A Preliminary Assessment of Specular Radar Cross Section Performance in the Sukhoi T-50  Prototype

Pelosi, Michael J.; Kopp, Carlo

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A Preliminary Assessment of Specular Radar Cross Section Performance in the Sukhoi T-50 Prototype

Air Power Australia Analysis 2012-03
12th November 2012

A Paper by
Dr Michael J Pelosi, MBA, MPA,
Dr Carlo Kopp, AFAIAA, SMIEEE, PEng
Text, computer graphics © 2012 Michael Pelosi, © 2012 Carlo Kopp

Sukhoi T-50 prototype public demonstration [click to enlarge]. The shaping design of the T-50 presents no fundamental obstacles to its development into a limited aspect coverage Very Low Observable design (KnAAPO).

	Abstract
	This study has explored the specular Radar Cross Section of the Sukhoi T-50 prototype aircraft shaping design. Simulations using a Physical Optics simulation algorithm were performed for frequencies of 150 MHz, 600 MHz, 1.2 GHz, 3.0 GHz, 6.0 GHz, 8.0 GHz, 12.0 GHz, 16.0 GHz and 28 GHz without an absorbent coating, and for frequencies of 1.2 GHz, 3.0 GHz, 6.0 GHz, 8.0 GHz, 12.0 GHz, 16.0 GHz with an absorbent coating, covering all angular aspects of the airframe. Modelling has determined, that if the production T-50 retains the axisymmetric nozzles and smoothly area ruled sides, the aircraft would still deliver robust Very Low Observable performance in the nose aspect angular sector. Conversely, if the production T-50 introduces a rectangular faceted nozzle design, and refinements to fuselage side shaping, the design would present very good potential for robust Very Low Observable performance in the S-band and above for the nose and tail aspect angular sectors, with marginal performance in the beam aspect angular sector. This study has therefore established through Physical Optics simulation across nine radio-frequency bands, that no fundamental obstacles exist in the shaping design of the T-50 prototype, which might preclude its development into a genuine Very Low Observable design with constrained angular coverage.

Index

Index
Introduction
T-50 Prototype Very Low Observable Airframe Shaping Design Features
Radar Cross Section Simulation Method / Simulator Design and Capabilities
- Aircraft Model Features and Limitations
- What the Simulation Does and Does Not Demonstrate
Specular Radar Cross Section Simulation Results
- Analysis of Shape Related Specular Radar Cross Section
- Analysis of Specular RCS with a RAM Coating
Conclusions
Endnotes, References and Bibliography
Annex A Scales, Bands, Geometries
Annex B Viewing RCS Plots
Annex C Glossary of Terms
Annex D What the Simulation Does Not Demonstrate
Annex E Comparative Analysis of Specular RCS - T-50 Versus J-20
Annex F Additional Notes on Physical Optics RCS Modelling

Introduction

The Russian Sukhoi/KnAAPO T-50/I-21/Article 701 PAK-FA (Перспективный Авиационный Комплекс Фронтовой Авиации) was the first manned combat aircraft design intended to possess low observable capabilities in the radar bands to be developed and publicly flown by a nation other than the United States, the first public flight shown in early 2010¹.

This paper extends earlier research focussed on the design of the T-50, and the Chengdu J-20, to provide a more accurate and quantitative preliminary assessment of the specular Radar Cross Section [RCS] of the T-50 design^2,3.

A full and comprehensive assessment of the RCS of any Low Observable [LO / -10 to -30 dBSM, Refer Table A.1] or Very Low Observable [VLO / -30 to -40 dBSM, Refer Table A.1] aircraft design is a non-trivial task, as careful consideration needs to be given to all major and minor RCS contributors in the design, of which there can be a large number in a complex design such as a combat aircraft.

If such an assessment is to be genuinely useful, it must consider the vehicle's RCS from a range of different angular aspects encompassing azimuthal sectors and also elevation or depression angles characteristic of the surface and airborne threat systems the LO/VLO design is intended to defeat [Refer Figures A.3 and A.4].

The assessment of RCS must always be performed at the operating wavelengths typical of the surface and airborne threat systems the LO/VLO design is intended to defeat [Refer Table A.2].

Definitions of these and other terms employed in this document are summarised in Annex C. Reference data for RCS scales, radio-frequency bands, engagement geometries are summarised in Annex A. A summary of representative threat systems is available in Annex A, in an earlier publication³.

The T-50 was developed specifically to compete against the F-22 Raptor in traditional Beyond Visual Range (BVR) and Within Visual Range (WVR) air combat. As a result, the T-50 shares all of the cardinal “fifth generation” attributes until now unique to the F-22 - stealth, supersonic cruise, thrust vectoring, highly integrated avionics and a powerful suite of active and passive sensors.

The PAK-FA therefore firmly qualifies as a “fifth generation” design. In addition, it has two further attributes not introduced in the F-22 design. The first is “extreme plus agility”², resulting from advanced aerodynamic design, exceptional thrust/weight ratio performance and three dimensional thrust vectoring integrated with an advanced digital flight control system. The second attribute is exceptional combat persistence, the result of an unusually large 25,000 lb internal fuel load. The former entailed some shaping compromises, at the expense of specular RCS performance.

The basic shaping design observed on prototypes of the PAK-FA will deny it the critical all-aspect stealth performance of the F-22, critical in BVR air combat and deep penetration operations. Despite this, the extreme manoeuvrability/controllability design features of the PAK-FA, which result in extreme plus agility, result in the potential for the PAK-FA to become the most lethal and survivable fighter ever built for air combat engagements.

The publicly displayed PAK-FA prototypes do not represent a production configuration of the aircraft, which is to employ a new engine design, and extensive VLO treatments which are not required on a prototype.

This assessment, like the earlier assessment performed on the J-20 design, cannot be more than preliminary for a number of important reasons:

The final airframe shaping remains unknown, and changes may arise through the development cycle, to improve aerodynamic performance, operational characteristics, and LO/VLO performance;
The state of Russian Radar Absorbent Materials (RAM), Radar Absorbent Structures (RAS) and radar absorbent coatings technology is not well understood in the West;
The state of Russian technologies for sensor aperture (radar, EO, passive RF) structural mode RCS reduction is not well understood in the West;
The state of Russian technologies for RCS flare spot reduction, in areas such as navigation/communications antennas, seals, panel joins, drain apertures, cooling vents, and fasteners is not well understood in the West.

Achievement of credible LO or VLO performance is the result of a design having intended RCS characteristics in all of these categories⁴.

Proper airframe shaping, as stated in Denys Overholser's famous dictum, is a necessary and essential prerequisite for good LO or VLO performance. If shaping design is deficient, no amount of credible materials application and detail flare spot reduction can overcome the RCS contributions produced by the airframe shape, and genuine VLO performance will be therefore unattainable. While this is self-evident, it is often not well appreciated.

If airframe shaping is credible, then careful and well considered application of Radar Absorbent Materials (RAM), Radar Absorbent Structures (RAS), radar absorbent coatings, aperture RCS reductions, and minor flare spot reduction techniques will yield a VLO design.

Modelling of the shape related RCS contributions of any VLO design is of very high value, as it determines not only whether the aircraft can achieve credible VLO category performance, but also where the designers will be investing effort in RAS, RAM and coating application to achieve this effect. Moreover, it exposes the angular extents within which the aircraft has poor RCS performance, and thus provides a robust basis for development of tactics and technique to defeat the design.

This paper will focus mostly on shape related RCS contributions, both due to the high value of knowing weaknesses in the design, but also due to the uncertainties inherent in estimating the performance of unknown technologies for RAS, RAM, coatings, aperture RCS reductions, and minor flare spot reduction. Where applicable, reasonable assumptions will be made as to the performance of absorbent material related RCS reduction measures.

T-50 Prototype Very Low Observable Airframe Shaping Design Features

Figure 1. The lower fuselage of the prototype displays interesting incongruities. There is an abrupt transition between the carefully sculpted faceting of the inlet nacelles, and the smoothly curved aft engine nacelles and conventional aft fuselage. The faceting strategy is similar to the F-22 design rules, with singly or doubly curved transitions between planes (C. Kopp/Sukhoi image)².

An extensive qualitative analysis of RCS reduction shaping feature design in the T-50 aircraft was performed in 2010. That analysis yielded the following observations, cited here for convenience²:

The forward fuselage is closest in general configuration to the YF-23, especially in the chining, cockpit placement, and hump aft of the cockpit canopy, although the blending of the upper forward fuselage into the upper carapace is more gradual.
There are important differences from the YF-23. The chine curvature design rule is purely convex, like the chine design on the F-22A. The nose height is greater, to accommodate an AESA with a much larger aperture than that intended for the YF-23 or F-22A.
If flare spots are properly controlled by the application of materials and serrated edge treatments around the canopy, and a good bandpass radome design using a frequency selective multilayer laminate is employed, the shaping related RCS contribution of the forward fuselage in the S/X/Ku-bands will be similar to that observed with the F-22A, YF-23 or F-35.
The edge aligned movable LEX are readily treated with leading edge absorbers and will not present a major RCS flare spot. The treatment of the movable join will present the principal challenge in this portion of the design. The obtuse angle in the join between the LEX and forward fuselage is characteristic of good design and is very similar to the angles used in the F-22.
The edge aligned trapezoidal main engine inlets are similar in configuration to the F-22, but with important differences. The inlet aspect ratio is different, and the corners are truncated in a manner similar to the YF-23. If properly treated with leading edge inserts and inlet tunnel absorbent materials, the inlet design should yield similar RCS to its US counterparts.
The placement of the engine centrelines well above the inlet centroids, in the manner of the YF-23, results in an inlet tunnel S-bend in the vertical plane. Sukhoi have not disclosed whether an inlet blocker will be employed. The use of an S-bend in the PAK-FA would permit an increase in the number of surface bounces further increasing attenuation and reducing RCS.
In the S/X/Ku-bands the basic shaping of the forward fuselage will permit the attainment of genuine VLO performance with the application of mature RAS and RAM, where the centre and aft fuselage do not introduce larger RCS contributions from the forward aspect.
The wing design from a planform perspective is closest to the F-22A, and the upper fuselage similar to the YF-23, permitting the achievement of similar RCS performance to these US types, from respective aspects.
Where the PAK-FA falls well short of the F-22A and YF-23 is the shaping design of the lower fuselage and side fuselage, where the general configuration, wing/fuselage join angles, and inlet/engine nacelle join angles introduce similar intractable specular return problems as observed with the F-35 Joint Strike Fighter design. These are inherent in the current shaping design and cannot be significantly improved by materials application. .... the PAK-FA prototype design will produce a large specular return in any manoeuvre where the lower fuselage is exposed to a threat emitter, and this problem will be prominent from the Ku-band down to the L-band.
This problem is exacerbated by the inboard ventral wing root fairings, claimed by some Russian sources to be pods for the concealed carriage of folding fin close combat AAMs, such as the RVV-MD/R-74 series. While these fairings do not introduce large RCS contributions from fore or aft aspects, they will adversely contribute to beam aspect RCS, especially for threats well below the plane of flight of the aircraft.
The tailboom shaping is reminiscent of the F-22 and F-35 designs, and will not yield significant RCS contributions from the front or aft aspects.
In the lower hemisphere, it will suffer penalties due to the insufficiently obtuse join angles between the wings and stabilators, and outer engine nacelles.
The upper fuselage fairings which house the all moving vertical tail actuators are well shaped, and the join angles are well chosen.
The outward cant of the empennage fins is similar to United States designs, and like the YF-23 tail surfaces, these are fully articulated with the VLO benefit of removing surface impedance discontinuities at the join of a conventional rudder control surface.
The axi-symmetric 3D TVC nozzles present the same RCS problems observed with the fixed axi-symmetric nozzles used in the F-35 JSF, and the application of serrated shroud treatments and tailpipe blockers as used with the F-35 JSF will not overcome the inherent limitations of this canonical shaping design. Observed from the aft hemisphere in the L-band through Ku-bands, the PAK-FA prototype configuration will produce to an order of magnitude an equally poor RCS as the F-35 Joint Strike Fighter⁵.
The centre fuselage beavertail follows a similar chine design rule as the forward fuselage does, and will not present a significant RCS contribution from behind.

These observations reflected the design of the first prototype. Subsequent prototypes, publicly displayed, do not fundamentally differ in any of these design features.

The qualitative analysis yielded the conclusion that with proper application of materials technology, detail feature RCS reduction treatments, aperture structural mode RCS reduction measures, the T-50 had potential to yield viable VLO performance in the forward sector, and with a nozzle design similar to the F-22A, had potential for viable VLO performance in the aft sector. Performance in the beam sector and lower hemsiphere were identified as problematic. This conclusion was a result of several specific shaping features, specifically the lower fuselage tunnel design, and the absence of obtuse angle joins between the aft fuselage sides and wing / stabilator joins, and the obtuse join angles in the fuselage tunnel.

Quantitative RCS modelling will demonstrate that these observations were valid.

Radar Cross Section Simulation Method / Simulator Design and Capabilities

The Physical Optics (PO) method is used to predict the RCS of complex targets, in this instance the Sukhoi T-50 prototype. The simulation software employed for this purpose was identical to that employed for the earlier modelling of the Chengdu J-20 aircraft, and is detailed in that document³.

A detailed discussion of the PO algorithm employed in POFACETS can be found in Chatzigeorgiadis and Garrido⁶.

To enhance data representation during analysis, a software tool was developed to produce a three dimensional representation of the PolyChromatic Spherical Representation (PCSR) presentation of RCS data, which can be rotated and zoomed by a user, interactively, refer Figure 2. PCSR format data for any given frequency could be processed into a coloured Stereo Lithographic format (StL) file⁷.

Figure 2. A screen dump of the pcsrgen tool output, using the VisCAM View 5.2 StL viewer tool (Petroulias).

No data in PCSR StL format will be presented in this paper due to the large size of the StL files, which for the baseline resolution employed in modelling are 207.4 Megabytes each, uncompressed. Presenting nine frequency bands, with two surface models, yields an aggregate storage requirement of no less than 3.7 Gigabytes uncompressed, and 0.54 Gigabytes, compressed with the zip algorithm. While this is acceptable for analytical use in a desktop environment, it is not practical for online deployment and web publishing.

Aircraft Model Features and Limitations

The model used was an extant public domain 25,967 facet representation constructed from publicly available high and medium resolution photographic imagery of the T-50 first prototype, observed since January, 2010. This model was compared extensively with photographic imagery to establish fidelity in shaping, especially in angles and join angles between flat surfaces.

As the T-50 model employs nearly eight times as many facets as the model employed previously for the J-20, it provides much better ability to capture the finer detail shaping of the vehicle.

All simulations presented are for a closed engine nozzle position, which is the most frequent case in operational use of such aircraft, and thus of most interest.

The nose and tail stinger mounted radar antenna radomes are assumed to be bandpass design, emulating United States fighter designs, and were assumed to be fully opaque at all frequencies of interest.

The model assumes an insignificant structural mode RCS contribution from the radar antenna faces and radar bay bulkheads, consistent with a properly designed bandpass radome in its stopband region. Given the absence of any useful data on the internal configuration of the radomes and antenna bays, a more elaborate model would be entirely speculative.

The engine inlet tunnels were modelled as Perfect Electrical Absorbers (PEA), as with earlier effort on the J-20. Given the absence of any useful data on the internal configuration of the inlets and tunnels, a more elaborate model would again be entirely speculative.

The exhaust tailpipe RCS contributions were also modelled as Perfect Electrical Absorbers (PEA), as with earlier effort on the J-20. Given the absence of any useful data on the internal configuration of the tailpipes, or any applied RCS reduction treatments, a more elaborate model would be, as before, entirely speculative. Importantly, this model reflects the prototype configuration, with an interim AL-41F1 engine. The nozzle design and tailpipe configuration for the full rate production engine has yet to be disclosed and could be very different in design.

The cockpit canopy transparency was modelled as a Perfect Electrical Conductor (PEC), to emulate the effect of a gold or other highly conductive plating layer in the polycarbonate laminate structure.

The photographic imagery of the T-50 prototypes was easily of sufficient quality to incorporate useful detail of panel join boundaries, door boundaries, and other surface features which produce RCS contributions due to surface travelling waves coupled to the aircraft skin. These features were not modelled, due to the small RCS contributions they present in a PO specular RCS modelling environment.

In summary, the model employed provides better shaping fidelity than the model previously employed in modelling the J-20, but is also constrained by similar fundamental limitations.

What the Simulation Does and Does Not Demonstrate

The specific limitations of the simulation tools employed are detailed in Annex D.

The combination of the T-50 aircraft geometry and the use of the PO method without the Mitzner/Ufimtsev edge current corrections will yield errors at the frequencies of interest of less than 1 dB for broadside backscatter sources in the beam aspect and tail aspect sectors, which both have dominant specular scatterers. The nose aspect angular sector results will strongly underestimate RCS, in part due to the absence of shallow angle specular contributions not modelled by the Mitzner/Ufimtsev edge current corrections, and by the absence of surface travelling wave backscatter contributions from surface features, gaps and trailing edges.

Demonstrably, the errors arising from the limitations of the PO computation method all fall into areas where well established RCS reduction treatments using RAS, RAM or coatings would be used, thus reducing the relative magnitude of the errors in the resulting RCS result for angles other than the peak mainlobes produced by these backscatter sources.

Importantly, even were the simulator capable of modelling shallow angle specular and non-specular RCS contributors, the Russian MoD would not permit sufficiently detailed disclosures on the RCS reduction treatments applied to the airframe design, as a result of which reasonable assumed parameters would have to be applied instead of actual values.

The latter underscores, as was the case with previous effort on the J-20 prototype, the difficulty in attempting to perform highly accurate numerical RCS modelling of foreign airframe designs, where access to high fidelity shaping data, surface feature data, and materials type and application is actively denied.

Despite its limitations, the PO method provides considerable utility:

The simulation can accurately capture the direction of mainlobes and sidelobes produced by specular backscatter returns, especially where major specular reflectors produce strong contributions; this includes broadside and lesser specular returns from the wings, control surfaces and major reflecting areas of the fuselage, inlet exteriors and nozzles;
For an untreated PEC skin, the simulation can accurately capture the absolute and relative magnitudes of mainlobes and sidelobes produced by specular backscatter returns, especially where major specular reflectors produce strong contributions; this includes broadside and lesser specular returns from the wings, control surfaces and major reflecting areas of the fuselage, inlet exteriors and nozzles;
In capturing mainlobes and sidelobes of major specular scatterers it permits an assessment of the angular extent in the nose and tail sectors where diffraction and surface travelling wave backscatter is dominant, and can still be suppressed effectively;

Importantly, if the results of the Physical Optics specular return modelling yield RCS values from key aspects, at key frequencies, which are consistent with stated VLO performance values in US designs, to an order of magnitude, it is reasonable to conclude that a mature T-50 design will qualify as a genuine VLO design.

Specular Radar Cross Section Simulation Results

Specular RCS of the T-50 prototype was modelled for full spherical all-aspect coverage, for nine frequencies of interest.

Frequencies were carefully chosen to match likely threat systems the T-50 would be intended to defeat in an operational environment. These chosen operating frequencies are:

150 MHz to defeat Chinese built VHF band Counter-VLO radars such as the CETC JY-27 Wide Mat, NRIET / CEIEC / CETC YLC-4, CETC YLC-8/8A and CPMIEC HK-JM2⁸;
600 MHz to defeat UHF band radars such as those carried by the E-2C/D AEW&C system, or the widely exported Russian Kasta 2/2E and P-15/19 Flat Face / Squat Eye series;
1.2 GHz to defeat L-band surface based search, acquisition and GCI radars, and the Northrop-Grumman MESA AEW&C radar;
3.0 GHz to defeat widely used S-band acquisition radars, and the E-3 APY-1/APY-2 AWACS system;
6.0 GHz to defeat C-band Surface-Air-Missile engagement radars such as the MPQ-53/65 Patriot system;
8.0 GHz to defeat a range of X-band airborne fighter radars, Surface-Air-Missile engagement radars such as the 30N6E Flap Lid / Tomb Stone, and 92N6E Grave Stone, and a range of Western and Russian Surface-Air-Missile seekers;
12.0 GHz to defeat a range of X-band airborne fighter radars, Surface-Air-Missile engagement radars, and Surface-Air-Missile and Air-Air-Missile seekers;
16.0 GHz to defeat a range of K_u-band airborne fighter radars, and Surface-Air-Missile engagement radars, and Surface-Air-Missile and Air-Air-Missile seekers;
28.0 GHz to defeat a range of K-band missile seekers, and Surface-Air-Missile engagement radars;

RCS simulation results are presented in PCSR and PCPR formats. The latter includes rulers to show the most important elevation/depression angle rings/zones, and the four azimuthal quadrants.

Analysis of Shape Related Specular Radar Cross Section

The results of the physical optics simulation modelling of specular RCS for the T-50 shape, using an idealised PEC skin for all external surfaces, are displayed in Tables 1 and 2, for a vertically polarised E component.

Results have been plotted in PCSR format for nine different aspects, and nine different frequencies. PCPR format plots have been produced for nine different frequencies.

Table 1. T-50 Specular RCS Model Results PEC [V-Pol] [Click Thumbnail to Enlarge]
Frequency		150 MHz	600 MHz	1.2 GHz	3.0 GHz	6.0 GHz	8.0 GHz	12.0 GHZ	16.0 GHz	28.0 GHz
θ	Φ	PEC Skin [Baseline]
0	0
180	180
090	180
090	0
090	270
045	225
135	225
045	315
135	315
dBSM Scale

Notation: The POFACETS simulator labels V-pol as “TM-z”, i.e. the magnetic H vector is transverse to the z-axis or vertical. This convention was retained for consistency in these simulation plots, with plots labelled TM being V-pol and plots labelled TE being H-pol⁵.

Table 2. T-50 Specular RCS Model Results PEC [V-Pol]
[Click Chart to Enlarge]

150 MHz

600 MHz

1.2 GHz

3.0 GHz

6.0 GHz

8.0 GHz

12.0 GHZ

16.0 GHz

28.0 GHz

Table 2 Legend:
NOSE ASPECT	Azimuthal Sector	90° centred on aircraft nose
TAIL ASPECT	Azimuthal Sector	90° centred on aircraft tail
BEAM ASPECT	Azimuthal Sector	90° centred on aircraft side
AERIAL THREAT	Depression Angle Ring	-5° - 3.7° aircraft at similar altitudes
SURFACE-AIR THREAT ~20 - 200 NMI	Depression Angle Ring	~3.7° - 20° SAM at 200 down to 20 NMI
SURFACE-AIR THREAT ~10 - 20 NMI	Depression Angle Ring	~20° - 36° SAM at 20 down to 10 NMI
SURFACE-AIR THREAT <10 NMI	Depression Angle Ring	~36° SAM inside 10 NMI
Assumptions: A.Distant threats CRPL exponential refractive atmospheric model; B.Near threats SBF refractive atmospheric model; C.Spherical earth model; D.Assumed aircraft altitude 36 kft; E.For higher aircraft altitudes the depression angles increase for nearer threats.

Threat depression angles as a function of type and missile kinematic range, for various contemporary and legacy SAM systems of Russian/Soviet manufacture (C. Kopp).

The starting point for any forensic analysis of the RCS of a new and hitherto unknown aircraft type is the study of the RCS of its shape, assuming a perfectly electrically conductive surface. This method was employed in the previous analysis of the J-20 and was also employed in this study.

The PO modelling has validated all observations in the earlier qualitative analysis.

Behaviour in the nose aspect angular sector, defined as ±45° in azimuth left and right of the nose, and between +5° in elevation, and -36° in depression, is mostly good across all bands simulated. This reflects attention paid to forward fuselage and inlet shaping and alignment, and presents no fundamental obstacles to attaining VLO performance in the nose aspect angular sector. No scattering sources introducing significant specular RCS contributions were observed at any of the modelled frequencies, although sidelobes from beam aspect scatterers begin to degrade the angular extent at UHF and VHF bands.

Behaviour in the tail aspect angular sector, defined as ±45° in azimuth left and right of the tail, and between +5° in elevation, and -36° in depression, is clearly dominated by the scattering behaviour of the pair of axisymmetric nozzles, which has major specular, cavity and diffractive scattering contributions. The behaviour of such nozzles is well detailed in earlier work covering the F-35 JSF and J-20 nozzles⁵.

Importantly, the T-50 prototypes employ an interim AL-41F1 powerplant, and associated three dimensional thrust vectoring nozzle developed for the conventional Su-27M2/Su-35S Flanker. Integration of this powerplant and nozzle introduces sub-optimal aft fuselage join geometry, and suboptimal axi-symmetric nozzles. To date there have been no definitive disclosures on the intended integration of the production powerplant, and its intended nozzle design. The aft fuselage geometry does not preclude the integration of a faceted VLO nozzle similar in concept to the F-22 design.

Therefore, tail aspect angular sector specular RCS for production T-50 aircraft might be much superior to the prototypes, and competitive against the F-22. This is important from the perspective of technological strategy, as the T-50, like the J-20, has the evolutionary potential for robust VLO performance in the tail aspect angular sector, unlike the F-35 JSF, which is constrained by commonality to an axi-symmetric nozzle.

The RCS of the untreated axi-symmetric nozzles observed on T-50 prototypes would be typically determined by the projected area of the aperture for a given aspect, and instantaneous position of the 3D TVC nozzle, and thus of the order of 1 m² in the aft sector, and presenting significant contributions in the nose sector. The location of the major lobes produced by the nozzle will depend strongly on the instantaneous position. Axi-symmetric nozzle contributions are discussed in some detail in previous work⁵.

Behaviour in the left and right beam aspect angular sectors, defined as ±45° in azimuth left and right of the beam, and between +5° in elevation, and -36° in depression, presents an interesting case study.

The grouping of primary scattering lobes in the beam aspect is quite unique in the T-50 design. The F-22 presents as a “two lobe” design and the J-20 presents as “three lobe” design, contrasting distinctly against the defacto “single lobe” design of the F-35, where complex lower fuselage convex and concave double curvatures effectively merge multiple lesser lobes into a single wide angle specular scatterer. The latter is the worst possible strategy for managing beam aspect lobes as it minimises the variation of specular return peak magnitude with elevation/depression angle.

The T-50 presents as a “six lobe” design, with specular slab reflectors and corner reflectors aligned to concentrate beam aspect backscatter into one normal ventral lobe, and five staggered lobes pointing sideways at different elevation/depression angles. This is depicted in Figures 3 and 4. The strongest peak is in the “C” lobe, centred at a depression angle of about -25° in depression.

Figure 3. The T-50 has five major lobes in the left and right beam aspect angular sectors, for convenience labelled A through E, with the flat lower fuselage mainlobe labelled F (KnAAPO image).

Figure 4. Mapping of the five major lobes in the left and right beam aspect angular sectors at 16 GHz (KnAAPO image).

Figure 5. The T-50 from behind, showing the corner joins in the inlet tunnel, and fuselage sides (KnAAPO image).

The association of the beam aspect mainlobes can be readily established from specific shaping features in the design.

Fuselage tunnel sides, partly masked by opposite inlet nacelle;
Aft fuselage engine duct join to lower wing and stabilator (corner reflector);
Inlet nacelle sides and vertical tails, forward fuselage side below chine;
Fuselage tunnel join to lower fuselage (corner reflector); ventral strake for missile carriage;
Lower wing to fuselage side join (corner reflector);

These are distinct and discrete lobes, which narrow with increasing frequency. The latter can also be observed in the horizontal plane, where lobe broadening arises with increasing severity below 3 GHz, a feature common to most fighter designs. The latter is quantified in Figure 6.

Figure 6. Frequency dependency of the angle off the longitudinal axis at which beam aspect lobe magnitude exceeds +2 dBSM, for depression angles of less than -25°. The horizontal angular width of the nose and tail aspect VLO range can be estimated by doubling the plotted value for the frequency of interest.

In summary, beam aspect specular RCS is dominated by the scattering behaviour of the almost flat slab sides, canted vertical tail surfaces, and specular return from the nozzles. This could be described as classical “bowtie” lobing behaviour, with the caveat that if the axisymmetric nozzle is retained in production aircraft, the detrimental impact of the nozzles will yield undesirable “pacman” lobing behaviour, not unlike the F-35 aircraft.

Some comparisons with other aircraft types are warranted, given the dominant effect of specular scattering mechanisms in beam aspect RCS, and the importance of beam aspect RCS in defence penetration, and air combat situations where fighter threats may present from any aspect.

The shaping of the T-50 is inferior to that of the F-22 Raptor. This is mostly a byproduct of the significantly more complex shaping of the lower fuselage area, the use of a tunnel between the engine nacelles, and the aft fuselage join between the aft engine nacelles, and fuselage at the wing and stabilator roots. The single narrow specular mainlobe produced by the careful shaping and fuselage joining of the F-22 presents a much smaller visible angular extent compared to the T-50.

The J-20, which largely emulates the advantages of the F-22 Raptor shaping configuration, is also superior to the T-50, but by a less distinct margin than the F-22 Raptor. Annex E presents a direct comparison of the specular RCS plots for both types. The J-20 performs better at higher frequencies, where the greater length of linear shaping features is better able to control mainlobe width.

The F-35 JSF exhibits similar, but in some respects more severe beam aspect specular RCS behaviour than the T-50. This is a direct consequence of the use of multiple complex double curvature convex and concave shaping features in its lower fuselage design, and lower wing root area, and a much shorter fuselage. The ventral shaping features were introduced in the SDD aircraft and were not part of the X-35 demonstrator design. Another unfortunate feature of F-35 shaping is the depression angle of the slab sides of the engine inlets, which is shallower than the F-22 and J-20 designs, and similar to the T-50, as a result of which the associated mainlobe peaks at a lesser depression angle, in turn degrading performance against long range surface based threats.

The conclusion which can be drawn from forensic analysis of the T-50 PAK-FA specular RCS modelling for a conductive surface is that its specular RCS performance will satisfy the Very Low Observable requirement that strong specular returns are absent in the nose sector angular domain. In this angular and frequency domain, i.e forward sector and S-band and above, the actual RCS performance of the design will be dominated by edge alignment to control diffracting edge mainlobe directions, and applied RAM and RAS, i.e. materials technology.

Analysis of Specular RCS with a RAM Coating

The results of the physical optics simulation modelling of specular RCS for the T-50 shape, using an idealised RAM coating model for all external surfaces, are displayed in Tables 3 and 4, for a vertically polarised E component.

Results have been plotted in PCSR format for nine different aspects, and nine different frequencies. PCPR format plots have been produced for nine different frequencies.

Images of unpainted T-50 prototypes indicate the use of multiple dissimilar skin panel materials. The likely approach that Sukhoi will pursue in surface coating will be a variation upon the “matched characteristic impedance” approach, with a conductive substrate coating applied to the aircraft's skin, and a multiple layer absorbent coating applied over the substrate⁹.

There have been no substantive disclosures on recent Russian research in absorbers, presenting difficulties in postulating even hypothetical coatings.

We opted to model the specular RCS of the T-50 with a trivial surface absorber model, mostly as it was the least challenging in computational time expended. The model employed a surface impedance of 377 Ohm / square, where Ohm / square is a measure of “sheet impedance”, in the same sense as sheet resistance. This is a low impedance model which does not contribute significantly to the attenuation of surface travelling waves, which are especially important in suppressing reflections in the nose and tail sectors.

The results of this modelling are included for completeness only, and should not be considered representative of an actual production quality treatment of surfaces. Observed lobing behaviour is identical to the PEC model, but with significant loss in the fine structure of the lobes.

Table 3. T-50 Specular RCS Model Results With RAM [V-Pol] [Click Thumbnail to Enlarge]
Frequency		150 MHz	600 MHz	1.2 GHz	3.0 GHz	6.0 GHz	8.0 GHz	12.0 GHZ	16.0 GHz	28.0 GHz
θ	Φ	377 Ohm/sq Skin Coating / PEC Substrate
0	0
180	180
090	180
090	0
090	270
045	225
135	225
045	315
135	315
dBSM Scale

Table 4. T-50 Specular RCS Model Results With RAM [V-Pol]
[Click Chart to Enlarge]

1.2 GHz

Chengdu_J-20_[2mm_Ferrite_-_4mm_CFC].mdb-01.20GHz-RsFromCoating-IncPol-TM-Pol-Theta

3.0 GHz

6.0 GHz

8.0 GHz

12.0 GHZ

16.0 GHz

28.0 GHz

Table 4 Legend:
NOSE ASPECT	Azimuthal Sector	90° centred on aircraft nose
TAIL ASPECT	Azimuthal Sector	90° centred on aircraft tail
BEAM ASPECT	Azimuthal Sector	90° centred on aircraft side
AERIAL THREAT	Depression Angle Ring	-5° - 3.7° aircraft at similar altitudes
SURFACE-AIR THREAT ~20 - 200 NMI	Depression Angle Ring	~3.7° - 20° SAM at 200 down to 20 NMI
SURFACE-AIR THREAT ~10 - 20 NMI	Depression Angle Ring	~20° - 36° SAM at 20 down to 10 NMI
SURFACE-AIR THREAT <10 NMI	Depression Angle Ring	~36° SAM inside 10 NMI
Assumptions: A.Distant threats CRPL exponential refractive atmospheric model; B.Near threats SBF refractive atmospheric model; C.Spherical earth model; D.Assumed aircraft altitude 36 kft; E.For higher aircraft altitudes the depression angles increase for nearer threats.

Conclusions

This study has explored the specular Radar Cross Section of the Sukhoi T-50 prototype aircraft shaping design. Simulations using a Physical Optics simulation algorithm were performed for frequencies of 150 MHz, 600 MHz, 1.2 GHz, 3.0 GHz, 6.0 GHz, 8.0 GHz, 12.0 GHz, 16.0 GHz and 28 GHz without an absorbent coating, and for frequencies of 1.2 GHz, 3.0 GHz, 6.0 GHz, 8.0 GHz, 12.0 GHz, 16.0 GHz with an absorbent coating, covering all angular aspects of the airframe.

If the production T-50 retains the axisymmetric nozzles and extant ventral fuselage design, the aircraft would still deliver robust Very Low Observable performance in the nose aspect angular sector, providing that effective RCS treatments are applied to suppress surface travelling waves, inlet and edge reflections.

If the production T-50 introduces a rectangular faceted nozzle design, and refinements to lower fuselage and side shaping, the design would present very good potential for good Very Low Observable performance in the S-band and above, for the nose and tail aspect angular sectors, with reasonable performance in the beam aspect angular sector. The extent to which this potential could be exploited would depend critically on the design of the nozzles and other shaping refinements.

In conclusion, this study has established through Physical Optics simulation across nine frequency bands, that no fundamental obstacles exist in the shaping design of the T-50 prototype, which might preclude its development into a genuine Very Low Observable design with constrained angular coverage.

Endnotes, References and Bibliography

1 Media Release, Компания "Сухой" приступила к летным испытаниям перспективного авиационного комплекса фронтовой авиации (ПАК ФА), OAO Sukhoi, 29th January, 2010.

2 Kopp, C. and Goon, P.A., Assessing the Sukhoi PAK-FA; Sukhoi/KnAAPO T-50/I-21/Article 701 PAK-FA; Перспективный Авиационный Комплекс Фронтовой Авиации, APA Analyses, Vol. VII, Issue 1, APA-2010-01, Feb 2010, URI: http://www.ausairpower.net/APA-2010-01.html.

3 Pelosi M.J. and Kopp C., A Preliminary Assessment of Specular Radar Cross Section Performance in the Chengdu J-20 Prototype, Air Power Australia Analyses, Vol VIII, Issue 3, APA-2011-03, Air Power Australia, Australia, pp. 1-35, Jul 2011, URI: http://www.ausairpower.net/APA-2011-03.html.

4 Knott, E.F., Schaeffer, J.F. and Tuley, M.T., Radar Cross Section, First Edition, Artech House, 1986; Knott, E.F., Schaeffer, J.F. and Tuley, M.T., Radar Cross Section, Second Edition, Artech House, 1993.

5 More recent quantitative RCS modelling of the J-20 axisymmetric nozzle design validates this observation in considerable detail. Please refer Kopp, C., Assessing Joint Strike Fighter Defence Penetration Capabilities, Air Power Australia Analyses, Vol.VI, Issue 1, APA-2009-01, 7th January 2009, URI: http://www.ausairpower.net/APA-2009-01.html, and Pelosi M.J. and Kopp C., A Preliminary Assessment of Specular Radar Cross Section Performance in the Chengdu J-20 Prototype, Air Power Australia Analyses, Vol VIII, Issue 3, APA-2011-03, Air Power Australia, Australia, pp. 1-35, Jul 2011, URI: http://www.ausairpower.net/APA-2011-03.html.

6 Chatzigeorgiadis, F., DEVELOPMENT OF CODE FOR A PHYSICAL OPTICS RADAR CROSS SECTION PREDICTION AND ANALYSIS APPLICATION, M.S. Thesis, NAVAL POSTGRADUATE SCHOOL, MONTEREY, CALIFORNIA, September 2004; Garrido, E.E. Jr, GRAPHICAL USER INTERFACE FOR A PHYSICAL OPTICS RADAR CROSS SECTION PREDICTION CODE, M.S. Thesis, NAVAL POSTGRADUATE SCHOOL, MONTEREY, CALIFORNIA, September 2000; Chatzigeorgiadis, F. and Jenn, D.C., “A MATLAB Physical Optics Prediction Code,” IEEE Antennas and Propagation Magazine, Vol. 46, No. 4, pp. 137-139, August 2004.

7 Kopp C., PolyChromatic Spherical Representation StL Format Generator Project Definition, August, 2011, Monash University, and Petroulias Z., Polychromatic Spherical Representation STL Format Generator, FIT1016 Final Report, Clayton School of Information Technology, Monash University, 11/16/2011.

8 Two publications detail a range of VHF radar types of interest, Fisher, R.D., Jr and Sweetman W., Too Little, Too Late, AirSea Battle concept may lag China’s capabilities, Defence Technology International, April, 2011 and Wise J.C., PLA Air Defence Radars, Technical Report APA-TR-2009-0103, Air Power Australia, January, 2009, URI: http://www.ausairpower.net/APA-PLA-IADS-Radars.html.

9 Yuzcelik, C.K, Radar Absorbing Material Design, M.S.Thesis, Naval Postgraduate School, Monterey, California, September, 2003.

Annex A Scales, Bands, Geometries

dBSM

-10

-20

-30

-40

-50

m²

1,000.0

100.0

10.0

1.0

0.1

0.01

0.001

0.0001

0.00001

Conventional

VLO

Table A.1 Conversion of RCS Values [dBSM] vs [m²]

Table A.2: US DoD Band Allocation Chart

Figure A.3: Threat depression angles as a function of type and missile kinematic range, for various contemporary and legacy SAMs of Russian/Soviet manufacture (C. Kopp).

Figure A.4: The impact of bank angles on threat depression angles as a function of type and missile kinematic range, for various contemporary and legacy SAMs of Russian manufacture (C. Kopp).

Annex B Viewing RCS Plots

Radar Cross Section plots in this document are represented in two formats, PCSR and PCPR. Both were devised with the intention of providing an easily interpreted graphical representation which can display information with much greater density than the traditional polar plots of RCS.

The use of PCSR and PCPR thus permits a significantly greater volume of data to be presented, compared to polar plots, but with some loss of resolution in magnitude due to the coarse quantisation of the colour scale. This quantisation error is acceptable given the logarithmic scale for RCS magnitude employed.

As this document is published in HTML, it permits easy viewing at a number of resolutions, determined by the browser employed.

All PCSR and PCPR plots are set up with HTML links to the original plots, which are PNG files with respective resolutions of 1000 x 1000 pixels and 1507 x 810 pixels. Clicking on the plot will display it in a user's browser window, or in a separate tab.

Different browsers display PNG graphics differently. Some, like Firefox, Chrome or Safari will initially display the plot scaled to fit the window size. If the window size is smaller than the graphic, clicking on the graphic will enlarge it to its native size on the user display.

It was intended that detailed viewing of PCSR and PCPR plots be performed in the latter fashion, and text font sizes have been set accordingly. A portion of a PCPR plot at native resolution is below.

Annex C Glossary of Terms

2D TVC / Two Dimensional Thrust Vector Control: A TVC arrangement which can control the direction of the engine thrust in a single geometrical plane, typically in the pitching axis.
3D TVC / Three Dimensional Thrust Vector Control: A TVC arrangement which can control the direction of the engine thrust in two mutually orthogonal geometrical planes.
AESA: Active Electronically Steered [Scanned] Array. A phased array antenna in which each element includes a solid state transmitter, receiver, and phase or delay beamsteering control component.
Azimuth Angles: The angle at which an illuminating emitter is seen in the plane of flight of the aircraft, relative to some datum such as the direction of flight.
CoG / Centre of Gravity: The center of gravity is a geometric property of any object. The center of gravity is the average location of the weight of an object [NASA GRC].
Carbon Nano-Tube (CNT): A CNT is one of eight allotropes of carbon, where the molecule is formed as a single or multiple walled tube, the walls of which are formed by connected hexagonal rings; sometimes CNTs are termed buckytubes.
CNT/Epoxy Absorbers: A RAM comprising an epoxy resin matrix loaded with Carbon Nanotube powder.
dBSM: deciBels with reference to a square metre; a logarithmic measure of RCS computed by multiplying the logarithm to the base of ten of the RCS in square metres by ten.
Depression Angle: The angle at which an illuminating emitter is seen below the plane of flight of the aircraft.
DSI (Diverterless Supersonic Inlet): A DSI is an inlet configuration where the inboard edge usually employed for boundary layer control is replaced by a blister shaped protrusion; in stealth design this is intended to remove the diffractive backscatter from the inboard inlet leading edge.
Elevation Angle: The angle at which an illuminating emitter is seen above the plane of flight of the aircraft.
EO (Electro-Optical) Apertures: a cover usually intended to protect an electro-optical sensor from the effects of its physical environment without degrading its optical performance; the optical mirror or lens system which focusses photons on to an optical detection device such as an imaging chip.
Ferrite/Epoxy Absorbers: A RAM comprising an epoxy resin matrix loaded with a ferrite powder.
Gap Treatment: An absorber material or shaping arrangement employed to reduce the RCS of a gap between two skin panels, or a movable surface or door and fixed skin panel.
Geometrical Diffraction: A method of computing RCS that is an extension of geometric optics that accounts for diffraction [Barton & Leonov].
Lossy Surface Coating: A type of RAM which is designed to produce electrical losses, but is not designed to necessarily suppress specular reflections.
Low Observable (LO): Early literature: any stealth aircraft; recent literature: a stealth aircraft with limited signature reduction, usually with an RCS between -10 and -30 dBSM.
Matlab Language: An interpreted computer language for mathematical expressions used by the Matlab code.
NPS POFacets Code: A Physical Optics RCS simulator program designed and implemented at the Naval Postgraduate School in Monterey, California.
Optics Scattering Regime: A scattering regime where the wavelength is smaller or very much smaller than the size of the object or shape scattering the wave.
Panel Serration: A serration is a repetitive triangular pattern used along an edge and intended to scatter surface travelling waves in directions other than the normal to the line of the edge.
PCPR Format (PCPR): PolyChromatic Planar Representation (PCPR) is such a representation in which a rectangular area is divided into tiles by aspect angle pair {θ, Φ}. The colour of each tile represents the RCS from the angular direction determined by the path between the tile and the centroid of the aircraft.
PCSR Format (PCSR): PolyChromatic Spherical Representation (PCSR) is such a representation in which a translucent sphere is rendered around a two-dimensional rendering of the aircraft, where the surface of the sphere is divided into tiles by aspect angle pair {θ, Φ}. The colour of each tile represents the RCS from the angular direction determined by the path between the tile and the centroid of the aircraft.
Perfect Electrical Absorber (PEA): A material with a characteristic impedance equal to that of free space and an infinite loss for all wavelengths of interest.
Perfect Electrical Conductor (PEC): A material with a characteristic impedance of zero for all wavelengths of interest; an idealised conductive metal.
Physical Optics (PO): A method of computing RCS for which the local current density at
each point on the illuminated portion of the body is assumed to be identical to the current density that would flow at that point on an infinite tangent plane [Barton & Leonov].
Phased Array: “array antenna whose beam direction or radiation pattern is controlled primarily by the relative phases of the excitation coefficients of the radiating elements.” [Barton & Leonov].
Radar Absorber: The term absorber refers to a radar absorbing structure or material (RAS or RAM), the purpose of which is to soak up incident energy and reduce the energy reflected back to the radar [Barton & Leonov].
Radar Absorbent Materials (RAM): A material, such as a coating, employed as a radar absorber.
Radar Absorbent Structures (RAS): A structural component, such as a leading edge, employed as a radar absorber.
Radar Cross Section (RCS): is “a measure of the reflective strength of a radar target.” The usual notation is σ. It is defined as σ = 4π P_s/P_i, where P_s is the power per unit solid angle scattered in a specific direction and P_i is the power per unit area in a plane wave incident on a scatterer from a specified direction [Barton & Leonov].
Radome: A radome is “a cover usually intended to protect an antenna from the effects of its physical environment without degrading its electrical performance.” [Barton & Leonov].
Raleigh Scattering Regime: A scattering regime where the wavelength is greater than the size of the object or shape scattering the wave; in Raleigh scattering, the backscatter is proportional to the inverse fourth power of the wavelength σ ∝ λ⁻⁴.
Resonant Scattering Regime: A scattering regime where the wavelength is equal to or similar to the size of the object or shape scattering the wave.
Specular RCS: RCS produced due to specular scattering effects only.
Specular Scattering: Scattering where a mirror-like reflection is produced by the scattering object or shape; usually the wavelength is smaller than the size of the object or shape scattering the wave.
Thrust Vector Control (TVC): Any gas turbine or rocket propulsion exhaust nozzle arrangement which permits the direction of the exhaust efflux and thus thrust to be controlled. Common arrangements include steerable nozzles, vanes or paddles.
Very Low Observable (VLO): a stealth aircraft with very good signature reduction, usually with an RCS smaller than -30 dBSM.

Annex D What the Simulation Does Not Demonstrate

The PO simulator at this time does not model backscatter from edge diffraction effects, although the resulting error will be mitigated by the reality that in a mature production design these RCS contributions are reduced by edge treatments;
The simulator at this time does not model backscatter from surface travelling wave effects. In the forward and aft hemispheres these can be dominant scattering sources where specular contributions are low. The magnitude of these RCS contributions is reduced by edge treatments, lossy surface coatings, gap treatments, and panel serrations;
The simulator at this time does not model backscatter from the AESA bay in the passband of a bandpass radome, due to the absence of any data on the intended design of same, the resulting error will be mitigated by the reality that in a mature production design much effort will be expended in suppressing passband RCS contributions within the bay;
The simulator at this time does not model backscatter from in- and out-of-band impedance mismatches between the radomes and the adjacent aircraft skin, and radomes are thus modelled as contiguous surfaces of equal complex impedance to the adjacent skin panels. The absence of data detailing the design of the bandpass radomes would present a major challenge should such modelling be attempted, and could be expected to degrade RCS performance results without necessarily providing an accurate representation of the actual design;
The simulator at this time does not model backscatter from the engine inlet tunnels or engine exhaust tailpipes, due to the absence of any data on the intended design of same. In the forward and aft hemispheres these can be dominant scattering sources where specular contributions are low. The magnitude of these RCS contributions is reduced by suppressing these RCS contributions with absorbers, and in the case of inlet tunnels, by introducing a serpentine geometry to increase the number of bounces;
The simulator at this time does not model structural mode RCS contributions from antenna and EO apertures, panel joins, panel and door gaps, fasteners and other minor contributors; although the resulting error will be mitigated by the reality that in a mature production design these RCS contributions are reduced by RCS reduction treatments.
The PO computational algorithm performs most accurately at broadside or near normal angles of incidence, with decreasing accuracy at increasingly shallow angles of incidence, reflecting the limitions of PO modelling. The simulator does not implement the Mitzner/Ufimtsev corrections for edge currents. While a number of test runs with basic shapes showed good agreement between the PO simulation and backscatter peaks in third party test sample measurements, even at incidence angles below 10°, characteristically PO will underestimate backscatter in nulls. This limitation must be considered when assessing results for the nose and tail aspects, where most specular RCS contributions arise at very shallow angles³⁹.
The PO computational algorithm performs best where the product of wave number and dimension ka ≥ 5, where k ≈ 2πf [Table 5.1 in (1)], yielding errors much less than 1 dB. Knott cites good agreement for cylinders as small as 1.5 wavelengths in diameter¹.
The simulator does not account for a number of environmental factors, such as air density profile at the aircraft skin boundary layer, thermal variations in absorbent material properties, and moisture precipitation. RCS contributions from these sources are negligible for the principal lobe magnitudes studied.

Annex E Comparative Analysis of Specular RCS - T-50 Versus J-20

Figure E.1. The J-20 has two major lobes in the left and right beam aspect angular sectors, for convenience labelled A and B, with the flat lower fuselage mainlobe labelled C (Chinese Internet image).

Table E.1. T-50/J-20 Specular RCS Model Results With PEC [V-Pol] [Click Chart to Enlarge]
150 MHz

600 MHz

1.2 GHz

3.0 GHz

6.0 GHz

8.0 GHz

12.0 GHz

16.0 GHz

28.0 GHz

dBSM Scale

Annex F Additional Notes on Physical Optics RCS Modelling

The numerical Physical Optics (PO) RCS computation method computes the specular monostatic RCS of an object by summing the respective RCS contributions, for a given angle of incidence, from all exposed surface facets forming the skin of the object being modelled. These RCS contributions are estimated in turn by the estimation of induced surface currents.

All object model surfaces are approximated using triangular facets, which is especially convenient as this technique is also employed in commonly used vector graphic modelling schemes for CGI, such as the Stereo Lithographic (StL) format.

The PO method is inherently limited as it does not consider edge contributions, and accuracy suffers as the angle of incidence departs from the broadside or normal to a contributing facet. The latter makes the PO method suitable for identifying major specular contributors to vehicle RCS, but not minor contributors.

An abbreviated summary of the basic principles of the PO method, cited from Chatzigeorgiadis and Jenn follows⁶.

The backscatter behaviour produced by a triangular facet represents a special case of the backscatter behaviour produced by a body of an arbitrary shape. The expression for the scattered field produced by a triangular facet can thus be derived from the expression which can be obtained for an arbitrary body. Consider an arbitrary scattering body placed at the origin of the coordinate system, with the observation point placed at coordinates (x, y, z), refer Figure F.1.

Figure F.1 Far Field Scattering from an Arbitrary Body (Jenn, 1995).

As we assume a far field geometry, the vectors r→ and R→ can be safely assumed to be parallel. If we assume the body has been divided into infinitesimally small volumes v' each at coordinates (x', y', z'), then the position vector to a point source is:

EQ.1

The unit vector for the coordinate axes is denoted with ^.

The unit vector in the direction of the point of observation is:

where u, v, w are defined as:

EQ.2

and where θ and Φ are the angular components in the spherical coordinate system, for the point of observation.

EQ.3

If we assume the magnetic volume current to be J→_m = 0, the field scattered by the body can be found from EQ.4:

Where:

J→ is the volume current;
Z₀ is the intrinsic impedance of free space;
k = 2π/λ or wave number; and g is defined to be:

EQ.4

EQ.5

The electric field has components only in the θ and Φ directions.

Now consider a triangular facet of arbitrary orientation in space, which is defined by three vertices, denoted 1, 2 and 3, in Figure F.2:

Figure F.2 Facet geometry and orientation (Jenn, 1995).

P is the integration point at (x_p, y_p, z_p), which corresponds to the coordinates (x', y', z') for the integration point in the arbitrary body previously discussed. We define its position vector as:

EQ.6

Because the facet is a planar object with infinitesimal volume, the volume integration collapses down to a surface integration, and the only current present is a surface current. Simplifying EQ.4 thus yields:

Where J→_s is the surface current, A the facet area, ds_p the differential surface area and g defined thus:

EQ.7

EQ.8

This simplifies the problem of finding the scattered field down to computing the surface current J→_s flowing across the facet, using PO, and performing the integration in EQ.7.

To perform this computation, we need explore the radiation integral for a triangular facet. Assume a triangular facet of arbitrary orientation, which has vertices in a cartesian coordinate system of (x_n, y_n, z_n), for vertices 1, 2 and 3. Vertices are labelled counter-clockwise, or if following a right hand rule, where the thumb of the right hand points in the direction of the normal to the facet face. This is depicted in Figure F.3.

Figure F.3 Facet geometry (Jenn, 1995).

Position vectors for each vertex are given as:

EQ.9

In turn we can find the edge vectors from the vertex coordinates as:

EQ.10

We can then determine the outward normal of any facet from the cross product of any two edge vectors, assuming a right hand rule. An instance is:

EQ.11

If we order the vertices in this manner, With this ordering of the vertices, the outward side of the facet is denoted as the front face with the opposite side being the back face. Given a plane wave incident from angle (θ_i, Φ_i) , which is propagating towards the origin, then its propagation vector is:

for which (u_i, v_i, w_i) are the direction cosine; and R^ is the radial unit vector between the origin to the source located at angle (θ_i, Φ_i).

EQ.12

If EQ.13 is satisfied, the front face is being illuminated:

EQ.13

The area of facet A can be found using a cross product of edge vectors:

EQ.14

To simplify integration, normalised areas are used, assuming subareas A₁, A₂ and A₃, as per Figure F.3b:

EQ.15

As the three subareas sum to unity, we can rearrange the expression for ξ thus:

EQ.16

This permits the integration to be rearranged as:

EQ.17

The induced surface current is proportional to the incident magnetic field. This yields two possible conditions for the surface current J→_s, where one face is illuminated and the other shadowed, and assuming the incident magnetic field at the facet surface to be H→_i:

EQ.18

The general expression for the incident field is of the form:

EQ.19

Using a series of substitutions, we find the magnetic field can be expressed as:

EQ.20

The PO approximation for the surface current flowing across the facet is then:

where h is defined thus:

EQ.21

EQ.22

We can rearrange EQ.21 thus:

EQ.23

There is no surface current in the direction of the facet normal, since the facet is planar, which permits further simplification.

To compute the scattered field produced by the induced current in the facet, we substitute the simplified expression into the radiation integral in EQ.7. This yields:

EQ.24

The integral component I_c, below, cannot be solved exactly, and is typically computed using a Taylor series expansion, commonly with five terms.

EQ.25

A more detailed treatment is available in Chatzigeorgiadis and Jenn⁶.

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