-Words: - Ekranoplan, CFD, Vortex Lattice method, AVL, Flight Ground Effect, A-90 Orlyonok.
Received: December 27, 2023. Revised: January 21, 2024. Accepted: February 1, 2024. Published: February 9, 2024.
1 Introduction
Wing-in-ground, WIG-craft, are aircraft vehicles
that fly near a surface, mostly above water surfaces.
The vehicles make use of the Ground Effect (GE)
being the increased lift curve slope and reduced
induced drag of the main lifting surfaces, [1].
GE effects are broadly understood as wing-span
and wing-chord effects, [1]. The wing-span
dominant GE is directly related to a reduction in the
induced drag, which is proportional to the wing’s
spanwise length. When a wing is close to the
ground, there is insufficient space for the full
development of wingtip vortices. Consequently, air
pressure leakage from under the wing to the upper
section is reduced. Additionally, the ground’s effect
pushes the vortices outwards, effectively artificially
increasing the wing’s aspect ratio beyond its
geometric value.
The wing-chord dominant GE involves an
increase in static pressure of the oncoming air
beneath the wing, which could be further enhanced
by utilizing wingtip side plates, [2]. The chord-
dominant GE enables the wing to generate more lift
per unit area, resulting in a higher lift coefficient for
the same power input, [1].
The distance between the wing and the ground
influences many of the effects experienced during
flight. Three distinct models have emerged from the
literature, each focused on a specific height zone
above the surface, [3], [4]. The first zone is the
operational region between the surface boundary
and a flight height corresponding to 20% of the
wing-chord length. In this In-Ground-Effect region
(IGE), the flow experiences significant constriction
in the vertical direction, leading to a predominantly
two-dimensional flow with restricted vertical
freedom. The second zone is referred to as the
region between one wing-chord length and ten
wing-span lengths above the ground. Within this
zone, the wing’s span dominates the model. Inviscid
flow models are commonly employed in this region
and demonstrate a marginal increase in the Lift to
Drag ratio (L/D), compared to the Out-of-Ground-
Effect (OGE) flight. A combination of the two
models is necessary to accurately capture the
aerodynamic behavior of wings operating in the
region between 20% - 100% of chord length, [4].
Above ten wing-span lengths, free-flight models
used in conventional aerodynamic theory for aircraft
design are applicable.
Distinct wing designs can be observed for WIG
craft throughout history. Russian Ekranoplans such
as the Korabl Market, the A-90 Orlyonok, and the
Lun-class craft, used a low aspect ratio straight wing
with minimal taper and twist. In contrast, the
German RFB X-114 and Chinese XTW had wings
with a significantly low aspect ratio, a very high
taper ratio, slightly sweptback leading and trailing
edges, and an appreciably large wing setting angle.
More recent WIG craft designs include the soon-to-
enter service Viceroy Seaglider by Regent, which
has a noticeably different wing planform with a high
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aspect ratio and quasi-organic shape. A part of the
aviation industry has shown interest in the
development of WIG-craft. The study below
showcases the use of computational time-efficient
aerodynamics tools capable of rapid design
evaluation, mostly applicable to the early
aerodynamic iterative aircraft design.
2 Ground Effect Flight
At the early aircraft design stages, namely at the
conceptual and initial design stages, a parametric
design space of all the aircraft features to be
determined is explored, for configuring the most
important variables from the design perspective. To
reach an optimum set of design parameters framed
by several constraints, usually rapid evaluation,
lower fidelity analysis computational tools are
employed. There are key aspects to be considered
upon selecting such tools, namely, time efficiency
and results accuracy relative to the maturity level of
the design stage.
The study herein, aimed at providing validation
and verification insights in the utilization of Vortex
Lattice computational fluid dynamics method
(VLM) applied to WIG-craft. For that purpose,
various analytical formulations and experimental
data were benchmarked against the numerically
VLM derived solutions.
2.1 Analytical Formulations
A thorough review of the analytical formulations of
a wing IGE shed light on various metrics for
efficiency comparison. The equations listed below-
maintained adherence to the operational parameters
analyzed in [5]. The main parameter utilized is the
ratio of the height of the mean aerodynamic chord
from the ground {hc} to the wingspan {b}, denoted
herein by h𝑐/b.
2.1.1 Induced Drag GE Reduction Factor
Derived from reference [6], various closed-form
relations are available in literature that can be used
to estimate the effect of IGE flight on the induced
drag. The drag reduction factor, [7], shown in
eq.(1), is the ratio of the induced drag in IGE flight
condition versus the OGE one. The equations
presented in [8], [9] for wings IGE are re-iterated
below in eq.(2) and eq.(3).
(1)
(2)
(3)
It has been noted in [10], that eq.(3) tends to
significantly underpredict the induced drag for h𝑐/b
< 1.
2.1.2 Induced Drag GE Influence Ratio
The induced drag coefficient over the lift coefficient
squared IGE to that OGE shown eq.(4), is referred
to as the induced-drag ground effect influence ratio,
[10].
(4)
Reference [10], derived several closed-form
relations to estimate the induced drag and lift
coefficients IGE. Starting from a review of earlier
equations, their first contribution improved the
approximation given in [7], by slightly modifying
the coefficients in eq.(5).
(5)
Equations (6) and (7), followed as a closed-form
relation for the induced drag IGE influence ratio,
verified via a comparison with results obtained from
numerical lifting-line solutions.
(6)
(7)
Noting that eq.(6) agrees mostly only at small
angles of attack, the correction factor {βD} in eq.(8)
is applied by multiplying the result of eq.(6) to
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increase the accuracy for higher angles of attack,
[10].
(8)
2.1.3 Lift GE Influence Ratio
The ratio of the induced drag coefficient over the
lift coefficient squared IGE to that OGE shown in
eq.(9), is referred to as the induced-drag ground
effect influence ratio, [10].
(9)
Derived in [10], K3 is presented in eq.(10).
(10)
(11)
A correction factor to improve the accuracy at
high lift coefficients was also suggested, [10], and
given in eq.(12).
(12)
ESDU 72023, [11], presented another equation
formed from the contribution of several studies,
such as that documented in [12], to estimate the
increment to the lift coefficient due to the ground
effect given by eq.(13). The derivation of each
parameter may be found in the ESDU method, [11].
(13)
For non-dimensional ground flight distance
of h𝑐/b < 1 and for small free-air lift
coefficients, experimental evidence highlights
the need to account for the wing thickness when
evaluating the GE on lift, [11]. The
approximation for the wing thickness correction
given by eq.(14), is suggested in the absence of
experimental data.
(14)
It is important to note that, in the context of the
presented ESDU method, eq.(14) assumes the
retraction of any high-lift devices at the same
aircraft incidence
2.2 Computational Tools
Various aerodynamic computational solvers can be
employed in the design synthesis of aircraft design.
The Navier-Stokes equations with turbulence
modeling could potentially offer the most realistic
prediction of the aerodynamic forces and moments
for complex geometries, [13]. Implementing Navier
Stokes solvers can be quite computationally time
inefficient, particularly when such tools are
implemented within multivariable design synthesis
optimization processes, [14].
The inviscid Euler equations, derived by
eliminating diffusion terms from the Navier-Stokes
equations, allow for the solution of rotational, non-
isentropic shock flows, predicting well enough
phenomena such as wave drag, [15]. Nonetheless,
Euler solvers cannot predict viscous drag and are
computationally expensive due to the need to solve
at least five coupled first-order partial differential
equation,s [16].
A need for lower fidelity yet faster aerodynamic
solvers is present, provided by non-linear and linear
potential flow solvers. Linear potential flow codes
based on the Laplace equations, are solved using
panel or Vortex Lattice Method (VLM).
Panel methods provide an approximate solution
distributed over the geometry’s surface and can be
enhanced by higher-order modeling and the
inclusion of lifting capability, unsteady flows, and
boundary layer effects, [17]. VLMs solve the
Laplace potential flow equations using singularities
on the mean surface of the geometry, [18].
However, VLMs and panel methods cannot handle
turbulence, viscosity, and flow separation, [17],
[18]. Nonetheless, VLMs are computationally
efficient and are currently widely used in the aircraft
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conceptual and initial design phases, [18], as well as
in other similar fields of engineering, [19].
2.2.1 Short Survey on VLM Aerodynamic Tools
For the present study, several open-source panel
methods and VLMs were surveyed, including
WINGBODY, PANAIR, XFLR5, and the Athena
Vortex Lattice, AVL software platforms.
WINGBODY [20], is a panel method useful for
simple 3D geometry analysis at subsonic and
supersonic conditions, though it lacks modeling
capabilities for wing twists and complex geometries
with multiple sections.
PANAIR [21], is a higher-order panel method
that supports the analysis of complex 3D geometries
in subsonic and supersonic aerodynamics. However,
it has limited aero-foil options and cannot predict
flow characteristics accurately for configurations
with different total pressures. Moreover, it requires
a commercial pre-processor for modeling flight
control surfaces.
XFLR5 [22], is an aerodynamic suite that
incorporates both VLM and 3D panel methods and
allows the modeling of more complex
configurations at various angles of attack.
Nevertheless, it involves complicated geometric
manipulation to swiftly model control surfaces and
lacks explicit stability and control derivatives.
The AVL method, [23], is based on VLM. It
supports aerodynamic analysis of simple and
complex geometries at subsonic conditions. It offers
quasi-steady flow analysis and includes
compressibility effects. AVL’s open-source nature
allows for remote operation, and it effectively
investigates geometric and aerodynamic twists and
control surface deflections, providing stability and
control derivatives without additional manipulation,
[17], [23]. To capture the effects of ground effect,
AVL has the capability of setting up a symmetry
plane whereby while the aerodynamic implications
of ground effect are taken into account, the forces
are not calculated on the image surfaces. This
method is similar in principle to the method in [24],
where the study explores reducing induced drag in
wings by employing an imaging method to estimate
the drag reduction factor.
2.2.2 Experimental Verification
The VLM verification exercise was based on the
findings of [5], which provided wind tunnel
experimentally derived aerodynamic properties of a
3D finite rectangular wing of NACA0012 profile at
relatively lower Reynold’s numbers. Although a
symmetrical aerofoil profile is generally not
recommended for WIG-craft to avoid possible
suction towards the ground, [1], the NACA0012
profile was used due to the lack of other publicly
available test data.
An identical wing to the experimental survey
was constructed in AVL, having a chord of 63mm
and a span of 400mm. The flight parameters were
set at a flow velocity of V∞=20ms-1, air density of
ρ∞=1.225kgm-3, and viscosity of μ∞=1.75×10-5kgm-
1s-1, which resulted in Re≈8.8×10-5. The
experimental study was performed for angles of
attack {𝛼} between -8° to 18°, at five non-
dimensional heights h𝑐/b equal to 0.4, 0.6, 0.8, 1.0
and 1.5. The value of h𝑐/b at 1.5 was considered
OGE by [5].
Results convergence testing was conducted for
the numerical VLM models generated grids via
systematic refinement of the discretisation of the
wing, to ensure that the solution is independent of
the element size. The results of the mesh sensitivity
are shown in Figure 1, Figure 2, Figure 3, Figure 4,
Figure 5 and Figure 6, in terms of calculated lift,
drag, and moment coefficients {CL, CD, Cm} for the
NACA0012 3D VLM modeled aerofoil section,
versus a number of elements used and for angles of
attack {𝛼} from -5° to +5°. The chart abscissa
values are the coefficients residuals, namely the
actual coefficient subtracted from the average value
of the coefficients calculated from the sum of the
tests for various numbers of elements at that angle
of attack. The charts are interpreted in terms of the
coefficient attaining a constant value after a certain
number of elements used in the mesh, an indication
of the results being mesh independent, as well as the
magnitude of the attained value being a measure of
the residual error. The numerical tests were
performed for OGE as well as for IGE at h𝑐/b =0.4.
The numerical mesh discretization sensitivity
testing, Figure 1, Figure 2, Figure 3, Figure 4,
Figure 5 and Figure 6, showed convergence of the
results for the coefficients in question after a certain
number of elements and above. For the IGE
scenario, a slightly increased number of elements
were required compared to OGE cases.
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Fig. 1: NACA0012, OGE residuals CL
Fig. 2: NACA0012, OGE residuals CD,i
Fig. 3: NACA0012, OGE residuals Cm
Fig. 4: NACA0012, IGE (h𝑐/b=0.4) residuals CL
Fig. 5: NACA0012, IGE (h𝑐/b=0.4) residuals CD,i
Fig. 6: NACA0012, IGE (h𝑐/b=0.4) residuals Cm
3 Results
3.1 Analytic Formulations Correlations
The induced drag reduction factor, K1, the induced
drag ground effect influence ratio, K2, and the lift
ground effect influence ratio, K3, of para 2.1 herein,
were evaluated and displayed in Figure 7, Figure 8
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and Figure 9. The results refer to the NACA0012
wing section described in para 2.2.2 herein, as a
function of the nondimensional height, h𝑐/b. The
numerical results from AVL were superimposed on
the figures as well.
Fig. 7: NACA0012, K1
Fig. 8: NACA0012, K2
Fig. 9: NACA0012, K3
It can be observed that the results generated by
the AVL VLM method correlate relatively well with
the results from analytical formulations, for higher
values of the non-dimensional distance from the
ground. The closer the distance to the ground, the
larger the deviation of the parameters in question.
3.2 Experimental Results Benchmark
The variation of lift and drag coefficients from the
work of [5], were benchmarked against AVL results
and are shown in Figure 10 and Figure 11. Given
that AVL is recommended for small angles of
attack, [23], simulations run in the range -8°≤ 𝛼
≤+8° and for the non-dimensional height off the
ground plane dictated in para 2.2.2.
Fig. 10: NACA0012, CL, experimental vs AVL
Fig. 11: NACA0012, CD, experimental vs AVL
The graphs revealed the congruence in the
trends between the VLM results and the
experimental data for the angles of attack range of
interest. There are certainly deviations to be noted,
related mostly to the negative angles:
In terms of the lift curves, the experimental data
have not captured a substantial increase in the lift
curve slope upon varying the h𝑐/b distance, as
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theory would require and evident for the VLM
simulations; the almost linear experimentally
derived lift coefficient were shown to be transposed
upwards rather than having a bigger inclination for
smaller values of h𝑐/b; the VLM results were more
congruent with what theory is dictating for the
ground effect change in the lift curve slope; at zero
angle of attack a more profound positive value for
the lift coefficient was captured in the experiments;
there are also a less aggressive lift curve slope than
the VLM derived ones; for the zero angle of attack
cases, the VLM showed a small increase in the lift,
if at all, almost indifferent to the h𝑐/b distance; for
the drag plot, the values spread across tenths of drag
counts so the relative importance of properly
assessing the drag seems crucial; in general, the
experimental data show an aggressive trend for the
negative angles of attack and a larger band of spread
depending on the h𝑐/b distance; it is fair to suggest
that the results for drag, whether they have been
deducted from the experiments or from the
simulations, are to be used only for comparative
initial design studies.
3.3 The A-90 Orlyonok Wing Case Study
Following the analytical results correlation and the
experimental results benchmark against the VLM
computational method for a symmetric rectangular
wing, the required adjustments were made to
simulate the wing of the A-90 Orlyonok WIG-craft.
The geometry of the wing profile and planform of
the A-90 Orlyonok was found in [25] and is
illustrated in Figure 12 and Figure 13.
Fig. 12: A-90 Orlyonok 3D wing representation
Fig. 13: A-90 Orlyonok 2D normalized chord length
wing profile
The analysis flow velocity was set to the
Orlyonok’s cruise speed of 104 ms-1, [4], while the
operational height was set to the typical value of
h𝑐/b = 0.4 for this WIG-craft. Given the differences
between the NACA0012 to the A-90 aerofoil
profile, area, and operational speed, the impact on
wing discretisation was re-assessed. A grid
dependence study was conducted for a typical range
of angles of attack, with the updated operational
parameters and geometry shown in Figure 14, the
results of which are presented in Figure 15, Figure
16 and Figure 17.
Fig. 14: Mesh sensitivity analysis for the A-90 wing
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Fig. 15: A-90 3D wing, IGE residuals CL
Fig. 16: A-90 3D wing, IGE residuals CD,i
Fig. 17: A-90 3D wing, IGE residuals Cm
The mesh sensitivity analysis showed that the
new aerofoil required a significant increase in the
number of elements in the grid. The study indicated
that a grid with approximately 2000 elements
provided results for the lift, drag, and moment
coefficients with a maximum error of 1%
approximately. The proposed grid was considered
appropriate for the given purpose to ensure accuracy
and reliability for subsequent parametric design
analyses.
4 Conclusions
The Vortex Lattice CFD method was used in the
present aerodynamic coefficient evaluation study for
WIG-craft, where a few hundred simulations were
performed efficiently in a relatively short amount of
time, concerning higher fidelity CFD methods. The
method is ideal for rapid model and results
generation, ideal for early design optimization
studies. Follow-on research, embedded the Vortex
Lattice method within a Python genetic algorithm
optimization script, aiming at optimizing the flight
performance of WIG-craft, by refining several
geometric parameters of various wing design
concepts.
The VLM method results for WIG-craft showed
a relatively good correlation with the analytic
formulations from the public domain, with
deviations occurring for closer to the ground
distances. The experimental results on the other
hand exhibited essential differences in the form of
the results generated, not uncommonly met when
benchmarking wind tunnel tests against
computational methods results. The take-away from
the study was that VLM can be used for
comparative initial design studies, but flight
performance should be judged with higher fidelity
computational models and flight testing.
Finally, the study showed that the VLM results
convergence does depend on the actual wing design
and that there can be an acceptable level of
convergence achieved for higher levels of
discretization.
References:
[1] Yun L, Bliault A, Doo J, WIG Craft, and
Ekranoplan: Ground Effect Craft Technology,
Springer US, 2010.
[2] Park K, Lee J, Influence of endplate on
aerodynamic characteristics of low-aspect-
ratio wing in ground effect, Journal of
Mechanical Science and Technology, 22(12),
2578–2589, 2008.
[3] Rozhdestvensky K, Pappas P, Karaminas E,
Stubbs A, Pohl T, Hudson M, Stinton D,
Thomasson P, Ekranoplans: The GEMs of
Fast Water Transport. Discussion,
Transactions of the Institute of Marine
Engineers, 109(1), 47–74, 1997.
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DOI: 10.37394/232013.2024.19.5
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Volume 19, 2024
[4] Halloran M, O’meara S, Wing in Ground
Effect Craft Review. Melbourne Victoria,
1999.
[5] Shirsath R A, Mukherjee R, Experimental and
computational investigations of aerodynamic
characteristics of a finite rectangular wing-
inground effect, Proceedings of the Institution
of Mechanical Engineers, Part G Journal of
Aerospace Engineering, SAGE Publications
Ltd, 2022.
[6] Prandtl L, Induced Drag of Multiplanes,
NACA-TN-182, 1965.
[7] Boschetti P J, Quijada G M, Cárdenas E M,
Dynamic ground effect on the aerodynamic
coefficients of a wing using a panel method,
AIAA Atmospheric Flight Mechanics
Conference. American Institute of Aeronautics
and Astronautics Inc., 2016.
[8] Suh Y B, Ostowari C O, Drag Reduction
Factor Due to Ground Effect, Journal of
Aircraft, 25(11): 1071–1072, 1988.
[9] Laitone E V, Comment on Drag reduction
factor due to ground effect, Journal of
Aircraft, 27(1): 96–96, 1990.
[10] Phillips W F, Hunsaker D F, Lifting-line
predictions for induced drag and lift in ground
effect, 31st AIAA Applied Aerodynamics
Conference. American Institute of Aeronautics
and Astronautics, 2013.
[11] Chapell P D, Allan J W, Wood S, Low-Speed
Longitudinal Aerodynamic Characteristics of
Aircraft in Ground Effect, ESDU 72023,
2015.
[12] Hoerner S, Borst H, Lift of Airplane
Configurations, Fluid Dynamic Lift. 2nd ed.
Bricktown, NJ: Hoerner Fluid Dynamics,
20.1-20.22, 1985.
[13] Amjad Sohail M, Chao Y, Ullah R, Younis
Yamin M, Computational Challenges in High
Angle of Attack Flow, World Academy of
Science, Engineering, and Technology, 56:
1148–1155, 2011.
[14] Anderson R, Willis J, Johnson J, Ning A,
Beard R, A comparison of aerodynamic
models for optimizing the takeoff and
transition of a bi-wing tailsitter, in AIAA
Scitech 2021 Forum. American Institute of
Aeronautics and Astronautics Inc, AIAA, 1–
17, 2021.
[15] Kupiainen M, Kreiss G, Effects of Viscosity
on a Shock Wave Solution of the Euler
Equations, in Hou T Y, Tadmor E, (eds)
Hyperbolic Problems: Theory, Numerics,
Applications. 1st edn. Berlin, Heidelberg:
Springer Berlin Heidelberg, 655–664, 2003.
[16] Maier M, Kronbichler M, Efficient Parallel
3D Computation of the Compressible Euler
Equations with an Invariant-domain
Preserving Second-order Finite-element
Scheme, in ACM Transactions on Parallel
Computing. Munich, Germany: Association
for Computing Machinery, 2021.
[17] Kier T M, Verveld M J, Burkett C W, (2015)
Integrated Flexible Dynamic Loads Models
Based on Aerodynamic Influence Coefficients
of a 3D Panel Method, in International Forum
on Aeroelasticity and Structural Dynamics.
Saint Petersburg, Russia, 2015.
[18] Okonkwo P, Jemitola P, Integration of the
athena vortex lattice aerodynamic analysis
software into the multivariate design synthesis
of a blended wing body aircraft, Heliyon.
Elsevier Ltd, 9(3), 2023.
[19] Solari P, Bagnerini P, Vernengo G, A vortex
Lattice Method for the Hydrodynamic
Solution of Lifting Bodies Travelling clos and
across a free surface, WSEAS Transaction on
Fluid Mechanics, 17:39-48, 2022.
[20] NASA-AMES WingBody Panel Code,
[Online].
https://www.pdas.com/wingbody.html,
(Accessed Date: February 5, 2024).
[21] The PANAIR Program for Panel
Aerodynamics, [Online].
https://www.pdas.com/panair.html, (Accessed
Date: February 5, 2024).
[22] XFLR5, [Online].
http://www.xflr5.tech/xflr5.htm, (Accessed
Date: February 5, 2024).
[23] Drela M, Youngren H, AVL, [Online].
https://web.mit.edu/drela/Public/web/avl/,
(Accessed Date: February 5, 2024).
[24] Wieselberger C, Wing Resistance near the
Ground, (Uber den Flügelwiderstand in der
Nahe des Bodens, Zeitschift für Flugtechnik
und Motorluftschiffahrt) Magazine for
aviation technology and motor aviation,
25(11): 145–147, 1921.
[25] Мараев P, Flying over the waves (Ekranoplan
‘Eaglet’) 1992, [Online].
http://www.razlib.ru/transport_i_aviacija/ayer
ohobbi_1992_02/p3.php, (Accessed Date:
February 5, 2024).
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- Karl Zammit: methodology, investigation, formal
analysis, software, validation, project
administration.
- Howard Smith: conceptualization, supervision,
project administration.
- Noel Sierra Lobo: investigation.
- Ioannis K. Giannopoulos: validation,
visualization, writing.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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