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3D Modelling of Potential Targets for the purpose of

Radar Cross Section (RCS) Prediction

Based on 2D images and open source data

Panagiotis Touzopoulos, Dimitrios Boviatsis and Konstantinos C. Zikidis

Department of Aeronautical Sciences, Hellenic Air Force Academy, Dekelia Air Base, Greece, e-mail: kzikidis@cs.ntua.gr

Abstract—The Radar Cross Section (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. All weapon

systems employ RCS reduction techniques, in order to minimise

their detection range and thus the reaction time of the enemy.

Evidently, there is significant interest in predicting the RCS of a

potential target. Towards this aim, a two-step approach is

proposed: At first, a 3D model of the potential target is created

with the help of suitable 3D editing software, based on available

data, such as photos, videos, blueprints etc. Then, the RCS is

calculated with the help of computational electromagnetics, and

more specifically, with the POFACETS 4.1 code, a MATLAB

application based on the Physical Optics method. The proposed

approach has been applied to the F-16 and F-35 jet fighters, as

well as to the Dong-Feng 15 (DF-15) short range ballistic missile,

yielding plausible results.

Keywords: Radar detection, radar cross-sections, electro-

magnetic propagation in absorbing media, solid modeling, physical

optics, computational electromagnetics.

I. INTRODUCTION

It is rather difficult to obtain closed form solutions of

Maxwell's equations in real world problems, unless the related

physical objects present a very simplistic form. In most cases,

computationally efficient approximations to Maxwell's

equations have to be employed in order to address real-life

tasks, an approach commonly known as computational

electromagnetics.

Concerning the application of computational electro-

magnetics to the issue of RCS prediction of a physical object,

there are exact and approximate methods. Exact methods tend

to be quite complex, while approximate methods usually offer

acceptable results with considerably less prohibitive

computational requirements.

Among the most common RCS prediction methods for any

arbitrary 3D target are the following: the popular Method of

Moments (MOM), the Finite Difference Method (FDM),

Geometrical Optics (GO) and Physical Optics (PO). The MOM

and the FDM are exact methods, yielding accurate results, but

are computationally intensive. GO and PO are approximate

methods. Even though it is easy to apply, GO is associated with

severe limitations, e.g., in case of flat or cylindrical surfaces,

where it simply fails to provide any results.

PO is a high frequency approximation that provides good

results for electrically large targets, in the specular direction, by

approximating the induced surface currents. The PO currents

are integrated over the illuminated portions of the target to

obtain the scattered far field, while setting the current to zero

over the shadowed portions. Since the current is set to zero at

the shadow boundary, the computed field values are inaccurate

at wide angles and in the shadow regions. Furthermore, surface

waves, multiple reflections and edge diffractions are not taken

into account. However, the simplicity of this approach ensures

low computational overhead [1][2][3].

The POFACETS 4.1 program, a MATLAB application,

developed at the US Naval Postgraduate School, is an

implementation of the PO method for predicting the RCS of

complex objects, with relatively modest computational

requirements. The program models any arbitrary target by

dividing it to many small triangular facets. The PO method is

used to calculate the induced currents on each facet. The

scattered field is computed using the radiation integrals [4].

In this paper, a two-step approach is proposed in order to

predict the RCS of any target. Firstly, a 3D model of the target

is created and refined according to available data, photos and

videos. Then, the POFACETS code is employed. More

specifically, this approach comprises the following actions:

Preprocessing of high def. 2D images (or still images

from videos) of the object under test, by converting

them to drawings, using software such as GIMP.

Estimation of the overall dimensions of the object.

Construction of a properly scaled 3D model, based

upon the above-mentioned drawings and dimensions,

e.g., in AUTODESK 3ds Max or in Blender 3D suite.

Fine-tuning of the 3D model, based on photos/videos.

Running simulations with the POFACETS program.

This approach elaborates on the idea which appeared in [5]

and was previously presented in [6]. In this work, a novel RCS

reference diagram for various targets is given, with respect to

the relevant detection ranges. Furthermore, new results are

provided, based on better target models. The results obtained

are consistent with RCS values available from open sources,

proving the viability of our approach.

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current

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https://doi.org/10.1109/MILTECHS.2017.7988835

http://ieeexplore.ieee.org/document/7988835/

Figure 1. RCS (in log scale) of various targets versus the respective detection range for the AN/APG-68(V)9 radar, assuming that a standard target of 1 m² RCS is

detected at 38 nautical miles. The targets are depicted with gray rectangles, the size of which depends on the estimation uncertainty of their RCS [7].

For each target, the distance from the left vertical axis represents the maximum range at which an F-16 fighter would detect that target.

II. RCS VALUES FOR VARIOUS TARGETS

Avoiding the formal definition of the RCS, which would

involve the strengths of the electric and magnetic fields, a more

intuitive definition states that the RCS of a target is the

projected area of a metal sphere which would scatter the same

power in the same direction as the target does [1].

The RCS, often represented by the symbol σ and expressed

in square meters (m²) or in dBsm (dB with respect to 1 m²),

depends on the actual size, the shape, and the reflectivity of the

target (i.e., on the materials used). In other words, for a certain

radar, the RCS can be expressed as the product of three factors:

σ = Projected cross section × Directivity × Reflectivity

The RCS is one of the factors in the radar equation. In fact,

the range at which a radar detects a target is proportional to the

4th root of the target's RCS. Therefore, reducing the RCS of a

target is crucial. The most important RCS reduction method is

shaping, thus affecting directivity. Radar Absorbent Materials

can be used to decrease reflectivity, further reducing the RCS.

As a target, i.e. an aircraft or a missile, moves in space, its

RCS exhibits significant fluctuations. However, a mean value

can be computed for the front sector of a target, offering an

estimation of the maximum detection range of this target for a

certain radar set. The mean RCS of any military aircraft or

missile is classified and would not be revealed by the

manufacturer. Nevertheless, the RCS can be measured in

suitable setups, such as test ranges, or predicted with the help

of computational electromagnetics, as proposed in this work. In

this way, mean RCS values for various targets have appeared

in the literature. A comprehensive RCS table for several targets

can be found in [7].

Similarly, detection/tracking ranges for aircraft fire control

radars are classified. On the other hand, there can be informal

"leaks", mainly from users. For example, concerning the

Northrop Grumman AN/APG-68(V)9 mechanically scanned

array radar, equipping recent F-16 jet fighters, there seems to

be a consensus among F-16 enthusiasts on the maximum

detection range, running into about 38 nautical miles (n.m.) for

a standard target of 1 m² RCS (see for example [8]).

Taking this value as granted (without confirming, nor

disproving it), the "detection range vs RCS" curve can be

derived from the classic radar equation. However, in Figure 1,

the inverse curve is shown, i.e., RCS (in m², log. scale) vs

maximum detection range (in n.m.) for the APG-68(V)9 radar.

In this way, the range at which an F-16 jet can detect each

potential target is shown in linear scale from the left axis.

Trying to depict the RCS of the various targets appearing in the

relevant table in [7], the gray rectangles shown in Figure 1 are

created, due to the uncertainty (min and max RCS estimated

values), corresponding to different detection ranges.

Looking at Figure 1, one can roughly define 3 categories:

a. Legacy fighters, whose RCS is more than 1 m². They can

be detected at ranges far more than 40 n.m.

b. Modern fighters with reduced RCS, from 0.1 to 1 m²,

with detection ranging roughly from 20 to 40 n.m.

c. Stealth fighters, with RCS less than 0.1 m². They can be

detected only at close ranges, up to 20 n.m.

III. TARGET MODELLING

A. Lockheed Martin F-16 Fighter

The venerable F-16 is a mature aircraft type, so it is not

hard to find specs, photos, and certain drawings. Therefore,

open source blueprints are used as a starting point to create a

3D model of the aircraft. This 3D model will be compared and

refined with respect to numerous photos, taken from various

angles.

In the AUTODESK 3ds MAX software, one can use

simple geometrical forms (geometries), like cylinders and

cubes, to create more complicated designs. Any simple

geometry can be an editable poly, consisting of vertices, edges

and polygons. By extruding and moving the elements, more

complicated geometries can be defined.

Figure 2. Adjusting the editable poly representing the F-16 fuselage,

according to the blueprints data.

For the F-16, a cylinder is first designed, representing the

fuselage. Then, the geometry is converted into an editable poly.

After editing the vertices, the fuselage can be modelled. The

next step is the modelling of the canopy. The polygons in the

front part of the fuselage, which can be edited to model the

canopy, are extruded and then edited by moving vertices to

represent the shape of the canopy. The use of reference photos

was necessary for the canopy.

Figure 3. The F-16 model with the radar nose cone. However, in the

simulation runs, the model used was without the radar nose cone, which is

more or less transparent to the radar transmission.

Regarding the engine exhaust nozzle, the edge on the end

of the fuselage is moved and then scaled. For the radar nose

cone, a sphere is created, scaled and divided in half. Then, it is

further edited, to approach the desired shape. In Figure 2, the

editable poly of the F-16 fuselage is depicted.

The main part of the model is now ready and will be used

as a base, to design and attach the remaining parts. The model

should be more or less symmetrical, therefore the command

symmetry will be applied. So, changes in one side will

automatically be applied to the other side, as well. As the

model is projected in front view, the deletion of half the model

is necessary. Then, by applying symmetry, the model is

mirrored. Also, the turbosmooth command is very useful, as

the flat areas are smoothed and curves are more accurate.

Figure 4. F-35 edited photo, used for reference.

The wings can be modelled by extruding the polygons in

the side of the fuselage where the wing root is located. Then by

scaling along the z axis the polygons that model the wingtip,

the wing will be modelled as the scaling affects all the

connected polygons. The stabilators will be modelled

separately by applying the same process. External armament,

pods or fuel tanks can be also modelled separately, and then

can be attached to the main model, if necessary. In Figure 3,

one can see the F-16 model with the radar nose cone.

Figure 5. An F-35 screenshot from a video, used to refine the F-35 model.

B. Lockheed Martin F-35 Fighter

For the F-35, a 3D model was created with the help of the

open source Blender 3D creation suite. This model was further

edited by comparing it to available photos and videos, such as

the ones in Fig. 4 and 5. Two models were created, one with

and one without the nose cone (which in fact is transparent,

from the RCS point of view). The model with the nose cone is

depicted in Fig. 6 and 7.

Figure 6. The F-35 wire model.

C. Dong-Feng 15 (DF-15) Missile

The DF-15 is a short-range ballistic missile developed in

China, in three variants (-A, -B, -C). Creating a 3D model of a

simple missile in CATIA v5 is a fast and accurate process. The

photo used as reference is inserted in CATIA v5 in Sketch

Tracer mode, having selected the front view. The image may

not be placed in the center of the axis system. The user can

move the axis system before accepting the inserted image. The

axis system should be placed in such a way that the z axis

divides the missile in two equal parts. Then, a new part is

inserted. In sketch mode the outline of the missile must be

drawn. Profile and spline are in most cases enough to complete

the half outline.

Figure 7. The F-35 3D model.

The next step is the shaft command. In the workshop mode,

the outline is selected. By applying shaft and selecting the z

axis as reference, the outline is rotated 360° and a solid missile

is created. Finally, the model is properly scaled, according to

available info on the dimensions of the missile.

The fins should also be modelled. In a new sketch, the

outline of a fin is created using the same process. Then, the

pad command is applied and the outline is extruded creating a

solid fin. Three other fins must be created symmetrically, by

using the circular pattern and placing each fin at 90° from the

previous one, while selecting the fuselage axis as reference.

Figure 8. DF-15 –C 3D model in CATIA.

IV. PHYSICAL OPTICS AND RCS PREDICTION WITH THE

POFACETS CODE

In a spherical coordinate system (r, θ, φ), the magnetic

incident field coming from a point source to any point is:

Ηi(r)=H0̂

hexp {jk ̂

r⋅r}

where

H0

is a constant,

̂

h

is the polarization vector (

̂

θ

or

̂φ

) for the magnetic field,

k=2π /λ

is the wavenumber,

r

is

the position vector and

̂r

the unit vector to the source. The

surface current density

Js

induced on the scatterer or the

Physical Optics (PO) current is approximated by the following

expression:

Js≈{2̂n×Hiin the illuminated region

0 in the shadow region

,

where

̂n

is the unit normal vector on each point on the

scatterer surface S. Now, the scattered field can be obtained by

the integral of the PO current. Using the far field expression

for the PO back-scattered field, the scattered magnetic field

Ηs(rs)

at any point

rs

is approximated by:

Ηs(rs)≈−jk

4π

e−jkr s

rs

∬

S

̂

rs×Js(r')⋅exp {jk ̂

rs⋅r'}d2S '

,

where S is the illuminated portion of the scatterer, r' is the

location of an arbitrary point on S,

̂n(r')

is the unit normal

vector on S at r' and

rs

is the magnitude of

rs

[3][9].

The POFACETS 4.1 code which was used to calculate the

target RCS with the help of the Physical Optics method is

running in the MATLAB environment. It can import .stl files

and convert them to .m files, to be processed by MATLAB.

The imported 3D models are considered to be Perfect Electric

Conductors. The monostatic RCS is computed, where the

transmitter and the receiver are co-located. As mentioned

above, scattering objects are approximated by arrays of

triangles (facets) and the scattered field of each triangle is

computed as if it were isolated and other triangles were not

present. Multiple reflections, edge diffraction and surface

waves are not taken into account. Shadowing is included by

considering a facet to be completely illuminated or completely

shadowed by the incident wave [4]. All parameters are set to

default values, unless otherwise specified.

Figure 9. RCS polar plot for the F-16 model, at 10 GHz and at the same

level (the aircraft nose is pointing upwards).

A. F-16 Model RCS Simulation Results

The RCS of the F-16 model was computed for a radar

transmitting at 10 GHz (X-Band), emulating a typical aircraft

fire control radar. The RCS pattern shown in Fig. 9

corresponds to the polar plot of the F-16 fighter RCS, observed

from the same level (θ=90° and φ ranging from 0° to 360°).

The mean frontal RCS, averaged from -30° to +30° in azimuth

(in steps of 1°) and from -15° to +15° in elevation (in 5° steps)

is -2.8 dBsm (0.525 m²).

The mean RCS of the F-16C is reported to be 1.2 m², while

the RCS of the F-16IN proposed in the context of the recent

MMRCA contest in India is at the 0.1 m² class (with an AESA

radar) [7]. Therefore, the result obtained from the proposed

approach (based on an F-16 model with AESA radar) is quite

reasonable, falling between these two RCS values. It should be

noted that if further RCS reduction measures had been taken

into account, such as the HAVE GLASS program, the RCS

would be even smaller, approaching the F-16IN RCS value.

Concerning the computational requirements, a complete run

calculating the F-16 RCS for φ ranging from 0° to 360°, with a

step of 1°, would require less than one hour on an ordinary

Intel i3 CPU, running at 2.5 GHz.

B. F-35 Model RCS Simulation Results

The F-35 model presented in the previous section was

imported to the POFACETS algorithm and was employed for a

series of simulation runs. The computed RCS does not take

into account the possible coating with a radar-absorbent

material (RAM), which decreases the RCS by distributed

loading [10]. The F-35 features advanced RAM (“fiber mat”),

which is more durable and requires less maintenance, with

respect to coatings of older stealth aircraft [7]. More recent

reports [11], refer to carbon nanotubes (CNT) technology,

absorbing electromagnetic waves over a wide range of

frequencies. Therefore, the actual RCS values are expected to

be lower than the ones obtained by POFACETS.

It should be noted that RAM coatings are frequency

selective, i.e., they are more efficient at specific frequency

bands, for example at the X-band. At lower frequency bands,

RAM coatings are less effective. To take into account RAM, a

rudimentary approach would be to subtract 10 dB from the

values calculated by the POFACETS code, at least concerning

X-band and higher frequency bands.

The mean overall RCS and the mean front sector RCS

(averaged from -30° to +30° in azimuth, in steps of 1°, and

from -15° to +15° in elevation, in steps of 5°) were calculated

at various frequency bands, from VHF to Ku-Band. The results

are shown in Figure 10, indicating that the RCS is not so small

in lower frequency bands. Considering that RAM is much less

efficient at lower frequencies, it turns out that VHF or UHF

radars seem to be a quite promising counter-stealth approach.

According to the results shown in Figure 10, the mean RCS

at 10 GHz (without the use of RAM) for the front sector is

-10.1 dBsm. Taking into account the use of RAM, the RCS

would be further reduced to the class of -20 dBsm, which

corresponds to 0.01 m², confirming that the F-35 exhibits a

really low RCS. This value is higher than but quite close to the

RCS values appearing in various sources, which estimate the

front sector RCS of the F-35 from 0.0015 to 0.005 m² [7].

In Figure 11, one can see the overall F-35 RCS, looking at

the target from below (10° depression angle), at a carrier

frequency of 10 GHz. The RCS appears to be relatively small

in a wide sector in the front, apart from the peaks produced by

the leading edges of the wings (approximately at 35° off-axis),

while it attains higher values at the sides (as expected, due to

the wings and the fuselage).

Figure 10. The mean overall RCS and the mean front sector RCS (averaged from -30° to +30° in azimuth and from -15° to +15° in elevation) of the F-35

model vs frequency. It is clear that the RCS is not so small at lower frequency bands. The indicated values do not take into account the use of Radar Absorbent

Material (RAM), which would further reduce the RCS, at least at higher frequency bands (S-Band and higher).

Figure 11. RCS polar plot for the F-35 model, seen from 10° below, at a

carrier frequency of 10 GHz (the aircraft nose is pointing upwards). The

average frontal and rear RCS are really low. Actual values are lower,

taking into account the use of RAM.

C. Dong-Feng 15 (DF-15) Model RCS Simulation Results

The simulation runs were performed on the DF-15 -C

model. Averaging the frontal RCS in a similar manner as

before, the result at 10 GHz is at the class of -17 dBsm.

Following the same approach, by subtracting 10 dB, as a rough

approximation of the use of RAM, the RCS becomes -27

dBsm, i.e., 0.002 m². At 150 MHz, the average head-on RCS

reaches -13 dBsm (0.05 m²). In the VHF-Band, RAM is quite

ineffective, without any considerable RCS reduction.

The RCS of the DF-15 missile has been reported to be

0.002 m² in the X-Band and 0.6 m² in the VHF-Band [12]. In

the X-Band, the above mentioned result coincides with the

reported RCS. In the VHF-Band, the computed RCS is higher

than the one at 10 GHz, but the difference is not as dramatic as

implied in [12]. However, it should be noted that the

POFACETS algorithm is expected to yield more accurate

results at the higher frequency range, closer to the optical

domain.

V. CONCLUSIONS

Trying to depict the RCS estimation for various targets in

parallel with the respective detection ranges for a certain radar

set, a novel “RCS vs range” diagram was given. In this

diagram, the maximum detection range of the F-16 fighter

radar for several targets is visualised. The importance of low

RCS is obvious, as well as the advantage of stealth fighters

against legacy fighters.

In order to estimate the RCS of a potential target, a 3D

model is created and further elaborated, with the help of

appropriate 3D editing software, in an attempt to minimize any

obvious difference with respect to available images. The

refined 3D model is imported to the POFACETS program,

running in the MATLAB environment, which is a

computational electromagnetics approach to the issue of RCS

prediction, based on the Physical Optics method. The proposed

approach has been tested on the F-16 and F-35 jets, as well as

on the DF-15 -C short range ballistic missile, with encouraging

results, which are fairly close to values appearing in the open

literature. The computer requirements were not prohibitive,

since a complete polar plot, with a step of 1°, would take less

than an hour, on a typical Intel i3 CPU. Taking into account the

above, it is evident that the Physical Optics method yields quite

plausible results, in reasonable time.

Concerning the F-35 stealth fighter, the proposed approach

confirmed that it exhibits a really small RCS at higher

frequency bands, such as the X-Band, in the class of -20 dBsm

or 0.01 m² (taking also into account the use of RAM – Radar

Absorbent Material). In other words, the F-35 RCS is expected

to be more than 100 times smaller with respect to the RCS of a

standard F-16 fighter. However, its RCS appears to be not so

small at lower frequency bands, such as the VHF-Band, where

RAM is also considered to be rather ineffective. Therefore, the

exploitation of lower frequency bands seem to be a viable anti-

stealth approach.

Figure 12. RCS diagram for the DF-15 missile, at 10 GHz and at the same

level (the missile is pointing upwards).

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