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EVALUATION OF DELTA WING EFFECTS ON THE
STEALTH-AERODYNAMIC FEATURES FOR
NON-CONVENTIONAL FIGHTER AIRCRAFT
Pedro David Bravo-Mosquera∗, Alvaro Martins Abdalla∗, Fernando Martini Catalano∗
∗Department of Aeronautical Engineering, São Carlos Engineering School, University of São
Paulo, Brazil
Keywords: RCS, Delta wing, Wave drag, CFD
Abstract
Survivability and maneuverability have become
the major design factors in the development of
future military aircraft with stealth ability. The
intake fully integrated into the fuselage com-
bined with an S-duct diffuser provide line-of-
sight blockage of the engine blades, satisfying
the requirement of low signature, lightweight
and low drag for the next generation of air-
craft. This paper aims to provide an insight
about radar cross section (RCS) and aerodynam-
ics of several delta platforms that would help
the need and amount of RCS suppression to es-
cape detection from surveillance radars and re-
duce wave drag. The stealth characteristics were
modeled using POFACETS software, which en-
abled the prediction of the RCS targets using tri-
angular facets. The aerodynamic characteristics
were evaluated through the investigation of the
wave drag phenomena of each delta platform, us-
ing a linearized mathematical model to intercept
the aircraft cross sectional area regarding the an-
gle of the Mach cone produced. These results
were compared with computational fluid dynam-
ics (CFD) simulations, which were performed us-
ing Reynolds-Averaged-Navier-Stokes (RANS)
equations, coupled with the Shear Stress Trans-
port (SST) turbulence model. Results showed
that the stealth and aerodynamic characteristics
of a non-conventional fighter aircraft can be opti-
mized through integration analysis processes.
1 General Introduction
The conception of non-conventional fighter air-
craft with the aim of achieving a certain perfor-
mance or operational improvement is undoubt-
edly, one of the most important objectives of
the aeronautical engineering. These improve-
ments involve: drag reduction, radar cross sec-
tion (RCS) reduction, noise reduction, shorten-
ing of take-off and landing distances, increase
of aerodynamic efficiency, armament weight in-
crease, among others. Therefore, the analy-
sis of delta platforms effects on the stealth-
aerodynamic characteristics are essential to up-
grade the conceptual design of this kind of air-
craft.
During the design of a fighter aircraft, there
are different techniques to reduce the RCS; the
most common is by modeling the surface of the
aircraft in such a way that radar waves be dis-
persed away from radar receiver. However, its ex-
ceptional form, manufactured by flat boards, are
aerodynamically unstable [1]. For that reason, in
this work was considered another approach to air-
craft design, which refers to the use of a thin air-
foil and a tailless delta wing design, with a top
mounted intake and single vector engine hidden
within the fuselage, highlighting a smooth com-
bination of the external surfaces and improving
the survivability and maneuverability aircraft ca-
pabilities.
The delta platform study continues to be a
1
BRAVO-MOSQUERA, P. D. ABDALLA, A. CATALANO, F.
subject of interest for most aircraft designers, due
to its advantages of significant reduction in struc-
tural weight, drag, and cost. The weight reduc-
tion and drag over traditional aircraft is achieved
by eliminating the empennage surface. There-
fore, the cost reduction comes by virtue of the
improved lift to drag and consequently reduced
fuel consumption [2].
This paper conducts studies of theoretical
models developed for the purpose of demonstrat-
ing the importance of the shape in the RCS and
wave drag of a non-conventional aircraft. The
configurations have the same airfoil, fuselage
length and intake location, however, five differ-
ent delta platforms were designed in order to de-
termine the configuration that best adjusts to the
mission constraints, performing an equilibrium
between low RCS and aerodynamics.
2 Delta wing planforms
Delta wings suffer from some undesirable char-
acteristics such as notably flow separation at
high angles of attack (swept wings have sim-
ilar problems), and high drag at low speeds
[3]. This originally limited them primarily to
high-speed, high-altitude interceptor roles. Since
then the delta design has been modified in dif-
ferent ways to overcome some of these prob-
lems. These include: Ogival delta wing, Stan-
dard delta with LEX (Leading Edge Extensions),
Compound delta wing, Canard delta wing, Dou-
ble delta wing (Fig. 1).
In this paper, the RCS of several planform
shapes of delta wings are studied, when the plan-
form has the same reference area, the same airfoil
at a constant angle of Attack and wing dihedral
angle at zero degrees. To ensure this, the Aspect
Ratio (AR) and taper ratio (λ) are varied so that
all the examples have an equal area but are rep-
resentative of the actual airplanes. It should be
noted that conceptual 3D digital models are de-
signed in SOLIDWORKS software.
The non-conventional fighter aircraft concep-
tually designed for this article is a kind of oper-
ational aircraft with a single seat, single vector
engine and dorsal intake configuration, since this
Fig. 1 Delta wing planform: (a) Ogival delta, (b)
Standard delta with LEX, (c) Compound delta,
(d) Canard delta, (e) Double delta.
configuration represents a low radar signature by
integrating the engine into the aircraft using an
S-duct diffuser, which prevents direct radar line-
of-sight to the engine face. (Table 1).
Table 1 Basic parameters of the conceptual design.
Parameter Value
Length 14.6 m
Height 4.5 m
MTOW 14000 kg
Empty weight 6600 kg
Weapons weight 4000 kg
Range 3000 km
Service ceiling 16500 m
Wing loading 415 kg/m2
T/W ratio 0.92
Engine Pratt & Whitney F100-229
Main airfoil wing NACA64a204
More specific details are found in Bravo-
Mosquera [4].
3 Radar cross section
The RCS is a measure of the ability of a target
to reflect radar energy, affecting the maximum
range at which this target is detected by a radar
set [5]. Concerning monostatic radars, RCS can
be defined as the power scattered from a target
to a certain direction, when the target is illumi-
2
EVALUATION OF DELTA WING EFFECTS ON THE STEALTH-AERODYNAMIC FEATURES FOR
NON-CONVENTIONAL FIGHTER AIRCRAFT
nated by electromagnetic radiation [6, 7]. There-
fore, a larger value of this measure means high
detectability by radar. Summarizing into a single
term, monostatic RCS, in terms of electric field
is:
σ=lim
r→∞4πr2|ES|2
|EI|2(1)
where ris the distance between the target and
the radar, ESand EIare the scattered and incident
electric fields, respectively.
The Eq. 1is valid when the target is illumi-
nated by a plane wave. It should be noted that
RCS values must be in square meters. However,
due to the large range of values, it is usually given
in a decibel scale. The conversion of scales can
be presented as Eq. 2.
dBSm =10logσ
1m2(2)
Radar cross section is a function of many fac-
tors which include the target configuration and its
material composition, frequency or wavelength,
transmitter and receiver polarizations, and the tar-
get aspect (angular orientation of the target) rela-
tive to the radar [8].
3.1 POFACETS software application
The POFACETS code is a MATLAB application
based on the Physical Optics (PO) method to pre-
dict the RCS targets (3D CAD models) using tri-
angular facets [8].
PO is a high frequency approximation that
provides adequate results for electrically large
targets, in the specular direction, by approximat-
ing the induced surface currents. The PO currents
are integrated over the illuminated portions of the
target to obtain the scattered far field, while set-
ting the current to zero over the shadowed por-
tions. Since the current is set to zero at the
shadow boundary, the computed field values are
inaccurate at wide angles and in the shadow re-
gions. Furthermore, surface waves, multiple re-
flections and edge diffractions are not taken into
account. However, the simplicity of this ap-
proach ensures low computational overhead [9].
Table 2 No. of cells for the different delta wing
planform.
Delta wing Area [m2]No. of cells at 10 GHz
Ogival 34.27 13549
LEX 34.12 13254
Compound 34.10 12459
Canard 34.01 11509
Double 34.35 11492
In this paper, a two-step approach is proposed
in order to predict the RCS for each configura-
tion. Firstly, a 3D model of the targets are created
and refined according to available data, i.e. fuse-
lage length, intake position and wing planform.
Then, the POFACETS code is employed.
For any signature shape, the low observability
of aircraft depends on the wavelength. Therefore,
it is one of the factors that determine the area of
the radar cross-section. This work only calculates
RCS considering high frequencies. The reason
of this is that radar operating in L-band (lower
frequencies) produces wavelengths with compa-
rable size to the aircraft itself and should exhibit
scattering in the resonance region rather than the
optical region [10].
3.2 Model description
Five aircraft of different delta wing shape are
modeled in SOLIDWORKS and discretized in
triangular facet surfaces using the ACIS Solids
module of POFACETS. (see Fig. 2).
Table 2lists the number of surface cells used
for discretization for the surface area considered.
The main objective is to study the RCS mea-
surements which aim to determine effective area
responsible for backscatter when hit by a radar
wave. In this way, some assumptions are re-
quired. As the radar is only monostatic case,
the target is involved with the high frequency (X-
Band) range.
Based on the assumptions described above,
the frequency bands chosen in this analysis fol-
low the guidelines of the Federal Radar Spectrum
Requirements [11].
On the polar coordinates of the RCS charac-
3
BRAVO-MOSQUERA, P. D. ABDALLA, A. CATALANO, F.
Fig. 2a. Ogival delta.
Fig. 2b. Standard delta with LEX.
Fig. 2c. Compound delta.
Fig. 2d. Canard delta.
Fig. 2e. Double delta.
Fig. 2 Triangular facet surface scheme of delta
wing planform.
teristics, the azimuth angle (Θ) is set between 0o
to 180o. The elevation angle (Φ) is set at 0oin or-
der to nearby RCS analysis in front of the aircraft.
It should be noted that no special materials were
used in the coating of the configurations, there-
fore, materials application to reduce wavelength
is beyond the scope of this research.
4 Wave drag estimation
The wave drag of the configurations was calcu-
lated based on the method proposed by Raymer
[12]. This uses several empirical tools and takes
into account both, the wing and fuselage dimen-
sions using a plane average method and Mach
cone method [13]. The following steps are fol-
lowed to obtain the areas to calculate the wave
drag.
•Use Computer Aided-Design (CAD) tools
to create the configurations.
•Create Mach cone planes defined by its re-
spective Mach angle.
•Intersect the geometry of the configura-
tions with the Mach cone planes regarding
the direction of flight (Fig. 3).
Fig. 3 Mach cone plane intersection with aircraft
geometry.
•Normalize the obtained area by the inter-
section of the configurations with the Mach
cone plane.
4
EVALUATION OF DELTA WING EFFECTS ON THE STEALTH-AERODYNAMIC FEATURES FOR
NON-CONVENTIONAL FIGHTER AIRCRAFT
•Create a point in the Z-direction in order
to obtain the profile of the area distribution
at each section of the models, as shown in
Fig. 4.
Fig. 4 Effective Mach cone area distribution for
different Mach numbers ranging from 1 to 2.
•Calculate the wave drag coefficient (CDW)
in relation to the area distribution obtained.
For preliminary wave drag analysis at
Mach ≥1.2, a correlation to the Sears-Haack
body wave drag is presented in Eq. 3.
CDW=EW D 1−0.386(M−1.2)0.57 1−πΛ0.77
LE
100 ···
···D
qSears−Haack (3)
where EWD is defined by the correlation be-
tween the aircraft and the Sears-Haack body
wave drag; also known as empirical wave drag
efficiency factor. ΛLE is the wing leading edge
sweep angle, given in degrees, and (D/q)wave is
the minimum possible wave drag for any closed-
end body of the same length and total volume,
given by Eq. 4.
D
qwave
=9π
2AMAX
l2
(4)
where AMAX is the maximum cross-sectional
area, determined from the aircraft volume-
distribution plot, and lis the overall aircraft
length.
Based on Hayes [15], the shock wave drag
for bodies immersed in transonic speeds only de-
pends on the longitudinal area distribution of the
system as a whole. Therefore, the Theodore von
Kármán formula for slender bodies of revolution
(Eq. 5) was used for Mach between 0.8 to 1.2.
CDW=ρV2
4πZx0
−x0Zx0
−x0
S00 (x)S00 (x1)Log|x−x1|dxdx1(5)
where S(x)represents the cross-sectional
area intercepted by a perpendicular plane to the
freestream, at a distance x from the tip of the
body.
5 CFD approach
CFD Simulations were carried out using the
commercial code ANSYS-FLUENT, which
solves the compressible Reynolds-Average-
Navier-Stokes (RANS) equations using a 2nd
order finite volume scheme. The solver uses the
Shear Stress Transport (SST) turbulence model
for all of the simulations. For the computational
domain, no-slip adiabatic wall boundary condi-
tions are imposed on the solid walls. Specified
inlet velocities are imposed at inlet boundary
regarding the flying Mach. The outlet condition
was imposed with no pressure gradient and walls
were set as non-friction (ideal) walls.
Multi-block structure mesh is generated by
Meshing ANSYS ICEM-CFD software. Figure
5shows a detail view of the surface grids around
the configurations. A series of grid with increas-
ing resolution is used to determine the grid sen-
sitivity involved in the numerical study. The final
grid of 5.8 million elements is adopted in the sub-
sequent numerical analysis.
Fig. 5 Mesh structure for delta wing configura-
tions: (a) Ogival delta, (b) Standard delta with
LEX, (c) Compound delta, (d) Canard delta, (e)
Double delta.
5
BRAVO-MOSQUERA, P. D. ABDALLA, A. CATALANO, F.
6 Results and Discussion
In this section, results are divided in two subsec-
tions. First, the RCS analysis is presented and
discussed. Then, the analytic wave drag estima-
tion is compared to CFD simulations.
6.1 Radar cross section
The monostatic RCS is computed, where trans-
mitter and receiver are co-located. As mentioned
above, configurations are approximated by arrays
of triangles (facets), and the scattered field of
each triangle is computed as isolated. Multiple
reflections, edge diffraction and surface waves
are not considered. All parameters are set to de-
fault values, unless otherwise specified.
The RCS of the configurations was computed
for a radar transmitting at 10 GHz (X-Band), em-
ulating a typical aircraft fire control radar. The
RCS pattern shown in the following figures cor-
responds to polar plot of all RCS configurations,
observed from the same level (Θranging from 0o
to 180oand Φset at 0o).
The configuration with lowest RCS signature
was the standard delta with LEX, with values be-
tween -10 and 40 dBsm (see Fig. 6). In this polar
plot, it is observed that the peaks occur in 0 and
180 degrees with a signature of 40 dBsm. In the
same way, in the region between 100 and 120 de-
grees, the RCS value was 10 dBsm. For other
regions, the RCS signature goes down to values
close to -10 dBsm.
On the other hand, the Double delta configu-
ration presents its maximum peaks at 0 and 180
degrees of around 55 dBsm and, in the region be-
tween 100 and 120 degrees with value around 12
dBsm. For other regions, the RCS signature goes
down to values close to 0.0 dBsm (see Fig. 7).
Finally, Ogival delta (8), Compound delta (9)
and Canard delta (10) presented similar signa-
tures, with peak values at 0 and 180 degrees of
around 55 and 60 dBsm. Furthermore, for 20 and
160 degrees, the average RCS signature was 20
dBsm.
Since all configurations have the same fuse-
lage, dorsal intake and vertical empennage, the
explanation of the RCS signature reduction for
the Standard delta with LEX and Double delta is
due to the planform of the configurations. Note
that Standard delta with LEX and Double delta
have different leading edges sweep, which en-
hances survivability by the non-uniform fringe
surfaces. By last, canards can potentially have
poor stealth characteristics due to their large and
angular surfaces that tend to reflect radar signals
forwards.
Fig. 6 LEX configuration, RCS characteristic curve.
Fig. 7 Double configuration, RCS characteristic
curve.
6
EVALUATION OF DELTA WING EFFECTS ON THE STEALTH-AERODYNAMIC FEATURES FOR
NON-CONVENTIONAL FIGHTER AIRCRAFT
Fig. 8 Ogival configuration, RCS characteristic
curve.
Figure 11 shows the linear plot of the RCS
analysis, where are compared all the configura-
tions tested. This figure allows to verify that for
this specific case, the standard delta with LEX
was the configuration with the lowest RCS signa-
ture. However, for more accurately results, it is
still necessary to evaluate more azimuth and ele-
vation angles on each configuration.
Table 3summarizes the results obtained in
the RCS analysis.
Table 3 RCS signature results.
Delta wing RCS min-max [dBsm]
Ogival 20 - 55
LEX -10 - 40
Compound 20 - 60
Canard 20 - 60
Double 0 - 55
6.2 Wave drag estimation
In this section, the analytical wave drag calcu-
lations are compared to CFD simulations. Fig-
ure 12 shows the wave drag coefficient (CDW) in
function of Mach number, between the analyti-
cal model presented and the CFD simulation for
the five configurations evaluated. It was observed
that for Mach = 1, the analytical CDWwere higher
Fig. 9 Compound configuration, RCS character-
istic curve.
Fig. 10 Canard configuration, RCS characteristic
curve.
Monostatic Angle, θ [Deg]
0 50 100 150
RCS [dBsm]
-20
0
20
40
60
80 Ogival
LEX
Compound
Canard
Double
Fig. 11 Comparison of linear plot, RCS charac-
teristic curves.
7
BRAVO-MOSQUERA, P. D. ABDALLA, A. CATALANO, F.
than CFD. However, for Mach >1, the analytical
CDwere reduced considerably.
These results are likely a product of the im-
precision of the analytical calculations to eval-
uate wave drag coefficients in transonic veloc-
ities. Nevertheless, the CFD wave drag values
were higher for supersonic velocities, mainly due
to the CFD simulations allowed to create condi-
tions closer to reality, at which not only the cross
section is considered, whereas also the compress-
ibility effects. Meanwhile, it was observed that
both curves presented the same behavior, where
the average margin of error for the five configu-
rations in the six velocities evaluated was 1.93%,
which allowed to conclude that the analytical
model developed were reliable.
The analytical wave drag comparison for the
five configurations tested are depicted in Fig. 13.
It is evident that the Ogival delta configuration
presents a reduced wave drag coefficient at Mach
= 1. However, for Mach = 2, the wave drag coef-
ficient is increased. This result is a consequence
of the relative increase of the cross-sectional area
of the Ogival configuration with the Mach cone
plane. LEX and Compound configurations are
the models with the lowest wave drag at all eval-
uated velocities. However, Canard and Double
delta configurations presented the highest wave
drag values.
Finally, similar results were obtained in the
numerical wave drag comparison for the five con-
figurations (see. Fig. 14).
7 Conclusions
In the present research, the stealth and aerody-
namic characteristics of five delta wing configu-
rations in the same aircraft geometry were ana-
lyzed.
The main results suggested that stealth-
aerodynamic characteristics of the non-
conventional fighter aircraft can be based on
the analysis process of the integration of stealth
aircraft conceptual design and aerodynamic
analysis.
The RCS calculations presented adequate re-
sults for preliminary stealth studies. However,
Mach number
1 1.2 1.4 1.6 1.8 2
CDW
0.01
0.02
0.03
0.04
0.05 Analytical
Numerical
Fig. 12a. Ogival delta.
Mach number
1 1.2 1.4 1.6 1.8 2
CDW
0.01
0.02
0.03
0.04
0.05 Analytical
Numerical
Fig. 12b. Standard delta with LEX.
Mach number
1 1.2 1.4 1.6 1.8 2
CDW
0.01
0.02
0.03
0.04
0.05 Analytical
Numerical
Fig. 12c. Compound delta.
Mach number
1 1.2 1.4 1.6 1.8 2
CDW
0.01
0.02
0.03
0.04
0.05 Analytical
Numerical
Fig. 12d. Canard delta.
Mach number
1 1.2 1.4 1.6 1.8 2
CDW
0.02
0.04
0.06 Analytical
Numerical
Fig. 12e. Double delta.
Fig. 12 Wave drag coefficient comparison, ana-
lytical and numerical methods.
Mach number
1 1.2 1.4 1.6 1.8 2
CDW
0
0.02
0.04
0.06 Ogival
LEX
Compound
Canard
Double
Fig. 13 CDWVs Mach number, analytical calcu-
lations.
8
EVALUATION OF DELTA WING EFFECTS ON THE STEALTH-AERODYNAMIC FEATURES FOR
NON-CONVENTIONAL FIGHTER AIRCRAFT
Mach number
1 1.2 1.4 1.6 1.8 2
CDW
0.01
0.02
0.03
0.04
0.05
Ogival
LEX
Compound
Canard
Double
Fig. 14 CDWVs Mach number, numerical simu-
lations.
more azimuth and elevation angles are still nec-
essary for a detailed analysis of the presented
designs. On the other hand, the aerodynamic
analysis has been successfully used to evaluate
the aerodynamic drag of transonic and supersonic
velocities.
In short, following the obtained results, the
Standard delta wing with LEX was the config-
uration with the lowest RCS signature. Like-
wise, this configuration presented adequate aero-
dynamic characteristics when comparing the an-
alytical and numerical models.
Acknowledgments
The authors express their gratitude to Maria
Luisa Bambozzi de Oliveira and Roberto Gil
Annes da Silva, members of the evaluation Jury
of the masters degree dissertation of Bravo-
Mosquera P. D.
The authors are thankful to CAPES (Coorde-
nação de Aperfeiçoamento de Pessoal de Nível
Superior) for the scholarship granted.
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8 Contact Author Email Address
mailto: pdbravom@usp.br
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