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THE IMPACT OF MAJOR STRUCTURAL MODIFICATIONS ON THE RADAR CROSS
SECTION OF A WARSHIP
Lt(N) P.D. Srnithers CD B.Eng P.Eng rmc Canadian A d Forces
A thesis submitted to the Department of Electricai and Computer Engineering
Royal Military College of Canada Kingston, Ontario
In partid IülfiIlrnent of the requirements for the degree of Master of Engineering
8 P.D. Smithcrs. 1999. This Wis may be u d withui the Depamnait ofNational Dcfcnoc howcva q - g h t for opai pubtication raiuins the poperry of the rmhor.
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ABSTRACT
The radar cross section (RCS) of a naval vesse1 is an important fàctor in its abiüty
to evade detection and localization by hostile forces. RCS plays a more cntikal mle in
self-defense against hostile guided weapoos anâ active radar firecontrol systems.
Modern warship design employs various methods to niinimiZe or reduce the RCS
of a warship. Complex objects such as warships are by their nature too complicated for
adytical aoalysis, but modem advances in digital Eomputer techwbgy have kilitated
the rapid and inexpensive prediction of RCS patterns by nuneriai modehg. This
facilitates RCS bpact analysis of p h r d changes to a ship's structure in the design stage.
When a warship undergoes substantial structural modifications, it's RCS may be
drasticdy changed During the TRWMP refits, Canada's IROQUOIS ckss destroyers
were subjected to major structural modifications wiihout coderation of the impact on
their RCS. Physical optics appro>cimations of the changes in the ROQtTOIS class RCS
due to the TRUMP modemLation are presented by a comparison of numerical models of
the TRIBAL and IROQUOIS class ships. Other investigations are conducted, including:
an iuialysis of the contriiution of multiple reflections to the RCS of the complete
IROQUOIS rnodel; the impact of various large structural modifications; the contniution
of numerous upperdeck lockers and other details; the contribution of a detailed mast and
guardrail stanchions; and, the contniution of cyIllidricai shapes to the RCS of the models.
The use of modular mode1 construction techniques and the development of a
method for accurately modehg cylindtical sbapes using m-sided polygonal cylinders
provide a simple and versatile means of exanvning the impact of structurai modifkathas
Kevwords: geornetric optics; IROQUOIS c h ; numerical rnetbods; physical optics; radar
cross sectioa; RAPPORT.
Sec*: The contents of this work are U N C L A S S I . . Qualifieci users may obtain
access to ciass5ed resuhs associated with this work through DREO Ottawa or NDHQ
OttawalDMSS 2-5-3.
ACKNOWLEDGMENTS
No graduate thesis is tnily an individuai effort, thus it is important to recogxüze the
contributions of the people w b heiped me wah the research which cuhinated in this
thesis. 1 am most gratetùl for the support and encouragement provided to me my principal
advisors, Dr Yahia Antar and Dr Satish Kashyap. The expert technical guidance, endless
patience and good humour of Dr Aloisius Louie of DREO was gteatiy appreciated. The
enthusiastic support of Mr Pbg Kwoiq DMSS 2-5-3, was a ktor in my choice of this
thesis topic. Finally, no acknowkdgment of this work wodd be cornplete without
recognizing the valuable advice and technical assistance provided by my colleagues LCdr
Marcel Losier and L t o Dave Winters, which helped guide me through the earîy stages of
the research,
1993 - 1994 Und-ter Weapons Project Ofiïcer Navai Eagineering Unit Atlaotic, Halifax. NS
1994 - 1995 Deputy Combat Systems Trials OfEcer Navai Engineering Unit Atlantic, Haiifax, NS
1995 - 1997 Combat Systems Engmeering Officer HMCS TERRA NOVA, HaiiIk, NS
1 997 - 1999 Graduate student of electrical en- Royal MELltary Coîiege of Caoada, hgstoo, Ontario
TABLE OF CONTENTS
Title ........................................................... i ...
Abstract .......................................................... LU
Vitae .............................................................. vi
........................................................ ListofPlots xiv
Chapterl-Introduction ................................................ 1 1.1 Background .............................................. 1 1.2 Sc0 pe ................................................... 6
................................................. 1.3 Method 7 1.4 Outline .................................................. 8
................................................ . Chapter 2 RCS Theocy 9 2.1 RadarBasics .............................................. 9 2.2 DefinitionofRCS ......................................... 11 2.3 Maxwell'sequations ....................................... 12 2.4 Wave equation ........................................... 13 2.5 Scatteri ng ............................................... 14 2.6 Polarization and received voltage ............................. 16 2.7 UnitsofRCS ............................................ 17 2.8 Simpleshapes ............................................ 17
2.8.1 Square plates ...................................... 20 2.8.2 Dihedral reflectors .................................. 21 2.8.3 Trihedral reflectors .................................. 22 2.8.4 Cyiindrical shapes ................................... 23
2.9 CompIex geometry ........................................ 24 2.9.1 GeometRc optics ........................... .. ....... 25
..................................... 2.9.2 Physicaloptics 26 ......................... 2.9.3 Geometric theory of difhction 29
2.9.4 U n i f o r m t h e o r y o f ~ n .......................... 30 2.9.5 Physical theory of diffhthn .......................... 30
..... 2.9.6 Method of Equivalent Cunents and Method of Moments 31
.................................... . Chapter 3 Method and analysis tools 32 ........................................ 3.1 Adysistecbnique 32 ........................................ 3.2 Simulation process 32
3.3 AutoC AD ............................................... 34 3.4 DIDEC ................................................. 35
.............. 3.5 Support p r o m developed with FORTRAN 90/95 37 ............................................. 3.6 JUNCTION 38
3.7 RAPPORT .............................................. 39 ....................................... 3.7.1 Background 40
......................... 3.73 Physicai optics approximations 40 ...................... 3.7.3 Ray tracing and multiple reflections 43
.............................. 3 .7.4 SurFace patch integration 44 .................................... 3.7.5 Input parameters 45
3.7.6 RAPPORTlimitations ................................ 47 3.8 MATLAB .............................................. 47
.................................... 3.9 Performance assessment 48 ...................................... 3.10 Modeling of cylinders 51
3.11 Discussion .............................................. 53
.......................................... . Chapter 4 Simulation Results 55 ................................ 4.1 The IROQUOIS CAD model 55
......................... 4.2 Simulation conventions and parameters 62 .................................... 4.2.1 Reflection limits 64 ................................... 4.3 Basehe RCS model plots 67
................................ 4.4 IROQUOIS detail additions -71
................................. 4.4.1 Forecastle additions 71 4.4.2 Forward superstructure additions ....................... 75 4.4.3 Toppartofship .................................... 77 4.4.4 Funnel exhausts and CIWS ............................ 79 4.4.5 Completing the IROQUOIS hull ........................ 81 4.4.6 Overall effect of detail additions ........................ 83
4.5 The impact of the ship's mast ................................ 85 .............................. 4.6 Reverting to the TRIBAL model 90
............................... 4.6.1 Lowering the waterline 91 ....................................... 4.6.2 FX additions 92
4.6.3 Forward superstructure modifications .................... 95 4.6.4 Toppartofship .................................... 97
................................ 4.6.5 Funnelandhangartop 99 ....................... 4.6.6 Completion of the TRIBAL huii 101
..................................... 4.6.7 TRIBAL mast 103 .............. 4.7 Comparison of the IROQUOIS and TRIBAL RCS 108
........................ 4.7.1 Funnel and hangar-top changes 110 4.8 Impactofguardrails ...................................... 114 4.9 Aiternatemastarrangements ................................ 117
4.9.1 Cylnidricalmast ................................... 117 .............................. 4.9.2 Box-Wremaststructure 119
....................................... 4.10 Impactofcylinders 121
Chapter 5 . 5.1
................................... Discussion and conclusions 123 E ~ t h e m e t h o d .................................... 123
........................ 5.1.1 Sources of error in the method 127 .................................. 5.2 Comments on the models 128
................. 5.2.1 Sources of modeling error ......... .. 130 5.3 Reviewofredts ........................................ 132 5.4 Futurework ............................................ 135 5.5 Conclusions ............................................ 137
Referenc es ......................................................... 139
Figurecredits ....................................................... 141
.............................. Annex A . FORTRAN 90/95 program listings A-1
Annex C . Resdts of RAPPORT performance assessrnent simulations ............ C-1
Figure 1-1
Figure 1-2
Figure 1-3
Figure 1-4
Figure 1-5
Figure 1-6
Figure 2- 1
Figure 2-2
Figure 2-3
Figure 2-4
Figure 2-5
Figure 2-6
Figure 2-7
Figure 2-8
Figure 2-9
Figure 3-1
Figure 3-2
Figure 3-3
Figure 3-4
Figure 3-5
Figure 3-6
LIST OF FIGURES
................... The design spirai for a ship's threshold signature 1
................ HMCS VANCOUVER, designed for RCS reduction 3
...................................... USNS SEA SHGDOW 4
LAFAYElTEClassfkigate ..................,................ 4
........... HMCS IROQUOIS several years before her TRUMP refit 5
....................... HMCS IROQUOIS after ber TRUMP refit 6
................ Block diagram of a basic conventional radar system 9
.............................. EM scattering problem geometry 14
........................... The power deosity dennition of RCS 17
........... RCS of a . isotropie sphere as a fùnction of electrical size 18
......................... RCSofaflatsq~areplatewithka=14.7 20
........... Reflection fkom a dihedral reflector with orthogonal sides 21
................. RCS of a trihedral reflector at various elevations 23
RCS of a right circulat cylinder as a furrtion of elevation ........... 24
.............................. Keller's cone of rays 29
Software process for the RCS analysis simulations ................. 33
TheVOstructweofDIDEC ................................. 35
.................. The RAPPORT developmeot scattering problem 40
Backward ray trachg to determine surfiioe patch iliumination ........ 43
A sample RAPPORT input parameter nle ....................... 45
Input parameter file for the square plate d y s i s .................. 48
Figure 4- 1
Figure 4-2
Figure 4-3
Figure 4-4
Figure 4-5
Figure 4-6
Figure 4-7
Figure 4-8
Figure 4-9
Figure 4-1 0
Figure 4- 1 1
Figure 4- 1 2
Figure 4- 1 3
Figure 4- 14
Figure 4-15
Figure 4-16
Figure 4- 1 7
Figure 4-18
Figure 4-1 9
Figure 4-20
Figure 4-2 1
Profle drawing of the post-TRUMP IROQUOIS ................. 57
......................... Origbd wire grid mode1 of IROQUOIS 58
IRûQUOISbasel9iemodeI#l ............................... 60
................................ IROQUOIS ùaseline mode1 #2 61
................................ I~%OQUOIS baseline mode1 #3 61
......................... NESTRA RCS range at Osborne Head 63
BaseLine # 3 with a breakwater adde cl. .......................... 72
Addition of FX details ..................................... 73
Superstructure detail additions ................................ 75
Addition of top part details ................................. 77
Addition of fhnel exhausts and CIWS .......................... 79
Completed IROQUOIS h d showing AX details .... .. ............ 81
TheIROQUOISmastmodeI ................................. 86
The complete IROQUOIS mode1 with mast fitted ................. 87
FXaiterations ............................................ 92
GMLSretrofÏt ........................................... 94
Retrofits to 02 and 03 deck .................................. 95
Deletions and re-arrangements on top part ship .................. 97
Changing the fiuinel configuration ............................ 100
The completed TRIBAL huii ................................ 101
TheTRIBAL mast ........................................ 104
..................... Figure 4-22 Complete TRIBAL mode1 with mast &ted 105
................ Figure 4-23 IROQUOIS d e l with guardrail stanchions fitted 115
....................... Figure 4-24 IROQUOIS with a cylindrical mast Mted 118
............... Figure 4-25 IROQUOIS mode1 with a box-like niast stnrtur~ 119
Plot 3-1
Plot 3-2
Plot 3-4
Plot 3-5
Plot 4-1
Plot 4-2
Plot 4-3
Plot 4-4
Plot 4-5
Plot 4-6
Plot 4-7
Plot 4-8
Plot 4-9
Plot 4-10
Plot 4-1 1
Plot 4-12
Plot 4-13
Plot 4-14
Plot 4-15
Plot 4-16
Plot 4-17
LIST OF PLOTS
.................. RAPPORT resuhs for a square plate with ka=14.7 49
............ . RAPPORT results for a trihedral reflector with O lm sides 50
......................... Modeiing a right ckuiar prolate cylmier 54
......................... Modehg a right circular prolate cyIinder 54
.......................... Contribution of multiple reflections 64-66
....................... RCS of the Grst b a s e h IROQUOIS mode1 68
...................... DBerence m RCS o f baseline models 1 & 2 68
.................... DBerence in RCS o f baseiine models 2 & 3 .-. 69
.............................. Impact of addmg the breakwater 72
...................... Cbange in IROQUOIS RCS due to PX details 74
............. Change in IROQUOIS RCS due to superstructure details 76
................. Change in IROQUOIS RCS due tc top part details 78
Change in IROQUOIS RCS due to furniel exhausts and CIWS ......... 80
.................... Change in IROQUOIS RCS due to AX details 82
Impact of aü detail additions to the IROQUOIS mode1 ............... 83
.................................. IROQUOIS mast in fke space 88
Impact of adding the mast to the IROQUOIS mode1 ................. 89
Lmpact of lowering the waterhe one foot ......................... 91
.................................... Effect of retrofÏtting the FX 93
Change in RCS due to repiacing the GMLS ....................... 94
......................... Change in RCS due to superstructure refit 96
plot 4-18
Plot 4-19
Plot 4-20
Plot 4-21
Plot 4-22
PIot 4-23
Plot 4-24
Plot 4-25
Plot 4-26
Plot 4-27
Plot 4-28
Plot 4-29
Plot 4-30
Plot 4-3 1
Changes in RCS due to top pact ship alterations ................... 98
Contri'bution of the RHIB crane column .......................... 98
Change in RCS due to retrofitting the f h l and AMR uptake ....... 100
Changes m RCS due to revision of the AX ....................... 102
Change in TRIBAL RCS due to addition of lattice mast ............. 106
Change in RCS of the IROQUOIS model due to TRUMP ............ 109
Impact o f restoring the bifiucated fumeis to IROQUOIS ............ 111
Contniiution of the fUnnel exhausts to IROQUOIS RCS ............ 112
Contriiution of the CIWS to IROQUOIS RCS ................... 112
Change in IROQUOIS RCS due to adding guardrail stanchions ........ 116
Effkct of replacing the lattice mast with a cylindrical mast ............ 118
Impact of replacing the lattice mast with a box-like mast ............. 120
Impact of cylindrical features on IROQUOIS RCS ................. 122
Impact of cylindrical features on TRIBAL RCS ................... 122
LIST OF TABLES
Table 3-1 Design parameters for prolate and obiate cylinder modeIs ............ 53
Table 4-1 Simulation statistics for IROQUOIS baseline models ................ 59
Table 4-2 Simulation statistics for the IROQUOIS detail additions ............. 84
Table 4-3 Major structurai modifjcations due to reversion to TRIBAL mode1 ..... 90
Table 4-4 Simulation statistics for the TRIBAL retrofit models .............. 107
Table 4-5 Simulation statistics for complete IROQUOIS and TRIBAL models ... 108
SYME3OL TABLE
The foiiowing symbol conventions are observeci throughout tbis thesis, unies otherwise noteci, with units as iadicated. Vector quantities . . are denoted in the text by an arrow above the symbol.
equivalent crou sectionai area, [dl mea, Wl magnetic ihur density, webers/m2] speed o f light, 2.997~ 10' d s electric disphcement, [CoulomWm2] electric field mag&ude9 ~ / m ] incident electric field magnitude, [Wm]
magnetic field strengtb, [Mm] complex CO-eilkient , ( fi ) current density, [ ~ h q
charge, [Coulombs] range, r d scattering matrix parameter radius, [ml time, [s] permittivÎty, or dielectric constant, p/m] propagation constant, [m-' ] intMsic impedance, [Cl ] &uth (bearing) angle, [O] wavelength, [ml permeability, w m ] pi electric charge density, [CoulomWm2] radar cross section, [dBsm] elevation angle, [ O ] soiid angle, [sr] angular frequency, [rads]
GLOSSARY OF ACRONYMS
AMR
AX
CAD
ClWS
CPF
DDG
DEC
DIDEC
DMSS
DREO
DXF
EFIE
EM
EPM
FCG
FMFCB
FX
GMLS
GO
GTD
HF
auxïkiry machinery room
quarterdeck
computer aided design
close in weapon system
Canadian Paîrol Frigate
guided missile destroyer
Digital Equïpment Corporation
Digitize, Display, Edit and Convert
Directorate of Maritime Ship Support
Defence Research Establishment Ottawa
Drawing Exchange File format, used by various CAD packages
electric field integral equation
electromagnetic
eiectronic preventative measures (formerly ECCM)
finite@ conducting ground plane
Fleet Maintenance Faciljty CAPE BRETON
fo recastie
guided missile launching system
geometric optics
geometric theory of difnaction
high fkequency (ka > 10)
HH
DWW'UAT
IR0
LIROD
LW08
M m
MMR
MOM
NESTRA
PC
PO
lEiAM
RAPPORT
RCS
RF
RHlB
RMC
SATCOM
SHrNCOM
sinc
SRBOC
SRGM
pardel horizontal poiarization
- * hternationai Mantme Satellite commuaications system
IROQUOIS ciass destroyer @ost TRUMP)
Lightweight radarfoptronic director
TRUMP air search radar system
magnetic field integration equation
main machinery room
method of moments
Naval Electronk Systems Test Range Atlantic, Osborne Head, NS
IBM Personal Cornputer
physical optics
radar absorbing niaterial
Radar signature Analysis & Prediction by Physical Optics & Ray Trachg
radar cross section
radio fiequency
ngid huiied idlatable boat
Royal Military College of Canada
satellite communications
Shipboard Integrated Communications system
Fourier transform of a sine fimction
Super Rapid Blooming Ofbard Chaffsystem
Super-Rapid Gun Mount
STIR
SVTT
SWIC
TDLC
TNO
TRIBAL
TRUMP
UNCLAS
USN
USNS
VDS
VLS
VMS
w
WM-22
2D
3D
Separaie Tracking & Iiiumhatkn Radar, TRUMP firecontml radar @em
surfàce vesse1 torpedo tubes
S u d k e Warning (radar), id Canadian
torpedo davit/light crane
Netherlaods Organization for Applied Scientific Research
c h name for the iROqUOIS ciass sbip prior to the TRUMP reM
TREBAL Class Update and Modernization b j e c t
unclassified
United States Navy
United States Naval Ship (USN awiliary designation)
variable depth sonar
Mk 41 Vertical Launch missile System
Virtuai Memory System @EC-Alpha operating system)
pardel vertical polarization
280 ciass firecontrol radar system
two dimensional
three dimensional
Cha~ter 1 - Introduction
1.1 Background
The purpose of a warship is to take weapons to the scene of an action and employ
them in the completion of a mission. In fulfilling this purpose, a naval vesse1 must O ften
either disguise its preseme nom hostile forces, or ahemately, defend itselfagahst hostiie
attack. The threat m either case is a potential enemy's ability to detect, localize and track
the ship. This may be accomplished umig any number of seosors. h m vinial sensor
apparatus to sensors based on acoustic, electromagwtic or thermal detection schemes.
Such sensors detect and classii a target based on that target's unique "signature" or
energy field pattern in the fiequency band of interest.
There are several ways to distract such sensors systems to varyÏng degrees by
employing active or passive countermeasures. However, the most critical aspect of
signature management occurs in the design stage of a warship's life cycle. In this stage,
every aspect of a vessel's design can be evaluated and adjusted to m h h k its various
signatures as much as is practical within the other design criteria [l].
Figure 1 - 1. The design spiral for a ship's threshold signature. (Figure credits are listed on p. 141).
For several centuries of nrttitime warfitre the only signature exploited by the
world's navies was the visual signature of a ship, as detected by the hunnui eye and later,
augmented by the use of opticai systems. Visual or optifal sensors were enipbyed with
- *
remarkable accuracy in all aspects of naval wa*, incltuhg co~~llll-ns, oavigatioa
threat detection and naval gunnery or fkcontrol These systems Wered h m a number
of disadvantages, c k f among them raoge limitations and high s u s c e p h i to
meteoroiogicd and iighting conditions [2].
The invention of the wireless telegraph led to the development of radio direction
hding, which was extended during the Second World War to produce the nrst naval
radar sets. Eariy 10 cm radar sets such as the Canadian SWl C radar were empioyed to
detect enemy warships and surbed submarines, dohg so with crude accuracy. As early
as the mid 1940's' work was under way to better d e s t a n d radio fiequency (RF)
scattering mechanisms, with the dual objectives of ùnproving radar performance and
decreasing the susceptibïlity of fkiendiy ships and aircraft to radar detection by hostile
forces.
The key to reducbg the probability of detection was the reduction of the amount
of RF energy reflected or "'scattered" back to a hostile radar receiver. This amount of
scattered energy is represented by the radar cross section @CS) of the given target. The
RCS of a target is defïned as the area of an isotropie sphere that produces a radar return
equivaient to that of the target. In layman's terms, it is a measure of a target's ab- to
reflect a transmitted radar signai.
Although it has been exploited for the detection of naval vessels s k e the Second
World War, thû aspect of signature management was iargely ignoreci m Canadian naval
construction untii the commencement of the Caoadian Patrol Frigate (CPF) project m the
late 1970's. The threat posed by modem radar-ho- anti-ship missiles and the tacticai
utility of Pealth" techoology made RCS reduction a major design criterion for the
HALIFAX class CPF. The RCS of that ship has been the subject of considerable study
[3,4], and work continues to tbk day towards the reduction of HALIFAX class RCS
through various passive techniques.
Figure 1 -2- The HALIFAX CIass ship HMCS VANCOUVER, me ofthe 6rst Canadian ships designed for RCS reduction-
The United States Navy bas piaced great empbasis on RCS reduction in its own
hture warship building plans. The USNS SEA S H A W W was built in 1980 as a
signature reduction technology demnstrator, and the success of that ship can be seen in
the conceptual designs for the proposed USN Surnice Combatant 21 platfonns [4].
Figure 1-3. USNS SEA SHADOW,
The state of the art in naval platform RCS reduction design may be seen in the
French LAFAYETTE class figate, which makes extensive use of shaping and RAM to
reduce its RCS. This class of ship is currently in s e ~ c e with three of the world's navies.
The LAFAYE'I-IE design is easiiy distinguishable nom conventional warships due to its
"garage doors" at the waist and a lack of aay visible upper deck fittings.
Figure 1-4- A LAFAYETTE Class fngate.
4
By contmst, RCS duction was mt considered m the original design the TRIBAL
class warship. 'Ihse large naval vesseis were designeci as destroyer-sinxi AS W platforms
ia the late 1960's and cotnmksioned in the eady 1970's.
The TRIBAL class ship sported the high freeboard and large, box-like forward
superstructure and hangar assemblies typical of American design practices at the t h e , as
seen in the SPRUANCE and PERRY c h ddgns. These features create a large "sail
area" or verticd surfàce b m ai l aspects, seemingly orakEg the ship's RCS quite large as
compareci to older ships of similar tonnage.
Figure 1-5- HMCS IROQUOIS, a TRBAL Class anti-submarhe destroyer, several years before hm TRUMP refit.
Almost two decades after the fkst TRIBAL class ship was co&oned, they
were radically redesigned and rebuiit to counter the new threats envisaged just pnor to the
end of the Cold War. The TRIBAL class Update and Moderaization Project (TRUMP)
changed the priniary role o f these ships h m AS W to area air defense and task group
command and control. Several existmg systems were modernized with new technology,
while the old radar, electronic wadm and anti-aircraft weapons suites were repiaced with
new, longer-range systems capable of defathg d e m air threaîs at long ranges.
- --
~ i & 1-6 HMCS IROQUOIS afier h a mUMP refit
Tne updated ships, re-christened the IROQUOIS c h , incorporated new ï d k e d
and acoustic signature management technology. However, no effort was made to reduce
the RCS of the ship due to the mounting cost of the project and the expense of structural
modifications [4]. Indeed, to the naked eye, it seems intuitive that the RCS of the ships '
may have been increased by the TRUMP modifications, as a resdt of the increased nnface
area of the funne1 casing and an increase in upper-deck protnisions on the superstructure.
1.2 Scope
This thesis shaii examine the RCS of the IROQUOIS class destroyer, as sirnulated
by numerical modeis generated using AutoCAD and processed by the RAPPORT physical
optics approximation code- The most compiete treatment of this topic wotild inchde a
detailed presentation and -sis of the TRUMP and TRIBAL RCS mode1 data.
However, that idormation is unsuitable for open pubücation as it is classified for defence
security purposes. Therefore, in order to sa* both academic d security requirernents,
this thesis presents the change in the RCS of this warship resuhiag nom the major
structural modifications of the TRUMP refit. Detailed models of the TRIBAL and
IROQUOIS c h desigas wiU be analyzed and particular attention wili be payed to the
mast and other cyiindrïcal f m s .
1.3 Method
The following methodology was proposeci in order to r e a k the aim of this
research:
a a iiterature survey, focusing on RCS theory, the amdelkg of complex
sbapes, and various numerical methods empioyed in hi& fiequency (HF)
RCS &sis;
-. . b. software fimhmation and modification of sohare tooIs employed in HF
RCS analysis at DREO to make them suitable for use at RMC;
c. alteration of an existing wire grid IROQUOIS mode1 to make it suitable for
the desired anaiysis, foiiowed by extensive detaii additions;
d. reverseengineering of the IROQUOIS mode1 to approxkte the TRIBAL
configuration;
e. performaace and anaiysis of the RCS computations; and,
F. documentation and discussion of the unclassified results.
1.4 Outhe
This work is presented m five chapters. This h t chapter htroduces the work and
places it within the conte= of -val signature management. The second chapter provides
an overview of RCS theory and discusses various methods of predicting RCS. Chapter
three focuses on the overall method employed in the research, with emphasis on the
numencal modeling method employed to ptedict the IROQUOIS RCS pattern. Chapter
four wïlI present the renilts of the RCS mode1 simulations. The noai chapter diseusses the
research, provide concludiag remarks and discuss potential fûture work.
Chaoter 2 - RCS Theory
2.1 Radar Basics
The word radar is an acronym for the phrase "radio detection and ranging". The
basic function of a radar system is to detect, localize and determine the range to a target,
by determinïng the time of füght of a radio ikquency electromagnetic (EM) pulse dong a
known bearing or elevatioa S k e EM energy traveis through fiee space at the speed of
light, an EM pulse will travel a round trip between a transceiver and a target a distance R
away according to the equation:
A block diagram for a basic conventional radar system is shown in figure 2- 1. In
simple t e m , the synchronizer is a trigger device that keys the transmitter to produce a
high-energy RF pulse. The redting EM pulse is routed through the duplexer to the
Figure 2-1. Block diagram of a h i c radar system.
9
anterma The puise travels to tbe target, where some of its energy is ~caftered back
towards the antenna Received energy is routed through the duplexer to the receiver,
where it is converted to a video or digital si& d timing m f o ~ i o n fiom the trigger
device is used to calculate and display the range to the target-
There are numerous mors that &kct the ability of a radar system to detect a
target. The benc radar equation relates the power received by a radar system as a
hction of the powa tnmsmined the range to the target and a number of terms that
descni power losses due to the radar system, the transmission medium, and scattering
fiom the target. One way of writing the basic radar range equation is 151 :
where: R- = maximum unambiguais range of the radar system [ml P, = transmitted power IW] G = directive antenna gain Sm, = minhum detectable signal [\KI A, = efkctive antenna area ("antenna aperture")[mq
Given a range R and a received power Pm equation 2.2 may be re-arranged to
isolate the impact of a target's RCS on the power received by the radar transceiver:
The second term in the expansion, which descriis power density losses due to
spherical scattering fkom the target, clearly demonstrates that the received power is
directly proportionai to the target's RCS.
Note tbat equations 2.2 a d 2.3 refa to the monostorie case: most modern radar
systems employ a CO-located transmitter and receiver; such systems are called monostatic
radars. A bi-static system employs a receiver and a transmitter thaî are not CO-locaîed.
2.2 D e m o n of RCS
The InstiMe of Eiectrical d EIectronics Enpineers defines RCS as [q:
"For a given scattering objecî, upcm wtiich a plane wave is incident, that portion of the scattering cross-section correspondmg to a specified polarkatioti coniponent of the scattered wave."
RCS is a quantined expression of an object's a b o i to reflect or cbscatter" iucident
EM energy. EM scattering may be defiaed as the dispersal of incident EM ewrgy in all
directions fiom an objet. The amount of incident energy tbat a target wili scatter is a
fiuiction of the:
a, target's geornetry (shape and size);
b. niaterial composition of the target;
c. angle of incidence, or "target aspect";
d. fkequency of the incident radiation; and,
e. polarization of the incident wave.
Consider RCS as the area of an isotropie sphere that would produce a radar echo
equal to that of the target 151. Given that RCS is of importame m the Eu field, it may then
be expressed mathematically as follows:
power reJlected towards source / unit solid angle I Z= -
incident power density
RCS is also known as "backscattering cross section", since it d e m i the portion
a = lim 4 z R~ R + a
of an EM field scattered back fiom a target. To understand scattering, it is necessary to
Es - 4
begin by examining Maxwell's equations, which are the basis for al l EM field theory. The
first equation is Faraday's Law, which states that a changing magnetic field produces an
eIectric field:
Converseiy, Ampere7s Law states that a changing electric field produces a
magnetic field:
The next Iaw states that the total magnetic flux through a closed surface is zero, ie
there is no such thing as a magnetic charge:
F i , there is Gauss' Law, which staîes tbai the o v e d electnc field pattern,
strength and direction on a point on a s d k e are determined by the charge distriion
around it:
v = B = ~ (2 Sd)
The electric and magnetic fields in an isotropic material with a lmown dielectric
constant, penneab'i and conduftivity are demibed by the equations:
2.4 Wave equation
AU electromagaetic waves may be represented by a single wave equation which
has a unique solution when modified by the ôouadary c o d o n s present in a problem. By
applying equations 2.5 and 2.6 in an isotropic medium m a region with no sources
( p =J=O) and employing the cu l of the e l d c and magnetic field vectors, we arrive at
the wave equation [q:
Equation 2.7 may also be used to describe the magnetic field by substituthg H for E. The
behaviour of the electromagwtic field at the boundary between two dinerent media is
descriid by bouodary conditions that break the fields into their respective nomial and
tangential components. In the special case where one meditun is a dieiectric (non-
conductinp) medium and the other is a perfect conductor, the boundary c o ~ o n s at the
interface between the media d u c e to [a:
where f i is the unit nonnal to the surface of the conductor.
2.5 Scatterhg
A typical EM scattering problem for a radar system involves EM scattering Eom a
target a large distance away fiom the radar transceiver. Figure 2-2 depicts a
representation of a bistatic case, where the traosmtter and observer are not CO-located.
Figure 2-2. EM scattering problem geometry.
14
An incident ray strikmg an object is partially absotbed and partially reflected or ~caffered
away fkom the object. The direction of tbe ~caftered ray will depend on the Wors listed
earlier in section 2.2. The scattered EM field may be determined by jkst nndnig the
current distriiution on the target's suthce. If the incident fieid is assumed to have unit
amplitude, for a range r the scattered field received at the radar may be reduced to [7]:
The term S in equation 2.9 is the scattering fùnction, a dimemionkss complex
vector h c t i o n which relates the scattering pattern for the target. S b x there is M, EM
field component in the direction of propagation, the electric field can be resolved into
distinct vertical and horizontal poiarizations or directions, and equation 2.9 becomes:
The value of each entry in the scattering matrix is found by setting the incident
field components each to zero in tmx
Lfwe treat the backscattering cross section a as baving amplitude and phase
compownts, the scattering mitrix is rekted to the backscattering cross section or RCS of
equation 2.4 by:
2.6 Polarization aad received voltage
The scattering ~natrix d e s c n i the relationship between tbe incident and scatterd
waves for a given target by its polaraation components. The actual voltage received by a
radar system can be desmbed in terms of the transmitter and receiver polarization as
foUows, ignoring system losses[8):
Where V= received voltage fi, = receiver polarization a, = transmitîed components ofeach polarïzatiori in direction of E,, and E,
The fonnal demion of RCS cm aIso be explained m tenns of power density, as
shown in figure 2-3. An incident power density P, strikes a target with a cross-sectionai
area a , then an intercepted power O f: is partially scattered and partially absorbecl as
heat. Assuming that the scattered power is radiated uniformiy m aU directions, then the
scattered power density P, is given by this relation, which is andogous to equation 2.4:
O?; watts
Incident Power Target of Cross Taqet Re-Radiates 'lux from Distant Section Area a Captured Energy
Transmitter Captures aPi watts 'lsotropicaiiy' of Energy
Figure 2-3, The power density definition of RCS,
2.7 Units of RCS
RCS is an equivalent area, thus it is customirily expressed in square metres. But
since ail but the moa simple ob&ts have cornpiex geometry, the physical size of an object
does not necessarily correspond to its RCS. Measurements be performed on objects
as srnaii as insects, or objects as large as buildings or ships. Tberefore it is convenient to
use a loganthmic scale for RCS measurements, referenced to one square meter:
2.8 Simpiesbapes
The importance of geometry in the RCS of complex objects is the subject of
considerable study [3,6,8- 101. Since cornpiex objects may be considerd to be composed
of a number of simple geometric shapes, it is necessstTy to exanime the RCS of simple
O bjects before discussing complex geometries. As @lied earlier, a perfèctly wnducting
sphere provides the basis for the definition of RCS and le& itsetfwell to a simple exact
solutioa The RCS of a perfèctly conducting sphere with radius o is a fhction of its
eiectricai size, given by:
Figure 2-4 iliustrates the relationship between the electxical sjze of the perfeçtly
conducting sphere and its RCS. As in aii scattering phemmena, the RCS of the sphere
niay be divided into three regions, each with Ïts own propert". In the Rayleigh region,
ka < I , ie the wavelength is much larger than the object: here, a sphere's RCS increases
proportional to the fourth power of its electrical size and the s k t h power of its radius
[8,9]. This region, sometimes referred to as the Iow-fkquency region, is of interest in
applications suc h as weather radars.
1.0
N O I= \ g 0.1 C O
6-
0.01
o.co1
t - - =- - - - - - - -
Rovle'gn regian Mie or resonance Ootïcot = regton reqion - - - - - - i - 7 - - -
1 . .
o. c---- i O 2 0.3 0.4 C ccumference 05 0.8 i O jwcvelencjth 2 = 3 2 rra/ 4 5 6 A 8 1 C 20
Figure 24. The RCS of an isotrqic sphere as a fûnction of eiectrïcai size.
In the Mie or Resonance region, RCS undergoes a decaying oscillation towards
unie as the eïectricai size hcreases. In this region the electrid ske is between one and
ten wavelengths. Tk oscillations are caused by creeping waves that propagate arouxxi the
nirface of the sphere, chanoin<r phase and mtetactiag comtnrtively and destructive@ with
direct-path specuiar reflections h m the '%onty' aspect of the spbere. RCS mgnitudes
in the Mie region are proportional to the square of the wavekngth,
In the Opticai region, aIso kwwn as the hi@-fkquency region, the sphereTs
dimensions are much hrger than one wavelength (b > IO). Creeping waws are aiso
present in the Opticai region, however their influence is limited as they are generaily
insignificant in cornparison to the other mechanisnrp that domhate it [8,11]:
a specuiar scatteringy w k the angle of reflection equals the angle of
incidence;
b. end-region scattering, which produces non-specular sidelobes;
c. dihction, or edge effects, which is end-region scattering in the specular
direction due to currents induced by edges or sharp curves; and,
d. multi-path, where energy reflects off more than one surface before
retuming to the observer.
In the Opticai region, RCS is asymptotic to za2 . High-fkquency RCS analysis is
of great interest to researchers in the field of signature reduction, notabiy with respect to
"stealth" technology such as h t presented m chapter 1. Note that in the following
sections, discussion is Iimited to the case where dimensions are much larger than  .
2.8.1 Square plates
An isotropic sphere presents the same RCS regardless of aspect; other simpie non-
isotropic shapes exhibit rehims that vary significantiy with the angie of incidence. Kmtt's
hierarchy of scattering shapes [12] descn'bes many of these shapes, providhg the reievant
formulas, fiequency and size dependance for RCS m each case. The moa basic shape is a
flat square phte, the RCS of which was demonstrateci by RA Ross in 1966 [13] and cited
in numerous works to date-
Figure 2-5. The RCS of a flat square plate with ka= 14.7
The RCS of a Bat square plate is cbaracterized by a hirge spike at n o d incidence
foilowed by a number of incfeasingly smaller d wider lobes as the angle of incidence
increases, appearing much iike a sinc fhction. Changkg the dimensiors of the plate in
figure 2-5 would change the magnitude and width and number of lobes in the RCS curves,
while their basic shape remajned simüar. The RCS of a fht square plate with sides of
length a, at n o d incidence, is given by:
2.8 -2 Dihedral reflectors
Corner reflectors are the most effective simple shapes for maximiPng RCS. A
dihedral comer reflector is composed of two plates (usually rectangubr) with a common
edge, oriented such that an incident ray reflects off both plates before teturniug to the
radar transceiver. The RCS of a dihedral rektor is a hction of the 'corner angie" as
weii as the size of the plates. By making the two plates orthogonal, an incident wave is
reflected back toward its source.
Figure 2-6. Reflection fiun a dihedral reflector with orthogonal sides.
The maximum RCS of a dihedral corner remor wîîh rectanguIar sides of length a and
height 6 occurs at specuiar incidence, and is given by 1121:
The trihedral reflector is the strongea cefiector in Knott's hierarchy, due to the
triple-reflection retums that it produces. Figure 2-7 demonsirates the RCS of a trihedral
corner reflector composed of equiIateral triangles, at various angles of incidence.
The large peaks at either end of each RCS plot occur as the incident ray becomes
tangentid with either of the two vertical sides of the reflector, effectvety "seeing" a flat
plate. The wide and gently-curved centrai lobe resuhs fiom triple-reflection retunis fiom
aii three faces.
The maximum RCS of a trihedral reflector composed of £lat square plates with
sides of Iength a is [12]:
Figure 2-7, The RCS of a trihedral reflectot at
various elevations.
2.8.4 C ylindrical shapes
Cyliaders are of particular interest to this research as there are numerous
cyhdricd shapes in the modelî ptesented later in this work. Cyiindricai shapes produce
higher RCS than spheres, and they are next only to the three precedmg examples m the
relative strength of their retunis. The RCS of a m e nght circular cyiinder is ody k t l y
proportional to fi-equency, however it Uicreases in proportion to the cube of the cylsder's
size. Like a sphere, it bas a high maximum RCS at normal incidence; like a square pkte,
the RCS drops off sbarply as the angle of incidence moves rowards an end" of the
cylinder. A plot of the RCS of a cylinder as a h t i o n of elevation is show m figure 2-8.
The maximum RCS of a right cin:ular cylinder of radius a and length b is [12]:
Figure 2-8- The RCS of a right cucular cyiinder as a hction of elevation.
The use of analyticai methods based on the preceding sections provides cornplete
and accurate solutions for the RCS of simple shapes, and they xnay be extended to analyze
shapes that are uncomplicated combinations of simple shapes. However, as the geomehy
of an object becomes more compIex, the correspondhg dytical solution to the RCS
problern becomes unmanageable. At thîs point, it becornes necessary to resort to
numencal methods, which provide approximate vice exact solutions.
HF prediction techniques are of particuiar mterest in this research sjnce at X-band
fiepuencies, an object the size of a ship as weil as many of the f e a . on Îts upper deck
are well inside the optics region They are relative@ simple in nature shce each part of a
complex body in the optical region scatters enagy independent of the other parts. This
makes estimation and integration of the individuai induced fields relatively uncomplicated.
2.9- 1 Geometric optics
The rnethod of geometric optics (GO) is based on the shdy of üght, m that it
assumes that EM scattering fobws the laws of ray optics 1141, behaving accordmg to
SnePs Law. The incident and reflected rays are in the same plane, and the angle of
incidence equals the angle of reflection Therefore, m the monostatic case, the reflected
ray only rehims directly to the source at normal incidence to the specular point. In the
case of muhipie reflectiom, as in complex geometry, the incident ray must be traced for
each reflection in order to determine whether or not it returns in the specular direction-
For a large &e that is doubly curved with rad5 a, and a, the RCS is calculated as:
There is no wavelength dependance in the above equation; the wavelength is
assumed to be at the iimit of zero since we are concemed with high-fkquency
approximation. GO has two principle weaknesses which malce it unsuitable for examihg
the RCS of anything other than doubiy cwed objects:
a Ït r e q h both dimensions m a given plane to have fjnîte radü. A flat
surfiice or a cyInidrical Nig bas at Ieasî one surîàce with infinite radius,
brefore the above quation bas no solution; and,
b. it fails to account for edge effects.
2.9.2 Physicai optics
Physical optics ïs of partic& interest m this research as it forms the basis for the
software used m the simulations desaiid in the following cbapters. PO approlcimates the
induced çurface currents at each point on an object and integrates them to obtain the
scattered field. In the case o f b t or sin& curved s b e s , this overcomes the limitation
of GO in that since the uiduced fields are fmite. the scattered fields are aiso finite [8]. PO
is based on a simplification o f the Stratton-Chu form of Maxwell's equations, also h o wn
as the electrîc field integration equation (EFIE) and magnetic field integration equation
(METE). The scattered fields are given by:
e" where y/ is the kee space Green's fiinction, = -
4x1- '
such that r is the distance between the surîkce patch US to the point of interest for the
scattering fields and f i is the unit normai to the scattering surfàce. The fkee spire Green's
function htroduces phase deky and mverse M d strength decay as a fbction of the range
f?om the observer to the scattera. The EFIE and MFIE are common starhg points in
m y high-fiequency numerical techniques.
In the case of PO, equation 2.22 is simpIified using two appro>mnatioas. First, the
far-field approximation is applied- In the fàr fieId, r is very large compared to the
dimensions of the object of interest. The gradent of equation 2.23 then becomes [a]:
where 3 is a unit vector representing the scattering direction and R is the range nom the
O bject to the observation point.
The second approximation is referred to as the tangent plane uppr~~mation. The
object king studied is asnimed to be perfèctiy flat and smooth at the SUTIàce patch rlS.
Assuming that the body is a p e r f i conductor, then the foilowing equalities can be
substituted for the tangentid field components of equation 2.22:
By restricting the surnice hiegral to those clS patches that are iiluminated, equation 2.25
equals zero for shaded patches [9]. The net effect is that only the fields on swbes of the
object that can be seen by the observer are evaiuated. The EFIE equation then becomes:
with a s i m k tesuit for MFIE. EvaIuatiag the E F E or MFIE and substitutmg the result
into equation 2.4 can then yiefd a much-siniplified expression for the RCS of an object.
For example, Knott [8] prodes this PO solution for the RCS of a rectanguiar Bat plate
with area A, and length I at incident angle 0, :
The PO solution for the monostatic RCS of a finite right circular cylinder is [a]:
a= 41s A cos 0, sin(kl sin 4 )
where a is the cylinder's radius and@, is the angle away fkom normal incidence.
Physical optics cannot account for edge difhction, so it does not address edge
effects or electrically smaii surnice discontinuities. It also M s to adequately account for
depolarization effects. PO generally gives better resuits as the angle of incidence
approaches the surface n o d of an objeçt's visible hce.
! sin(# sin 0, )
COS@, kl sin ei
2
2.9.3 Geometric theory of difEaction
Both of the numerical methods diseusseci so fàr n3 to adequately account for
difhction &om edges or nu$ce discootmuiues, or for the impact of changes m
po larization. Keiier's geometric theory of ciBiaction (GTD) considers the scattering of
EM waves by a straight wedge in order to ad- these problems, as weii as to overcome
the wide-angle reflection errors inherent in PO. GTD assumes tbat a ray striking an edge
generates a "cone* of di5acted rays such tbat the M-angle of the eone equals the angle
between the incident ray and the edge.
Figure 2-9. Keller's m e ofdificting rays-
GTD assigns an amplitude and phase to scattered field compownts ifthe
observation point lies on the cone; otherwise, the cWhcted fiehi is equal to zero. The
field amplitude depends on a cornbition of a di8iaction coefficient and a divergence
factor, and the phase depends on the phase at the edge and the distance fkom the
difnractmg edge element to the observer. The difnaction coefiients thenselves are also
dependent on phase, ami they account for polarization effects. The divergence f'actor
ïntroduces a decay in amplitude as tbe difnacted rays spread h m the edge. 16,101
GTD does not work mrrectly in shadow and reflection boundaries due to
singulanties in the difhction coefficients, and in it a h incorrectiy gives innnite results at
caustics, where an infinite number of rays converge.
2.9.4 UniformtheoryofdifEaction
The uniform theory of difhction overcomes the singularities in GTD's d i h c t i o n
coefficients by rnultiplying the difraction coefficients by a Fresnel integral This technique
removes the singuiarities, but it does not deal with GTD's inability to account for the
convergence of idhite rays at caustics (81.
2.9.5 Physical theory of d ihc t ion
Uhtsev ' s physical theory of dif lkt ion 0) was developed to impmve upon
physical optics using a solution involving scattering eom a wedge. Unlike Keller, he used
wedge s c a t t e ~ g to apply a correction fkctor to the PO solution. He distinguished
between unifom currents, which are the PO surfàce currents, and non-unfonn currents,
which are due to the edge [15]. The total field is represented as the sum of the incident
wave, the PO contri'bution and the edge contrî"bution Since this s u m must equal the exact
solution, the edge cont r i i ion can be found by subtracting the others fiom the exact
solution Considering the cases where each of the two wedge faces is by the source,
both individudly and together, PTD uses two diffi.action coefficients for each case,
ultimately having six difhction coefficients where GTD uses o d y two.
Although PTD d o w s the calcuiation of scattered fields outside the Limits of GTD,
ït is ultimately a l e s complete solution It must be used in conjuaction wiîh another
method, such as PO, since it accounts only for the scattered fields at edges.
2.9.6 Method of Equivalent Currents and Method of Moments
The method of quivalent currents is based on the k t that a nnite current
disaibution produces a finite result m the fàr field wben the distriiution is summed in a
radiation integrai. By nnding the proper current d i s t r i i n , the caustîc proMems of GTD
can be avoided. This method has been the subject of considerable study and refinement,
however ultimately it is UIlSUitable for the analysis of complex bodies because of a huge
computationai burden generated by three highly complex dZbction coefficients [6,8].
The method of moments (MOM) is a popular technique that converts to EFIE or
MRE ïnto a set of algebraic equations for solution by niatnx inversion Harrington [16]
developed this method as a meam of solving numerous EM field problems. RCS
calcuiation using MOM has been impiementeci in modern low fiequency EM anaiysis
software such as NEC, however the high computatiod burden resulting fkom extensive
matrix inversion cdculations d e s the method of moments unsuitable for HF d y s i s .
None of the first four theories adequately addresses surfàce waves, wkch are
important when a component of the incident waves is taagentid to a long mu>oth d c e .
Such waves c m have a significant contri-bution by operating in an end lire mode.
The software used in this research is a hybrid code that uses elements of PO and
GO to perform HF RCS &sis. SSpeciGc details of this code, caiied RAPPORT, wül be
discussed in the next chapter.
Cha~ter 3 - Method and aaalysis tools
Thus fàr we have discussed the practicai problem presented at the outset of this
research, and examined the pertinent tbeory in radar cross-section adysis. The next step
is to examine the software tools and numerical models employed in the research, with
particular emphasis on the RCS analysis software, its capabilities and iimitations and its
application to the problem of IROQUOIS class radar cross section
3 1 ADalysis technique
The numerical RCS a d p i s process employed in this research starts with a
simplified line drawing based on ship's drawings, which models an IROQUOIS or
TR[BAL class ship [ 1 7,181. It ends with polar plots of the computed RCS of those
models. The joumey fiom the beginnïng to the end of this process is quite cumbemme,
involving a number of commercial software packages and specialized FORTRAN
programs, interspersed by considerable file conversion. The process fobwed is
essentially that employed by Losier [3], with a number of improvernents made to speed up
the error-checking, file re-fomtting and data presentation subprocesses.
3.2 Simulation process
A sïmplified rnodeling and analysis process flow chart is shown in figure 3- 1. Once
a suitable CAD mode1 is produced, it is saved in Drawing Exchange File 0 format, a
comon graphics ille format compatible with DIDEC. DIDEC is employed to convert the
DXF file to Electric Field I n t e w o n Equation @FI) format. The E H output nle is
modifïed slightiy to convert it to another nle format (*.O02 fofmat), then read into
jlJNCTION. JUNCTION checks the mode1 for geornetry errors and converts the data îïle
to PLA file format.
File ooriverslon
PRE-PROCESSING POST-PROCESSING
Figure 3-1, The software process for the RCS analysis simulations.
The PLA forniat is the native geometry input file format empioyed by RAPPORT-
Mer processmg the PLA file, RAPPORT produces its output as an ASCII text (*.RPO)
me, which descn'bes the sïmuiation paraaieters and lists the wmputed RCS data The
resdts are then extracted fiom the RAPPORT output fiie and plotted ushg MATLAB.
The simulations were perfonned on a variety of hardware platforms, sbi.ting with
a Pentium 166 desktop PC and later moving to Pentium II conputers with processing
speeds of 233 MHz and 450 MHz, with 128 M b and 256 Mb RAM respectively. On
occasion. work was verifïed at DREO ushg their considerably fàster DEC-Alpha 3600.
3.3 AutoCAD
AutoCAD is a powerfd computer-aided drawing software package which can be
used to produce fU-size drawings of highiy detailed complex objects. It d o w s drawings
to be saved in a number of Merent füe formats, including a DXF file format compatible
with DiDEC, These features made AutoCAD the tool of choice for building and
mod-g the triangular fàcet models of the IROQUOIS and TRIBAL class ships.
AutoCAD release 13 was used for this research; one limitation of release 13 that caused
considerable delay and extra work in the mode1 development was the inability of the
software to convert objects fiom line drawings to three dimensional fàces or face&, and
vice versa. As we& although there are numerous powerfid commands available that aüow
the user to quickly constnict simple or complex three-dimensional shapes, these routines
produce extraneous lines that lead to modeling errors in the pre-processing stage. In sorne
cases, such as the " 3 D comrnand, they produce 3D shapes as '%locks" of fkets tbat are
not recognized or processed by DIDEC. As a d, although these features could be
used as modehg guides, it is oecessary to build most 3D structures in the ship models as
iine drawings, one line at a t8sie.
3.4 DIDEC
DIDEC (Digitize, Display, Edit and Convert) is a versatile program originally
developed by Concordia UnÏversity for DREO m the late 1980's to mate wire ~d mode$
of complex geometrk shapes to fàciiitate their electromagnetk interaction adysis using
various time domain a d fiequency domain codes. Extensive modification of the original
program by DREO has added the ability to create and manipulate nirface patch and celi
models, as weii as numerous other capabllitKs. Figure 3-2 shows the VO structure of the
DIDEC program. Accepting input fkom a variety of sources, DIDEC can be used to
create, m o d e or convert numerical modeis that xnay be saved in formats used by NEC,
EFZE, TWTDA and FDTD codes. Cl91
N urnerical input
Digi tizing tablet
Simple geome tric shapes
Figure 3-2- The VO structure of DIDEC.
Ln this research, DIDEC was used maidy as a fïie conversion utility, to convert
AutoCAD DXF output mes mto EFI fite format. AutoCAD's inability to convert line
drawings to 3D &et drawïngs was overcome by reading DXF line drawings into DIDEC
and then writhg them back to AutoCAD as "3D fàce" drawings. The reverse procedure
was employed to speed up the construction of cyhdrical objects. DIDEC also has a
number of usefiil graphic user interfàce features that assisteci greatly in debugging the
various CAD modeis and eliminating errors during the model design process-
The principle limitations of DiDEC are piatfonri-refated: aithough the program has
k e n upgraded regularly by DREO, it is built around the obsolete HALO graphics driver
for an early version of MS-DOS, which is not entirely compatiile with modem Microsoft
Windows 95, Wmdows 98 and Wmdows NT 4 DOS enviromnents. CompatiibiiÏty
problerns ranged fiom very slow mput file processhg to an k b i i to &play the EGA-
based graphics images properly on many PC platforms. Reading the DXF file for a
relatively simple ship mode1 initially took over ninety minutes ushg DIDEC; the input file
processing was sped up greatly, at the expense of meen clarity, by changing the desktop
PC's video mode to large-character resolution. Another Iimitation imposed on the
research by the age of the program was the MS-DOS "640 Kb Mer"; in order to ensure
that DIDEC's memory requirements did not exceed 640 Kb, a fixed Limit of 2000 vertices
was set in the code for the TO EFlE commaod. This necessitated breaking up the CAD
models into parts with no more than 2000 vertices each, As a result, models had to be
pre-processed as up to eight separate mes that were subsequently johed together after
conversion to PLA format.
3 -5 S u p p a programs developed using FORTRAN 90/95
FORTRAN appears to be the lingua haca of the EM field analyss research
commmity, insofk as the software employed m this pmject is c o ~ i c e n d The origmal
code for DIDEC, JUNCTION and RAPPORT was ail written in FORTRAN 77, with
subsequent updates written using later versions of that venerabk matheniatical language.
The JUNCTION and RAPPORT code acquired h m DREO for this research was
modikd for the W d o w s 9 5 N 4.O/DOS 8.3 desktop PC environment ushg downward-
compatible FORTRAN 90 and FORTRAN 95 compilers. As well, a number of short
FORTRAN 90 programs were d e n to perform the followiag fhctions:
a, convert EFi format files to 002 format;
b. extract multiplicity m o t messages fiom the JUNCTION diagnostic output
fïie (two programs based on DEC Alpha FORTRAN at DREO were re-
written for the PC environment);
c. convert one o f the KJNCTION output file formats to PLA format;
d. splice together PLA files representing mode1 sections, to create one
RAPPORT input file; and,
e. extract azimutb, elevation and RCS prediction data fiom RAPPORT
output files.
The source code listings for the above programs are found in Annex A.
3.6 JUNCTION
JUNCTION is an EFIE anaIysis code o ~ ~ y written at the University of
Houston, Texas in the 1980's. A tnmcated version of this soAware was employed as an
error-checkhg routine and another step in the process of creatmg a RAPPORT-
compatible input file- Since the EFiE analysis component of JUNCTION was not used in
this work, the EFIE analysis routines were removed fiom the program by DREO.
Subsequently, at RMC some extraneous code was removed in order to speed up the
program. JCTNCTION was written in FORTRAN 77 to be run on a variety of hi&-speed
platfonns ranging fiom a VAX system to a CRAY supercomputer. The DREO version
lent to RMC for this work is normaüy run on a DEC Alpha 3600 computer system.
Several changes to the JUNCTION software were required to run the program on a PC;
despite the change in platform, there was no apparent l o s in computational speed.
JClNCTION performs one other vital fùnction not dexn'bed earlier- Given an
input file consisting only of a list of vertices and edges of triangular fàcets, JUNCTION
examines each closed body in the model and assigns an outward normal to each facet. It
then writes the coordinates for the base of each unit normal into a * .FAC output file dong
with the facet coordinates. The outward normals are required by RAPPORT m order to
determine the PO resuit for each fàcet.
,IUNCTION7s most sienificant limitation is the user-unfiiendliness inherent in its
geometry diagnostics output file (*.O03 me). This me con& a comprehensive list of
model geometry data such as general body parameters, lists of fàces defioed by their
edges, edge-vertex connectivity, various mode1 parameter statistics, definitions of edges
by vertices and a fâcet orientation check. For complex models with numerous fàcets, this
file can be dozens of pages in le@ The daficulty m interpreting this f i T s contents is
overcome by the use of two post-ptocessing programs provided by DREO,
CHECK-MULT and CHECK-VER, which extract relevant error messages fiom the
*.O03 file and iden* edges and vertices containing modeiing errors. Again, miwr
modifications were made to these programs to port them fiom the DEC VMS
enviromnt to a desktop Windows/MS-DOS sheii. O f k importance, the version of
JUNCTION employed for this researcb producecl output data mes with four decimal
places accuracy. Although this limitation was insigdicant for the purposes of this
research, four decimal places accuracy were used as a guidelme for DXF fik format
accuracy and in ail FORTRAN program devebpment.
3.7 RAPPORT
RAPPORT @idar signature mysis and -Prediction by Dysical Qptics and Ray
Tracing) was developed by Dr M.G.E. Brand of the Netherlands Institute for Scientific -
Research (TNO) to perfonn HF RCS analysis of simple or complex O bjects 1201. The
program was written in FORTRAN 77, to be nin in a Unix environment on a DEC Alpha,
Sun station or similar high-speed compter. Version 3.0 of the RAPPORT code was
extensively modined by DREO for their use. In previous work by Losier 131, DREO's
code was rnodified to be run in the PC environment. For the purpose of this research,
Losier7s code was f'urther modifieci and adapted to more modem IBM PC hardware. The
following paragraphs desccli. the theory and main features of RAPPORT.
3.7.1 Background
RAPPORT is based on a combination of the PO and GO high-fkequency aaalysis
methods discussed earlier. B d employs a PO solution similnr to tbat presented in
section 2.9, and uses a ray trackg algorithm to detemine which surnife patches are visible
to the observer for the given angle of incidence.
3 -7.2 Physical optics approximations
In order to develop RAPPORT'S hybrid irnplementation of PO and GO, consider
the scattering problem presented in figure 3-3. An observer at point P is a distance R fkom
the origin, observing an object a distance r away, whose d a c e patch ds ' bas a normal
fi . An incident plane wave, consisting of an electric field with magnitude E, and direction
êi and a magnetic field with magnitude Ho and direction 6 travels in the direction f and
is scattered in the direction s . Note that this dennition applies to both the mowstatic
and bistatic scattering cases-
Figure 3-3. The RAPPORT development scattering problem-
Staaing with the EFIE and MFIE equations 2.22, RAPPORT a p p b the tangent piane
approximation for a non-perfktiy conducting plane; m this case, the reflection coeiEcients
for the reflected wave m w depend on the polarvation of the incident wave as weiî as the
angle of incidence. For a plane constnicted of a materiai with a kwwn dielectric constant
E, and permmMty p, the incident fieki at any &en pomt may be considered as having an
incident component Ê, and a normal component Ë, with respect to the incident piane.
Equations 2.25 can then be r e - d e n as the four foIlowing relations 1201:
where coefficients R, and RA are the Fresnel reflection coefficients:
p, cos 4 - JPrq - sin2 R =
Pr COS^, + ,/-
Equat ion 3.1 reduces to equation 2.25 in the case of a perfedy conducting
scattering surfixe, whae R,=l and R p 1 . Using figure 3-3, the EM fields are: [20]
The scattered field components can be detemimed by substituting equations 3.1
and 3.3 into equation 2.22. The perpendicular-polarued component of the scattered field
is given by [2O]:
The parallel-polarized components of the scattered field are given by:
The above equations, which are the PO equations used by RAPPORT to predict
the RCS of an illuminatecl area, are valid for both the monostatic and bistatic cases since
there are no restrictions on the incident and sçattered field vectors. As weU the use of
reflection coefficients aiiows for the use of one or more non-perfectly conductmg
materials in the object to be analyzed.
3.7.3 Raytracingdmultipierefiections
RAPPORT a d y z e s the flat fàcets in an object by suMividmg each k e t kto a
number of small trianguhr swfàce patches, each of wbich Ïs illuminateci sepatateiy. A ray
tracing algorithm based on Sneii's law is 4 to determine w k h of tk triaoguQr nirntce
patches in a given làcet are exposed to an incident ray or a ray rekted ftom another
surface patch on the object. The ray trachg method is referred to as b a c h d ray
tracing, because the v i s i i of a sinnre patch to an incident wave is determined by nring
a ray from the centre of the patch towards the source of the wave, as show in figure 3-4.
I f the backward ray strikes an object before it reaches the incident wave source, that patch
is considered to be m a shadow zone, and no field contriiution is calcuiated for it.
- ray fired patch A contributes to first relieetion patch 6 is shadowed by part of object
Figure 3-4. Backward ray tracing to determine sucface patch illuminaîïon.
To account for multiple refiections, RAPPORT fint uses this backward ray tracing
implementation of GO to determine which SLnface patches on an object are visible to the
radar beam. It then calculates the fïrst order reflection fkom the object uskg the PO
approximations of equations 3.4 through 3.7. Next, GO is used to determine which
nirface patches are illuminated by the scattered field fiom the fim reflection, ushg Snell's
law. The contn'bution to the o v d scattering k k l h m the second rekt ion is then
calculated by applyïng PO to these nuface patches. This pro~ess is repeated for the thad
reflection and so on, untd the reflection b i t specined by the user is reached.
3 -7.4 Surfàce patch integration
Mer the object's polygonal surfàces are divided into triaaguiar surfkce patches
and the IIiuminated patches have been KlentineQ the ~cattered field for each polygon is
determined by modifieci versions of equatiom 3.4 and 3.6, tbat sum the sllrface patch
contniutions [20 1:
where the summation is over the iilummiited patches and the integration is over the
individual patches. The last term in each equation in 3.8 is a phase integral that can be
waten as fo Uo ws [20] :
9 Y = 1 - S and the mangular patch has vertices al. 02. a3 and al where
One of RAPPORT'S streogths is the flexi'bility inherent in its broad choice of input
parameters. The user bas considerable control over the RAPPORT simulstion through the
parameters specined m an RPI He, as shown m figure 3-5. Many of the perametm are
seIf-explanatory - certain parameters of interest are exphined m the fobwing paragraphs.
Figure 3-5. A sample RAPPORT input parameter file.
RAPPORT allows the user to speciQ the maximum number of reflections to
calculare for each ray. When analyzing simple shapes, the maximum number of reflections
to spec@ is intuitive. For example, there is no need to specify more than one reflection
when analyzing a Bat plate. However, for complex shapes the number of reflections that
rnake significant contri'butions to the RCS on object is heavüy dependent upon the target
aspect. This parameter was set to a value o f 3 in previous work [3], as this is the value
commonly used in similar such simulations at DREO. Given the more complex nature of
the ship mode1 a d y z d in this research, it was feh prudent to aaalyze the impact of
increasing the maximum numbef of reflections that RAPPORT would calculate when
analyzhg the IROQUOIS modeL Tbe results of the retlection iimit andysis are presented
in the kginning of chapter 4.
RAPPORT breaks each facet in a mode1 into nuniemus triangular surfàce patches
to facilitate ray traçing- AhUSIZE is a scaiing &or that is used to determine the
maxirnurn size of the surfàce patcties. This influences RAPPORT'S ability to determine
the area of a given &et in a complex object that is exposed to a ray. Decreasing
MAXSIZE increases the accuracy of the RCS cdculation, but at the cost of a dramatic
increase in processing the.
The transmitter/receive configuration parameter is decepiive in that only the
monostatic case is available m DREO's modiki version 3.0 of RAPPORT. In any event,
the monostatic case is the one of interest, since it pertains to naval radars, active missile
seekers and firecontrol systems.
The type of calnrlation may be specified as RCS, ISAR, HIST, Mü'LTI or VISI.
The choices of interest in this research were RCS, used for simple shapes without ground
planes, and MULTI, that provides a multi-path mechanism including a g r o d plane. The
groundplane data iine following MULTI is a program modification made by DREO that
specifies a finitely conducting seawater gtound plane @CG) in this case. This feaîure is of
course a necessary requirernent m the RCS analysis of seagoing pbtforrns. As noted in
[3], the more user-fiiendly XPATCH code for RCS anaiysis does not simulate an FCG.
3 .%6 RAPPORT Limitations
The limitations of the RAPPORT code are discuss;ed in detail in 131. The major
limitation of RAPPORT that was central to this re-h effort is the software's ïnability
to process cwed swhes . Any curved surke m an object that is to be d e l e d must be
represented by a nurnber of h t k t s arrangeci to approximate the c w e d siirface. in the
case of a gently curved swface, this is eady approxiirrated with a smail number of
triangies. Where the object bas sharp curves or is ~ y ~ c a l in shape, it becomes
necessary to approximate the object with a large number of triangles i~ order to acbieve
acceptable accuracy in the physical sbape and di.iiensions of the object. in Losier's work
[3] it was not necessary to mode1 c w e d surfiaces since the HALIFAX class has no curved
major structurai fatures- By contrast, both the IROQUOIS and TRIBAL classes have an
abundance of cytindrical smf3ces in their architecture; as weil, the higher level of detail
desired in this work necessitated the modehg of many such d a c e s . The modehg of
cylùiders for analysis by RAPPORT shall be discussed in detaii later in th chapter-
3.8 MATLAB
MATLAB version 5.2 was used to produce the various graphs and polar plots
displayed in this chapter and chapter 4. This version of MATLAB include an infiemile
polar plotting routine that is incapable of producing accurate and easily readable polar
plots of quantities measured in dB. Moa wtably, the POLAR M o n plots negative
radial values as if they were positive numbers rotated 180 degrees. To overcome this
h w , a ssharware polar plottnlg routine that aiiows user control over moa plotting
parameters was obtained h m Mathworks [21] and modined substantiaily to automate the
selection of plot parameters. The modined MATLAB script (iisted m Annex B)
autornatically calculates the radial lia& and grid spacing for each plot.
3.9 Performance assessrnent
A number of simple shapes and existing models were processed with RAPPORT
eariy in the research, m order to gain experknce w i ' the program and assess îts
agreement with theoretical RCS calculations. To demonstrate RAPPORT'S ability to
predict the RCS of simple shapes, two examples were processed.
The fïrst example is a h t square plate presented by Ruck [22], the results of which
are show in figure 2-5. The RAPPORT simulation was done at 1 1.2 GHz; using
ka = 14.7, this corresponds to a square with sides of 6.260 cm. The smiulation was
conducted using WH polarization and a MAXSIZE of 0.005.
RCS computation of Ruck's square plate 1 Number of objects to process rucksqar-pla Object file narne 3 Number of reflections to calcutate 0.005 MAXSIZE (maximum patch size scale Factor) monostatic Tx/RX configuration RCS Type of result elevation scan Type of scan 0.0 0.0 0.0 Azimuth range & step 0.0 90-0 1-0 Elevation range and step SINGLE firequency Frequency parameter (single or sweep) 1 1.2 0.0 0.0 Analysis 6equency ( G k ) horizontal Trammitter polarkation horizontal Receiver polarization mcksqar.rpo Result file name
Figure 3-6 - The input paramder file for the square plate analysis.
The EFI, 002, PLA and RPO files for this simuIation are iisted in Annex C. The
result, sho wn in plot 3- 1, shows good agreement with Ggure 2-5. As anticipata the
larges disagreement with the experimentai case occurs as the angle of incidence
shpe of the curve closely foliows tbat of figure 2-5; the d ciifferences in mgnitude
may be due to the mteriai specifications king Merent, the choice of MAXSIZE, or
Radar Cmss Section of RudCs square plate with ka=14.7
Plot 3- 1. RAPPORT analysis resuIts for a square plate with ka= 14.7.
The second trial simulation is an analysis of the trihedral reflector presented by
Brand [20]. This simulation was conducted to examine RAPPORT'S multiple-reflection
processing capabiiity, as weil as to ver@ the correct operation of software after the
modifications made to DREO's version of RAPPORT. The anidysk was conducted at a
fiequency of 15 G a using a MAXSIZE of 0.005 and KH p o b t i o n .
Piot 3-2. RAPPORT analysis results for a trihedrai reflector with O, i m sides.
The r e d s shown in plot 3-2 were obtained for an elevation of zero degrees fiom
the horizontal, such that the specular direction is dong the axis of symmetry of the
reflector, as in [20]. The shape of the curve foliows that of the curves shown in figure 2-7
and agrees weil with Brand's results (wt shown), The peak RCS occurs at specular
incidence witb the reflector's point of symmetry' and the lobes to either side of the main
Iobe correspond to the case where the observer "sees" a dihedral reflector. because one
face of the trihedrai is parailel to the incident ray. As expected, the results show perfect
agreement with Brand The results are almost identicai to the exact solution, and have fàir
agreement with measured data [20].
3.10 Modeling of cylinders
As stated earlier, RAPPORT lacks the abiüty to process curved surf'aces. A right
circular cylinder of !hite length is most easïiy modeled as many-sided polygon extruded
over the length of the cyLiader, In order to achieve the desireci level of accuracy in the
RCS of this model, it was necessary to investigate the optimum number of sides that the
end cap polygons should have. Previous work by DMSS on an improved HACIFAX
ciass mode1 restricted the modehg of dl cyinidriccd ob@ts to six-sided modeis (ie. using
hexagonal end caps). S~ulaîioas of cylindrical abjects by D E 0 have used models with
varying numbers of sides. A critical analysis of various hexagonal cylinders in the CPF
model revealed that the bexagonaily-capped cylinders did not provide an RCS close to the
theoretical redts. A literature w e y reveald m y cyljndrïcal models but no clear
formula for determining the optimum number of sides for the end caps when modeling a
right circular cylinder.
The cylindrical sbapes used in the IROQUOIS and TRIBAL models analyzed in
this research corne in a variety of sizes, with radiï ranging fiom 3.6 centimetres to 1.2
metres, and lengths ranghg fiom twenty centimetres to twelve metres. At a simukition
fiequency of 1 1.2 GHz, the wavelength of interest is 2.676 cm and the wavenumber, k, is
234.8 m-'. The HF d y s i s region is defimi as ka > IO and I > il , where o and 1 are the
radius and length of the cyhder respectiveiy [22]. Usmg this critenon, cylinders of 3.6
cm radius would fàii just outside the lower bound of the HF anaiysis region, at h=8.45.
Bearing m mind that the Isnits of the HF region are approximate (81, and the possibiiity of
meamrenient errors arising fiom the scale of the ship's drawings [17,18], aii cylinders in
the models were assumed to fàii within the HF anal* region. In this region, equation
2.27 provides a satisfkctory solution for the RCS of a cylinder 1221.
To determine a rnethod for accurateiy modeling cylinders in the IROQUOIS
model, two cases were considered: the prolate case, where the cylinder radius is stnalier
than the length, and the oblate case, where the radius is larger than the length. The prolate
RHIB craw pedestal and the oblate cruise e n g k exhaust outlet on IROQUOIS were each
modeied a number of rimes* with each successive mode1 ushg a larger number of sides.
Azimuth scam of the models were pediormed at normal incidence in elevation. The
average results ofeach scan were then compared to the adytical specular RCS.
Azimu-averaged results were eniployed because the RCS would Vary with azimuth: as
the observer's position rotates about the cylinder model, the model's aspect changes. On
one bearing the incident ray may be normal to a Bat plate; on the next it may strike a plate
at an angle, or strike an edge formed by two plates. The RCS of the model varies with
azimuth as a fùnction of the number of sides in the end caps.
The results of these investigations are summarURd in plots 3-3 and 3-4. The
theoretical RCS of each cylinder was obtained using equation 2.19 with the parameters
listed in table 3-1. In both cases, the average RCS over 360 degrees of azimuth slowly
converged towards the theoretical speculat value. Starting with a four-sided cylinder, the
results were considerably lower than the theory, with only a 3 to 5 dBsm improvement in
the hexagonal case.
The results for the prolate cyiinder converged d e r the 30-sided model, and at the
50-sided model in the oblate case. Experiments with prolate and oblate cyiinders of other
sizes produced s i m k resuits, estabhihg the trend that for a @en fkquency and radius,
the number of sides requeed in the end caps increases as the shape of the cylinder
becomes more oblate.
Parameter RHIB Cohmm Cniise Exhaust
Frequency 1 11.2 GHz 1
Specular RCS (dBsm) 18.85 dssm 1
Table 3- 1. Design parameters for prolate and oblate cylinder models.
He;@
Radius
3.1 1 Discussion
Some confidence in the developed method was estabijshed fiom the resuits
presented in the previous section Since these r d t s provided good agreement, tbey were
used as guidelines in the modeling of right circuhr cylinders in the IROQUOIS and
TRUMP models: each cylinder was initially modeled with 30 sides (in the prolate case) or
50 sides (in the oblate case), the modeis were evaluated using RAPPORT, and then
adjusted to bring the aljmuth-averaged RCS to witbin 0.1 dBsm of the theoretical
specuiar value at normai incidence.
The next step in the research was to obtain and analyze results liom the RCS
analysis of the IROQUOIS and TRIBAL class ship models. These resuits are presented in
the next chapter.
3.12 m
0.312 m
0-624 m ,
0.84 m
Azïmuth-averaged RCS of simulated prolate cylinder at 1 1 -2GHz
1
Maximum Minimum - - Average
L
I 15 20 25
# of sides in end-cap polygon
Plot 3-3. Modeling a right circular proiate cyluider using m-sided cylindrical polygons.
Azimuth-averaged RCS of simulated oblate cylinder at 11 -2GHt
5 10 15 20 25 30 35 40 45 50 # of sides in end-cap polygon
Plot 3 4 , Modeling a right circular oblate cylinder using rn-sided cylindrical poiygons.
Cha~ter 4 - Simulation Results
This chapter will discuss the development of the IROQUOIS and TRIBAL CAD
models, and present the resufts of the RCS anaiysis of them. A large number of simulation
resuits are presented, with dhgmms of modincatitions under study, polar plots of the
changes in RCS which result h m these modifications, and a brief discussion of each
result. The redts presented represent only a sniall subset of a huge number of analyses
possiile due to a modular mode1 design approach, however they are sufEcient to address
the ami of this research.
4.1 The ROQUOIS CAD model
An early drawing of the pst-TRUMP IROQUOIS class ship is show in figure 4-
1. The numerical RCS mode1 of IROQUOIS was developed using the A u t o 0 model
employed by Wmters (hereafter referred to as Wie Wmters model") as a prototype CAD
drawing. The Wmters modei, show in figure 4-2, was originally designed as a
rectangular-mesh wire grid model for near-field HF antenna pattern analysis [23]. It
required signi6icant redesign in order to be suitable for RCS analysis using RAPPORT.
Major changes to the protoSrpe inçIuded:
a breaking up model blocks and converting its numetous polygons into
triangular fkcets of varying sizeq
b. addition of a waterline layer to produce a W y enclosed 3D structure; and,
c. validation of the mode1 using JUNCTION,
The above changes to the Wmters model actuaiiy only constituted the beginning of
a long series of m n s which culminated in a bighiydetailed IROQUOIS class
mode1 with many upper deck features and a detailed mast. Before the detail additions
started, it was necessary to produce a processable model, correct structurai mors m the
prototype, and add aii of tbe details that were cornmon to di later models. Three baseliw
models were produced to address these requirements. The simulation statistics associated
with these modeis are presented m table 4-1.
Baseline model # 1 is the srniplest possible mode1 of the ship. The wire antennas
and 2D surfàces in the Wmters model were removeci, its rectanguiar mesh was replaced by
a much less complex triangular làcet gn4 and a waterline layer was added to fiilly enclose
the modeL While a lack o f detail ~Ililkes this model unsuitable for detailed adysis of the
ship's RCS, it is useful as a benchmark for conprisons with later mociels.
The second baselme mode1 corrects a structurai approximation in the Wmters
model: to simplify the modeling process, the sides of the superstructure were made flush
with the hu1.L While this approximation may have been valid for HF antenna pattern
analysis, the above details were considered signifiant for RCS analysis, since they
introduce a variety of dihedraî and trihedral corner reflectors of varyïng size,
The thkd baselÏne model replaces the 2D surfàces ofthe prototype with thin 3D
plates, to preserve the closed form of the ship model. This modification accurately @es
these structures some thickness, removing the requirement to check normais m the *.PLA
fdes. Structurai dzerences in the port and starboard sides, beneath the flight deck
overhang, were also incorporated iato baseline model # 3.
Graphics file (*-DXF) size 1 162 Kb E I
# of vertkes in mode1 1 335 1 374 1 498 1 I 1 I
# of &a in mode1 1 999 1 1113 1 1458 1 1 R I
# of fâcets in mode1 1 658 1 742 1 972 I I I I
1 Avenne RCS (dBsm) 1 56-3 1 1 56.30 1 57.86 1
Prclcessinp; t h e (Plil233 CPU)
Minimum RCS (dBsm)
Maximum RCS (dBsrn)
~able4- 1 Simulation statistics for the LROQUOlS Baseiine models.
36 min
13.86
85.2 1
38 min
16.63
83.18
44 min
17-65
80.79
4.2 Simulation conventions and patanieters
It is now appropriate to discusses the conventions used in the models and the
simulation redts throughout the remabder of this report. The Z=0 plane is the waterinie
or ground piane, and the ship travels along the positive X axis. The origsi of the
coordinate system is at the bow in the 2 4 plane. The bearings in the polar plots
correspond to the relative bearing of the observer as seea h m the ship, with dative
azmiuth hcreasbg wunterclockwise: 0 O is dead ahead and 1 80" k dead asterq 9û0 and
270" are on the port and starboard beams respeaively.
Except where mted, ail simulations were conducted at 1 1.2 GHz one of maay
fkequencies used by the RCS measurement equipment at NESTRA m Obsorne Head, NS
1241. Vertical p o b t i o n is specified for both the reçeiver and transmitter in ail cases.
Choice of this fiequency and p o b t i o n facilitates comparison between t h work a d
previous work done on a HALIFAX class mode1 131.
An elevation angle of 89.5" fiom the vertical axk is used in ail simulations, as thk
corresponds to the 0.5 O depression angle of the NESTRA equipmenî, as shown in figure 4-
6. Caiculations are conducted m 0.5 O steps over 360 O of azimuth.
RAPPORT'S MULTI resuIt format is used in the ship simulations, to include a
finitely conducting seawater ground plane [25j at Z=O as a fkctor in the andysis. A
MAXSIZE of 0.00 1 is employed throughout, as a compromise between accuracy d
computationai time.
The majority of the polar plots in this chapter are plots of the change m RCS of the
mode1 due to a given modification to h The change in RCS is calculated by subtracting the
old (pre-mo~catioo) RCS h m the new @est-modifbtion) RCS. The result is rneasured
in dB vice dBsm, Smce subtmcting quantities in logarlthmic scales is quivalent to dividsig
their scalars, such that the reference dimension (square metres, in this case) drops out.
Note also that the radial scale of the polar plots is not consistent.
RCS Radar Antennes
rnd
Figure 4-6 NESTRA RCS range at Osborne Head, NS.
4.2.1 Reflection limits
As stated m &on 3-75, RAPPORT allows the user to specaj. the maximum
number of reflections to calculate for each ray trace. In previous work, the reflection limit
was set to 3, as this was d d suEcknt for the level of detail presented. In the case of
the more detaüed IROQUOIS modei, experiments were cooducted with various reflection
limits to determine the iïmit most suitable for this research. To foniialize these
experiments, a complete IROQUOIS mode1 with the lanice mast and guardrails iastalled
was analyzed, using one to eight retlections. This mode1 was chosen as it reptesents the
most complex shape to be aoalyzed. effectively a Worst case". The results of the study are
shown in plots 4-la to 4-1 h inclusive, which display the cuntri'bution of successive
reflections to the overali RCS of the modeL
Cbange in RCS due to Successive Refiectioas (dB) vs h u t b (degrees)
Plot 4-1 a. Contribution of 2d reflection, Plot 4-1 b. Contribution of 3d reflextion.
Plot 4- id. Contri'butim of 5<b reflection. Plot 4-lc. Contribution of 4* reflection.
Plot 4-if, Conbi'butim of reflectïori- Plot 4- le. Cmtri'butioa 0 f 6 ~ refleccian,
Plot 4- 1 g. Contributkm of 8& refleaiori, Plot 4- 1 b, Overall contnùution of multiple reflecticms.
Clearly, the second reflection accounts for the largest component of the overd
RCS. However, signifiant contriibutions continue to be made even at the eighth reflectioo,
that bas several spikes of approximateiy 3 dB. The overall contribution of the i k t eight
reflections @lot 441) effectively illustrates the cornplex.@ of the complete IROQUOIS
model by showing a great change in the RCS of the mdel due to multiple reflections.
Based on the above resuhs, the decision regarding the limit to set for the model
simulations became a compromise between processing t h e and afcuracy of resuits.
Simulation time for the complete mode1 increased by approxbtely one hour on the
PIIL23 3 for each increment in the reflection Limite Notmg that plot 4-1 f shows a ievel of
alrnost coasistently O dB, it uui be inferreci that the seventh reflection does wt conmie
much to the RCS of the model; therefore a limit of six reflections was estabkhed for al i of
the ship model simulations.
4.3 B a s e h model RCS plots
The RCS of the fïrst baseüne model, sbwn in plot 4-2, demonstrates a feature
common to ali later ship models, including the TRIBAL modeis. The large lobes in the
stem arcs of the ship are due to a large corner rektor fo& by the flight deck and the
hangar doors. It is intetestmg to note that the RCS drops by more than 30 dBsm close to
180"; this is due to the slight inward cant of the port and sbrboard hangar doors, that
prevents a specular return fiom îhem at or near a bearnig of 1 80 O. The high average r e m
of 42-82 dBsm is aiso due to the iarge number of upright sutfaces in the ship's forward
aspect, and the presence of two large dihedral corner reflectors on the forecastle, formed
by the upper deck, the gun house and the bridge face.
Baseline mode1 #2 was created by narrowing the hangar by 0.48 metres and
forward superstructure by one metre, as weii as adding mEor details to the hangar/fiumel
interface. These changes introduce a series of long dihedral corner reflectors with one
small side and one iarge side. As expected, the results of the modifications, shown in plot
4-3, indicate Little or no change in RCS over the stem arcs with considerable variation
forward. The pattern displays the expected symmetry about the long axis. The iarge spikes
in the forward quadrants are due to the influence of the dihedral corners formed by the
superstructure ''Iedge" and the angled corner fices of the SRGM house, while the changes
to the hangar top introduce a small variation in RCS fiom almost directly astem
270 Plot 4-2. RCS of the first baseline ROQUOlS model,
RCS (dB) versus Azimutb (degrees)
30 -- .- . 120 50 . 60
' 40 - . . . - .. . . --
30.. ' . . - . .
150 '
180 . . . . . . ... . . -. . . .
21 0 . . . . . . . . - . - . . . . . . . . .
. . . . . . . .
, _ . . - ' - . . ... . 240
- ...--. -. _ . . . 300
270 Plot 4-3- Difference in RCS of k l i n e models 1 and 2: the impact of narrowing the superstructure and hangar.
The Wmters prototype was designeci for purposes other than RCS adysk; as such,
certain design feanires were uns&able for a d y s k by RAPPORT. Wmters' two-
dimensional &es couid be proçessed by RAPPORT; however, they were better
represented as 3D surlàces to r e k t the k t that they have some thickness, and to simple
the mode1 fa&-fiading process. The 2D surfaces were re-introduced in baseline mode1 # 3,
with thicknesses dictated by the as-fitted drawings, In order to change the incorrect
symmetry of the rnodei, minor changes were made in the port and starboard breezeways as
weii as the VDS weii. Plot 4-4 displays the resuiting change in RCS.
RCS (dB) vemus Azimutb (degrees)
270 Plot 4-4- Difference in RCS benVeen badine models 2 and 3- impact of restoring 2D sudàœs and introducing asymmetry in the breezeways.
Some structurai detaiis were not included m these or suôsequent IROQUOIS
models due to difficulties in modehg or these practicai consideratioru:
a. a number of features, such as the TDLC's, could not be modeled corzecw
in three dgnensions due to inaccwsacies or lack of adEcknt detail m the
curator drawings;
b. some features were omitted as a compromise between mode1 complexity
and the time taken to build and process it. For exampleJ a capstan would
require over 500 nicets, while baseiïne mode1 # 3 wahout the two capstans
consisted of just over 2000 facets;
c. some prominent features m the slips are constructeci fiom nonmetalac
materials that are traasparent to radar and thus electrically insignifiant. For
example, the torpedo tubes, CITKS d o m e and SRGM gun shield are
constnicted of glass-reinforceci plastic;
d. the ship's various rotating antenna were mt modeleci, due to the rnodulating
influence that r o t a t a antenna have on RCS; and,
e. the internai components of the 76mm SRGM were not modeled. The gun
mechanism mi@ have some contribution to RCS, but it is composed of
numerous d mechanical parts of various complex shapes and sizes; it
was decided to disregard them in order to reduce the complexity of the
modeL
4.4 IROQUOIS detail additions
With a complete baseline, the next step in the mode1 design process was to add a
high level of detail to the beseline modei. Whiie the la, b a s e h mode1 is a complex shape
in as own right, it Iacks a number of signincamt structurai fatures, such as the breakwater,
the LW08 pedestai and the AMR air ktake. Additiordy, the curator drawings for the
IROQUOIS class [18] include many upper-deck nnings a d structural features such as
hatch combings upper deck lockers of various sizes and various cylindrical piUaR. A total
of ninety-eight structural features, lockers and pi- were added to the third baseline
model not including the toast and guardrail stanchions (these last two features shall be
discussed later)- Additions to the baseline mode1 were constnicted as separate cbsed
bodies and then added to the mode]; this moduht design approach kilitated easy changes
to the complete mode1 m the later stages of the work For the sake of discussion, the
additions to the mode1 and the impact that they have on the RCS of the mode1 are grouped
in sections, starting at the forecastIe (FX) and rnoving aft to the quarterdeck (AX).
4.4.1 Forecastle additions
The IROQUOIS class has very few protnidaig features on its FX, creating a pair of
large dhedral reflectors out of the upper deck, the SRGM house and the bridge face.
Detaii additions on the FX are limited to the breakwater, the VLS, and a smaii number of
hatch combings as seen in figure 4-7. The breakwater is of mterest because it is a cornplex
feature by itself, forming trihedral corner reflectors with the upper deck at all angies of
incidence. PIo t 4-5 illustrates the impact of adding the breakwater module to the ship.
Figure 4-7. Basdine 3 wîth breakwater added to FlC Inset port aft view of the breakwater.
RCS (dB) versus AWmotb (degrees)
Plot 4-5. impact of adding the breakwater module to the forecastie.
The asymmetricai resdts in plot 4-5 were expected, as the breahater itselfis
asymmetrical. The spikes in t%e forward arcs are due to the approximateiy 70" dihedrals
formed between the fbrward faces of the breakwater and the hulL On a number of bearings,
the complex shape of the -ter açts to "trap" rays and prevent them h m returning to
the observer; this is most notable in the starboard aft arc, where the observer c ' ~ ' ' the &er
side of the breakwater.
The remahder of the FX additions are an assortment of rectangular shapes
representing three hatch combings, the forward king post busing and the VLS mount. The
king pst housing is a prominent feature, M e the hatch combings rise only up to 13 cm
above the deck.
Figure 4-8. Addition of FX details. inset: sbtboard aft v i e ~ of3 hatch combigs, VLS and king post housing.
Plot 4-6. Change in CROQUOIS model's RCS due to adding FX details.
As expected, the addition of FX details had no sigdïcatlt impact over the stem arcs.
There is also little impact within 30" either side of the bow: this is kely due to the forward
dope of the FX masking the hatch combings and other objects fiorn view inside this arc.
Despite the low profile of most objects on the FX, they have sigoiscant impact. A
maximumof 20.36 dB occurs at 40°, witha minimiunof-27.9 dB close by. It should be
noted that these results include the influence of the breakwater: a quick comparison of plots
4-5 and 4-6 suggests that the influence of the breakwater in the starboard aft quarter is
negated by the presence of the king post hou* and the aftermost hatch combing.
4.4.2 Forward superstructure additions
The major additions at this stage are the LW08 pedestal and the AMR air intake. A
large number of upper deck k k e r s and antema mounts are also found on 02 and 03 decks.
The locken are typicaily mounted a few centimetres above the deck and away fkom
bulktieads (where appticable). This can create nanow cavities that act like many-sided
reflectors, trapping rays and uitimaîely reflectïng them in various directions. In this modei,
the iockers were mounted ten centimetres above deck, and the same distance away h m
buikheads as required.
These detail additions produced a large increase in RCS in the forward arcs, notabiy
at 15 O either side of the bow, wtiere a maximum of 35-56 dB occurs, A large number of
spikes exceed 10 dB. The ovewhelming Muence of the fiïght decic5ngar corner reflector
remains evident aster= The increase m RCS between 180" and 21 5 O is likely due
Figure 4-9. Superstructure detail additions. Insets: close-up and abjects, starboard side afi view
- -
240 300
270
Plot 4-7 Change in [ROQUOIS model's RCS due to addition of superstnicture detaiIs-
to the large tocker beside the starboard STIR phtfiorm supports. The a:-try in t
stem arcs may also be due to the k t tbat the starboard SRBOC lockers are in different
locations tban their port counterparts. Plot 4-7 also shows a number of relative decreases in
RCS, iIlustrating tbat the abundance of upper deck lockers on the superstructure creates
sigdicant destructive interference.
4.4.3 Top part ofship
The top part of ship is characterïzeâ by a passageway between the port and
starboard sides, flanked by Large trhedd and tetrahedral reflecton formed by the upper
deck, the forward superstructure, and the hangar. A small number of lockers and equipmnt
are added to each side of top part at this stage. As we4 three large cylinders are added:
two mast base supports and the support column for the RHIB crane.
Figure 4-10. Addition of top part details, insets: added objects, seen fiom starbard side aft; port Rde cl- UP-
Addition of the upper deck lockers and cylinders to top part caused a large change in
RCS across the entire azimuth, as expected. Due to the central location of these features,
and the large corner reflectors formeci by the hangar, upper deck and superstnicture,
multiple reflections are scattered back to the observer at di angles of incidence. A low
average change in RCS of 0.1367 dB in plot 4-8 is likely due to the fàct tbat many reflected
rays can pass tbrough the waist ami out the other side of the sùip, cather than reflecting back
towards the obsewer. This is supporteci by the change of approximately O dB at 90" and
270". The low average change is deceptive, snice the range of vaiues m this case is 46.97
dB.
RCS (dB) versus Azimuth (degrees)
Plot 4-8, Change in IROQUOIS mode1 RCS due to adding top part ship details.
The top part additions are symmetrical for the most part, except for the addition of
the RHZB C r a n e pedestai. The influence of this large cylinder can be seen m the larger
4.4.4 Fuanel exbausts d CIWS
This set of additions inchdes four large oblaîe cyiinders, a wmplex phtfiom and
two boxes representhg the CIWS support equipment cabkts. The ClWS mount itselfwas
not modeled due to its compiexÏty and the transparency of its radorne.
Figure 4- 1 1. Addition of fiumel exhausts and CIWS. Insets: four exbausts and CIWS cabinets; close-up.
These additions produced some surprishg resuhs. Although the average diBirence
in RCS of plot 4-9 was practically negligii at 0.0875 dB, there are a number of spïkes of
interest. Many large spike iocludiag a maximum of 16.16 dB occur m the fonuard arcs.
Since the CIWS mount is largely obscured fiom forward viewpoints, many of the changes m
RCS may be due to mutti-paîh i n t ~ t i o n s between the fume1 exhausts a d aaroundiag
SUffàces at the hinnei top and top part of 'Ibis particuhr modiocation is si- in
that the cylindrical features dominate the changes to the d e l ; mih the fiRy sides m the
cniise exhausts and fifty-two sides m the mains exbausts, high direct-path d secod-order
reflections are possible fiam numerous angles of incidence. A more detailed analysk of
these features wiii be presented iater m this chapter.
RCS (dB) venus Azimuth (degrees)
240 300
no Plot 4-9. Change in IRûQUOlS model's RCS due to addition of h e l exhausts and CWS-
4.4.5 Completing the IROQUOIS hdl
The nnal set of additions inc1udes the quarterdeck locken and batches, the torpedo
tube seats, and the INMARSAT pedestal. A number of these o b m are located "inside"
tetrahedral reflectors f o d by the upper deck, the sides of the superstructure, and the
underside of the flight deck overbang.
/'- -- ---, -- -- --_____.-'
Figure 4-12. Completed [ROQUOIS hull sbowing AX deâails- Insets: port side ail view of AX lockers, TDLC controllers. various lockers, CNMAWAT post and batch combhgs; close up fiom port aft-
RCS (dB) versris Azimuti (d-)
Plot 4- 10. Change in LROQUOIS model's RCS due to addition of AX lockers, hatch combings, INMARSAT p e d d and SVTT pedestals-
These additions ciearly illustrate the impact of çomplex geometry on tlae RCS ofa
warship, due to the numerous spikes m plot 4-10 and the wide data range of over 42 dB.
The additions to the exposed area of the quarterdeck are esentially symmettid the
maximum of 23-76 dB at 37" is likely due to the two lockers and SVTT pedestal added to
the port breeze way interacting with the tetrabedral reiiector forrned by the flight deck, port
buikhead and the upper deck. Although the importance of average RCS values is arguable,
this change resulted m the kgest overall decrease m RCS, with an average of -0.2264 dB.
4.4-6 Overail effect of detail additions
The impact of di of the detail additions to the IROQUOIS huli model is shown in
plot 4- 1 1. The changes had considerable impact, with an average of 1.235 dB, a maximum
of 37.2 dB and a minimum of -25-66 dB.
RCS (dB) versos Azimutb (degrees)
Plot 4- 1 1. hpact of d l detail additions to the IROQUOIS model,
The influence of the hangadight deck corner reflector is still very much apparent,
as the greatest changes in RCS occur in the forward arcs- In addition to c a u s a large
second-order retunis, the hangar face and flight deck also obscure much of the rest of the
ship ûom rnany angles of incidence. By contrast, in the forward arcs a considerably larger
number of small dihedrals, trihedrals, larger-order reflectors and cyiindricai object ma. be
'seen" by an observer. The higber-order rektiom that resuit are evkient in this and
previous plots,
As expected, there are large changes m RCS h m 35"to 75" either side of the bow.
These are undoubtedly due to the new additions causing additionai reflections to mach
dihedral and trihedral corners formed by the ship's bullrbeads and the upper de& most
notably at top part ship. Tabk 4-2 summarks the statistics associated with the IROQUOIS
detail additions,
Detail addition Break- 1 Fore 1 Super- water cade structure
# of edges in model
# of facets in model
Rocessùig time (PiU233)
Minimum change in RCS (dB)
Maximum change in RCS (dB)
Average change in RCS (dB) Table 4-2. Sim lation sbt&ics for the IROQUOlS it modeis.
4.5 The impact of the ship's mast
The final step in the development of the IROQUOIS ship model was to design and
add a cylindncal-pipe lattice mainnast to the drawing. This design effort consurned much
thne and effort due to the high detail required and the large number of vertices m each pipe
that makes up the mast. The mast itselfstaods 41.5 metces hi& supportmg three distmct
radar and communications antenna platforms It has in excess of two hundred pipes in its
lattice. The pipes are right cùcular cyiïuders of varying length and radius-
For rnodeling purposes, each pipe was represented by a cyiinder wah polygonal end-
caps. The cylinders were d e s i d fiom fjrst principles ushg the procedure d e s c n i in
section 3.10. This procedure wouid be repeated mtil simulation and theoretical results
agreed to within 0.1 dB. Initially a very tirne-consurning process, d e r a few iterations it
became possible to predict the trends in the resuh, ifmt the required number of sides itself;
with reasonable accuracy. Modehg the niast's structural members m this manner was not
without its drawbacks, such as a very high computationai burden: the graphies nle for the
completed IROQUOIS lattice miut was considerably larger than the fle containing the rest
of the ship modet The complete mast modei, shown in figure 4-13, was composed of 7,124
vertices, with 20,154 edges and 13,463 3D fàcets. By contrast, the mast-less IROQUOIS
contains only 3,744 b a t s . In order to overcome DIDEC's EFIE output restriction, it was
necessary to split the mast He into five separate graphics mes for pre-processing. Pre-
processing these segments consumeci over two hours, and the complete IROQUOIS model
with mast fitted took 1 1.5 hours to process with RAPPORT.
Figure 4-13, The [ROQUOIS mast model-
86
Resuits f?om an analysip of the mast alone Pi k space are show11 in plot 4- 12.
The plot bas an approxitmte bilateral symmetry, as expected, with an average RCS of
14.98 dB= Peaks over 30 dBsm occur 4S0, 90" and 135" either side of the bows. At
some angles of incidence, destructive mterference causes a large drop in RCS. The mhor
lack of s-try m the plot is likely due to modehg enors: sltbough the mast structure is
symmetrical, some mast members had to be moved slightly in order to avoid DIDEC or
JUNCTION errors rehthg to vertex prolàmlty and excessive muttipiicïty.
RCS (dBsm) vemus Azîmutb (degrees)
1 ; ' O .t... .
240 300
270
Plot 4-12, IROQUOIS mast in fiee space-
Plot 4-13 shows the merence m the RCS of the IROQUOIS mode1 due to the
addition of the lattice mast- The average change in RCS was -0.79 dB, however
significant kreases in RCS are apparent at approximately 45 de- either side of the
b w due to the large lobes present at those bearings. Except for a few small spurious
spikes fiom 150" to 210 O , it appears tbat the addition of the rnast has m Bnpact over the
stem arcs, due to the overpowering idluence of the aght deck corner reflector. Besides
the small ciifferences due to modeiing error, the lack of symmetry in this plot is
undoubtedy due to the inûuence of the ship's as- upper deck, which has the
effèct of adding an uneven metal groundpkne beneath the mast.
RCS (dB) vemus Azimuth (degrees)
Plot 4- 13- Impact of addimg the mast to the IROQUOIS model.
4.6 Reverting to the TRIBAL d e l
Mer RCS analysk of the IROQUOIS model was pediomed, the IROQUOIS
mode1 was reverse-eagIaeered to t e k t the ship's design prior to the TRUMP refit.
Design details were lifted nom curator's drawings obtasied h m FMFCB [IV. This
redesign effort Hicluded the eleven major structurai modifications listed in table 4-3 m
addition to the removal or relocation o f a number o f lockers and other d protrusions.
12 I S R G M ~ - 1 Removeci and replaced with GMLS mag 1
Mod #
1
1 3 1 ~ ~ 0 8 ~ e s t a l 1 Removed 1
--
Subject
VLS
-
Detail
Removed
4
5
1 O AMR uptake Replaced " i
6
7
8
9
I I RHIB m e column Removed I Table 4-3. Major structural modifications due to reversion to the TEUBAL model.
Mainmast
COMIS chaffpedestals
The changes to the IROQUOIS model were progressed fkom bow to Stern,
changing structural details as required and re-amangiog or replacing upper deck features.
The modular approach to the IROQUOIS detail additions saved some time and effort,
however it was still necessary to make large scaie structural changes to the cioseci bodies
representing the ship's huil and hangar. For couvenience, the mode1 changes are grouped
Changed to 280 configuration 1
Added -
WM-22 radar pedesîais
SATCOM p l a t f m s
Funnel Casing
CIWS pedestal
- --
Added
Removed
Changed to bifincated fiwiel configuration
Removed
by sections corresponding to parts of ship. The pbts in this section show the RCS of the
mode1 with the featured mOdifiC8tiOn, minus the RCS of the ptevious modeL To kiiitaîe
easier cornparison with eark resuits and to reduee the computational burden, aü but the
Iast of these analyses were conducted using mast-less rnodels.
4.6-1 Lowering the waterline
the ships effectively sa& a fmt. To incorporate this change in the mdel, it was raiçed
0.3048 rnetres; then the huii sides and waterline iayer were stretched back d o m to the
groundplane and corrected for the dope of the hulL The resuits are shown in plot 4-14.
RCS (dB) versus Azimuth (degrees)
Plot 4-14. Impact of Iowering the waterlbe m e fbL
The resuhs show m plot 4-14 are noteworthy m that ahhough the average change
in RCS is low, at 0.5738 dB, the difference in RCS varies widely over the plot, h m -24
dB to 33.7 dB. Most of the high values are in the forward arcs, in contrast to resuits
obtained fiom simiiar woik with the CPF mode1 [3]. The differenee in measurenients is
hi& where the h d has a promunced outward slope, and reduces drastïdy aft of the
beam, where the h d is essentjally perpeadicular to seawater grodplane. S h the
fonvard dope of the hua hrms an acute dihedral with the groundplane, the iarge huii
surface resulting fiom raisiag the ship -tes a iarger dihedd, and thus a higher retum.
4.6.2 EX modifications
The modifications to the forecastle consist of a number of remvals, a new
breakwater, and one major structurai change, as show by figure 4-15. The SGRM house
was removed and replaced with the larger GMLS iauncher and magazine compartment,
The upper deck changes and superstruchue modification are shown in figures 4-1 5 and 4-
16.
Figure 4- 15. FX alteratkm- inset: TRlBAL breakwater and deck with VLS and one hatch rmoved-
RCS (dB) versus Azimuth (degrees)
, ,
240 - . . - - . . . " 300
270 Plot 4- 15- Effect of retrofitting the FX.
As expected, the change of breakwaters and removal of other FX features d t e d
in no RCS changes in the stem arcs. Small spikes were evident just af t of 90° and 270 O in
plot 4-15, perhaps due to reflections h m the ioner faces of the breakwater. The most
sigdicant results are the large decrease in RCS at *45 O fkom the bow. The symmetry in
the plot suggests that this is due to the TRIBAL breakwater, which is fùrther aft than the
one it replace& and thus "iess visi'ble" to the observer; additionalty, tfiis breakwater forms
a less acute dihedrai, thereby giviag lower retunis.
Figure 4-1 6. The GMLS retrofit Inset: ciose-up v i e ~ .
RCS (dB) versos Azimiith (degriees)
270 Plot 4-16, Change in RCS due to replacing the GMLS house-
As shown m plot 4- 16, the replacement of the GMLS bouse on the forecade
resulted in a large increase in RCS on most fonuard bearhgs, while hawig no effect
astem. This change produced a range of RCS changes of 55-66 dB; the average chauge of
2.145 dB was the highest average RCS change thus $r in the research. This is due to the
hcrease in size of the dihedrals formed by the upper deck and the GMLS bulkheads.
which are much taler snd longer than the IROQUOIS SRGM buse.
4.6.3 Fonvard superstnicture modifications
The most compiex modifications to the ship's geometry occu.md on the fornard
superstructure: vimially every structural feaîure and cbsed body addition to 02 and 03
decks was rnoved or replaced Most mtably, the SATCOU, STIR and LW08 platrom
are renmved, and the WM-22 pedestais and Corvus chaffmounîs are a d d d The chaff
mount modules are extremely compiex; composed of over two hundred fêcets eacb, they
required considerabLy more design effort than any other feature in the ship d e l .
Figure 4- [ 7. Retrofits to 02 and 03 deck hets: close-ups of h m r d anci aft of02 & 03 deck-
95
RCS (dB) versas Azimutb
Plat 4- 17. Change III RCS due to superstructure retrofit
The results of this sïtnulation are shown in plot 4-17. Once again, a large
dinerence in RCS is evident in the fonvard arcs. The large WM-22 cylinders, the WM-22
piatform and its supports appear to more than make up for the loss of the dihedrais fonned
by the LW08 pedestal and the caMties created by the STIR and SATCOM platforms. The
approxïmate concave curve of the chaffmunts acts as a dish reflector to concentrate rays
arriving near 90" and 270 O .
The high ciifferences m RCS just forward of the beam are undoubtedly caused by
multiple reflections fiom these new objects, which remah obscured to the observer when
the ship is viewed &om aft.
4.6.4 Top part ship
The ody rriajor cbange to this ares is the removal of the RHlB crime column. The
remainder of tbe changes involved smiply re-bcating e* upper deck lockers.
, ./ %- I I . . ' " -
Figure 4-1 8. Deletions and ce-arrangements on top part ship. ïnsets: re-arranged abjects; starbard side close-up showing removal of RHIB @estai.
Plot 4- 1 8 shows thaî the changes to the model's RCS due to these modifications
are greatest on the starbard side, as expected. This is due to the remval of the RHIB
column cyluider, that caused scattering in all directions m the IROQUOIS modeL Of
particular interest is the iarge drop m RCS at 85 O; this too is likely due to the loss of direct
and multiple reflections h m the RHIB Crane coliuirn_ that is only partMy obscureci fiom
the port side at this angle of incidence (as show in figure 4- 10).
Another simulation was run in order to assess the impact of the RHIB crane
column. in this case the mode1 show in figure 4-17 was compared to the same mode1
with the RHIB Crane column removed. Plot 4-19 shows the results of this cornparison.
RCS (dB) versus Azimagh (degms)
Plot 4-18, Changes in RCS due to top part ship deletions and te- arrangements-
Plot 4-19. Contriilmion of RHLB crane column to plot 4-1 8.
Plot 4-19 demonstrates the iarge c o n t n ~ n of the RHIB crane colunm to the
overail RCS of the ship. Situated man area surrounded by trüiedral and tetmhedd
reflectors, its cyiindricai d e refiects energy in aiI directions. Although tbe average
RCS Werence in the plot is 0.0256 dB, Wèrences over 3 dB happen on numerous
bearings. A difference of approxhnately 20 dB occurs just forward of the starbard beam.
Most surpnsingiy, the maximum Merence m RCS occurs on the port beam, at 85".
Here, multiple reffections off the RHIB colunni on the starboard skie of the ship actualIy
pass through the waist and exit out the port side. The impact of multiple reflections miay
be seen throughout the plot, with numemus spikes everywhere except IO0 eaher side of
the bow.
4.6.5 Funnel and hangar top
This set of revisions inçludes the mst prominent change to the TRIBAL cIass ship
as a result of the TRUMP refit: the bifkcated or "bunny earsn finml arrangement was
replaced with a larger, single box-like structure. The changes to the modei, shown in
figure 4- 19, include the removal of the CIWS mount and its replacement with the AMR
uptake. The size of the IROQUOIS fiuinel intuitively suggests that it increases the RCS of
the ship, however replacing it with the oki TRIBAL fbmels demonstrates that the
opposite may mdeed be the case. Plot 4-20 shows that the change to the TRIBAL fumiels
actually increases the RCS of the mode1 by as much as 9.77 dB on the beam and seven dB
near 180°, with very little impact on most other bearings. The average cbange in RCS is
one of the lowest recorded thus tàr m the research, at O@ -0.0998 dB.
Figure 4- 19. Changing the -el corrfiguratim, inset: close-up of hnnels-
RCS (dB) versos Anmuth (dqrees)
PI& 4-20. Change in RCS due to retrofitting the TRBAL bels and AMR uptake.
The impact of the fumiels and the associated IROQUOIS class féahnes will be examineci
in more detail laîer m îhis cbapter.
4.6.6 Completion of the TRIBAL huil
The snai changes needed to reverse-engineer the IROQUOIS hull bacL to
D A L configuration mvolve minor changes to the ship's structure, removal ofthe
figure 4-20.
Figure 4-20. The coaipleted TRiBAL hull. lnsets: AX additions & close-up wew to starboard. Note that the exhaust Fan housing under the Qight dedc in the sbrbaard breeze way has been rernoved.
The change in RCS resulting 6om these modifications is shown m plot 4-21. The
changes to the ship's structure included tbe deletion of one hatch combing and the removal
of the damage control exhaust fàn on the starboard side breez way. The exhaust fan that
was added to the IROQUOIS mode1 with the baseline # 3 changes formed a rectangujar
cavity with the ship's structure forward of ît and a tetrahedral reflector behiad it. Removal
of thû feature in combination with movbg three upper de& lockers d t e d in a surprishg
increase in the RCS of the model as sbown m plot 4-21. It is possible that the exhaust
fan's presence was creatnig destructive miderence between 180 and 200" m previous
models. It is also interesting to note that there is a roughly symmetrical iactease in RCS on
near 90 O and 270 O; this may be due to the insertion of extra tectangular life jacket lockers
in the breezeways, or loss of destructive interference fiom the removed INMARSAT
pedestal.
RCS (dB) venus Azimuth (deg-)
240 300
270
Plot 4-2 1 - Changes in RCS due to revision of AX to TRlBAL configuration.
4.6.7 TRIBALmast
The TRUMP refit &ed m a n& of cbanges to the mast in order to support
new sensors and co~nmuniations antemas. These changes klwied:
a rernoving sponsons for the WSPS-501 and ANISPQ-2D radars,
b. removing four comm unications antenna sponsons and replacing them with
larger structures that supporteci new radar antennas as well as
communications antennas;
c. removing a number of s d sponsons for EW equipment; and,
d. shortening the mast slightiy-
The TRIBAL class mast evolved considerabiy in the over twenty years that the
ships were in service. Many cliffereut systems wcre fit to the ships individualy or as a
ciass, as new equipment or for triais, and work was p e r f o d by a variety of contractors.
As a result, there were many possiile mast configurations to choose fiom. In the end,
1986 curators drawings provided by FMFCB 11 7] were used as a guide in building the
TRIBAL mast, altbough some design assu~~lptions bad to be made as only side view
drawings were available, Construction was sped up by the k t that the "oil derrick" stages
in the lattice mast remaïned iargely unchanged by TRUMP: to change the main IROQUOIS
mast sections to TRIBAL contiguration required only the construction of one more level of
fiamework- The simpler design of the TRIBAL tnast aiiowed it to be built and processed
as four files, as opposeci to f ie m the IROQUOIS case; as we& the rnast s e p n t
composed of the fïrst four levels of the lattice b w o r k was common to both mast
models. The completed TRIBAL mast is shown m figure 4-21.
Figure 4-2 1. The TRIBAL mast,
104
RCS (dB) versrs Azimith (degrees)
4-22, Change in TRIBAL mode1 RCS due to addition of lattice ma=
Adding a laîtice mast to the TRIBAL mode1 produced very different d s than
the same action with the IROQUOIS mode1 The impact of the niast addition is small to
negligiile except for arcs h m 40' to 90" either side of the bow, and a small arc directly
astem. The average change in RCS shown in plot 4-22 is only -0.0219 dB m this case,
with very iittle variation over a range of 20 dB. The contributon of this mast to the RCS
drectly astem is approlcimately 3 dB higher than the IROQUOIS case. Except for three
large spikes the plot is essentially symmetrid, suggesting tbat the spikes are due to either
spurious multiple reflections off asymmetricai features, or possibly due to modeling errors
(as discussed in section 4.5).
Table 4.4 sutuniarizes the statistics associated with the ttansition h m the
IROQUOIS mode1 to the TRIBAL d e L
4.7 Comparison of IROQUOIS and TRIBAL RCS
Having completed the changes in the original IROQUOIS ship model to convert î t
to a TRIBAL class modei, and f ï t h g a mast to both slips, it is mw possibk to CO-
the RCS of the two ships. This comparkon was performed by processing the two ship
models, complete with k i r masts. The statistics associateci with each model are found m
table 4-5.
The result, as shown in plot 4-23, is the change in RCS resulting fkom the
conversion of the TRIBAL ciass ship model to the LROQUOIS class shïp rnodeL This
may be taken as representative of the change in RCS of the TRIBAL class ship due to the
TRUMP refit. The difference between the results fiom the two ship models varies widely,
fÏom a minimum of -3 1.97 dB to a maximum of 27.6 dB, with an average of -2.276 dB.
The overwheirning influence of the hangar door/fiïght deck dihedral on the RCS of the
stem arcs remaïm evident in this cornparison
TRlBAL ,
3,924
7,968
22,292
14,850
10:O 1
Mode1
Graphics file (*.DXF) size (Kb)
# of vertices in mode1
Table 4-5 Simulation staîistics for the complete IROQUOIS and TRiBAL rnodels.
JROQUOIS
4,180
9,187
# of edges in mode1 25,770
# of Iacets in mode1 17,180
Processing t h e (Piy233) (hhnim) 11:16 L
RCS (dB) vernis Azimith (degrtes)
Plot 4-23. The change in RCS of the lROQUOIS class ship mode1 due to the TRUMP refit.
It is hteresting to note that the RCS over the forward arcs has decreased
sigdlcantly on most bearings. Given the highly complex nature of the rnodels, t is
unlikely that there is one snigle cause for this phenomeaon, however a quick revïew of the
TRIBAL development plots suggests that this decrease in due to Muences fiom the
forecastle, GMLS and superstructure acting in concert with the mast. Indeed, the kgest
change in RCS appears ou the approxktely the same bearings as the larger returns nom
the IROQUOIS mast addition (plot 4-13).
Another point of interest is the iack of syrnmetry along the long axk: this may be
accouated for by the cMEzence in the placement of hatch combmgs and a small number of
upper deck lockers, as weii as iamor asyimnetncal structurai htures m the two modefs
nich as the 03 deck ladder piatfionn m the TRIBAL mode1 and the starboard exhaust fàn
housing in the IROQUOIS modeL
4.7.1 Fumel and hangar-top changes.
On inspection of the results obtained m sections 4.4.4 and 4.6.5, it was decided to
investigate the contriibutions of the fbmeis and the IROQUOIS hangar-top htures in
more detail. The most prominent feature of either chss of sbip is their f'unnek: what
would the impact on the ship's RCS have been ifthe ' % u ~ y ear" funnels had been left
intact by TRUMP? To investigate this question, the biicated fuaaels and AMR uptake
were imtdled in the IROQUOIS model; since the CIWS mount was an interfierence item,
it was moved to the position it occupied on the Persian GuJf-modifieci TRIsALs, and the
INMARSAT pedestal was moved to the former position of the after SATCOM mount,
between the after ends of the f i l s . The resuiting change in the RCS of the complete
IROQUOIS mode1 is show m plot 4-24.
The plot shows some symmetrical variations in RCS on either beam, as well as a
number of isolated spikes of varyjng size. A maximum of 15.48 dB occurs at 340°, and a
minimum o f - I 1 -08 dB occm at 190 O. Unlike many previous rnodels, the larger values
do not seem to be cfustered around the starboard side of top part ship. The approxbateiy
10 dB spikes near 30" are mteworthy in that their cause is wt apparent, ahhough it is
obviously a hct ion of multiple reflectiom involving asymmetrical upper deck features.
RCS (dB) vernus Mmath (degrees)
Plot 4-24. impact of restdng the bitiircated h n e l s to the lROQUOIS model.
The next feanires of interest are the IROQUOIS' fbnnel exhaust ports and the
CIWS mount. Plots 4-9 and 4-20 suggest that these items create large retunis on a
nurnber of distinct bearings. Simulations were run using the complete IROQUOIS model,
isolathg fist the exhaust ports @lot 4-25) and then the C W S @lot 4-6).
The results of these simulations suggest that, as expected, the fùnnel exhausts do
wt contniute much to the overall RCS of the ship mode1 Their average contniution of
-0.028 dB has iittie variation except for one 4 dB maximum and a siagle spike showing a
large reduction of -1 1.4 dB.
RCS (dB) venus Azimiitb (degreu)
Plot 4-25. Ccmûi.hdion of fini-el -exhnusts to CFtOQUOIS RCS.
Fig. 4-26. Contn'butim of the CIWS to the IROQUOIS RCS.
The CIWS produces a slighîly higher average contnibution of 0.072 dB, aiso with
iittle variation. However its maximum value is much larger: tbe 1 8-24 dB spike at 342 O is
prominent w t ody in this pbt, but in piot 4-9 as weiL Thus, it is apparent that the renihs
of plot 4-9 may be attriIbuted nuiinly to the iduence of the CIWS.
4.8 Impactofguardtalls
TheupperdecksofmostCanadianoavalve~~eIs~Mtsdwiihsafetyguardrails
that consist of thm metal stanchions supporthg a plastic-coated wire rope barnet. In
modern construction these guardrail stanchions have been grodeci to the hdl to
minimize any electmmapetk mterference with Wed ship's equipment. in geneial
discussion it bas been theoiized that the guardrails might also have some impact on the
RCS of the ship, as weiL This theory if supported by the design of the LAFAYETTE
Class destroyer in France: the LAFAYETTE was designed b m the outset with RCS
reduction in min& and that class of ship sports no guardrails on Ïts upper deçks (see figure
1 -4).
The impact of the guardrail stanchions on the RCS of the IROQUOIS class was
examined by cornparhg the RCS of the completed IROQUOIS model, iitted with the
mast, with the same mode1 having aii of the guardrail stanchions installed. The wire rope
barriers were not included in the design for practicai reasons of time and effort, as weli as
the small electrid size of the wire's cross-section. The wire rope is les than 2 cm in
diameter and there is in excess of one kilometer of it on the upper decks: to simulate this
wodd require use of a tkquency severai GHz h i e than that used for most of tbe
simulations m this work; but more iinportantly, given that a minimum vertex separation of
0.0 1 metres was employed m the design and pre-processing of ali of the CAD models,
neither JUNCTION nor RAPPORT would have recognized the wire rope models as
cylinders, and they would have been dmegarded durhg pmcessing.
The guardrail stanchions were buiit with dimensions of 3 c m by 5 c m by one metre.
In order to meet the physical optics lgnitation for RAPPORT, a fkquency of 16 GHz was
chosen for this simulation 'This choice is considered vaad as the fkquency is withm the
band wrmally used by naval fkcuntr01 d tracking radars. A total of 228 guardd
stanchioas were iostalled in the complete IROQUOIS mode4 as shown in figure 4-23,
adding 2736 more fâcets to the RAPPORT @ut me. The model took approximately 13.5
hours to process with these additions.
Figure
Plot 4-27 dispiays the effect of adding the guardrail stanchions to the other-
complete IROQUOIS ship model. The asymmetri*cai RCS pattern of the plot niay be
explained due to two factors: first, the asymmetrical nature of other upper deck features in
pro- to the guardrd stancbions; and second, the stancbns themselves are not
instalied symmeiricaiiy about the long axk of the ship. In particuhr, there are no
nanchioas dong a lengthy section of port quarterdeck. Thk and the notch in the
starboard side of the VDS w e l explains the obvious Merences m the port and starboard
sides of the plot over the stem arcs.
RCS (dB) versos Azimith (degreu)
Plot 4-27, Change in IROQUOIS mode1 RCS due to adding guardrail stanchims.
The average contr'bution of the guardrail stauchions was -0.0543 dB, with a
ma>cimumof 14.4 dB at 3" and aminimwnof-14.42 dB at 335". The guardrail
stanchions act as long, thin plates m their outward aspect, and thin dihedd reflectors that
fàce away fkom the observer. Plot 4-27 demonstrates how they can cause destructive
interference on some bearings, ie 45 O either side of the bow here, while increasing the
RCS on others. The larger return h m observation angies closer to the fore/& lnie of the
ship cm be explained by the aspect of the sbachions at those angles: fiom bearings near
dead ahead or dead astern, the 5 cm fiices of the stanchions are dominant; as well, the
observer would see the greatest number of them fkom the bow, foilowed by the stem.
4.9 Alternative mast arrangements
One of the origiœl mtents m this reseerch was to examine the impact o f a detailed
mast mode1 on the RCS of the ship, The lattice mast examined earlier in both the
TRLBAL and IROQUOIS clsss designs is w t a conmion n.atrne of modem naval vessels,
therefore it was decided to examine the impact o f difErent niast configurations on the
IROQUOIS modeL The two modern coniigurations chosen for comparative study were
k d on the cyLmdrical raked mast of the USN's ARLEiGH BURKE c h DDG and the
tapered box-like structure of the French Navy's LAFAYETTE class f?igate.
4.9.1 Cylindrical mast
The ARLEIGH BURKE class is fitted with a mabmast consisting of one long,
wide cylinder with an approimnate 15" att rake, supporteci by two smaller cylindrical
members. This mast provides supprt for at least one radar antenna as w d as various
electronic watfare and communications antennas. A mast with a similar configuration was
created for the IROQUOIS mode1 by building a 48-sided cylinder with a radius of one
metre, height of 19.8 metres, and a backward slope of approximately 15 O, such tbat the
UHF polemast antenna at the masthead remahed in the same position as Ït does m the
original IROQUOIS mast model. As s h o w in figure 4.24, two thinner and shorter
cylinders support it fiom the rear, with th& bases at the same points as the afler "ail
derrick" pylons o f the original mast model.
Figure 4-24, CROQUOIS with a cy1Ïndrical mast fitted, Inset: the cylhdncal mast-
RCS (dB) venus Azimath (degrecs)
240 - - -.. ... - . 300
270 Pfot 4-28- Effect of replacing the lattice mast with a cylîndrical mast,
The net effect of ntting a c y W d mast to the IROQUOIS mode1 was almost
negligiile, with an average change in RCS of ody -0.0323 dB. As seen in plot 4-28, there
are a number of significmt spikes wbere the RCS is greatiy decreased, notably at
approximaîely 40" either side of the bw. A number of small increases occur at the bow
itself, and a 3dB hcrease occurs at each beam. The cornplex geometry of the moQl
comes into play at 1 75 O, where the= is a lone asymnietricai reduction of approlmnatefy -6
dB.
4.9.2 Box-like mast structure
The French LAFAYETTE class and various Brkkh aud Russian warship claîies
are fïtted with enclosed, box-like mIimmasts that niay be easily modeled as one enclosed
shape. An enclosed kt-nded mast of arbitrary configuration was created for the
IROQUOIS model by building a single, twenty-sided cbsed body. This structure was one
metre narrower than the lanice mast on each side, but the same beight. As in the previous
case, the MMR air imake had to be removed to make way for the mast.
Figure 4-25. lROQUOIS m&l with a box-like mast stnrcturestnrcture
RCS (dB) vernis Azimuth (degrces)
Plot 4-29. impact of teplacing the lattice mast with a box-Iike structure.
Plot 4-29 shows thaî the box-like niast configuration had a more signifïcant impact
than the cylindricai case. The range of values is twice that of the cylindtical case, with a
minimum of - 17.73 cU3 and a tuaximum of 1 1.53 dB. The average change in RCS is
higher, at -0.107 dB. Once again, there is a &est increase in RCS at the bow, and a
roughly symmetrical iocrease on the beam; however, this modincation caused a number of
asymmetricai spikes at various locations, suggesting a high degree of mteraction with
~ û i c a i features on the upper deck. The preponderamx of high values betweem
270 O and 3 15 O suggests multiple reflections mvolving features on the starboard side of top
part ship, ie the RHIB crane column.
4.10 Impact of cyliders
The nnal study to be presented is an a d p i s of the impaft of the cyliadrical
objects dded to the IROQUOIS and TRIBAL models. Results obtained thus suggest
that modehg the cyüadrral surfaces m the two models CO@ is cniiail to obtainiog
meaningful and accurate results. Both anaLyses were conducteci using models with masts
fitted, in order to niaràmize the impact of multiple reflectbns.
The contri'bution of the cylindncal shapes m the IROQUOIS model is shown in
plot 4-30. The cylinders have an average cornfin of -0.3 12 dB, with extremes of
20.16 dB and -28.8 dB. The influence of the cyiinders is apparent in the niany spikes in
the plot, most notably on the starboard side. This suggests tbat the RHIB crane colunm
does indeed have considerabte influence on the ship's RCS. In the stem arcs, there is
some variation in RCS b e e n 160 O and 240 O, possibiy due to the INMARSAT p e d d
The contn'bution of the cylindrical shapes m the TRIBAL model is shown in plot
4-3 1. As expected, the average contriition is higher than the IROQUOIS case, and there
is considerably more variation in the entire 360" of the plot. The average change in RCS
due to removing the cylinders fiom the TRIBAL model was 0.13 1 1 dB, with a maximum
of 17.6 dB and a minimum of -14.87 dB. While the range of values is narrower than the
IROQUOIS case, it is clear fiom the plot that there is more variation in RCS in the
TRIBAL case.
RCS (dB) vernus Azimath (dcgrrcs)
Plot 4-30. Impact of cylindrical features on IROQUOIS RCS.
240 ' - - - . . ... ...-.. ... ... 300
270 Plot 4-3 1. impact of cylindricai features ai TRJBAL RCS.
Cha~ter 5 - Discussion and Conclusions
The initial ami of this research was to fùrther devebp the work of Losier [3] on
the HALIFAX class model by producing a more detailed anaSysis of the IROQUOIS chss
ship, examine the change in the ship's RCS brought about by the TRUMP refit, a d study
specifk etements of the effect of complex geometry on RCS. It was assumed that the
signïfïcant differences in the geometry of the two ships wodd provide much usefid
information for study; that assu~llption proved correct &en the number of curved features
to be mdefed in the IROQUOIS and TRIBAL class ships. Advances in computing
power, use of the Wmters mode1 as a prototype and the development of some time-saving
fïIe conversion utilities reduced the effort required m model development and cut
processing time drasticaüy, making it possible to improve on previous work and increase
the level of detail in the models. The aims of the research remained essentiaiiy uacbanged
throughout the work, the objectives being to study the changes in RCS due to TRUMP
and the impact of cylindrical geornetry m the models. The scope of the work was later
expanded to hclude a study of the impact of the mast and the ship's guardrail stanchions.
This chapter s h d discuss the validity of the rnethod and models used to obtain the RCS
resuits, and then comment on the results themselves with a view towards the impact of
complex geometry on the RCS of a warship.
5.1 Examiningthemethod
The method employed in this research centred around RAPPORT, which was
obtained on loan iiom DREO. As might be expected when working with non-commercial
software, much of the tmie and effort expenàed m getting the desired resuits out of
RAPPORT was devoted to the pre-processing and pst-procashg around it. Tutorials at
DREO outlined an effective procedure for pre-processhg CAD models on UMX-based
DEC Alpha computer systems, and Losier [3] had proven tbat DREO's metbod wuld be
ported to the MS-DOS environment. Armed with this hrowledge, m o n the software
provideci by DREO became an exercise in FORTRAN progranmiing and a certain aniount
of patience. Procurement of Losiet's PC-~endiy code sped up the process meaSurabiy,
d e r some modifications to tador the pre-processjng software to personal requirements.
The possibiiity of running RAPPORT and JUNCTION on a SUN station at RMC was
considered but uitimately discarded because of the author's * . with UNLX, the
requirement to do any UNIX work in situ at RMC and the already hi@ amount of
software fimhma .. . tion needed for the work.
The modeis were b d t and modEfied using AutoCAD re1- 13. Triais with
release 14 suggested that it would add no value to the design effort due to version
compati'biiity problems. SpeciGc i ssws related to the models wdi be discussed in the wxt
section.
DIDEC proved to be a versatile tool for file conversion and d e l de-bugging. Its
abiiity to label vertices sped up the process of k ü n g modelinp errors, and the variety of
usefid fiinctions in its c o d set aiiowed for easy translation h m Line drawings to
facets and vice versa. However, DIDEC was d e n for now-obsolete computer systems,
with oId drivers based on MS-DOS 3.3. This created compati'b'i problems with three of
the four PC platfonns used in this researcb, ranging fiom an inabiiity to print graphics
directly fiom DIDEC to unacfeptably Long exmution times under m s t video modes.
Given the fàst pace of change in desktop PC technology, Ït niay be onIy a short tnne
before DIDEC wili mt run under the successors to Wdows 98 and NT 4.0. If f'urtiaer
work is to be done with DIDEC in a PC environment, a software upgrade may be rquired
to bring it up to date.
Aithough originaMy seen as a Iimitation, DIDEC's 2000-vertex Iimit in translating
to EFIE format proved to be very usern large mode1 segments that were common to
many modeis needed to be processed oniy once; subsequdy, the *=A or *DXF nle
associated with that segment could be easiiy inserted into other models as required.
JUNCTZON's role as an error-checking program proved crucial to the work. The
mimer in which it presents error messages in the *.O03 file is inherentiy difl6icult to digest,
but Dr AH. Louie's CHECK-VER and CHECK_MULT pro- made the error-finding
process quicker and easier to understand. Late m the research, it was discovered that
these programs do not report aiI errors detected by JUNCTION; investigation of a
çuspiciousiy erroneous plot uncovered a serious modeling error that necessitated
rebuilding aU of the CAD models, and many results obtained by that point were negated as
a result. This could bave been overcome, time permitting, by writing a diagnostic program
to idente and extract locations of inconsistent fke orientations fiom the *.O03 file. A
more complete understandhg of JUNCTION would have sped up the software
modification process considerabiy eariy in the work, and saved much effort devoted to
debugging errors that produced slltially mysterious error messages. Having the source
code at hand proved useu however the iack of documentation for the program made the
JUNCTION learning curve quite steep.
A certain amount of mamuai nle editing was neçessary at DREO and in previous
work. The time spent writing FORTRAN 90 programs to automate these He conversion
processes sped up the processing time mxmmbly and eriminrited much time at the
keyboard once simulations were d e r way. This had the additionai bene& of elinhaî@
potential operator enors in pre- and pst-processing. Gnien that FORTRAN 77 is the
lingua h c a of ail of the other specIalized progranis used in this work, the effort to re-
learn FORTRAN &er 1 1 years away h m it was tirne well spent. The FORTRAN
programs iisted in Annex A are i U y portable to any DOS or WINDOWS based cornputer,
with attention paid to directory management.
RAPPORT'S flexible input parameter selection allows the user a high degree of
control over simulations: every action requjred for this research was easiïy accommodated
by RAPPORT. As a DOS program, it too may require an upgrade to take it into the
fùture, ifTNO or the other agencies ushg it wish to use it in a PC environment in the
fùture. Having said that, the ody things found lacking m the curent ïmplementation were
detailed error messages d indicators for elapsed time and estiniated nin-tirne.
As stated earlier, one of the objectives of this research was a higher degree of
detail and precision than m previous work, given a ten-fold krease in proceshg power
o f desktop PC resources available at RMC. Simulations previously done in four hours [3]
could now be accomplished in twenty minutes usmg &house resources. To take
advantage of this leap m processing capab'üity, more detail was added to the models and a
higher number of reflections was calculated. This iecreased the cornputaional burden
such that it was considered mwise to decrease the value of MAXSIZE in RAPPORT
beyond 0.00 1 ; the accuracy achieved at this vaiue was deerned sufEcient for the work,
given that changing MAXSIZE to 0.0001 effkctivety changed the processing time f?om
hours to days. The reflection iimÏt was initially capped at four rektions; &et adding the
mast and guarcirails, it was re-assesseci and mcreased to six. The cost of increasing the
reflection limit translated mu& as one hour per additionai reflection using the most
cornplex mode! produceci.
RAPPORT'S ASCII text output was the source of more work m FORTRAN
programrning and uitimately, a search for a robust polar-plotting routine. None of the
many mathematid simulation packages availabie at RMC were capable of producing
polar plots that handled negative radials (ie -10 dB) correctly. The user support web site
set up by Mathworks Ied to a shareware Matlab routine that solved this problem, after
some customization to automate radial L i . assignment, Mathworks has since made two
more advanceci polar plotthg routines available as sbareware: they were not adopted by
this research due to time constraints.
5.5.1 Sources of error in the method
The principal sources o f error that may be attn'ited to the method are as foilows:
a. four decinial p k e s were used m al calcuiations, FORTRAN programs and
AutoCAD work, as this is the fixeci accuracy in the JUNCTION code;
b. as discussed above, a bwer value of MAXSIZE would increase the
precision of the simulation;
c. material specifbthn errors. Om 'btal" material specincation was used
to represent a i i d inthe d e l , whenmfactnot allofthe surfaces
are n e c e made of the same m a t a
d. as discussed in chapter 2, the PO approximation yiek worse resuhs as the
angle of incidence approaches the tangentid case. Unfortunateiy, the
resultam diseRpancy in resuhs is impossiiiiie to quanti@ m very complex
geometries; anci.
e. RAPPORT fails to account for edge effects, although they too may have
iittie impact in the case of complex geometries of this nature.
5.2 Comments on the models
Previous work on RCS and EM field adysis at RMC started by creaticp CAD
models by lifting vertices directiy fiom curator's drawings, or by reading them in wiih a
digitïzing tablet. The decision to use the Wmters model as a prototype s i e d fiom a
lack of digitizing resources at RMC and an assumption that a long lead time wodd be
required to obtain ship's drawings. While that assumption proved to be incorrect, the use
of the Wmters model did ailow a much earlier start to the work than bad k n expected.
There were drawbacks in this approach, none the iess. As discussed in chapter 4, the
Wmters model containeci a number of approximations that had to be corrected to &-&te
RCS analysis. Despite best efforts at validating the prototype drawing against cmtor's
drawings obtained fiom FMFCB, some of these approximations were not apparent until
weil into the model design process. For example, although the overaii length of the model
was correct to two decinial phas, it was discovered tbaî flight deck and ''admin cornplex"
structure beneath it were one metre too long, with the excess iength being hiciden by a
shortened quarterdeck. The nartowing of the superstnicture was not completed until late
in the work, after suiEcknt experknce with AutoCAD made it a simple task.
To cut down processing time by reducing the number of Iacets as much as
possible, almust every k in the prototype was eventually combnied with adjacent lines,
deleted or redrawn in the ptocess of cteating b a s e h #l. This also rem- thaî
JUNCTION processes a straïght lïne composeci of X Lme segments as an X-sided polygon
with zero enclosed arm Severai weeks of effort were expendecl on learning AutoCAD
and changing the prototype to a model suitable for processing by RAPPORT. Subsequent
changes and detail additions were mede by üfüng dimensions off ship's dtawings.
Mer some experiniwting with trea- the enîire ship mode1 as one closed body, it
was decided to discard this approach in fàvour of adding each new detail as a new and
separate closed body. Treating the complete IROQUOIS model as one closed body
would have made it extremeiy difEcult to add the 98 separate details that distinguish the
mas-les IROQUOIS model fiom baseline rnodel #3, or the 78 m the TRIBAL model. It
certainly would have been impossible to mdel tbe niast under those constraints.
Experimentation with rectangular boxes of various sizes and orientations determined that
srna11 interference between closed bodies (on the order of O to 0.02 metres at 1 1.2 GHz)
was permissible and did oot affect the RCS results. Therefoce it was acceptable to place
one body "on top" of another by hahg its bottom fhe m the same plane as the top Gice
of the object under it.
The most obvious advantage of this method is the modulanty of the desiga It
dows a user to easily change the mode1 by smiply addmg or delethg enclosed sbapes as
required Taken to an extreme, it allows P=3.169~1@ possible combinations of model
components for d y s i s . The adysis of the CIWS, frnml exhausts, RHIB cohimn and
alternative masts presented m chapter 4 take advantage of thk modularity: m each case,
the module representing the feature d e r study was deleted h m the complete ship
mdel. This stripped mode1 was then adyzed under RAPPORT, and the contribution of
the object under study was calculateci by suaractmg the RCS of the saipped model h m
the RCS of the complete modeL The modular design approach was extended to the basic
huil design to a limited extent (Iimited oniy by time coostranits): the LW08 pedesta
MMR intake, hangar, flight deck supports and breeze way 'Wets'' were separate closed
bodies. Of course, the 228 guardtaEls added in section 4.8 were a single closed body'
copied and pasted to a new location 227 times!
5.2.1 Sources of modeling error
Potential sources of error attniuted to the design of the models include:
a. possbie d e h g errors that may have been mis& in the prototype;
b. inaccuracies in ship's drawings, ranging fiom omissions of details known to
exist, to inwrrectiy drawn lines (for example, fiont view dimensions of the
TRIBAL mast had to be interpolateci as the curator's drawings provideci
oniy a side view. This was not seen as a serious cause for concern, since
the dimensions appmximate those of the IROQUOIS mast, which were
available in three views);
C. measurement errors introduced when liftiog dnnensions off ship's drawings
when additg details;
d. vertex-identification errors m DDEC due to the pro* of vertices m
the modeL DIDEC's DXF input routine requins a ''vertex separation"
limit specifieà by the user. In this wotk, a iimit of 0.01 m was specified m
aiI modek, s k e this is much smaiier than the HF approxhatbn Iimit of
ka> 10, and aU details have no dimensions d e r than 1 1 mm Distinct
vertices h m separate objects that are closer than 10 mm wodd be
recogoized as one common vertex. This does not always generate an error
message f?om JUNCTION. Although none of these enors are believed to
ex&, the high number of vertices in the mast d e s it a possi'bility; and,
e. unrecognized or uwietected modeluig mors m the AutoCAD drawings.
One signifiaint modehg error that was the source of some good humour relates
to the coordinate system used in RAPPORT. The correct coordinate system is descri i
in chapter 4. Durhg the mode1 devebprnent stage, it was discovered that the IROQUOIS
modeis had aIl been built 180° out of alignment on the X &. Over 75 models of various
configurations of the two ships had built by this pomt, and AutoCAD inexplicably
generated erroneous DXF files i f these rnodels were smiply rotated 1 80 O. Therefore a
FORTRAN program was m e n to "rotate" the RAPPORT output data 180" in pst-
processing. This program, d e d COLDMOVE, is iisted m Annex A.
5.3 Review of resuhs
At the outset of tbis research it was assutœd tbat the addition or deletion o f large
items on the ship models would resuit in cowspondiogly large changes m RCS.
Investigation showed that tbis was mt mdeed always the case- Addiiion of the large
CIWS mount to the IROQUOIS hangar top d e d m an average increase m RCS of O@
0.0875 dB, whereas the addition of a few s d features to the fotecastle resuited in aa
average hcrease o f 0.4545 dB. Whüe the size of an object c k l y has an impact on its
RCS, when added to anotber complex object, the overall cbange m RCS is as much a
hct ion of the surrounding geometry as Ït is a h t i o n of the object 's size.
The baseline modifications adequately demonstrate the e f f ? of adding various
corner reflectors and asymmetrical fatures to an object: the 33 dB spikes m plot 4-4
(comparing baselines 2 and 3) correspond to the retum expected h m a square plate
44.67 metres to a side, or a sphere o f 25 metres radius. None of the features in tbat
modification approach that physicai s k . Indeed, the resuhs nom the addition of the
breakwater show that a relative& s m d but complex object can generate high returns, as
seen by the 14 dB maximum and -1 5-78 dB minimum obtained in that case. The small
corner reflectors introduced by the IROQUOIS FX modij6ications support this as weil,
generating peaks as high as 20 dB.
The simple shapes examined in chapter 2, aiong with Knott's hierarchy of
s ca t t e~g shapes, provide a good background for understawling the influence of simple
geometry on RCS. For exampie, the overwheiming influence of the flight deck/hangar
doors corner reflector thughout the resuhs is easiiy understood. While it was important
to understand that the RHIB cram colunm would cause direct returas fiom aU angles of
incidence, any understanding of its actual impact on the ship's RCS bas to take &O
account its position - located at top part, it is surrounded by large trihedral and four-sided
corner reflectors, as well as numerous s d corner reflectors of various shapes. This
knowledge becornes l e s significant as the complexity of an objeft increases, as seen in
many of the plots that descrik changes in RCS due to additions or deletions forward of
the beam,
The reflection limit study presented at the beniryiing of chapter 4 demonstrates the
impact of multiple reflections quite eEectively. The second reflections make a massive
contribution to the overall RCS of the model, suggesting that the average RCS of the ship
is dominated by second-order reflections fiom dihedral corner reflectors. By contrast, the
third reflections contriiute very iittle, except on diçcrete bearings. Statements by Brand
[20] and Losier [3] that three reflections are d that is needed are not supported in the
case of the IROQUOIS d e i , as fourth-order reflections retum over 20 dB on a numkr
of bearings in this case. The average cona'bution of the higher-order reflectioris may be
low, but for an RCS anaiysis to have any tacticai utility it must place emphasis on discrete
karings as weli as abreragesY in order to define sectors where the RCS of the ship is an
increased liabilïty, or to determine the best aspect to present upthreat. In the end, the
choice of reflection limit for this research was a compromise between accuracy and
computatiod t h e , as individuai contributions of over 3 dB were still present at the
eighth-order reflections.
The progressive development of the IROQUOIS class and the retrofit to the
TRIBAL ciass mode1 provideci considerable insiit into the impact of complex geomtry
and highlighted the iadividuai c o n t n i n s of a srnail number of upper deck features for
more detailed mdividuai m d y s k -sis of upper deck fkatures grouped by parts of
ship gave some Ïnsight mto proper warship design for RCS ceducfion, notably by
highlighting the si-t contriiutions to the ship's RCS made by daails on the
forecastle, top part and superstructure. Those results and the consistentiy minimai
variation of RCS in the stem arcs suggest tbat a aish-decked design similar to that of the
LAFAYETTE c h m a t e is ideal for RCS reduction.
The considerable time and effort spent designing, drawing and and@ng the
IROQUOIS and TRIBAL c h masts was worthwhile in that it demonstratecl a technique
for simuIating right circular cyiînders with some degree of accuracy using RAPPORT.
M y P n g the IROQUOIS mast in k e space and as 6tted to the ship was a fùrther
ciemonstration of the impact of compiex geornetry, in that an average lke-space RCS of
approximately 15 dB= resuh:ed in an average change of l e s than 1 dB when the mast
was attached to the ship. Here again, the addition of this complex object produced large
returns fkom ahead, with negiigiile impact astem.
It is important to note that not ali changes m RCS due to complex geometry result
in increases in RCS. The replacement of the SRGM house with the GMLS magazine @lot
4-1 6) resulted in the highest average RCS change of alI of the modifications, at 2.1452
dB; however, the plot displays numerous inward radial spikes, some ceaching -20 dB.
This effectively demonstrates that complex geometry can help as weii as hiwler RCS
reduction.
The W observation to discuss relates to the effèct of cylndrical objects in the
two ship models, since the modeiing of cylinders was one of the principle focuses of this
work. The technique developed in chapter 3 for the design of polygonal end-capped
models of nght circuiar cylinders allowed cytindncal objects on both ship &eh to be
simuiated with some accuracy. Given the number of such obhts În the models, this
undoubtedly promoted greater accuracy in the overall simuhion resuits- The fiaal two
plots in chapter four suggest that the c y b d r h i féanires had sipÏfkant impact on
average, as compared to other simulaions m this report. The RHIB crane colu~nn in
particular has a large impact on the RCS of the IROQUOIS class ship, most notabiy on
both beams.
5.4 Future work
As can be expected in tirne-iimited studies of this nature, there is always room for
additional work to improve the accuracy of the IRûQUOIS RCS model and the
understanding of the impact of complex geornetry on RCS. Specinc improvements to the
model could include:
a more accurate modehg of the rounded corners on the FX and the hangar;
b. additional complex details such as boliards or SHINCOM weather deck
tenninals;
c. an assessment of the impact of various sea states on the model's RCS;
d. use of dinerent materiai specifications as required. In this mariner a
numerid mode1 of the impact of RAM pads may be produceci; and,
e. a mxms for accurateiy simuiating the Hnpact of tbe various antemas and
weapoas mormts Wed to the ships.
Once a more accurate mode1 of IROQUOIS bas been pmduced, an investigation
could be conducted mto the RCS of the ship in bwer radar baads, such as those used by
naval s u r f k e search radars, to assess the impact of RCS with respect to long-fange
counterdetection concem.
The recent trend towards ever-Wer personal cornputers may also bave s i g d h ~ ~ t
impact on this field of eadeavour in the future, as commercially available off-the-sheif
PC's begin to rival higber-end cornputer hardware suçh as Sun stations and DEC -Alpha
machines m processing speed and addressable RAM size. In the meantirne, as much of the
software used in this research was written for old DOS versions, tbere is a danger that PC-
resident versions of these programs may mon befome obsolete. Consideration should be
given to produchg updated versions of DIDEC, JUNCTION, a d RAPPORT that take
Ml advantage of the Microsoft Wtndows environment.
5 -5 Conclusions
Despite a nwnbet of bumps in the road on the way to completing this re~eafch, the
initial objectives were met d additional interesthg work was added in the pmcess.
Ideally, an exhaustive RCS aaalysis would have exammed each and every upper deck
addition to the ship models, m haa; however, this was impractid 8i view of the
constraints, and it wouid serve little educational value d e r the fkst few iterations. The
modeling methods employed are none the les valuabte as they validateci the concept of
modular construction for RCS a d p i s , provideci a technique for accurately shulating
right circular cylinders using RAPPORT, and most importantly acted as a vehicle for
1eacning about the RCS of complex objeçts.
When the research was completed, over thirty-seven large-de simulations had
k e n produced for this report, and numerous others were conducted to mvestigate
intermediate designs and explore potential areas of study. The main practical deliverable
of this research was the comparison between the IROQUOIS and TRIBAL models RCS.
Assuming that any process or modeling error in the research is consistent across both
final ship models, and that a sdiicient level of detail was added to the models, it may be
concluded that the TRUMP refit caused a signifiant decrease in the average RCS of the
IROQUOIS class ship, as conipared to its pre-TRUMP configuration However, the new
configuration caused large increases in RCS on a number of discrete bearings near 145"
fkom the bow and abeam to starboard- It is also apparent that the placement of mmy
objects on the upper deck creates an abundance of corner reflectors that cause large
increases in RCS on many forward bearings, as well as directiy aster=
The use of modular construction techniques ailowed the simulation of a number of
what ifscenarios, which demonstrate that:
a the new IROQUOIS furniel configuration impmved the ship's RCS;
b. the guardrails staiic:hions sigmncaotly cbanged the RCS of the ship, most
wtabiy in large kreases near the port bow and the starboard beam, and in
large deçreases 45 O either d e of the bowy
c. replacing the niast with a large cylindri-cal mast would have Mie effect on
RCS; and,
d. a box-like mast structure would resuh in wide variation in RCS due to the
asymmetry of the surrounding upper deck feahues.
The research produceci the secondary bene& of creating a nurnber of specialized
FORTRAN programs that speed up the RCS anaiysis process by automating the fle
conversions and pst-processing necessary when working with RAPPORT. It also
reinforced the utility of performing RCS calculations on a desktop PC, a k t i o n nondly
the province of highend CCsupercomputers" such as DEC-Alphas, Sun stations or Crays.
As a final comment, the most valuable lessons learned in this effort were
undoubtedly the experience gained fiom the research process and the knowledge that,
despite all that was learned about the field of RCS sntdies, there cemains a great portion of
the body of knowledge about RCS that may still be learned.
References
Kwok, P. et al, "Sltrface Ship Above Water Signanne Management - a Naval Architect's PetSpectiYe", unpublished submission for the Mantrme
. . Emheerhg Journal, 1998. Frieden, David R (ed). Princkles ofNaval Weawns Svstems. Naval Mitute Press, Maryland, 1956. Losier, M. "An Investigation into the Signincance of Geometry m the RCS of a Ship". Master's thesis, Royal Military Cokge of Canada, 1 997. Personal discussions with Mr P. Kwok, NDHQ/DMSS 2-5-3. Skolnik, Merril 1. Introduction to Radar Svstems.. McGraw-Hill, New York, 1980. Bhattacharyya, kK, Radar Cross Section Anahsis and ControL Mech House, Boston, 1991- Stutzman, Warren L. Polarization in Electroniaaaetic Svstems. Artech House, Boston, 1993. Knott, E.F., Radar Cross Section, 2d ed. Artech House, Boston, 1 993. Skolnik, M e d 1 (ed). Radar Hhdbook, 2"d ed. McGraw H . New York, 1990. Ruck, G. T. et al. Radar Cross Section Handbook, vol 2. Plenum Press, New York, 1970- Fuhs, Allen E., USNPS Radar Cross Section Lectures. Amencan hstitute of Aeronautics and Astronautics, New York, 1982. Knott, E.F., Radar Cross Section, 1" ed. Artech house, Boston, 1985. ROSS, RA "Radar Cross Section of Rectangular Flat Plates as a Fwt ion of Aspect Angle", IEEE Ttans Ant . Prop, Vol AP-14, No. 3, May 1966, pp 329-33 5. Mika, R Cornouter Techniaues for Elechomaenetics.Permagon Press, New York. 1973. Knott, EX. "A Progression of High-Frequency RCS Prediction Techniquesn, IEEE Proceedings, Vol 73, No 2, Febniary 1985. Harington, Roger F. Field Comutation bv Moment Methods. EEE Press, Piscatway, NJ, 1993- "General Arrangement DDH 28 1 " , DND Curator Drawing #GN-D28-28 1-60500- 0 1, 1 :48 scale. Last change 27 May 86. "General Arrangement DDH 28OW, DND Curator Drawing #28O-D28-562-OOO-Ol, 1 :48 scde. Origmai drawiag dated 28 Feb 95. Dion, Marc et al. "A Sophisticated CAD Tool for the Creation of Complex Models for EIectromagnetic Intedon Anafysis", DREO Technid Note 9 1 - 16. Defence Research Establishment Ottawa, June 1 99 1. Brand, M.G.E. ''Radar Signature Analysis and Prediction by Physical Optics and Ray Trachg. The RAPPORT Code for RCS Predictiony', 'IN0 Report FEL-95- A097. TNO Physics and Electronics Laboratory, The Hague, Netherlands, 1996. Mathworks Inc resources web site, www.mathworks.codresource.shtml Ruck, G. T. et al. Radar Cross Section Handbook, vol 1. Plenum Press, New York, 1970.
[23] Wmters, D.T. "A Numerical Investigation of Shipboard HF I n d d Radiation Hazards", Masters thesis, Royal Müitary CoUege of lanada, 1997.
[24] 'TROQUOIS Class Radar Cross Section (RCS) Datan, MARCOMHQ N3(N3 1-2) 1995- 1 - 19, SECRET
[25] Louie, AM. 'The RCS of Objects on Seawatei'. haft paper for Defnre Research Establishment Ottawa, May 1997.
F i m e Credits
The figures listeci below were obtanied h m the fobwing sources. Figures not listed are attniuted to tbe author. Figures h m published texts were reproduced with permission fiom the publisher.
Kwok, P. et al, "Surface Sbip Above Water Signature Managemmt - a Nav Atch's Perspective", unpublished submission, 1998. KMCS VANCOUVER h o m e , www.islardnet.com/-~gar.hmil USN Navy Fact File web page, www.chmfo.navy~~vpaliW~~e/ships/ship-dtml DCN Intemational web page, www~vat-technoIogy.cod~~ntractots/warShip/ddde~,htmI TRIBAL C h web page, wwwuss-salem,org/navhist/~postwar/tri'baLhtml HMCS IROQUOIS homepage, www.niatlbt.hlfjtdnd.Ca/Il~~~uoislpbtnim,html Frieden, David R (ed). Priacibles of Naval W m n s Svstems. Naval Mitute Press, Maryland, 1986. Bhattacharyya, A.K. and Sengupta, DL. Radar Cross Section Analvsis and Control. Artech House, Boston, 1991. Knott, E.F. Radar Cross Section, 2"6 ed. Artech house, Boston, 1993. Skolnik, Merril 1. Introduction to Radar Svstems, Zd ed. McGraw Hill, Toronto, 1980. Ruck, George T. Radar Cross Section Handbook, Vol 2. Plenum Press, New York, 1970 Knott, 2* ed. Ruck. Knott, 2& ed. Dion, Marc et al. "A Sophisticated CAD Tool for the Creation o f Complex Models for Electromagnetic interaction AnaEysis", DREO Technid Note 9 1-1 6. Defence Research Establishment Ottawa, June 199 1. Brand, M.G.E. "Radar Signature Anaiysis and Prediction by Physical Optics and Ray Tracing. The RAPPORT Code for RCS Prediction", TNO Report FEL-95- A097. TNO Physics and Electronics Laboratory, The Hague, Netherlands, 1 996. Brand. C'Trumping the TRIBALS: A Progress Report''. Canada's Navy Annual, 1986 edition- Corvus Publishing, Calgary, 1986. Wmters, D.T. "A Numerid Investigation o f Shipboard HF Induced Radiation Hazards", Masters thesis, Royal Military Coilege o f Canada, 1997. UNCLAS diagram fiom "IROQUOIS Class Radar Cross Section @CS) Data", MARCOMHQ N3(N3 1-2) 1995- I - 19, SECRET
FORTRAN 90195 PROGRAM LISTINGS
This amiex contains source code listings for the foiiowing FORTAN 90 or FORTRAN 95 programs Wriften m order to automate the nle fommt conversion p m used m pre-processbg data for RAPPORT -sis a d exîracting output data for presentation.
002MAKER converts a DIDEC EFIE output nL to JUNCnON *.O02 input file format.
PLA-MAKER converts a JUNCTION *IAC output nle to *.PU format for RAPPORTT
SPLICEIU combines hwo separate *9LA files mto one larger *.PLA me, to overcome a 2000-vertex limit in DiDEC's TO EFLE output routine.
DATA-EXI' extracts the azimuth, eievation and RCS data h m a RAPPORT output file.
COLDMOVE reverses the RCS teadings listed m an extracted data 61e 180 degrees, to correct the plot orientation.
CHECK-MULT.FOR and CHECK-VERFOR are modified versions of multiplicity error-checking codes origïnaily writîen by Dr AH, Louie o f DREO.
! Pmgram 0002MAKER ! ! Version 1 witten by Lt(N) P.D- Srnithers ! ! This program prompts for the name of a DDEC *EFI output file, reads ! in the file and convers it to JUNCTION input Ne (*.002) format. Note that filenames ! must have eszictly eight cbcters - ! ! Variable dcclantions 1
character*S filename integer edges,edg~vertices,vertex,vertex t ,vertex2 mai &y,z
! ! Prompt for the input Ne n m e and open the files !
~ ~ t e ( 6 , * ) What is the name ofthe *.EFï file? read(5,lOO) filename opcn(2,statusc-'n&,fi14ename/f .002',m*agecontro~='1iSt') open(3,status-'olb,fil~Ien8md~.e~,~ageccmtrol='list')
! ! Writc the header !
wite(2J00) md(3, *) vertices,edges ~wite(2,3ûû)vertices,edges
! ! Writc the vertes List !
do 10 i= 1 ,vertices read(3, *)vert%x,yz r~~ite(2,400)vert%&y,~
10 continue ! ! Writc the cdge list !
do 20 j= 1 ,edges read(3 ,*)edge,vertex 1 ,vertex2 write(2,500)edge,vertex 1 .vertex2
20 continue ! ! Writc the footcr !
clo~e(3 ,status-'kq') ~rite(2,*)' 0' write(2,*), û' 1wïte(2,*)' 0' write(2,*)' 0' ~~tç(2,')'E''
Mite(2,*)' 90.0 0.0 0.0 0.0 2-654421E-3 0' write(2,*)' 10 1.OE9 1.OEY ciose(2,status-lcéep')
! ! Format staternents ! 100 format(A8) 200 format(2x,'- 1 ',S&*O') 300 format(IS,lx,I5) 400 f o r m a t ( 1 4 ~ 8 . 4 J @ 8 - 4 ~ 8 . 4 ) 500 fonnat(I4,2xJ4~4)
stop end
! h g n m PLA-MAKER ! ! Version 2 wrïtten by L t O P.D. Srnithers I
! This program reads in the JUNCTION output file FOR0 L2,FAC and c o ~ e r t s it t to *.PLA format using a î l e name spedied by the user. Note the fiIe name must be c'rad'. ! cight characters long ! ! Variable dcclatau'ons !
chanaer88 filename character* 12 h a m e integer fàces,body,edges,îàcarea real syz
! ! Prompt for the output file narne and open the files !
print*,'What do you want to name the PLAN file?' read(*, 1OO)filename open(2,staw-'~lb,fiIe=~forO 12,fac',~agecortwol='list')
! 1 Go to the end of the input file and rctrieve the information for the output header !
rcad(2,600)tàcname read(2,200)faces ofEx!t=6*Faces do 10 I=l ,offkt
read(2,') 1 O continue
read(2JOO)facarea I
! Open the PLA file and -rite the header !
opcn(3 ,stahrs'"ned,fiIe"fiiename/r .pla1,camagecontrol~list') wri te(3 ,* )fimame \\-ri te(3,300)îàcarea miind(2) read(2,*) md(2,*)
! ! Writc thc facets to thc output file !
do 20 J= 1 ,hcarea read(2,*)&y;t ~vrite(3,400)x,y,z md(2,jbody wntc(3,500)body read(2, *)edges mi te(3 ,500)edges
do 30 k=l,edges read(2, %YJ h W 3 , 4 0 0 h y ~
3 O continue 20 continue
ciose(2,status-'keep') cIose(3,status"keep')
! ! Format statements ! 100 format(a8) 200 f o ~ ( 5 x , i 4 ) 300 format(Sxj4, I w! FACES WilH AREA > t sq cm') 400 format(&fl1.7,2qfl t .7,2x.flL .7) 500 format(8x,i 1) 600 format(a 1 1)
stol' end
! Program SPLICER ! ! Version 2 wïtten by Lt(N) P-D. Srnithers ! ! The purpose OF this program is to input mo *PLA files and create a riw
! *.PL A file from their contents. Note h t file nama must k exactly 8 characters long ! ! Variable dedarations !
characteP8 in file 1 ,infiie2,outfile chancter* 12 hcname integcr faces 1 .fàces2,fhces,body,edges
LYP ! ! Get thc file names and open the files r
printt,'What do you waat to name the new PLAN file?' rcad(*, 1 ûû)outfTIe prïnt*,'What is the name of the nrst input file?' rad(*, 100)infileI open(2,stahis--'old',file=infilel/f .pla',carriagecoatrol='list') read(2.600)facnarne md(2,.200)f%ces 1 p~t* , 'What is the name of the second input file?' rad(*, 100)infile2 open(3,status='old',file=infiIeUf .pla',cacriagecoamFW)
read(3 , î O O ) f i ~ d !
! Wntc the output file header !
open(4,stanis-'new',file~0~tfi1df .pla',m*ageconttol='1ist1) wvrite(4,*)fâmame fac&ces 1 +faces2 ~Tite(4,3OO)!àces
!
! Rcad the ciam from the first file into the n m fiIe 1
rewi nd(2) =m,*) =w,*) do 30 k=l,EicesL
read(2, * )%y,z nTi te(4,400)x,y,z read(2, *)body write(4,5ûû)body md(2, *)43= wcite(4,500)edges do 40 L=l ,edges
100 format(a8) 200 format(i9) 300 format(i9,IW!FACESWTHAREA>lsqcai') 400 format(2x,fl1.7~xJi 1.7,2x,fl1-7) 500 format(8-i 1) 600 format(Al1)
stop end
! Program DATA-€Xi ! ! Version 1 ~ritten by Lt(N) PD. Srnithers 1
! The purpose of this program is to extract the azimuth eievation and RCS data h m a ! RAPPORT output file. ! ! Variable dechrations !
chancter*9 plotdata rwl azhnuth,eivat~m,rcs
!
! Open the file and advance to the first data m r d 1
open(2,status='old'~1e='iro.rpor,-ag~troL='list') 20 md(2,1oo)plot&ta
if(plotdata.eq.'#PLOTDATA') goto 10 gotu 20
! ! R a d !!x desircd &ta and \vrîte ir to the new file ! 10 0pen(3,status-'nd~fi~~'r~~~&tamat',~agec0tltro~~~id') 40 ~ d ( 2 ~ 0 0 , e n d = 3 0 ~ m u t h 7 e l v a t i m 7 r ~
wvri te(3,300)aPmuth,elvation7rcs goto 40
3 O continue close(2,status='k~') cIose(3,stanis='keep')
1
! Format statcments I
1 O0 format(a9) 200 format(4~,Iri.2,4~,@3 J l~fl2) 300 f0rmat(t752,4~f152~4x,f72)
QOP end
! Prograxn COLDMOVE ! ! Version f nlitten üy Lt(N) P.D. Smithers ! ! The purpose of this program is to cead in a ! three coIumns. the f i of which contains azimuth
72 1 -record data file of readings. and nrite out
! thc same file. wî th the mimuth readings rotated 180 degras. ! ! Variable declarations !
character*S filename &YJ
! ! Gct the filename !
wrïte(6,*) ' What is the narne of the *.MAT file? (8 characters rquired)' rcad(5, f 00) filename
! ! Crcatc a working filc copy of the originid filc !
opcn(2~nis'old',fil~1ename/Fmatw,~~~~ol='l~) opcn(3,status-'n~,file='tempfile.mat',-agec0ntrol='1i~ do 10 j=I,î2I
read(2, *)r~y , z write(3 ,*)x,y,z
10 continue !
! Dclcte the old file !
close(2,status-'delete') ! ! Rmcrse the data and w-rite it to the new file !
teuind(3) open(4,status-'n&,file=filenamdf .mat',carriagecwtrol='list'~ do 20 i= I ,72 1
read(3,*,end=20)x,y,z if(x.ge. 1 80,O)then
X=X- 180.0 clsc
x=x+ 180.0 cndif rvri te(4, *)&y,z
20 continue clos(3,status-'delete') close(4,status='keep')
1 O0 format(A8) stop end
C C CHECK-VER - CHECK IF ALL VERTICES IN A *O02 FlLE ARE CONNECTED TO AN EDGE C
PARAMETER(MAXVER= 10000) MTEGER LOUVER (MAXVER), NCONN(2,MAXVER) ,BNDEDG(SOO) OPEN( 1 ,FILE='FOROOS.IN* ,STATUS=*OLDT) OPEN(2, FILE='VERTEX.TXT' ,STATUS=*NEW ,CARRIAGECONTROL=' LIST') R E m 12ow READ(1, *)VERTICES,EDGES DO I= 1 ,VERTICES
LOUVER(I)=o READ(1 J W
m i m DO I= 1 ,EDGES
READfL*) ~~ LouvER(IA)=LoVVER(IA)+ 1 LOuvER(IB)=LOUVER(IB)+ 1 NCONN(1, IE)-I A NCONN(2, IE)=iB
ENDDO DO C= I ,VERTICES
IF(LOUVER(QEQ.0) WRITE(2JOO) 1 LF(LOUVER(i).EQ. 1) WRITE(2,400) 1
ENDDO C C GET BOUNDARY VERnCES C
OPEN(3,FILE='MUL.TO.Txl",STATUS='OLD') NUMBE=O DO 1=1,500
READ(3,500,END=6Oû,ERR=600) BNDEDûO NWMBE=UMBE+ 1
ENDDO 600 NUMAP-1
il=NCONN( I ,BNDEDG(l)) 12=NCONN(2,BM)EDG( 1 )) BNDEDG (IW
650 WRITE(2,')' VERTICES OF BOUNDARY APERTURE ',NUMM WRITE(2,*) n WRiTE(2,*) 12
700 DO 1=2.NUMBE IF(BNûEffi(i) NE.0) THEN
IF (I2.EQ.NCONN(I ,BNDEDG(I))) THEN Q=NCONN(S,BNDEDGo) BNDEDG (Ij==o ff(I2.EQ.Il) GOTO 750 -(2,*) 12 G r n o 700
ELSEIF(I2.EQ.NCONN(2,BNDEDû(I))) THEN
iî=NCONN(i,BM)EDü(i)) BNDEDG(I)=o IF(l2EQ.11) GOTO 750 -(2,*)12 GOTO 700
ENDiF ENDIF
ENDDO 750 NUMAPNTJMAP+l
Do I=2,NUMBE E(BNDEDGO.NE.0) THEN
11 =NCONN(i,BNDEDGO) Iî=NCONN(2BM)EDc(C)) BNDEDG(Ip GOTO 650
ENDCF ENDDO
200 FORMAT(1X) 300 FORMAT(' VERTEX ',14,' CS NOT CONNECTED TO ANY EDGE') 400 FORMAT(* VERTEX ', 14,' IS CONNECTED TO EXACTLY ONE EDGE') 500 FORMAT(7X, 15)
STOP END
CHECK-MULT - PICK OUT A U EDGES WITH MULTEPLlCrrY NOT EQUAL TO 1 Version 1. IR - written to run on a PC at RMC
This program requins a JUNCTION geometry file names FOR003.0UT as input I t outputs trvo files named MULTO-TXT and h4üLTX.TXT- CKPiCTER*8 FILNAM, L M E CHARACTER*4 EDGE OPEN(I,FILE='FOR003 .O~*,STATUS='OLD*) OPEN(2~ILE='MULTO,TXT,STATUS='NEW*,CARRLAGECONTROL=' LIST') OPEN(3 ,.FILE='MULTXTXT',STATUS='NE W',CARRIAGECONTROL='LIST') FTLNAM='CDGE-VERTEX CONN' REAfy1,100)LINE IF(LlNE.NE-RLNAM)GOTO 10 READ(I,lQO)LME NEDGE=O READ( 1,20O)EDGE,LEDGE,MüLT rF(EDGE,NE-'EDGE')GOTO 900 NEDGE=NEDGE+I IF(MULT.EQ.O)THEN
WRITE(2,300)LEDGE,MüLT ELSElF(MUL.T.NE-1)THEN
WFUTE(3 JOO)LEDGE,MüT.,T ENDff GOTO 20 STOP FORUAT( 14-8) FOELMAT(3 XS\4 J5, t OX,I2) FORMAT(3X,*Edge',[S,' has mult= '-12) END
This annex contains source code tistings for the fohwing MATLAB 5.0 progmns, whkh were written to perfonn post-pfOCeSSmg of RAPPORT output data &er it bad been extracteci into an ASCII text file.
POLARHG is a shareware fiinction which creates polar plots with a high degree of user control over plot parameters.
RCS-POLAR produces poiar pbts of RCS data using POLARHG as a plot fbnction, and calculates the minmiun, rmuamUm and average RCS vaiues.
RCS-COMP produce polar plots of the d i f f e ~ e ~ : e between two RCS data files, usign POLARHG as a pbt fbction, and caculates the minimum, maximum and average RCS ciifferences.
~nct ion H = polarhg(theta,rho,pl ,VI .p2,v&p3,v3,p4,v47p5,v5,pd,v6,p77v7,p8,v8) 9 6 "/o POLARHG is similar to polar, honmrer. it is possiile to set sorne
pscudo-propcrties. Bclow is a table of the pseudo-propertics O/o thcir function. and senings: ?/o PSEUDO- O/o PROPERTY O ! / O - 96 thctrt O h rho O 4 tdir 941 rlim 9.0 rtick 96 tsrcp 9.8 O43 torig 4.6 color ?/o Linestyle
N = nargin;
96 Crcatc the propcw namcfproperiy vdue string a m y s FropFIag = zeros(l,7); for X = 1 :(N-2)/2 p = eval(['p',inQstr0()1); v = evai(['vg ,in t2str(X)]); i f X = 1
Propersr-Names = p; Roperty-Value = v;
else Property-Names = str2mat(Roperty-Nam-p); Praperty-Value = str2mat(Pr--Value,v);
end if strcmp(p,'co Io r' )
PropFIag(1) = 1 ; color = v;
ciseif strcmp(p,'rtick') PropFlag(2) = 1; rtick = v;
eIscif strcmp@,'rlirn') PropFlag(3) = 1; rlim = v;
clscif strcmp(p,'tdir') PropFlag(4) = 1 ; tdir = v;
elscif strmp(p,'tstep') PropFlag(5) = 1 ; tstep = v;
elseif mcmp@,'tong')
RopFlag(6) = 1 ; torig = r,
elseif strcmp(p,'iinesiyIe') RopFIag(7) = 1 ; linestyle = v;
else error(E'1rxvaiid pscudo-property name: ',pl)
end end
Oh Dclcrminc which propcrties have not ben set by the user NotSet = !hd(PropFlag = 0); Defàuit-Settings = ["-" 1 ,
7
NaN 1.
9
'NaN 1. . "'munterclockt~ue" '; '30 1.
7
"'nght" 9 -
w '8,-'i '1;
Property-Names = ['color '; 'rtick '; 'rlim '; 'tdir ': 'tstep '; 'torig '; 'lines~le'] ;
for 1 = 1 :length(NotSet) evai([h.operty-Names(NotSet(r),:),'=',DeFa~lt~Setthgs(NotSet~,:),':'])
cnd
O 4 start CurrentAxes = newplot; NextPlot = get(CurrmtAxes,WestPlot'); HoldFlag = ishold; AxisCoIor = get(Currenthes,'XColor');
if -HoldFiag hold on % rnrzke a radial grid if -isnan(rlirn) % rIim is defined
MinRho = find(rhoCmin(r1im)); % Minimum rho fimit MaxRho = fuid(rhdmax(r1im)); % Maumum rho limit rho(minRho,MaxRho])fl; theta([MinRho, MaxRho])=u;
end Temp=W([O max(theta(:))l,[O max(aWho(:)))l); % Initialize plotthg info AxisLirn = [get(CurrentAxes,'M) get(CurrentAxes,~Iim')]; NumTicks = length(get(CurrentAxes,>.tick')); delete(Temp);
% chcck ndial limits and ticks if isnan(rtick) % rtick not defineci if -isnan(rlim) % rlim is defineci
Rmin = rlim(1); % InÏtialize Rmin Rmax = rlim(2); % Initidize Rmas
else % rIim is not defincd Rmin = O; % Set Rmin = O Rmz. = AxisLim(4); % Set Rmax = mxirnum y-a'(iS d u e
end NurnTicks = NumTicks-1; ?'O Number of circIes if NumTicks > 5 % sce if ne can &ce the number
if rem(NurnTicks,2) = O NumTicks = NumTicks/T;
elseif rem(NumTi&s,3) = O NumTicks = NumTicW3;
end end Rinc = (Rmax-Rmin)/NumTicks; % Distance bchvecn circles rtick = (Rmin+Rinc):Ruic:Rmax; % radu of tirdes
clse % rtick is defmed if isnan(r1im) % rlim is not defincd
Rmin = 0; % set M n = O Rmax = max(rtick); % set Rmxx = m m rtick caiue
elsc % rlim is defined Eùnin = min(r1im); % set Rmin = minimum rlim Rmax = max(r1im); % set Rmax = ma\;imum rlim RtickMin = find(rtick<Rmiri); % End elements OF rtick < min(r1im) RtickMax = find(nick>Rmax); % find elements of rtick > mx(rIim) rtick([RtickMin,RtickMax]) = 0; % remove thcse vducs from rtick
end rtick = [Rmin,rtic~Rrnax]; % the new ratai set(CurtentAxes,Ylim',~inRmax~) %xttheY-limitsto[RmÏnRmaxl NumTicks = length(rtick)-1; % numbcr of circles
cnd
?4 plot spokes th = ( 1 :.5*360/tstep)*2*pi*tstep/360; % definc ùic spokcs cst = cos(th); snt = sin(th): Cs = [-cst; cst]; m = [-nit; snt]; CS = [cs;NaN.*& 1 ,:)]; sn = [sn;NaN.*sn(l,:)J; % plot the spokc h h ~ i o t ( ( R m a x - R m U i ) * & : ) , ( R m a x - R m i n ) * w - .
'lincuidth', 1 ); set(O,'UserData',hh)
Rt = 1.1 *(Rmax-Rmin); for i = I :m ax(size(th)) text(Rt*cst(i)~*snt(~,int2stt(i*tstep),%orizontalalignment','c; if i = max(size(th))
loc = int2-O); else
Ioc = int2str( l8û+i*tstep); end text(-Rt*cst(i),-Rt*snt(~,l~'horfiontalaLignmentf;cente~);
end
'!,6 sct vicw CO 2-D. Use the appropriate ~ i e w (tdir) tdir = lowexftdir); torig = Iower(torig); if strmp(tdir(l:5),'count') & strcmp(tdg,'right') view(0.90); InitTh = 0;
elscif strcmp(tdir(1 :5),'count1) & strcmp(taig,'l&) view( 180,90); InitTh = 1;
elscif strcmp(tdr( ! :5),'count') & strcmp(torig,'up') view(-90,90); InitTh = 2;
elscif strcmp(tdir(1 :5),'countf) & strcmp(torig,'down') view(90,90); initTh = 3;
clseif strcmp(tdir( 1 :S),'dock') & strcmp(tcnig,'rightg) view(0,-90); InitTh = 0;
dseif strcmp(tdir(l:5),'clock') Br strcmp(torig,'left') view( 180,-90); InitTh = 1;
elseif strmp(tdir( 1 :S),'clock') & strcmp(tm*g,'upf) view(90,-90); initTh = 2;
c i w i strcmp(tdir(l:S), CLKK ) & strcmp(torig, aoib ii ) view(-90,-90); InitTh = 3;
cksc error('Inva1id Tûir or TOng')
end if strcmp(torig,'up') 1 strcmp(totig,'down') axis square
end
% dcfinc a circle th = O:pi/75Ppi; m i t = cos(th); yunit = sin(th);
96 This codc has bcen vectorized so that only one line 96 is used to dnw the circles. MultFact = rtick-Rmin; m,w = size(Mu1tFact);
= size(xunit); XUNIT = [MultFact' * ones(1 ,NNN)] .* [ones(NN, 1) xuniq; YUNIT = wultFactl * ones(i ,NNN)] -* [ones(NN, 1) -yuait]; XUNIT = XUNIT; YUNIT = W T ; XX = ~T;NaN,*XUNIT(l , : ) ] ; YY = fYUNIT;NaN,*YUNIT(I ,:)]; hhh = p l o t ( X X ( : ) , Y Y ( : ) , ' : ' , ' C o I o i & i C o l ~ , 1);
Add the L ~ X T and make sure t h t it dways silirts zit the origin 96 and movcs up. for i = MultFact
if [nitTh = O ?6 Right Xt = 0; Yt = i;
clseif InitTh = 1 % Left Xt = 0; Yt = 4;
elseif [nitTh = 2 % Up Xt = i; Yt = 0;
clseif InitTh = 3 % Down Xt = 4; Yt = O;
clse Xt = 0; Yt = i;
cnd textmt, Yt~um2str(i+Rmin),'Verti~ignment','botto4, ...
'Ho&ontalAlignrnent','left'); end
Or;, innsform data to Cartcsian coordinatcs. xx = (rho-Rmin).*cos(theta); % I'm not sure if this is correct yy = (rh*lùn in).*sin(theta);
9'0 plot ciam on top of grid 9 = PM=?YY); if isrnarker(linesty1e)
set(q,'Color',color,~rker',Iinestyle) else set(q,'Color',coIor,'lincstyle',line~le)
end
if nargout > O n = q;
end if -HoldFIag
h axes=ge t(gcf, 'CurrentA..es'); set(haxes, 'DataAspcctRatio', [I 1 11, Vible', '00;
end
O/; rcsct hold statc if -HoldFiag, set(CurrentAxes,We.utP1ot*~extPIot); end
funcuon y = ismarker(symbo1) O6 t S i W R rctum 1 if the speciftcd symbol is a valid 96 rnarker property value and returns O othernise. 94,
Esample: 9.0 >=isrnarker('square') if nargin =O error('A qmbol must be specified')
end markefS = (t+yol;t*Lt , . '-1 , x A.' , squarc';'diarnond';
8 \ .*;lnt;*>o;*<e.t , pen tagram';'he.agram';'none') ;
for i= 1 :length(markers) val=strcmp(rnarkers ( i) , symbol); if v a l e l
break end
end if nargouP0 v a l ;
end
% PROCRAM RCS-POLAR % VERSION 1.3 Y0 O 6 Writtcn by Lt(N) P.D. Smithers. Scp 1998 Y0 ?/0 The purpose of this program is to produce polar plots of 96 RCS rncasurements in dbsrn versus azimuth, The input fLTe is 941 a &ta file ex-cted from the PC-RAPPORT output N e *.RPO. 96 The program makcs usc of a shamvare MATLAB routine d e d %O P0LARHG.M to produce ri customized polar plot not availabic in % the standard MATLAB POLARM fiiuidon. POLARHG-M m s also ?G inodi fied by the author to automate tarious display panmeters. Y0 clc; clf; clear; CI- al1 5% Clear the workspace '"O
?6 Input the RCS &ta and convert it to polar coordinates O/n
load irofïnal -ascii % Load the RCS data file theta=uofmal(:, l)*pi/l80; % Calcdate the azimuth in radians rho=irofinal(: J); Oh Isolate the merisurement O/o
O/o Dttcrmine Lirnits of the RCS measuremcnts "6 and find the rho data m g e for the plot "4 rmin=round(min(rho)/l @OS)* 1 O; nnax=round(max(rho)/ 1 DtO.5). 10; "/O *6 Plot the data using thc modifIed POLARHG routine. oh
figure( 1) polarhg(th~rho,'tdii.'counte~~10~h~ise','rlim', [min rmax], ..-
'rtick'.(rmin: 1 O:max),'nep'$O,'torig','nght','color','r') "6 94 C;ilculations %O
Minimum=min(rho) Maximum=mri(rho) Average--mean(rho) ?6 End of program
% PROGRAM RCS-COMP V2.0 % % Tlte purpose of this program is to produce p o l x plots of % RCS mcasurcments in dbsm versus azimuth. The input files are 96 an output data file prodiced by PC-RAPPORT. The pro- displays 941 the differcnce between the data in files RCS-DATAMAT and % RCS1.MAT ?'O
% Thc data files should be sct up such that RCS 1 contains the % basclinc data and RCS-D ATA contains the badine plus the change % to be rinalyzcd ?A cic; clf; ci-, close al1 % CIear the workqxlcé O,'
9.6 Input data and convert to polar coordinates Y0 load rcs-data -ascii % Load the RCS last data file theta=rcs_data(:, l)*pi/ 180; % CaIcdate the azimuth in radians rho t =rcs-data(:,3); % Isolate the fast measurernents load rcs 1 -ascii % Load the Eirst RCS data file rho2=rcs 1 (:,3); % Isolatc the first measurements O 6
O 6 Calculate the differcnce in the RCS rneasurernents 96 rh0=rhoI-rho2; average-differenc-ean(rho) m aximum=max(r ho) minimum=min(rho) ?/O "/O Dctcrrninc limits of the RCS measurements I / o and find the rho dam range for the plot ?h min=round(min(rho~leO.5)* 10; rmax=round(max(rho)/1 û+û.S)* 10;
?'O Plotting routine O/*
fiEwe( 1 polarhg(theta,rho))tdir'~counterctwkni~'~riim~,[nnin rmax],.,.
'rtick',[rmin: I O:max],'tstep',30,'torig','right';mlo~) % End program
Results of RAPPORT ~erfo~nance assessrnent simulations
The raw data correspondkg to the results of the square plate and trùiedral rrflector sbulations performed m section 3.9 is presented as fobws:
a input parameter (RPI) file;
b. EFIE data fle;
c. JUNCTiON output data (002) file;
d. IUNCIlON output diqpstic (003) file;
e- PLA data file; and,
f. RAPPORT output (RPO) file.
1. Square date withka=14,7
RCS computation of Ruck's square plate 1 Number of 0bject.s to p- ~ocess mcksqar.pia Object file name 3 Number o f reflections to calculate 0.005 MAXSIZE (maximum patch size scale -or) monostatic Tx/RX dgurat ion RCS Type of tesuit elevation scan Type of scan
0.0 0.0 0.0 Azimuth range k step 0.0 90.0 1.0 Elevation range and step
SiNGLE fiequency Frequency parameter (single or sweep) 1 1.2 0.0 0.0 Andysis fkequency (GHz) horizontal Transmitter polarization horizontal Receiver polarkation rucksqar.rpo Result file aarne
b. EFI Listmq
CL CL FOR003 .OUT CL NUMBER OF IMAGE PLANES= O IMAGE PLANE NOTATCON:
O=NO GROUND PLANE l=A P.M.C. GROUND PLANE
-l=A P.E.C. GROUND PLANE O M THE X=O PLANE O IN THE Y=O PLANE O IN THE Z=O PLANE
VERTEX COORDINATE LIST See input geanetry file 002 See input geometry file 002
IPAT= O : IF IPAT.GT.0 FAR FIELD PATTERNS ARE COMPUTED
FACE ARRAY ITREE IN BODY 1 SUBTREE 1 ( 2 ENTRLES = ( 1 -> 2) : 1 2
FOR BODY NUMBER: 1
FACE 1 HAS EDGES 1 2 5 WITH VERTICES 3 1 2 FACE 2 HASEDGES 3 4 5 WITHVERTICES 1 3 4
EDGE-VERTEX CONNECTION LIST
EDGE 1 HAS MULT= O EDGE 2 HAS MULT= O EDGE 3 HAS MULT= O EDGE 4HASMULT=O EDGE 5 HAS MULT= 1
BODY PARAMETER LIST
NUNBER OF VERTICES= 4 NUMBER OF EDGES= 5 NUMBER OF FACES= 2 NUNBER OF EDGES iNCLUDING MULTIPLICITY= 1
MODELMG PARAMETER LIST (METERS)
SURFACE AREA OF THE SCATTERER= 39 188E-02 SQMETERS AVERAGE EDGE LENGTW -88530E-01 METERS MAXIMUM EDGE LENGTH(EDûE NO. 5 )= -88530E-O 1 METERS
( 3-> 1) MINIMUM EDGE LENGTH(EDGE NO. 1 )= -62600E-0 1 METERS => %Y THE LAMBDM RULE, MAMMUM RELIABLE FREQUENCY BASED ON
AVERAGE EDGE LENGTH= 6.77269EM8 Hz MAXIMUM EDGE LENGTH= 6.77î69E-tO8 Hz MINIMUM EDGE LENGTH= 9.57804E+08 Hz
AVERAGE FACE AREA = .l9594E-O2 SQ,METERS MAXIMUM FACE AREA (FACE NO. 1 >- -19594E-02 SQMETERS MMIMUM FACE AREA (FACE NO. 1 )= - 19594E-02 SQ-METERS MINZMUM FACE HEIGHT TO BASE RATIO (FACE NO, 1 )= .5000€+00
EDGE 1 IS ATTACHED TO FACES 1 EDGE 2 IS ATïACHED TO FACES 1 EDGE 3 IS ATTACHED TO FACES 2 EDGE 4ISATTACHEDTOFACES 2 EDGE SISAITACHEDTOFACES 1 2
FACE ORIENTATION CHECK: **ALL FACE ORIENTATIONS ARE CONSISTENT
RUCKSQAFLFAC 2 ! FACES WITH AREA > 1 sq cm
.O000000 .0000000 1.0000000 1 3
.0000000 .oooO000 .O000000 -0626000 .O626000 .O000000 ,0000000 -0626000 .O000000 .O000000 .O000000 1.0000000
1 3
.O626000 .O626000 .O000000
.0000000 .O000000 .0000000
.O626000 -0000000 .O000000
# RAPPORT V3.0
Y TNO Physics and Eldaronics bboruory - #- Radar signature Analysis and Predictioa - #- bY - #- Physid Optics and Ray Tncing - ik # RAPPORT V3.0
#RCS cornputanon of Ruck's square phte # # PARAMFfER FILE
RCS computation of Brand's trihedrai reflectoc 1 Numbcr of objects to proass brandîri.pla Object file name 3 Number of reflectims to calculate 0.005 MAXSLZE (maximum pich size scale -) monostatic T x / R X c u r i f i ~ m RCS Type of result azimuthscan Type afscan -60.0 60.0 O S Azimuth range & step 90.0 0.0 0.0 Elevation range and step SMGLE fiequency Frequency paramda (single or v) 15.0 0.0 0.0 Analysis fhquency (GHz) horizontal Transmitter polarizaticm horizontal Receiver polarizaticm brandtri.rpo Result file name
CL CL FOR003 .OUT CL NUMBER OF MAGE PLANES= O MAGE PLANE NOTATION:
&NO GROUND PLANE I=A P.M.C. GROUND PLANE
-1-A P-E-C. GROüND PLANE O M THE X=O PLANE O M THE Y=O PLANE OrNTHEZ=UPLANE
VERTEX COORDUVATE LIST See input gecnnetry file 002 See input geometry file 002
LPAT= O : IF IPAT.GT.0 FAR FELD PATTERNS ARE COMPüTED
FACE ARRAY ITREE CN BODY 1 SUBTREE 1 ( 4 ENTRES = ( 1 -> 4) : 1 2 3 4
BODY 1 IS A CLOSED BODY WITH VOLUME = -1.66575E-04 CUBIC METERS
BODY 1 HAS NEGATIVE VOLUME: NBOUM) ARRAY RE-ARRANGED = FACE 5 ISAMONGTHE EDGES 2 1 3 FACE 5 ISAMONGTHE EDGES 1 6 2 FACE 4 ISAMONGTHE EDGES 6 4 3 FACE 5 IS AMONG THE EDGES
FOR BODY NUMBER: 1
FACE 1 HAS EDGES 2 1 3 WITHVERTICES 1 3 2 FACE 2 HAS EDGES 5 1 6 WITHVERTICES 2 4 1 FACE 3 HAS EDGES 2 4 6 WITH VERTTCES 4 2 3 FACE 4 HAS EDGES 4 3 5 WITHVERTICES 1 4 3
EDGE-VERTEX CONNECTiON LIST
EDGE 1 HAS MULT= 1 EDGE 2HASMULT=1 EDGE 3HASMULT=l EDGE 4HASMULT= 1
EDGE 5 HAS MULT- 1 EDGE 6 HAS MULT= 1
BODY PARAMETER LIST
NUMBER OF VERTICES= 4 NUMBEROF EDGES= 6 NUMBER OF FACES= 4 NUMBER OF EDGES iNCLUDiNG MULTIPUCITY= 6
MODELiNG PARAMETER LIST (METERS)
SURFACE AREA OF THE SCAlTERER= Z65SE-û 1 SQMETERS AVERAGE EDGE LENGTW= .1207OE+OO METERS MAXIMUM EDGE LENGTH(EDGE NO- 1 )- . l4144E+OO METERS
( i -> 2) MINIMUM EDGE LENGTH(EffiE NO. 3 )= -99962E-0 1 METERS => BY THE LAMBDAIS RULE, MAMUUM RELIABLE mQUENCY BASED ON
AVERAGE EDGE L E N G W 4.%742E+08 Hz MAXIMUM EDGE LENGTW 423920E+08 Hz MlNMüM EDGE LENGTH= 5.99812E+08 Hz
AVERAGE FACE AREA = -59 l38E-ûî SQ-METERS MAXIMUM FACE AREA (FACE NO. 2 )= .86607E-02 SQ.MEî'ERS MINIMUM FACE AREA (FACE NO. 4 )= -49962E-02 SQMETERS MMTMUM FACE HEIGHT TO BASE RATIO (FACE NO- 4 )= -4998Et00
EDGE 1 IS ATTACHEDTO FACES 1 2 EDGE 2 ISATTACHEDTOFACES 1 3 EDGE 3 ISATTACHEDTOFACES 1 4 EDûE 4 ISATTACHEDTOFACES 3 4 EDGE 5 ISATTACHEDTOFACES 2 4 EDGE 6ISATTACHEDTOFACES 2 3
FACE ORXENTATiON CHECK: **ALL FACE ORIENTATIONS ARE CONSISTENT
e. PLA listing
DIDEC and JUNCTION processed the origioai cira- file as a closed body, ie that there is a fourth fàcet in the thewing, denned by the h n t three vatices. In order to accurate& mode1 the trihedral reflector, iî is necessary to remove the fourth fixe h m the PLA file. In addition, when JUNCTiON processed the tribedral as a four-sided closed body, it assigned outward norrnals to each face. Since the reflectiag smkces of the trùiedral are actually on the innde of the body, it is necessary to reveme the signs on the mrmai coordinates and re-arrange the vertex Listing to eosure that normal assignment obeys the n'ght-hand rule:
OnW PLA listing
! FACES WITH AREA > I sq cm -7069454 .4080085
Correcteci PLA Iisting
BRANMIRI - EAC 3
-5777174 1 3
,0577000 ,0577000 ,0000000 -577 7174
1 3
.O577000
.0000000 ,057 7000 -5773497
1 3
.O577000
.0000000
.O577000
! FACES WITH AREA > I sq Qn
-,7069454 -.4080085
C-Y
RPO Listing
# d RAPPORT V3.0
#nie object description is taken h m the 6id.s): # bnuidtn'.pla whichcontaiils 3 poiygmm #The x-min and x-max of the objcct a . .O0000 .OS770 #ïhe y-min and y-max of tbe objaa are -.O7070 -07070 #The z-min and zaiax ofthe objcicr uc -.O4080 -08 170 #The area of the abject oq& .O 1499 # #INTERNAL OBJECT DESCiUPTiON
#An objcct desniption wirh 768 ptches isobiriod # # R A ~ C I N G INFORMATION
#The maximum numkr of rcflcnions accouatod fk - 3 # #TYPE OF CALCULATION
# P e r f i a moaostadc calculrtion: mnrmitar d #-vaarelocacedatEbesamcposigon # #TYPE OF RESULT # #ïhe RCS aiter the tocal n u m k of refIactioris # #SCAN MODE
#An azünuth sain is pafamd, #sœhng6romazimuthuigk = -60.000000 #aidmg at azimuth angle = 60.000000 # w i t h imxement - 5OOOOO #a? a fixez! elevatim angle of 90.000000 tilpsa # #FREQüENCY INFORMATiON
