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MEMORANDUM REPORTBRL–MR-3383

SOLID GEOMETRIC MODELING – THE KEY TOIMPROVED MATERIEL ACQUISITIONFROM CONCEPT TO DEPLOYMENT

Paul H. Deitz

September 1984

APPROVEDFOR PUBUC RELEASE;DISTRIBUTIONUNUMITED..:

.JS ARMY BALLISTIC RESEARCH IJiBORATORYABERDEENPROVINGGROUND,MARYLAND

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B R L

MEMORANDUM REPORT BRL-MR-3383

SOLID GEOMETRIC MODELING - THE KEY TO IMPROVED MATERIEL ACQUISITION FROM CONCEPT TO DEPLOYMENT

Paul H. Deitz

September 1984

APPROVED fOR PUBUC RELEASE: DISTRIBUTION UNU .. ITED.

US ARMY BALLISTIC RESEARCH LABORATORY ABERDEEN PROVING GROUND, MARYLAND

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Destroy this report when it is no longer needed.Do not return it to the originator.

Additional copies of this report may be obtainedfrom the National Technical Information Service,U. S. Department of Commerce, Springfield, Virginia22161.

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The findings in this report are not to be construed as an officialDepartment of the Army position, unless so designated by otherauthorized documents.

The use of trade names or manufacturers’ names in this reportdoes not constitute endorsement of any commercial product.

Destroy this report when it is no longer needed. Do not return it to the originator.

Additional copies of this report may be obtained from the National Technical Information Service, U. S. Department of Commerce, Springfield, Virginia 22161.

The findings in this report are not to be construed as an official Department of the Army position, unless so designated by other authorized documents.

The use of trade names or manufacturers' names in this report does not constitute indorsement of any commercial product.

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MEMORANDUM REPORT BRL-MR-3 383

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Solid Geometric Modeling - The Key to ImprovedMateriel Acquisition from Concept to Deployment Memorandum

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Paul H. Deitz

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ATTN : AMXBR-VLDAberdeen Proving Ground, MD 21005-5066 lL162618AH8fl

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USA Ballistic Research Laboratory September 1984ATTN: AMXBR-OD-ST 13. NuMBEROF PAGES

Aberdeen Proving Ground, MD 21005-5066 39

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19. KEY WORDS (Contfnue on r.v.rmo aido ifnecoeauy -d fdentify by bfock number)

Solid Modeling Weights and MomentsComputer Graphics Infrared ModelingWeapons Engineering RaycastingBallistic AnalysisNuclear SurvivabilityZQ A3tSnACT@acz@w*-m?-’0rU sfdkfifnecn—ty adiderttffyby block number)

At its most abstract level, the business of materiel acquisition involves amassive task of information processing which starts with a concept and, ifultimately successful, ends with a deliverable. Most system analysts as wellas program managers are aware that the key to increased productivity in such acomplex process lies somehow in the application of automation. Some may viewautomation as the use of computer-aided drafting tools in a concept phase.Others might see it as computer-based system analyses of predictive performance

(See other side for continuation. )--—..

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MEMORANDUM REPORT BRL-MR-3383 4. TITLE (and Subtitle) 5. TYPE OF REPORT a PERIOD COVERED

SO 1 i d Geometric Nlodeling - The Key to Improved Memorandum Materiel Acquisition [rom Concept to Deployment 6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(e) 8. CONTRACT OR GRANT NUMBER( .. )

Paul H. Deitz

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK

USA Ballistic Research Laboratory AREA a WORK UNIT NUMBERS

J1.TTN: AMXBR-VLD Aberdeen Provi ng Ground, MD 21005 -5066 1 L162 6] 8AH80

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I~ SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on rev.r ••• Ide If n.c .... ery and Id .. ntlly by block number)

Solid Modeling Weights and Moments Computer Graphics Infrared ~odeling Weapons Engineering Raycasting Ballistic Analysis Nuclear Survivability

2Q. ABSTl'lACT ("Coatlaue _ ""'r_ ale Ff"........" ani Idenllfy by block number)

At its most abstract 1 evel , the business of materiel acquisition involves a massive task of information processing which s ta rts with a concept and, if ultimately successful, ends with a deliverable. Most system analysts as well as program managers are aware tha t the key to increased productivity in such a complex process 1 i es somehow in the application of automation. Some !'lay view automation as the use of computer-aided drafti ng tools in a concept phase. Others might see it as computer-based system analyses of predictive performance

(See other side for continuation.)

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or processor-controlled manufacturing procedures. Yet other observers may seeword processing and electronic mail as centerpieces in the automated environm-ent of the future. However, the real key to fundamental advances in the waymateriel is concepted, analyzed, manufactured and delivered rests in ourability to describe and analyze geometry. By geometry we mean the complete anunambiguous mathematical definition of a system in three-dimensional spacetogether with its complete material and functional properties, tolerances, etcFrom this single unified model a series of engineering analyses can be exer-cised to judge the suitability of a concept to a set of requirements before aprototype is built. Later this file can be used to automate the manufacturingprocess.

This fact is what computer-aided design/computer-aided manufacturing(CAD/CAM) is about but with a crucial ingredient. Most CAD systems on the market today perform mainly as automated drafting stations. Because the math-ematical files used for rendering generally do not describe object surfaces ormaterial properties, they cannot be used as input to a collection of engineer-ing analyses necessary for materiel evaluation. By contrast, an emergingtechnology called solid modeling is characterized by its robust, or complete,description of three-space material. Such geometry can be used as crucialinput to predictive models dealing with ballistic protection, nuclear survivalinfrared and structural integrity mobility, and the like.

By virtue of its long history in the analysis of materiel in both thenuclear and conventional ballistic environments, the Ballistic Research Laboratory has developed extensive experience in advanced geometric techniques. Inthis paperlthe key role solid modeling can play in weapons engineering isdiscussed; in addition, examples of enqineerinq analyses driven by solidmodeling illustrate the-capability such-sition process.

1For a discussion of computer-aided ales”air-vehicle survivability problems, seeModeling in Survivability/Vulnerability

techniques bring to the materiel acqui

gn techniques applied to ground andE. P. Weaver and P. H. Deitz, “Solid“ Proceedings of the Second JTCG/AS

Workshop on Survivability and Computer-Aided Design, Vol. 1, 18-20 May 1982,USAF Museum, Wright-Patterson AFB, OH, sponsored by the Joint Technical Coordinating Group for Aircraft Survivability and other papers in the proceedings.

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or processor-controlled manufacturing procedures. Yet other observers may see word processing and electronic mail as centerpieces in the automated envi~on­ment of the future. However, the real key to fundamental advances in the way materiel is concepted, analyzed, manufactured and delivered rests in our ability to describe and analyze geometry. By geometry we mean the complete an unambiguous mathematical definition of a system in three-dimensional space together with its complete material and functional properties, tolerances, etc. From this single unified model a series of engineering analyses can be exer­cised to judge the suitability of a concept to a set of requirements before a prototype is built. Later this file can be used to automate the manufacturing process.

This fact is what computer-aided design/computer-aided manufacturing (CAD/CAM) is about but with a crucial ingredient. Most CAD systems on the mar­ket today perform mainly as automated drafting stations. Because the math­ematical files used for rendering generally do not describe object surfaces or material properties, they cannot be used as input to a collection of engineer­ing analyses necessary for materiel evaluation. By contrast, an emerging technology called solid modeling is characterized by its robust, or complete, description of three-space material. Such geometry can be used as crucial input to predictive models dealing with ballistic protection, nuclear survival, infrared and structural integrity mobility, and the like.

By virtue of its long history in the analysis of materiel in both the nuclear and conventional ballistic environments, the Ballistic Research Labora­tory has developed extensive experience in advanced geometric techniques. In this paperlthe key role solid modeling can play in weapons engineering ;s discussed; in addition, examples of engineering analyses driven by solid modeling illustrate the capability such techniques bring to ~he materiel acqui sition process.

I For a discussion of computer-aided design techniques applied to ground and air-vehicle survivability problems, see E. P. Weaver and P. H. Deitz, "Solid Modeling in Survivability/Vulnerability," Proceedings of the Second JTCG/AS Workshop on Survivability and Computer-Aided Design, Vol. 1, 18-20 May 1982, USAF Museum, Wright-Patterson AFB, OH, sponsored by the Joint Technical Coordi nating Group for Aircraft Survivability and other papers in the proceedings.

UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(M"," Dlltll Entered)

TARLEOF CONTENTS

Page

LIST OF ILLUSTRATIONS ............ ........................................... ..................... 5

1. INTRODUCTION ................................................ ............................... ............. 7

H. WHAT IS SOLID MODELING? . ................................................ ........ ............. 8

HI. MANIPULATION OF COM-GEOM ...... ........................................................13

IV. THE GEOMETRIC INTERFACE ........................................................ ........ ..16

V. EXAMPLES OF SOLID MODEL APPLICATTONS ................................... ..19

A. Ballistic Analysis .............. ............... ............ ................................... ... ..........19

B. Nuclear Survivability .......................... ...................................................... ..21

C. Weights and Moments ............................... ................................... ... ..........24

D. Susceptibility of Vision Elements .................. ............................... .............26

E. Infrared Modeling .......................................................................................28

w. suMMARY ............................. .................................................. .....................30

REFERENCES ...................... ...........................................................................33

DISTRIBUTION LIST .................. ................... ................................................35

TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS ............................................................................ 5

I. INTRODUCIlON ............................................................................................ 7

II. WHAT IS SOLID MODEl...ING? ..................................................................... 8

m. MANIPULATION OF COM-GEOM .............................................................. 13

IV. Tlffi GEOMETRIC INTER.FACE .................................................................. 16

V. EXAMPLES OF SOLID MODEL APPLICATIONS ..................................... 19

A. &l1istic Analysis ......................................................................................... 19

B. Nuclear Survivability .................................................................................. 21

C. Weights and Moments ............................................................................... 24

D. Susceptibility of Vision Flements .............................................................. 26

E. Infrared Modeling ....................................................................................... 28

VI. SUMMARy .................................................................................................... 30

REFERENCES ................................................................................................. 33

DISTRIBUTION LIST ..................................................................................... 35

3

LIST OF TLLUSI’RAT?ONS

I?gm

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Geometric IMta is Processed Through an Interf&e Where itis Combined With Other (Nongeometric) Information for Process@gin an Applications Model ......................................................................... .......... 7

Ability to Evaluate Geometry Removes Ambiguities inTmage Interpretation ..................................................... ............................... ......11

Illustration of Subdivision for an Implicit Boundary Representationand Various Degrees of Refinement . ................................................................12

Color-Shaded Image of the Exterior of the Ml Tank ................. .....................14

Similar image of the Ml Showing the Interior After the ExteriorStructure has been Removed ...................................................................... ......14

Image of the Exterior of a Soviet BMP Generated from aCom-GeOm Description ..... ....................... ................... .....................................15

Interior Detail of the EMP ...............................................................................15

Color Image of the New Army Fast Attack Vehicle (FAV) ................. ..........16

Color Image Showing a Set of Shot.lines One Inch Apart in aHorizontal Plane through the M48 Vehicle Below the Turret Ring ....... ........ ..l7

Same Rendering as Shown in Figure 9 for a Vertical SliceThrough the M48 Center Line ... ....................... ................................................18

Illustration of Mobility and/or F~epower Kills for a Test ThreatAgainst an M48 Tank ......... ....................................... ........................................20

A Color Plot Showing the Absolute DiRerence BetweenFigures lla and b .................................................. .................................. ..........21

Ray Diagram Showing the C!alculational Geometry for theVehicle Code System (VCS) ................. ............................... ........ ........ .............22

False-Color Image Showing Results of Neutron Transport Calculationfor a Concept Vehicle Called Tank Test Bed (Tl13) ........................... ... ..........23

Schematic Showing Orientation of Axes for Moment and Center-of MassCalculations for M60A3 ......... .............................................. ................... ..........25

Color Shaded Image of Soviet BMP ............ ....................................................27

LIST OF TLLUSI'RAnONS

Figure

1 Geometric Data is Processed Through an Interface Where it is Combined With Other (Nongeometric) Information for Processing in an A pp lica tio ns Mooel .......... ,................................................ ..•..... ......• ..•. •... .. 7

2 Ability to Evaluate Geometry Removes Ambiguities in Image Interpretation ......................................................................•..•..•..••.••.••... 11

3 Illustration of Subdivision for an Implicit Boundary Representation and Various ])egrees of Refinement .............................................. ~ ....••.....•...... 12

4 Color-Shaded Image of the Exterior of the M1 Tank .......................••............. 14

5 Similar Image of the Ml Showing the Interior After the Exterior Structure has been Removoo ............................................................................ 14

6 Image of the Exterior of a Soviet BMP Generated from a Com -Geom IJescription .......................................................................•............ 15

7 Interior ])etail of the BMP ............................................................................... 15

8 Color Image of the New Army Fast Attack Vehicle (FA V) ...................•....... 16

9 Color Image Showing a Set of Shotlines One Inch Apart in a Horizontal Plane through the M48 Vehicle Below the Turret Ring ...••............ 17

10 Same Rendering as Shown in Figure 9 for a Vertical Slice Through the M48 Center Line .......................................................................... 18

11 Illustration of Mobility and/or FIrepower Kills for a Test ThWJlt Against an M48 Tank ........................................................................................ 20

12 A Color Plot Showing the Absolute Difference Between Fig-ures Ila and b ...............................................................................•.............. 21

13 Ray Diagram Showing the Calculational Geometry for the Vehicle COOe System (VCS) ...............................................................•....•........ 22

14 False-Color Image Showing Results of Neutron Transpon Calculation for a Concept Vehicle Called Tank Test Bed (TIB) ........................................ 23

15 Schematic Showing Orientation of Axes for Moment and Center-of Mass Calculations for M60A3 .................................................................................... 25

16 Color Shaded Image of Soviet BMP ................................................................ 27

5

LIST OF ILLUSTRATIONS(cent’d)

ngwz? Page

17

18

19

20

A Polar Plot Illustrating the Fraction of the Commander’s ForwardSite Ilkuninated by an Optical Source as a Function of Azimuth Angle

(Zero Degrees Elevation) ...................... ................ ............................................28

A Color Shaded Tmage of a T62 Tank When Viewed From a(90,45) Degree Asp=t A@e ............................... ............................................29

m Infrared Image of a T62 Which has Been Generated by MappingMeasured Radiances onto a Solid Model .......... ................................................30

A Diagram of the R&D (upper half) and Manufacturing(lower half) Phases of Materiel Development ..................................................32

LIST OF TLWSTRATIONS (cont'd)

F1gure

17 A Polar Plot Illustrating the Fraction of the Commander's Forward Site Illuminated by an Optical Source as a Function of Azimuth Angle

Page

(Zero Degrees Elevation) .................................................................................. 28

18 A Color Shaded Image of a T62 Tank When Viewed From a (90,45) Degree Aspect Angle ........................................................................... 29

19 An Infrared Image of a T62 Which has Been Generated by Mapping Measured Radiances onto a Solid Model. ......................................................... 30

20 A Diagram of the R&D (upper half) and Manufacturing (lower half) Phases of Materiel Development .................................................. 32

6

I. INTRODLKXION

Geometry plays a central role in the evaluation of military equipment for its suitabilityto fuIfill a particular role. Essentially every question that can be raised about system per-formance -- survivability, mobility, weighh maintainability -- are a function of geometry.Thirty years ago geometric dam w extracted from blueprints by hand to make simpleestimates of bullet penetmtion into ahcraft structures or unk hulls. As system evaluationsgrew more complicated, vulnerability analysts sought ways to automate the process of pass-ing geometry information to subsequent ana!ysis codes.

At the Ballistic Research Laboratory that search resuhed in the devel pment of a?

geometric modeling technique called Combimtorial Geometry (ComGmm) which is aparticular example of what is known today as Solid Modeling (sM). When an applicationscode is to be rum the geometric files used to represent ob.iect design are interrogated by ageometric interface and passed to the applications code itself (see Figure 1).Nongeometric data is also passed dtiecdy to the code where some system evaluation ismade.

\

KzE1/’IAPPLICATIONS MODEL I

Figure 1. Geometric Data is Processed Through an Interface Where it isCombined VWh Other (Nongeometric) Information for Processing in an

1 The originalMathematical

Applications Model.

Com-Geom method was produced under contract for the BRL byApplications Group, Inc., Elmsford, NY and was an early precursor for a

current product marketed under the name Synthavision. For example,

“A Geometric Description Technique Suitable for Computer Analysis of Both Nucka.rand Conventional Vulnerability of Armored Military Vehicles,” MAGI-6701, AD847576,August 1%9.

“The MAGIC-SAMC Target Amlysis Technique,” Vol VI, AMSAA TR14, April 1%9.User Manual 1971.

7

I. INTRODUcnON

Geometry plays a central role in the evaluation of military equipment for its suitability to fulfill a particular role. Essentially every question that can be raised about system per­formance -- survivability, mobility, weight, maintainability -- are a function of geometry. Thirty years ago geometric data was extracted from blueprints by hand to make simple estimates of bullet penetration into aircraft structures or tank hulls. As system evaluations grew more complicated, vulnerability analysts sought ways to automate the process of pass­ing geometry information to subsequent analysis codes.

At the Ballistic Research Laboratory that search resulted in the devel~pment of a geometric modeling technique called Combinatorial Geometry (Com-Geom) which is a particular example of what is known today as Solid Modeling (SM). When an applications code is to be run., the geometric files used to represent object design are interrogated by a geometric interface and passed to the applications code itself (see Figure I). Nongeometric data is also passed directly to the code where some system evaluation is made.

GEOMETRIC FILES

GEOMETRY INTERFACE

\

NONGEOMETRIC DATA

r APPLICATIONS MODEL J

Figure 1. Geometric Data is Processed Through an Interface Where it is Combined With Other (Nongeometric) Information for Processing in an

Applications Model.

1 The original Com-Geom method was produced under contract for the BRL by Mathematical Applications Group, Inc., Elmsford, NY and was an early precursor for a current product marketed under the name Synthavision. For example,

"A Geometric Description Technique Suitable for Computer Analysis of Both Nuclear and Conventional Vulnerability of Armored Military Vehicles," MAGI-6701, AD847576, August 1969.

"The MAGIC-SAMC Target Analysis Technique," Vol VI, AMSAA TR14, April 1969. User Manual 1971.

7

In the past fifteen Years the princiwl uses of Solid modeling at the BRL have been tosupport various vuhembility/lethality codes and neutron r.tansport models In this paper,we want to highlight two particular issues 1) The first relates to current progress in thegeneratio~ display, and mtifimtion of solid geometry. 2) The secmnd is to discuss thewider application of solid geometric modeling and to give some specific example% Table1 shows a partial listing of uses for solid models. This list is by no means exhaustive, butgives some hint of the powerful and varied uses of geometry.

II. WHAT IS SOLID MODELING?

Solid Mtieling is an analytical framework within which three-dimensional material is completely and unambiguously defined.

This might seem to be a straight form.rd requirement of geometry, but the mqjority ofcommercial computer-aided design systems today do not structure their data files so as tomeet the above requirement. Such systems are known as wire-frame or 2 1/2-D modelersand are quite useful for drafting and visualization. However it is not possible, for exam-ple, to pass an arbitrary ray through a wire-frame model file and know at every point alongthe ray the material properties.

Another way of looking at SM is the following:

Solid Modeli ng is an analytical framework which serves as graphical inmttas well as graphical output.

This is an important property of SM data files. They are equally useful for passinggeometry on to other computer codes as they are for viewing geometry.

There are generally two approaches to solid modeling.2 They are

(A) Constructive Solid Modeling,(B) Boundary file Representation

(1) Explici~(2) hnplici~

2

MAGIC Computer Simulatio~

MAGIC Computer Simulatio~71-7-2-2, May-1971.

Vol. 1, User Manual, 61JTCG/ME-71-7-1, July 1971.

Vol. 2, Analysts Manual Parts 1 ati 2, 61JTCG/h@

For an excellent review paper covering solid modeling approache$ see A. A. G.Requicha and H. B. Voelcker, “Solid Modeling An Historical Summary& ContemporaryAs=ssmenL “ IEEWCS Computer Graphics& Applicatio~ March 1982.

8

In the past fifteen years the principal uses of solid modeling at the BRL have been to support various vulnerability/lethality codes and neutron transport models. In this paper, we want to highlight two particular issues: 1) The first relates to current progress in the generation, display, and modification of solid geometry. 2) The second is to discuss the wider application of solid geometric modeling and to give some specific examples. Table 1 shows a partial listing of uses for solid models. This list is by no means exhaustive, but gives some hint of the powerful and varied uses of geometry.

II. WHAT IS SOLID MODELING?

Solid Modeling is an analytical framework within which 1hree­dimensional material is completely and unambiguously defined.

This might seem to be a straight forward requirement of geometry, but the majority of commercial computer-aided design systems today do not structure their data files so as to meet the above requirement. Such systems are known as wire-frame or 2 1I2-D modelers and are quite useful for drafting and visualization However it is not possible, for exam­ple, to pass an arbitrary ray through a wire-frame model file and know at every point along the ray the material properties.

Another way of looking at SM is the following:

Solid Modeling is an analytical framework which serves as graphical input as well as graphical output.

This is an important property of SM data files. They are equally useful for passing geometry on to other computer codes as they are for viewing geometry.

There are generally two approaches to solid modeling.2 They are:

(A) Constructive Solid Modeling, (B) Boundary file Representations,

(I) Explicit, (2) Implicit.

MAGIC Computer Simulation, Vol. 1, User Manual, 61JTCGIME-71-7-1, July 1971.

MAGIC Computer Simulation, Vol. 2, Analysts Manual Parts I and 2, 61JTffiIME-71-7-2-2, May 1971.

2 For an excellent review paper covering solid modeling approaches, see A. A. G. Requicha and H. B. Voelcker, "Solid Modeling: An Historical Summary & Contemporary Assessment, " IEEE/CS Computer Graphics & Applications, March 1982.

8

TABLE 1. A LIST OF SOME OF THE APPLICATIONS CODES AND USES TOWHICH SOLID MODELS PLAY A KEY ROLE AS INPUT.

● Nuclear Survivability

● Ballistic Penetration/Behind-&mor Damage:- Armor Design/System Configuration- Survivability/Lethality Predictions- SPARC/Logistics Model Support

● Weights and Moments- Calculation of M of I Matrix- Overturning moments for Nuclear Blast Problem- Use of moments for Servo Fire Control

calculation

● Infrared/Millimeter Wave Signatures- All surfacxx and materials are defined in 3 space- Accounts for perspective- Passive radiometer prediction- Radar Cross Section Prediction- Side-Looking Radar Prediction

● Finite Element Mesh Generation (viaPreprocessor):- Generation of 3-D Elements- Variable Level of Subdivision- Exterior Mesh for Signature Models- 3-D Mesh for Heat Flow Modeling- Static/Dynamic Stress Analyses- Blast/Shock Predictions

● Fiie Control/Vision- Susceptibility of Vision Elements to Laser

Radiation- Field-of-View of Vision Blocks

● Aerodynamic/Fluid Flow Amlyses

● Mobility Models

● System Intergration/Engineering Optimization

● wtional Link:Mission Ikqukements --> Quantitative

System Specs

9

TABLE 1. A LIST OF SOME OF THE APPLICATIONS CODES AND USES TO WHICH SOLID MODELS PLAY A KEY ROLE AS INPUT.

• Nuclear Survivability

• Ballistic Penetration/Behind-Armor Damage: - Armor Design/System Configuration - Survivability/Lethality Predictions - SP ARC/Logistics Model Support

• Weights and Moments: - Calculation of M of I Matrix - Overturning moments for Nuclear Blast Problem - Use of moments for Servo Fire Control

calculation

• InfraredlMilIimeter Wave Signatures: - All surfaces and materials are defined in 3 space - Accounts for perspective - Passive radiometer prediction - Radar Cross Section Prediction - Side-Looking Radar Prediction

• Finite Element Mesh Generation (via Preprocessor): - Generation of 3-D Elements - Variable Level of Subdivision - Exterior Mesh for Signature Models - 3-D Mesh for Heat Flow Modeling - Static/Dynamic Stress Analyses - Blast/Shock Predictions

• Fire ControllVision - Susceptibility of Vision Elements to Laser

Radiation - Field-of-View of Vision Blocks

• Aerodynarnic/Fluid Flow Analyses

• Mobility Models

• System Intergration/Engineering Optimization

• Rational Link: Mission Requirements --> Quantitative

System Specs

9

Com-Geom belongs to class 1;3 it is a system which uses certain geometric building blocks

called primitives. Examples of pimitives me wious tit-surfaced volumes of four to eightsides, conic sections and ellipsoids. These entities are placed in space, possibly overlappingone another; the m=~ng of the overlaps is resolv~ by U* of Wol-n (or logical)definitions of the three following types

● Intersection

. Difference”

Figure 2a) shows an example of these operations. A section of a connecting rod is

modeled using a combination of plain prfii~ves and cylinders (A through E). In itsunprocessed form shown in a), the file is termed unevaluat~ using only this visual

prompting, the meaning of the logical operations indicated beneath a) is difhcult to infer.An evaluated or boundary file is shown in Figure 2b) and illustrates the actual results ofthe primitive shapes when processed according to the illustrated logic operation.

3 For a discussion of Com-Geom and a technique for interactive editing, see P. H. Deitz,“Solid Modeling at the US Army Ballistic Research Laboratory,” Proceedings of theThird Annual Conference and Exposition of the National Computer GraphicsAssociatio~ Inc., held 13-16 June, 1982, Vol. II, pp. 949-960.

●

The Union operation takes the combined volume of two intersecting primitives. TheIntersection o~ration takes the common volume of two intersecting primitives. TheDifference operation subtracts the intersecting volume of the second primitive from thefirst.

10

Com-Geom belongs to class I; 3 it is a system which uses certain geometric building blocks called primitives. Examples of primitives are various flat-surfaced volumes of four to eight sides, conic sections and ellipsoids. These entities are placed in space, possibly overlapping one another; the meaning of the overlaps is resolved by use of Boolean (or logical) definitions of the three following types:

• Union

• Intersection

• Difference*

Figure 2a) shows an example of these operations. A section of a connecting rod is modeled using a combination of planar primitives and cylinders (A through E). In its unprocessed fonn shown in a), the file is tenned unevaluated; using only this visual

prompting, the meaning of the logical operations indicated beneath a) is difficult to infer. An evaluated or boundary file is shown in Figure 2b) and illustrates the actual results of the primitive shapes when processed according to the illustrated logic operation.

3 For a discussion of Com-Geom and a technique for interactive editing, see P. H. Deitz, "Solid Modeling at the US Anny Ballistic Research Laboratory," Proceedings of the Third Annual Conference and Exposition of the National Computer Graphics Association, Inc., held 13-16 June, 1982, Vol. II, pp. 949-960.

* The Union operation takes the combined volume of two intersecting primitives. The Intersection operation takes the common volume of two intersecting primitives. The Difference operation subtracts the intersecting volume of the second primitive from the first.

10

c

A- B- C-D+E

Figure 2a Wueframe Representationsof Corn-Geom Building Blocks withLogic Operations

Figure 2b. Wwefrarne Representationsof COm-Geom Building BlocksEvaluated Boundary File of ProcessedGeometry

Figure 2. Ability to EvaluEte GeometryRemoves Ambiguities in Image Interpretation.

Constructive Solid Geometry is a rather good way to start building objects (since it startswith a variety of commonly used shapes), but often the final tuning of surfaces is diflicult.

Some modelers use no primitives at all, but deal entirely with surface descriptions.This approach is called the Boundary File Representation (BFR) and can be chamcterizedby large numbers of flat polygonal approximations to the surfaces being modeled. Such anapproach is called Explicit because the data base actually stores the coordimtes of the sur-face facets. The data may actually be many sampled points over the surface on an actualobject. Explicit representation has a number of serious problems among which are storageof many data points and the fixed polygonal patch size characterizing the surface at thetime it is modeled. On the other han~ BFRs generally can model compound surfacesmore easily than Constructive Solid Systems, and hence often have an advantage at theend of the modeling process.

A Boundary Ftle approach which has come into use more recently is called an ImplicitRepresentation. In this approach the surface of a modeled object is represented by athreedimensioml analytical function which itself is characterized by a set of parameters.Examples of analytical forms for these implicit representations are the Bezier patch andvarious forms of splines. When the surface is to be displayed or utilized in some applica-tions code, points on the surface are calculated anew at the optimum spacing (or resolu-tion) required to serve the competing constraints of surface accuracy and calculation time.

11

C

A-B-C-O+ E

Figure 2a. Wrreframe Representations of Corp-Geom Building Blocks with Logic Operations

Figure 2b. Wrreframe Representations of Com-Geom Building Blocks Evaluated Boundary File of Processed Geometry

Figure 2. Ability to Evaluate Geometry Removes Ambiguities in Image Interpretation.

Constructive Solid Geometry is a rather good way to start building objects (since it starts with a variety of commonly used shapes), but often the final tuning of surfaces is difficult.

Some modelers use no primitives at all, but deal entirely with surface descriptions. This approach is called the Boundary File Representation (BFR) and can be characterized by large numbers of flat polygonal approximations to the surfaces being modeled. Such an approach is called Explicit because the data base actually stores the coordinates of the sur­face facets. The data may actually be many sampled points over the surface on an actual object. Explicit representation has a number of serious problems among which are storage of many data points and the fixed polygonal patch size characterizing the surface at the time it is modeled. On the other hand, BFRs generally can model compound surfaces more easily than Constructive Solid Systems, and hence often have an advantage at the end of the modeling process.

A Boundary File approach which has come into use more recently is called an Implicit Representation. In this approach the surface of a modeled object is represented by a three-dimensional analytical function which itself is characterized by a set of parameters. Examples of analytical forms for these implicit representations are the Bezier patch and various forms of splines. When the surface is to be displayed or utilized in some applica­tions code, points on the surface are calculated anew at the optimum spacing (or resolu­tion) required to serve the competing constraints of surface accuracy and calculation time.

11

This capability is known as setting the degree of refinement. This particular method of geometric modeling holds some promise for advanced requirements where precision sur­face representations are required. 4,5

Figure 3 illustrates both the use of implicit boundary representation and four degrees of refinement (or resolution).·

Figure 3. Illustration of Su1:xiivision for an Implicit Boundary Representation and Various Degrees of Refinement. The same (implicit) spline representation of a sphere is used to calculate four renderings, each at different levels of refinement. None of the surface points used for rendering are stored in the data base; they are recalculated as required for a specific purpose. 'The cost for higher resolution in display is paid in computer cycles. (Courtesy U. of Utah, Ref. 8)

4 E. Cohen, R. Lyche, R. Riesenfeld, "Discrete B-Splines and Su1:xiivision Techniques in Computer-Aided Geometric Design and Computer Graphics," Computer Graphics and Image Processing, Vol. 14, No.2, Oct. 1980.

5 E. Cohen, "Some Mathematical Tools for a Modeller's Workbench," Proceedings of Symposium on Computer-Aided Geometry Modeling held Apr 20-22, 1983 at NASA Langley, Hampton, VA .

• Private communication with R. Riesenfeld, U. of Utah.

12

The same spline represenmtion of a sphere is used to dculate the four renderirtgs each atdifTerent levels of refi~men~ None of the surfs= poin~ used for rendering are stored inthe data base, they = r=lculat~ m ~uia for a sr=ific purpose. The cost for higherresolution in display is paid for in computer cycles.

III. MANIPULATION OF COMGEOM

At the core of any geometric model is a large set of numbers which represents the 3-space geometry being descri~. UnfOfiUIU@Y even a modest sized obkxt requires a largenumerical file for its description In Com-Geom, for example, a simple box having aninner and outer dimension togefier with fuel is descri~ by approxknatdy 100 numbers.Any change in orientatio~ shape, or mamru enmils changing a significant portion of thatfile.

Because of the di.fllcuhy in genemting and tiidating files with great quantities ofnumbers, the task of building Com-Geom descriptions was historically quite time consum-ing. A full-scale tank complete with inuxior components could take as many as 18 monthsto assemble and validate. Because of this critical path “ the process of vulnerability

ranalysis, the BRL developed a graphical editor called GED. This code runs on a minicom-puter and gives immediate visual feedback to an operator who can initiate commands tochoose viewing planes, add or delete components and modify dimensions. me organiza-ticm of GED is hierarchic in nature3 so that tie designer can traverse UP or down thetree structure to initiate an opemtio~ To move higher in the tree structure is to increasethe number of geometric bodies and vice Ver=

GED has been used by the BRL for nearly two years and has significantly decreasedthe time to generate and modify geometry. Savings factors from five to eight have beenexperienced.

In addition to the editing process itself, the BRL has exploited advanced techniques inimage rendering made possible by current frame-btier technology. Such processes areuseful in the interpretation and validation of geometric files. Some examples of theserenderings are shown in Figures 4-8. The descriptions of the Ml and Soviet BMP wereeach built in preGZD days. However, the FAV (Fast Attack Vehicle), shown in Fig. 8,was built entirely with GED in about 12 hours. Various armament options (not shown)have been added to its description-

6 M. J. Muus$ K. A. Appli~ J. R. Suckling C. A. Stanley, G. S. Moss and IZ P. Weaver,‘GED: An Interactive Solid Modeling System for Vulnerability Assessment% “ BRLTechnical Repor~ ARBRL-TR-02480, March 1983 (UNCLASSIFIED) (~ ‘126657).

13

The same spline representation of a sphere is used to calculate the four renderings, each at different levels of refinemenL None of the surface points used for rendering are stored in the data base, they are recalculated as required for a specific purpose. The cost for higher resolution in display is paid for in computer cycles.

III. MANIPULATION OF COM-GEOM

At the core of any geometric model is a large set of numbers which represents the 3-space geometry being described. Unfortunately even a modest sized object requires a large numerical file for its description. In Com-Geom, for example, a simple box having an inner and outer dimension together with fuel is described by approximately 100 numbers. Any change in orientation, shape, or material entails changing a significant portion of that file.

Because of the difficulty in generating and validating files with great quantities of numbers, the task of building Com-Geom descriptions was historically quite time consum­ing. A full-scale tank complete with interior components could take as many as 18 months to assemble and validate. Because of this critical path IJt. the process of vulnerability analysis, the BRL developed a graphical editor called GED. This code runs on a minicom­puter and gives immediate visual feedback to an operator who can initiate commands to choose viewing planes, add or delete components and modify dimensions. The organiza­tion of GED is hierarchical in nature3 so that the designer can traverse up or down the tree structure to initiate an operation. To move higher in the tree structure is to increase the number of geometric bodies and vice versa..

GED has been used by the BRL for nearly two years, and has significantly decreased the time to generate and modify geometry. Savings factors from five to eight have been experienced.

In addition to the editing process itself, the BRL has exploited advanced techniques in image rendering made possible by current frame-buffer technology. Such processes are useful in the interpretation and validation of geometric files. Some examples of these renderings are shown in Figures 4-8. The descriptions of the Ml and Soviet BMP were each built in pre-GED days. However, the FAV (Fast Attack Vehicle), shown in Fig. 8, was built entirely with GED in about 12 hours. Various armament options (not shown) have been added to its description.

6 M. 1. Muuss, K. A. Applin, 1. R. Suckling, C. A. Stanley, G. S. Moss and E. P. Weaver, "GED: An Interactive Solid Modeling System for Vulnerability Assessments, " BRL Technical Repor4 ARBRL-TR-02480, March 1983 (UNCLASSIFIED) (AD A126657).

13

Figure 4. Color-Shaded Image of the Exterior of the Ml Tank This model has been built using Com-Geom.

Figure 5. Similar Image of the Ml Showing the Interior After the Exterior Structure has been Removed

Certain interior components (such as the turbine engine) have also been removed.

14

Figure 6. Image of the Exterior of a Soviet BMP Generated from a Com-Geom Description

Figure 7. Interior Detail of the BMP

15

Figure 8. Color Image of the New Army Fast Attack Vehicle (FA V)

A final point of these renderings, particularly the vehicle interiors, is the complete 3-space description of geometry. In addition, all geometric structures are tagged with material attributes appropriate to subsequent analyses.

IV. THE GEOMETRIC INTERFACE

Although the solid modeling file describes the three-dimensional make up of a vehicle, the analysis code seldom sees this file itself. The geometry file is generally interrogated by an interface code which extracts certain data from the solids model and passes the infor­mation to the applications code. There are in general four geometric interface techniques. They are:

1) Shotlining (Raytracing or Raycasting), 2) 3-D Surface Mesh Generation, 3) 3-D Volume Mesh Generation, and 4) Analytic Representation.

The first, shotlining or raycasting, is by far the most used technique in vulnerability ana­lyses. A series of rays are passed through the Com-Geom descriptions. The intersections to the primitives are calculated, the logic operations are performed, and the material assignments are made.

16

The code that BRL uses for this operation is called GIFT7,8 (Geometric Information For Targets) and it is used to calculate typically thousands of ray trajectories through a target description.

Figure 9 and 10 illustrate the output of the GIFf code.·

Figure 9. Color Image Showing a Set of Shotlines One Inch Apart in a Horizontal Plane Through the M48 Vehicle Below the Turret Ring.

Various material structures are broken out by color.

7 L. W. Bain, Jr., and M. J. Reisinger, "The GIFT Code User Manual; Volume I, Introduction and Input Requirements (U)," BRL Report No. 1802, July 1975. AD# A078364.

8 G. G. Kuehl, L. W. Bain, Jr., M. J. Reisinger, "The GIFT Code User Manual; Volume II, The Output Options (U)," USA ARRAOCOM Report No. 02189, Sep 79, AD# A078364 .

• These results are plotted by a code called RunShot written by L. M. Rybak which takes input from GIFT and plots color shotlines on a Megatek display system.

17

Figure 10. Same Rendering as Shown in Figure 9 for a Vertical Slice Through the M48 Center Line.

Normally in vulnerability calculations, a 4 inch x 4 inch grid is superimposed over a target from a chosen aspect angle. A single ray is fired into each grid square over the entire view. In these illustrations, the shotline density was increased to a one inch grid. In Fig­ure 9, a horizontal set of rays has been intersected with the target description of an M48 tank. The various materials have been coded by color. White is a default color and gen­erally includes the armor and suspension system. Green denotes crew air, yellow the ammunition, red the personnel, and burgundy the engine air. These color assignments are arbitrary and can be modified easily by the user. Figure 10 shows a similar set of rays for a vertical slice through the same vehicle.

Although shotlining provides the great bulk of geometric information to vulnerability programs, new applications require geometry information in a completely different format. Currently the BRL is developing an interface from Com-Geom to a finite element mesh (FEM) preprocessor.· This particular code is capable of generating 3-dimensional meshes on the surfaces of solid objects (Le. a polygonal patch model) or optionally, a true 3-

• Private communication with G. S. Moss who is writing an interface between Com-Geom and a FEM preprocessor called PATRAN-G. PATRAN-G is a product of PDA Engineering, Santa Ana, CA.

18

dimensional Solid mesh of the solid oh-t itself. The former m~tility is usefd for thoseapplication codes that - polygo~ ~tch approximations to compound surfacegeometry. The size of the patch approximations is user definable, and can be set for theprecision required in the application. Such surface information is key to the exploitation ofvarious signature calculations of the following types:

● Radar Cross Sections● Side-boking Radars● Optical Scattering● Susceptibility of Detectors to Radiation● Camouflage EfTects● Pattern Recognition● Image Perspective Kkpende-

Three dimensional mesh generation is important for many static and dynamic structuralstudies as well as the following in which complete interior and exterior material informa-tion is needed

● Heat Flow leading to Surface (and Volumetric) Temperatures● Acoustic Signatures● Magnetic Signatures

FhxdIy there are certain applications in which the formal mathematical structure of asolid mcxlel may relate in closed form to an attribute of vehicle assessment. For example,the radar reflection from an armored vehicle is described by the spatial Fourier transformof the electric field over the target itself. If a solid model is based on an implicit boundaryfile having a mathematical form which can be directly evaIuated by such a transform, thenthe resulting signature might be evaluated by direct analytical techniques

V. EXAMPLES OF SOLID MODEL APPLICATIONS

In this section we will describe a few examples of applications codes which depend onsolid geometric models for input. The first is an example of one of a number of pointburst models in use at the BRL.

A. Ballistic Analysis

TheT

icular model used here is called SLAVE (Simple Lethality and VulnerabilityEstimator) and is used to evaluate the effect of antiarmor weapons against ground

9 F. T. Bro~ D. C. Bely, and D. A. Ringersj ‘The Simple Lethality and VulnerabilityEstimator (SLAVE): User’s Manual,” BRL Technical Report ARBRL-TR412282 (AD#B055277), January 1981.

D. A. Ringers and F. T. Brow ‘SLAVE (Simple Lethality and V~nembflity l%timator)Analyst’s Guide,” Technical Report ARBRL-TR42333 (AD#B059679L), June 1981.

19

dimensional solid mesh of the solid object itself. The former capability is useful for those application codes that need polygonal patch approximations to compound surface geometry. The size of the patch approximations is user definable, and can be set for the precision required in the application. Such surface information is key to the exploitation of various signature calculations of the following types:

• Radar Cross Sections • Side-Looking Radars • Optical Scattering • Susceptibility of Detectors to Radiation • Camouflage Effects • Pattern Recognition • Image Perspective Dependence

Three dimensional mesh generation is important for many static and dynamic structural studies as well as the following in which complete interior and exterior material informa­tion is needed:

• Heat Flow leading to Surface (and Volumetric) Temperatures • Acoustic Signatures • Magnetic Signatures

Finally there are certain applications in which the formal mathematical structure of a solid model may relate in closed form to an attribute of vehicle assessment. For example, the radar reflection from an armored vehicle is described by the spatial Fourier transform of the electric field over the target itself. If a solid model is based on an implicit boundary file having a mathematical form which can be directly evaluated by such a transform, then the resulting signature might be evaluated by direct analytical techniques.

V. EXAMPLES OF SOLID MODEL APPLICATIONS

In this section we will describe a few examples of applications codes which depend on solid geometric models for input. The first is an example of one of a number of point burst models in use at the BRL.

A. Ballistic Analysis

The ~icular model used here is called SLAVE (Simple Lethality and Vulnerability Estimator) and is used to evaluate the effect of antiarmor weapons against ground

9 F. T. Brown, D. C. Bely, and D. A. Ringers, "The Simple Lethality and Vulnerability Estimator (SLAVE): User's Manual," BRL Technical Report ARBRL-TR-02282 (AD# 0055277), January 1981.

D. A. Ringers and F. T. Brown, "SLAVE (Simple Lethality and Vulnerability Estimator) Analyst's Guide," Technical Report ARBRL-TR-02333 (AD#B059679L), June 1981.

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vehicles. Following perforation of a vehicle armor shell by a penetrator, SLAVE uses a simplified subroutine to evaluate behind armor spall. Basically spall is described by a cone behind the point of armor penetration. If soft components are located anywhere within the spall cone, they are counted as killed by the behind-armor debris. Hard components survive unless they are impacted by the main penetrator. This code, formerly a batch model, has been port1'b to various minicomputers and runs in an interactive mode with optional color plotting.

Figure 11 illustrates two color-coded diagrams generated with SLA VB; these results show the performance of a particular KE penetrator against the M48 tank.

••••• ••••••• •••••••• ••••••••••• ••••••••••••••••••••••• •••• •••••••••••••••••• ••• •••••••••••••••••• • ••••••••••••• • ••• .. ................... . ... ............. . .. . ..........•...... . ••••• •••••••••••• • • •• ••• ••••••• •••••••• •• • •••••• ••• ••••••• •••• •••• •• •• ••••••••

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•

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· •• ••• ••• •• • •••••• •••••••••• •••••••• •••••• • ••• • · .. •• • ••• •• • ••••• ••••••••••• •••••••••••• ••••••• ••••••• ••••••• •••••••

Figure 11. Illustration of Mobility and/or Firepower Kills for a Test Threat Against an M48 Tank. Color key (see Figure 12) implies numerical range from zero (white) to one (orange). Left result shows the effect of main penetrator only. Right image shows combined result for both main penetrator and spall.

The left figure illustrates the probability of an M and/or F kill (mobility and/or fire-power kill) in which only the effect of the main penetrator is assessed. The numbers are bounded by zero and one, and can be interpreted by means of the scale (below) in Figure 12. White represents zero and orange represents one.

10Ref . 1 and A. Ozolins and D. A. Ringers, "ISLA VE: Interactive Simple Lethality and Vulnerability Estimator," pp. 91-99.

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••••• ••••••• •••••••• • • ••••••• ••• ••••••••• • ••••• •• • ••••••••••••••••• • ••••••••••••• • •••••••••••••••••• • · .... .......... .. · . . ......... 1.. . .. . ................ . .. ............... . .. . ••• ••• • • ........... I ••••

•••• • ... . . . ......... 1 __ •••• ....... ....... ... . ............. . ........ ............... . ....... . ........................... . ..... . ................................... ..................................... ........ ...... . ............. - ... . •••••••• ••• • ..... _ ••••• 1 I .. . .............................. __ ... . ....... ................... . ..... . ••••••••••• ,4:,':::' ••••••••••• ...................... . .......... . ••••••• • •••••• ••••••• • •••••• ••••••• • •••••• ••••••• • ••••••

• • ••••••

Figure 12. A Color Plot Showing the Absolute Difference Between Figures lla and b. Numerical range of color key as described in previous caption.

On the right the calculation has been repeated evaluating the effect of behind-armor spall as well as the main penetrator. Clearly more of the target is represented in orange, indicating higher kills. Figure 12 illustrates a feature of the interactive SLAVE model-­the option to subtract any two runs from each other. Here the spall and nospall calcula­tions have been differenced showing for this penetrator/vehicle configuration the contribu­tion of spall to the overall M/F kill. And for this particular threat/target combination, the contribution of behind armor spall to the overall system damage is clearly illustrated.

B. Nuclear SurvivabilitY

When a nuclear weapon is detonated, several threats to equipment and personnel exist. Among these threats are blast, thermal radiation, EMP and nuclear radiation. The last can be further divided into initial and residual radiation, the latter often being referred to as fallout. The BRL is primarily concerned with the initial nuclear radiation but evaluates other effects as well.

The initial radiation output from a nuclear weapon is either a prompt neutron, a neutron-induced gamma (sometimes called a secondary gamma) or a prompt gamma. In our analyses we usually only consider the total dose effects. The calculational technique

21

used at the BRL is Vehicle Code System (VeS),11,12 actually a combination of three codes. Referring to Figure 13, the first code calculates detenninistically the transport of radiation from the source to an envelope that surrounds the vehicle. The second code makes a stochastic calculation to detennine the relationship between the radiation at the source envelope and a detection point inside the vehicle. This calculation is done in what is known as the adjoint mode which amounts to a calculation backward in time for scatter­ing from the detector point to the source envelope.

x x x x x x x x x

Figure 13. Ray Diagram Showing the Calculational Geometry for the Vehicle Code System (Ves). The Discrete Ordinate eode (DOT) calculates the transport of nuclear radiation from the source to an envelope surrounding a vehicle. A second calculation relates the radiation at the envelope to the total dose at some interior portion of the vehicle. The vehicle geometry itself is described using Com-Geom.

liW. A. Rhodes, "Development of a Code System for Detennining Radiation Protection of Annored Vehicles (the VCS Code)," ORNL-TM-4664, Oak Ridge National Laboratory, Oak Ridge, TN, October 1974.

12W. A. Rhodes et aI., "Vehicle Code System (VCS) User's Manual," ORNL-TM-4648, Oak Ridge National Laboratory, Oak Ridge, TN, August 1974.

22

A Monte Carlo procedure is invoked as a given particle is traced through the Com-Geom target description. The adjoint mode is adopted for computational efficiency. A third code matches the first two codes at the source envelope boundary.

Recently such a calculation was performed for a particular US tank concept called the Tank Test Bed (TTB).* The results are illustrated in Figure 14.

Figure 14. False-Color Image Showing Results of Neutron Transport Calculation for a Concept Vehicle Called Tank Test Bed (TIB). Total dose reaching driver was calculated by summing radiation leakage through all exterior vehicle regions. Results have been normalized to the driver's hatch (which contributed the greatest portion of radiation). Note the low-detail Com-Geom description used for this study. Color key at bottom represents range of normalized radiation dose from zero (dark blue) to unity (white).

There are two principal points. The first is that the description of the TTB illustrated here is austere --- there is a minimum of detail that can be observed in the exterior detail of the vehicle. The same holds true for the interior of the vehicle. This is because neutron

* J. W. Kinch and A. E. Rainis, "Nuclear Vulnerability Analysis of the Tank Test Bed (TTB) in an Initial Nuclear Radiation Environment," BRL Technical Report ARBRL-TR-02552, March 1984 (AD B080980) .

23

transport problems are sensitive on.lY to mther gross dhribution of material and thusgeometric detail is insigticant in such analyses. Second, the vehicle is displayed using afalse coloring scheme. In this study the toti radiation dose reaching the driver’s head wascalculated while monitoring the specfic emrior portions of the vehicle through which theradiation leaked. In Figure 14, an attempt has been made to render the portions of thevehicle contributing most greatly in brighter colors, those contributing less in the dullerpart of the spectrum. The results have also been normalized to the radiation enteringthrough the driver’s hatch; 60% of the total drive~s dose was delivered through the hatch,and for the illustration that amount of radiation has been normalized to unity. Radiationentering through other exterior vehicle parts is scaled to the hatch flux according to thecode shown in the figure.

C. Weights and Moments

As is well appreda@ moments and Productsof inertia play a central role in the designof military vehicles. Particularly for aircrafq the center-of-gravity and inertia-related

-e~rs me key KI favomble Performs= and s~bility. Even for ground vehicles theseparameters are important. Total weights for ground vehicles are always needed for assess-ment of air transportability. Applications of moments of inertia range from calculating theprobability that ground vehicles will turn over due to a nuclear air blast to predicting aim-ing errors of stabilized fire-control systems mounted on vehicles traversing rough terrain

The estimate of moments and products of iT!f

k is a straightforwar~ but somewhatlaborious calculation for a solid modeling system. That the calculation is straightfonvardcan be seen by again examining Figure 9. The shotlines illustrated wem calculated onone-inch centers. The various obbts (indicated by color) each have an assigned density.In effech each shot-line is broadened by one half inch above and below, and left and right.This gives a (one-inch) square cross section of uniform mass between material interfacesas the shotline progresses through the vehicle description. The laborious aspect of the cal-culation involves setting the effective density of various components properly and sing

that the predominant vehicle constituents are in place.

13See for example G. A. Bias% “Theoretical Physi~” AppletonUmtury<rof@ NY(1%2), PP. 102 m. BY these techniques dculations of the principal second momentsand cross products of inertia can also be made. Often these mechanical designparameters have been umvailable to the traditional engineer due to the computationaloverhd.

24

transport problems are sensitive only to rather gross distribution of material and thus geometric detail is insignificant in such analyses. Second, the vehicle is displayed using a false coloring scheme. In this study the total radiation dose reaching the driver's head was calculated while monitoring the specific exterior portions of the vehicle through which the radiation leaked. In Figure 14, an attempt has been made to render the portions of the vehicle contributing most greatly in brighter colors, those contributing less in the duller part of the spectrum. The results have also been nonnalized to the radiation entering through the driver's hatch; 60% of the total driver's dose was delivered through the hatch, and for the illustration that amount of radiation has been nonnalized to unity. Radiation entering through other exterior vehicle partS is scaled to the hatch flux aa:ording to the code shown in the figure.

C. Weights and Moments

As is well apprecia~ moments and products of inenia playa central role in the design of military vehicles. Particularly for aircraft, the center-of-gravity and inertia-related parameters are key to favorable perfonnance and stability. Even for ground vehicles these parameters are important. Total weights for ground vehicles are always needed for assess­ment of air transportability. Applications of moments of inertia range from calculating the probability that ground vehicles will turn over due to a nuclear air blast to predicting aim­ing errors of stabilized fire-control systems mounted on vehicles traversing rough terrain.

The estimate of moments and products of iIlfjljia is a straightforward, but somewhat 1aboriou~ calculation for a solid modeling system. That the calculation is straigh tforward can be seen by again examining Figure 9. The shotlines illustrated were calculated on one-inch centers. The various objects (indicated by color) each have an assigned density. In effect, each shotline is broadened by one half inch above and below, and left and right. This gives a {one-inch} square cross section of unifonn mass between material interfaces as the shotline progresses through the vehicle description. The laborious aspect of the cal­culation involves setting the effective density of various components properly and seeing that the predominant vehicle constituents are in place.

13See for example G. A. Blas~ "Theoretical Physics," Appleton-Century-Crof~ NY (1962), pp. 102 ff. By these techniques calculations of the principal second moments and cross products of inertia can also be made. Often these mechanical design parameters have been unavailable to the traditional engineer due to the computational overhead.

24

Momentaf-inertia and center of mass dc~ations were performed recently” using theCom-Geom description of the M60A3. The changes of the N version over the Al includea new suspension system, a new turret and fire control system, and new tracks. A orie-inch shotline grid was used and the calculation was performed along each of the principalaxes (See Figure 15). The total number of shotlines computed came tothe results of the three runs were averaged.

z

about 76,5(MJ and

Y

Figure 15. Schematic Showing Orientation of Axes for Moment amlCenter-of-Mass Calculations for M60A3.

(Origin of coordinates resides at the center of the turm ring.)

Table 2 shows the calculation of center of gravity comparing the Project Manager’s dataand the BRL calculations. The origin of the coordinate system resides at the center andbase of the turret ring. Given the length of this vehicle (approximately 20 feet), the PM’sand calculated results are within a few percent agreement. The results for moments ofinertia are given in Table 3. Again the agreement is quite good.

● Private communication with J. H. Waker.

25

Moment~f-inenia arxi center of mass calculations were performed recentl~ using the Com-Geom description of the M60A3. The changes of the A3 version over the Al include a new suspension system, a new turret and fire control system, and new tracks. A Orie­inch shotline grid was used and the calculation was performed along each of the principal axes (See Figure IS). The total number of shotlines computed came to about 76,500, and the results of the three runs were averaged.

z

x y

Figure IS. Schematic Showing Orientation of Axes for Moment and Center-of-Mass Calculations for M60A3.

(Origin of coordinates resides at the center of the turret ring.)

Table 2 shows the calculation of center of gravity comparing the Project Manager's data and the BRL calculations. The origin of the coordinate system resides at the center and base of the turret ring. Given the length of this vehicle (approximately 20 feet), the PM's and calculated results are within a few percent agreement. The results for moments of inertia are given in Table 3. Again the agreement is quite good .

• Private communication with J. H. Walter.

25

TABLE 2. A COMPARISON OF THE CENTER OF GRAVITYFOR THE M60A3 W BATTLE TANK.

The upper figures are due to the Project Manager, M60, amlthe lower numbers are the result of a GI~ CalculationCoordinate axes are shown in Figure 15. Origin resides atthe center of the turret ring.

XYZPM M60 FIGURES: -15.4 -0.6 -14.4 INCHES

GIFT CAWLJLATION -20.3 4).4 -15.6 INCHES

TABLE 3. MOMENT OF II~~IA ( in lbm-ft2) ABOUT THE CENTEROF GRAVITY FOR THE M60A3 TANK. Left are the PM M60 dauq

right are the results of the GIFT Calculation.

PM M60 DATA G~ CALCULATION

1= 1.67 X 166 1.55 x 106

Iv 4.95 x 106 5.12 X 106

1= 5.46 x 106 5.59 x 106

One further application of these calculations worthy of mention is their use in fire-control predictions. Clearly the slew rate for a tank turret depends on the distribution ofmass. Using our graphics editor, it is a straightforward process to add or delete ammunit-ion in a turret bustle or to reconfigure the armor and rerun GIFT for each configurationto generate various sets of moments. Each set can be fed in turn into a servo-controlmodel to see how the fire control mechanism is affected by configuration.

D. Susceptibility of Vision Elements

The BRL was recently asked to evaluate susceptibility of mious vision ports onarmored vehicles to optical irradiation. One vehicle for which this study was made is theSoviet BMP, illustrated again in Figure 16. This rendering is different from that shown inFigure 6 for here the commander and driver vision blocks are illustrated in blue. The

.26

TABLE 2. A COMPARISON OF THE CENTER OF GRAVITY FOR THE M60A3 MAIN BATILE TANK.

The upper figures are due to the Project Manager, M60, and the lovw:r numbers are the result of a GIFT calculation. Coordinate axes are shown in Figure 15. Origin resides at the center of the turret ring.

PM M60 FIGURES: x y

-15.4 -0.6 Z

-14.4 INCHES

GIFT CALCULATION: -20.3 -0.4 -15.6 INCHES

TABLE 3. MOMENT OF INERTIA (in 1 bm-ft2) ABOUT THE CENTER OF GRAVITY FOR THE M60AJ TANK. Left are the PM MOO data;

right are the results of the GIFT Calculation.

PMM60DATA GIFT CALCULATION

Ixx 1.67 x 166 1.55 x 106

Iyy 4.95 x 106 5.12 x 106

Izz 5.46 x 106 5.59 x 106

One further application of these calculations worthy of mention is their use in fire­control predictions. Clearly the slew rate for a tank turret depends on the distribution of mass. Using our graphics editor, it is a straightforward process to add or delete ammuni­tion in a turret bustle or to reconfigure the armor and rerun GIFT for each configuration to generate various sets of moments. Each set can be fed in turn into a servo-control model to see how the fire control mechanism is affected by configuration.

D. Susceptibility' of Vision Elements

The BRL was recently asked to evaluate susceptibility of various vision pons on armored vehicles to optical irradiation. One vehicle for which this study was made is the Soviet BMP, illustrated again in Figure 16. This rendering is different from that shown in Figure 6 for here the commander and driver vision blocks are illustrated in blue. The

26

GIFT code was modified- to calculate the area of a particular vision block exposed to opti­cal radiation from a given aspect angle.

Figure 16. Color Shaded Image of Soviet BMP. The blue colors highlight the commander and driver vision blocks.

For this study the elevation angle was held at zero and the azimuthal angle was varied over the frontal arc. Figure 17 shows the results for the commander's forward periscope. The cardioid plot gives the percent area of his vision block that would be illuminated by a laser versus azimuth angle. The large reduction in illumination on the commander's right is due to the obstruction caused by the mounted sagger missile.

-Private communication with G. G. Kuehl.

0°

80 -80°

\ 0061,0

Figure 17. A Polar Plot Illustrating the Fraction of the Commander’sFo~d Site Illuminated by an optical Source as a Function of

Azimuth Angle (Zero Degrees Elevation).

An important related problem with which vehicle builders must deal is the design andplacement of the vision elements so as to optimize the exterior field-of-view for the vehi-cle occupants. When the viewing system for a current fighting vehicle was initially built(presumably without the assistance of a computer-aided vision program), the result WS asubstantial blind spot in one portion of the commander’s field-of-view. At some expensethe system was redesigned to eliminate this problem.

With the appropriate application code, a solid model can be used with inside-out ray-casting to give the view from inside a vehicle through any vision port or window. Such anoption is available in a solid modeling package called Euclid* and could be indispensable inthe design of vision systems.

E. Infrared Modeli~

Solid Modeling can also be applied to the problem of infrared signature analysis. In thedesign of smart munitions it is important to know the nature of vehicle signatures owm arange of detection bands and signal processing schemes. In order to estimate the infrared

● Euclid is a product of MATRA Corporation of France and is distributed by MATRADATAVISION, Inc., BostorL MA.

28

80 -800

1.0

Figure 17. A Polar Plot Illustrating the Fraction of the Commander's Forward Site Illuminated by an Optical Source as a Function of

Azimuth Angle (Zero Degrees Elevation).

An important related problem with which vehicle builders must deal is the design and placement of the vision elements so as to optimize the exterior field-of-view for the vehi­cle occupants. When the viewing system for a current fighting vehicle was initially built (presumably without the assistance of a computer-aided vision program), the result was a substantial blind spot in one portion of the commander's field-of-view. At some expense the system was redesigned to eliminate this problem.

With the appropriate application code, a solid model can be used with inside-out ray­casting to give the view from inside a vehicle through any vision port or window. Such an

option is available in a solid modeling package called Euclid- and could be indispensable in the design of vision systems.

E. Infrared Modeling

Solid Modeling can also be applied to the problem of infrared signature analysis. In the design of smart munitions it is important to know the nature of vehicle signatures over a range of detection bands and signal processing schemes. In order to estimate the infrared

-Euclid is a product of MA TRA Corporation of France and is distributed by MATRA DATA VISION, Inc., Boston, MA.

28

perfonnance of one smart system called SADARM, 14 a series of measurements in the 8-12 micron bandwere made for a Soviet T62 tank under various operating conditions. For each set of conditions, a complete thermal signature was gathered over the vehicle surface. The measured temperatures were then associated with the corresponding exterior regions of the Com-Geom description. Such an approach, although not predictive, assures that the effect of sensor aspect angle is accurately accounted for in the subsequent simulation.

Figure 18 shows a (Com-Geom generated) color-shaded image of a T62 Soviet tank. And Figure 19 shows a thennogram of the tank from the same aspect angle (90,45). The false color image illustrates the signal strength in the 8-12 micron band; this data was taken during clear night time operating conditions, and the color scale represents a range of about 18 to 35 Degrees C. Although this is not an example of predictive modeling, the solid mcxlel serves an invaluable role in achieving true image perspective in the sensor simulation.

Figure 18. A Color Shaded Image of a T62 Tank When Viewed From a (90,45) Degree Aspect Angle.

1~. R. Rapp, "A Computer Model for Estimating Infrared Sensor Response to Target and Background Thennal Emission Signatures," BRL Memorandum Report ARBRL-MR-03292, August 1983 (AD B076976L).

29

Figure 19. An Infrared Image of a T62 Which has Been Generated by Mapping Measured Radiances onto a Solid ModeL The use of the solid model in this way assures the proper effect of aspect angle in later analyses.

Actual predictive IR modeling is possible based on solid modeling but it is considerably more difficult. To make predictions it is necessary to calculate a complete heat budget throughout the vehicle accounting for all sources and sinks of heat among all components including the ratfs of heat flow as well. The methodology to do this was developed but never validated. Generally thermal models are developed around an FEM structure. Heal flow is calculated from node to node with mesh links characterized by coupling coefficients.

VI. SUMMARY

In this paper we have described -some of the principal techniques used in solid modeling as well as illustrated ways in which this discipline can be applied. We have asserted that e5Sentially all engineering models which attempt to predict system performance must be

15 J. R. Rapp, "A Computer Model for Predicting Infrared Emission Signatures of An M60A1 Tank," BRL Report No. 1916, AD#B0l341IL, August 1976.

30

SUppOrted by solid geometric descriptions. Although solid modeling MS &veloped princi-pally for ballistic and nucka.r studie$ iw applimtion is fm wider than commonly realized.

The applications described abo~ belong wholely to the R & D cycle of weapons SYSterns. The title of this paper implied a much kger rde for solid modeling, and indeed ithas one. Materiel development gene~lys- with a Wgue concept. In a seriesof itera-tive analyses, the concept is progressively refined. At some point the concept is eitherpassed on for prototyping or abandoned. we beliew that Solid Modeling should play akey role in providing the critical geometricimateriel AW base to suPPort a broad group ofengineering a~yses. Subseqwnt tO this pha=, the ~m - should be passed over to themanufacturing cycle where subsmntti wings in time and improvements in accuracy couldbe made. For in fut much of the Computer-aidd manufutwing tim would already havebeen generated.

Figure 20 attempts to illustrate the process of materiel ~uisition from concept (in theR & D phase) through manufactming. At the h- of the process is the Solid GeometricModel (sGM) data base. In the upper half, layered around the data base are the applica-tions codes for suitability uses~en~, the supporting electronic environment makes itpossible to move and share data quickly. In the lower half the refined concepts becomereality through computer-aided manufacturing techniques. Somewhat ironically, the hnyhas paid considembly more attention to the automaton of this latter stage of materiel&velopment than to the concept and engineering phases. Based on the enormous mone-tary commitments made to the manufacturing cycle, this attention is not surprising. How-ever, the potentti to achie~ maximu =mndesign optimimtion can only occur in theengineering ph=s of devdopmen~ not by ~tering COnStrUCt materiel by means of pro-duct improvements (PIPs) after manufacturing. Only by means of mmputer-aidedgeametric techniques carefully and broadly applied to weapons engineering can we expectto achieve the optimum performance, reliability and timely &livery of future military sys-tems.

31

supported by solid geometric descriptions. Although solid modeling was developed pnncl­patly for ballistic and nuclear studies, its application is far wider than commonly realized.

The applications described above belong wholely to the R &: D cycle of weapons sys­tems. The title of this paper implied a much larger role for solid modeling, and indeed it has one. Materiel development generally starts with a vague concept. In a series of itera­tive analyses, the concept is progressively refined. At some point the concept is either passed on for prototyping or abandoned. We believe that Solid Modeling should play a key role in providing the critical geometric/materiel data base to suppon a broad group of engineering analyses. Subsequent to this phase, the data base should be passed over to the manufacturing cycle where substantial savings in time and improvements in accuracy could be made. For in fact much of the computer-aided manufacturing data would already have been generated.

Figure 20 attempts to illustrate the process of materiel aa:tuisition from concept (in the R &: D phase) through manufacturing. At the heart of the process is the Solid Geometric Model (SGM) data base. In the upper half, layered around the data base are the applica­tions codes for suitability assessments; the supponing electronic environment makes it possible to move and share data quickly. In the lower half the refined concepts become reality through computer-aided manufacturing techniques. Somewhat ironically, the Anny has paid considerably more attention to the automaton of this latter stage of materiel development than to the concept and engineering phases. Based on the enormous mone­tary commitments made to the manufacturing cycle, this attention is not surprising. How­ever, the potential to achieve maximum weapon-design optimization can only occur in the engineering phases of development, not by altering constructed materiel by means of pro­duct improvements (PIPs) after manufacturing. Only by means of computer-aided geometric techniques carefully and broadly applied to weapons engineering can we expect to achieve the optimum performance, reliability and timely delivery of future military sys­tems.

31

Electronic Connectivity

M

A

N.

Automated OiTlce Environment

Automated Factory Environment

Figure 20. A Diagram of the R&D (up&r half) and Manufacturing (lower half)Phases of Materiel Development. At the heart of both mtir cycles is the SolidGeometric Model (SGM) data base which unites geometry with material(attribute) properties. Around the shared data base are the supporting codes andprocesses all linked via electronic media.

32

t R

&: D

M

A

N.

!

An aly'i is

Weight. Strength

Cost Performance

CAM

Figure 20. A Diagram of the R&D (upper half) and Manufacturing (tower half) Phases of Materiel Development. At the heart of both major cycles is the Solid Geometric Model (SGM) data base which unites geometry with material (attribute) properties. Around the shared data base are the supporting codes and processes all linked via electronic media.

32

1.

2.

3.

4.

5.

. .

6.

7.

8.

The original Com-Geom method WM produced under contract for the BRL byMathematical Applications Group, Inc., Elmsfoti m and was an early precursor fora current product marketed under the name Synt.havkion. For example,

“A Geometric Description Techtique Suimble for Computer Analysis of BothNuclear and conventional Vulnerability of Armored Military Vehicles,” MAGI-6701,AD847576, August 1969.

‘The MAGIC-SAMC Target Analysis Technique,” Vol VI, AMSAA TR14, April1969. User Manual 1971.

MAGIC Computer Sirnulatiou VO1.1, User Manual,61JTCG/ME-71-7-1, July 1971.

MAGIC Computer Simulatio~ Vol. 2, Analysts Manual Parts 1 and 2,61JTCG/ME71-7-2-2, Mlly 1971

For an excellent review paper covering solid modeling approaches see A. A. G.Requicha and H. B. Voelcker, “Solid Modeling An Historical Summary & Contem-porary Assessment” LEEE/CS Computer Graphics& Application March 1982.

For a discussion of ComGeom and a whnique for interactive editiw see P. H.Deiw “Solid Modeling at the US Army Ballistic Research Laboratory,” Proceedingsof the Third Annual Gnference and Exposition of the National Computer GraphicsAssociation Inc., held 13-16 June, 1982, Vol. II, pp. 949-960.

E. Coheu R. Lyche, R. Riesenfel& “Discrete B-Splines and Subdivision Techniquesin Computer-Aided Geometric Design and Camputer Graph ics,” Computer Graphicsand Image Processing, Vol. 14, No. 2, Oct. 1980.

E. cohe~ “Some Mathematical Tools for a Modeller’s Workbench,” Proceedings ofSymposium on Computer-Aided Geometry Modeling held Apr. 20-22, 1983 atNASA Langley, Hampto~ VA.

M. J. Muuss, K. A. Appli~ J. R. Suckling, C. A. Stanley, G. S. Moss and E. P.Weaver, “GED: An Interactive Solid Modeling System for Vulnerability Assess-men~” BRL Technical Repor~ ARBRL-TR-02480, March 1983 (UNCLASSIFIED).(ADA126657) .L. W. BaiL Jr., and M. J. Reisinger, “The GIFI’ Code User Manua~ Volume I,Introduction and Input Requirements (U),” BRL Report No. 1802, July 1975. AD#A078364.

G. G. Kuehl, L. W. BaiL Jr., M. J. Reisinger, “The GIIW Code User Manual;Volume II, The Output Options (U),” USA ARRADCOM Report No. 02189, Sep.79, AD# A078364.

REFERENCES

1. The original Com-Geom method was produced under contract for the BRL by Mathematical Applications Group, Inc., Elmsford, NY and was an early precursor for a current product marketed under the name Synthavision. For example,

"A Geometric Description Technique Suitable for Computer Analysis of Both Nuclear and Conventional Vulnerability of Armored Military Vehicles," MAGI-6701, AD847576, August 1969.

"The MAGIC-SAMC Target Analysis Technique," Vol VI, AMSAA TR14, April 1969. User Manual 1971.

MAGIC Computer Simulation, Vol. I , User Manual, 61ITCGIME-71-7-1, July 1971.

MAGIC Computer Simulation, Vol. 2, Analysts Manual Parts 1 and 2, 61JTCGIME-7I-7-2-2, May 1971

2. For an excellent review paper covering solid modeling approaches, see A. A. G. Requicha and H. B. Voelcker, "Solid Modeling: An Historical Summary & Contem­porary Assessmen4" IEEE/CS Computer Graphics & Applications, March 1982.

3. For a discussion of Com-Geom and a technique for interactive editing, see P. H. Deitz, "Solid Modeling at the US Army Ballistic Research Laboratory," Proceedings of the Third Annual Conference and Exposition of the National Computer Graphics Association, Inc., held 13-16 June, 1982, Vol. II, pp. 949-960.

4. E. Cohen, R. Lyche, R. Riesenfeld, "Discrete B-Splines and Subdivision Techniques in Computer-Aided Geometric Design and Computer Graphics," Computer Graphics and Image Processing, Vol. 14, No.2, Oct. 1980.

5. E. Cohen, "Some Mathematical Tools for a Modeller's Workbench," Proceedings of Symposium on Computer-Aided Geometry Modeling held Apr. 20-22, 1983 at NASA Langley, Hampton, VA.

6. M. J. Muuss, K. A. Applin, J. R. Suckling, C. A. Stanley, G. S. Moss and E. P. Weaver, "GED: An Interactive Solid Modeling System for Vulnerability Assess­ments," BRL Technical Repor4 ARBRL-TR-02480, March 1983 (UNCLASSIFIED). (AD AI26657).

7. L. W. Bain, Jr., and M. J. Reisinger, "The GIFT Code User Manual; Volume I, Introduction and Input Requirements (U)," BRL Report No. 1802, July 1975. AD# A078364.

8. G. G. Kuehl, L. W. Bain, Jr., M. J. Reisinger, "The GIFT Code User Manual; Volume II, The Output Options (U)," USA ARRADCOM Report No. 02189, Sep. 79, AD# A078364.

33

9. F. T. Bro~ D. C. Bely, and D. A. Ringer% The Simple Lethality and Vulnerability

10.

11.

12.

13.

14.

15.

Estimator (SLAVE): User’s Manual,” BRL Technical Report ‘ARBRL-TR42282(AD# B055277), January 1981.

D. A. Ringers and F. T. Brom “SLAVE (Simple Lethality and Vulnerability Estima-tor) Analyst’s Guide,” Technical Report ARBRL-TR-02333 (AD#B059679L) June1981.

Ref. 1 and A. Ozolins and D. A. Ringers “ISLAVE Interactive Simple Lethality andVulnerability Estimator,” pp. 91-99.

W. A. Rhode% “Development of a Code System for Determining Radiation Protec-tion of Armored Vehicles (The VCS Code),” ORNL-TM-4664, Oak Ridge NationalLaboratory, Oak Ridge, TN, October 1974.

W. A. Rhodes ~., “vehicle Cde System (VCS) User’s Manual,” 0RNL-TM-4648,Oak Ridge National Laboratory, Oak Ridge, TN, August 1974.

See for example G. A. Bias% ‘Theoretical Physic%” Appleton~ntury-Crof@ NY(1962), PP. 102 R. BY these tihniq~s mlculatiom of the principal second momentsand cross products of inertia can also be made. Often these mechanical designparameters have been unavailable to the (traditional engineer due to the computa-tional overhead.

J. R. Rapp, “A Computer Model for Estimating Infrared Sensor Response to Targetand Background Thermal Emission Signatures,W BRL Memorandum ReportARBRL-MR413292, August 1983 (AD B0769TGLJ.

J. R. Rapp, “A Computer Model for Predicting Infrared Emission Signatures of AnM60A1 Tank,” BRL Report No. 1916, AD#BOl 341 IL, August 1976.

34

9. F. T. Bro~ D. C. Bely, and D. A. Ringers, "The Simple Lethality and Vulnerability Estimator (SLAVE): User's Manual," BRL Technical Report ARBRL-TR-02282 (AD# 0(55277), January 1981.

D. A. Ringers and F. T. Brown, "SLAVE (Simple Lethality and VulnerabilitY &tima­tor) Analyst's Guide," Technical Report ARBRL-TR-02333 (AD# B059679L) June 1981.

10. Ref. 1 and A. Ozolins and D. A. Ringers, "ISLA VE: Interactive Simple Lethality and Vulnerability &timator," pp. 91-99.

11. W. A. Rhodes, "Development of a Code System for Determining Radiation Protec­tion of Armored Vehicles (The VCS Code)," ORNL-TM-4664, Oak Ridge National Laboratory, Oak Ridge, TN, October 1974.

12. W. A. Rhodes et al., "Vehicle Code System (VCS) User's Manual," ORNL-TM-4648, Oak Ridge National Laboratory, Oak Ridge, TN, August 1974.

13. See for example G. A. Blass, 'Theoretical Physics," Appleton-Century-Crofts, NY (1962), pp. 102 if. By these techniques calculations of the principal second moments and cross products of inertia can also be made. Often these mechanical design parameters have been unavailable to the traditional engineer due to the computa­tional overhead.

14. J. R. Rapp, "A Computer Model for &timating Infrared Sensor Response to Target and Background Thermal Emission Signatures," BRL Memorandum Report ARBRL-MR-03292, August 1983 (AD B076976L).

15. J. R. Rapp, "A Computer Model for Predicting Infrared Emission Signatures of An M60Al Tank," BRL Report No. 1916, AD#BOI3411L, August 1976.

34

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