Studies in Radar Cross- Sections - XVIII Airborne Passive Measures and Countermeasures (Offense with, and Defense Against, Bomber Decoys (S)) by K. M. Siegel, M. L. Barasch, J. W. Crispin, R. F. Goodrich, A. H. Halpin, A. L. Maffett, W. C. Orthwein, C. E. Schensted, and C. J. Titus. Contract AF 33 (616)- 2531 December 1955 2260-29-F 2260-29-F - RL-2047 The University of Michigan Engineering Research Institute Willow Run Laboratories Willow Run Airport Ypsilanti, Michigan This document contains information affec g thejtonbl defense of the United States within the meaning of the Espionage Laws, (Title YB S. C., Sections 793 and 794). Its transmission or the revelation of its contents in any m o an unauthorized person is prohibited by law.

CONIFI DE1NIT /AL UNIVERS ITY OF MICHIGAN 2260-29-F STUDIES IN RADAR CROSS-SECTIONS I Scattering by a Prolate Spheroid, F.V. Schultz (UMM-42, March 1950), W(038)-ac-14222. UNCLASSIFIED II The Zeros of the Associated Legendre Functions Pnm(t') of Non-Integral Degree, K. M. Siegel, D.M. Brown, H.E. Hunter, H.A. Alperin, and C.W. Quillen (UMM-82, April 1951), W-33(038)-ac-14222. UNCLASSIFIED III Scattering by a Cone, K. M. Siegel and H.A. Alperin (UMM-87, January 1952), AF 30(602)-9. UNCLASSIFIED IV Comparison Between Theory and Experiment of the Cross-Section of a Cone, K. M. Siegel, H.A. Alperin, J.W. Crispin, H.E. Hunter, R.E. Kleinman, W.C. Orthwein, and C.E. Schensted (UMM-92, February 1953), AF 30(602)-9. UNCLASSIFIED V An Examination of Bistatic Early Warning Radars, K. M. Siegel (UMM-98, August 1952), W-33(038)-ac-14222. SECRET VI Cross-Sections of Corner Reflectors and Other Multiple Scatterers at Microwave Frequencies, R.R. Bonkowski, C.R. Lubitz, and C.E. Schensted (UMM-106, October 1953), AF 30(602)-9. SECRET (UNCLASSIFIED when Appendix is removed) VII Summary of Radar Cross-Section Studies Under Project Wizard, K.M. Siegel, J. W. Crispin, and R.E. Kleinman (UMM-108, November 1952), W-33(038)-ac-14222. SECRET VIII Theoretical Cross-Sections as a Function of Separation Angle Between Transmitter and Receiver at Small Wavelengths, K. M. Siegel, H. A. Alperin, R. R. Bonkowski, J. W. Crispin, A.L. Maffett, C.E. Schensted, and I.V. Schensted (UMM-115, October 1953), W-33(038)-ac-14222. UNCLASSIFIED IX Electromagnetic Scattering by an Oblate Spheroid, L. M. Rauch (UMM-116, October 1953), AF 30(602)-9. UNCLASSIFIED X The Radar Cross-Section of a Sphere, H. Weil (2144-6-T, to be published), DA 36(039)SC-52654. UNCLASSIFIED XI The Numerical Determination of the Radar Cross-Section of a Prolate Spheroid, K. M. Siegel, B.H. Gere, I. Marx, and F.B. Sleator (UMM-126, December 1953), AF 30(603)-9. UNCLASSIFIED XII Summary of Radar Cross-Section Studies Under Project MIRO, K. M. Siegel, M.E. Anderson, R.R. Bonkowski, and W.C. Orthwein (UMM-127, December 1953), AF 30(602)-9. SECRET XIII Description of a Dynamic Measurement Program, K. M. Siegel and J. M. Wolf (UMM-128, May 1954) W-33(038)-ac-14222. CONFIDENTIAL XIV Radar Cross-Section of a Ballistic Missile, K. M. Siegel, M. L. Barasch, J. W. Crispin, I. V. Schensted, W. C. Orthwein, and H. Weil (UMM-134, September 1954), W-33(038)-ac-14222. SECRET XV Radar Cross-Sections of B-47 and B-52 Aircraft, C.E. Schensted, J. W. Crispin, and K. M. Siegel (2260-1-T, August 1954), AF 33(616)-2531. CONFIDENTIAL XVI Microwave Reflection Characteristics of Buildings, H. Weil, R.R. Bonkowski, T.A. Kaplan, and M. Leichter (2255-12-T, May 1955), AF 30(602)-1070. SECRET XVII Complete Scattering Matrices and Circular Polarization Cross-Sections for the B-47 Aircraft at S-Band, A. L. Maffett, M. L. Barasch, W. E. Burdick, R. F. Goodrich, W.C. Orthwein, C.E. Schensted, and K. M. Siegel (2260-6-T, June 1955),AF 33(616)-2531. CONFIDENTIAL XVIII Airborne Passive Measures and Countermeasures (Offense with, and Defense Against, Bomber Decoys (s)), K.M. Siegel, M.L. Barasch, J.W. Crispin, R. F. Goodrich, A. H. Halpin, A.L. Maffett, W.C. Orthwein, C.E. Schensted, and C.J. Titus (2260-29-F, December 1955). AF 33 (616)-2531. SECRET -E E culnlF lnlrl/

UNIVERSITY OF MICHIGAN 2260-29-F PREFACE In the series of Studies in Radar Cross-Sections, this paper, Studies XVIII, is the first report which is a final report for the contract under which it was written. As a result its style and approach are different from the rest of the series. It contains many analyses which are incomplete-such being the intent of both the United States Air Force and The University of Michigan. This situation, and indeed the very nature of any report dealing with the employment of bomber decoys (because they are not operational today), has fostered the inclusion of discussions which are both philosophical and factual. However, considerable care has been taken by the authors to document statements of fact with figures, appendices, and references to other existent work. It is intended, therefore, that this paper should serve as a summary of our thinking as well as an introduction for future investigations by others relative to the decoy problem. This paper is the eighteenth in a series of reports growing out of Studies in Radar Cross-Sections at the Engineering Research Institute of The University of Michigan. The primary aims of this program are: 1. To show that radar cross-sections can be determined analytically. 2. To elaborate means for computing cross-sections of objects of military interest. 3. To demonstrate that these theoretical cross-sections are in agreement with experimentally determined values. Intermediate objectives are: 1. To compute the exact theoretical cross-sections of various simple bodies by solution of the appropriate boundaryvalue problems arising from Maxwell's equations. _ _- ___ _ SW[l

r r LC_ UN I VER SITY OF 2260-29-F MICHIGAN __ 2. To examine the various approximations possible in this problem and determine the limits of their validity and utility. 3. To find means of combining the simple body solutions in order to determine the cross-sections of composite bodies. 4. To tabulate various formulas and functions necessary to enable such computations to be done quickly for arbitrary objects. 5. To collect, summarize, and evaluate existing experimental data. Titles of the papers already published or presently in process of publication are listed on the back of the title page. K. M. Siegel ii -

r= Lr- r-__ UN I VERSITY OF MI C 2260-29-F TABLE OF CONTENTS H 1 G A N __ Section Title Page i Preface List of Figures vi ix List of Tables I Introduction and Summary II Offense with Decoys 2. 1 Offensive Decoys for B-36, B-47, and B-52 2.2 Chaff III Defense Against Decoys 3. 1 The Circular Polarization Method 3. 2 Bistatic Radar Method 3. 3 The Frequency Comparison Method 3.4 The Broadside Discrimination Method 3. 5 Scintillation and Glint Method 3.6 Conclusions IV Countermeasures to the Enemy's Defense 4. 1 Circular Polarization Method 4.2 Bistatic Radar Cross-Section Method 4. 3 The Frequency Comparator Method 4. 3. 1 Use of Corner Reflectors with Curved Faces to Obtain Frequency Independent Cross -Section 4.4 Conclusions V Conclusion Appendix A Monostatic Radar Cross-Sections for the B-36 and the Duck Vehicle A. 1 Duck A. 2 B-36 Radar Cross-Section Computation A. 3 Experimental Data A. 4 New Arrangement of Nose Reflectors for Duck 1 4 4 12 15 15 18 20 20 20 23 25 25 25 26 27 30 33 34 34 40 45 45 iii. XC-l

UNIVERSITY OF MICHIGAN 2260-29-F TABLE OF CONTENTS (Continued) Appendix Title Page B Evans Signal Laboratories Experimental Data on the Radar Cross-Section of the B-47 Aircraft 51 C Experimental Scattering Data Obtained by Microwave Radiation Company, Inc. 59 D Monostatic Radar Cross-Section of Elliptical Corner Reflector 72 D. 1 Introduction 72 D. 2 Projection of the Equivalent Aperture 72 D. 3 The Intersections, Semi-axes, and Orientations of the Curves 75 D.4 Discussion of Results 81 E Graphical Techniques for Radar Cross-Sections 103 E. 1 Stereographic Projection 103 E. 2 Application to Change of Coordinates 104 E. 3 Application to Polarization-Independent Cross-Sections 105 E.4 Graphical Transformation of Coordinates 106 F Effect of Fuel on the Radar Cross-Section of Corner Reflectors 113 F. 1 Radar Cross-Section of Fuel-Filled Circular Corner Reflector 113 F. 2 Comparison of Results with Experiment 116 F. 3 Resume of Experimental Results (obtained at Microwave Radiation Company, Inc.), for Radar Cross-Section of Corner Reflectors as a Function of Fuel Level 119 G Circular Polarization Analysis for a Square Corner Reflector 123 H Bistatic Radar Cross-Section of the B-47 Aircraft at S-band 134 I iv ~5, = - - 1r

r - i 7r UNIVERSITY OF MI CHIGAN 2260-29-F TABLE OF CONTENTS (Concluded) Appendix Title Page I Corner Reflector Experiments at the Ohio State University References Distribution 158 164 169 II v rr 7 F-\ r- -

U N I VE R S I TY OF MICHIGAN 2260-29-F LIST OF FIGURES Number Title Page 1 Cross-Section Curve of Composite B-47, B-52 As Compared with Cross-Section Curve of Typical Decoy for Zero-Degree Elevation at S-Band 5 2a Cross-Section of Duck As Compared with Theoretical and Experimental Cross-Section of B-36 6 2b Suggested New Arrangement for Nose Reflectors in Duck 7 3 Cross-Section of the B-47 Aircraft at ZeroDegree Elevation 10 4 Cross-Sections of the F-86 Aircraft 14 5 Forward Scatter and Back Scatter from F-84F Airplane 19 6 Bispherical Reflector 29 7 Bispherical Reflector 29 8 Spherical Cap 29 9 Cross-Sections for a Sphere of Radius a and for a Disk of Radius a (at normal incidence) 31 A-1 Elliptic Cone Geometry 41 A-2 Suggested New Arrangement for Nose Reflector in Duck 47 A-3 An Alternative Reflector Arrangement 50 B-l Coordinate System for Airplane Reflection Coefficient Patterns (as used by the Evans Signal Laboratory) 52 vi I 11 ~-ii77

U N I VE RS ITY OF MI CH I GAN 2260-29-F LIST OF FIGURES (Continued) Number Title Page B-2a Cross-Section of the B-47 Aircraft at 150 Mc 53-58 through B-2f C-1 Elliptic Cylinder No. 10 64 C-2 Elliptic Cylinder No. 9 65 C-3 Polar Plot of Cross-Section of Perpendicular Flat Plates 68 C-4 Polar Plot of Cross-Section of Perpendicular Flat Plates 69 C-5 Experimental Arrangement 71 D. 2-1 Orientation of Corner Reflector 73 D. 3-1 Six-Sided Area for L< M + N 78 D. 3-2 Four-Sided Area for L>M + N 79 D.4-1 A, for Unit Edge Circular Corner Reflector 83-102 through D. 4-20 E.4-1 Stereographic Projection of Sphere 109 E.4-2 Stereographic Projection of Rotated Sphere 110 E.4-3a Stereographic Projection of Unit Edge Circular Corner Reflector Whose Edges Lie Along Positive x-, Positive y-, and Negative z-axes 111 E. 4-3b Stereographic Projection of Corner Reflectors in Transformed Coordinate System 112 F-la Ray Paths Through a Spherical Lens 114 vii E-LF E-ir

r 1 ) UNIVERSITY OF M ICH IGAN 2260-29-F LIST OF FIGURES (Continued) Number Title Page F-lb Sectional View of Ray Paths Through a Spherical Lens 114 F-2a Radar Back-Scattering Cross-Section of XQ-4 and Reflector Assembly as a Function of Amount of F-2b JP-4 Fuel in Reflector Pod 121-122 G-1 Basic Coordinate System Used in Determining the Cross-Sections 127 G-2 Comparison of Cross-Section of the B-47 and through Square Corner Reflectors at S-Band 128-133 G-13 H-1 Coordinate System for the Ogive 135 H-2 Coordinate System for the B-47 Aircraft 137 H-3a Coordinate System for the Loop 142 H- 3b Definition of Parameters 146 H-4 Bistatic Radar Cross-Section for the B-47 Aircraft for 9T = 9R = 15~ 150 I-1 Double-Double Bounce Corner Used in Ohio State University Measurements 159 I-2 Reflection Patterns of "Double-Double Bounce" Corners (four-inch square aperture, horizontal polarization, measured at K-Band (X = 2 inch)) 160 I-3a Coverage Diagrams-Triangular Corner Reflector 163 I-3b Coordinate System for Coverage Diagrams 163 viii rrI \

cDFr) LE ir U N I VE R SIT Y OF MI C H I GAN 2260-29-F Number 1 A-1 D. 3-1 D. 3-2 D. 3-3 H-1 through H-7 LIST OF TABLES Title Contributors to the B-36 Cross-Section Comparative Cross-Section, Old and New Arrangements for Duck Nomenclature for Intersection Points Location of Intersection Points Ordering of Intersection Points Bistatic Cross-Section for the B-47 Aircraft Page 8 49 75 76 76 151-157 k ix l I r-\ ---

UNIVE R S I TY OF MICHIGAN 2260-29-F I INTRODUCTION AND SUMMARY On 1 May 1954 The University of Michigan commenced an investigation directed toward the determination of the proper electromagnetic characteristics of decoys. Bomber decoys are vehicles with performance similar to a bomber during one flight only; these vehicles are much smaller and cheaper than a bomber yet simulate the electromagnetic characteristics of a bomber to a probing search radar. The philosophy of the offense was that, when a main offensive thrust was being made at a given location, the need for the bombers and pilots in a diversionary raid at a different location should be eliminated if at all possible. In other words, it was highly desirable to save the lives and bombers lost from such diversionary efforts and simultaneously it was also desirable to increase the probability of success of the main mission. It was conceived by the Rand Corporation (Ref. 1) and others that if some of our large bombers could carry decoys, then this unnecessary loss of life and bombers from a diversionary raid could be avoided. It was also foreseen that since a bomber could carry many decoys, the probability of success of the prime effort could be increased. As a result the United States Air Force made an effort to have decoys designed so that they could be carried by a B-36 (the Duck vehicle) and a B-47 and B-52 (the Quail vehicle) and so that these decoys, since they are carried by the bomber, could be used against the local defense radars of the USSR. It was also foreseen that long-range decoys (the Goose vehicle) with the capability of fooling the enemy's long-range search radars should be based in the United States or in friendly bases. In our defensive picture, we can foresee that the Russians could use decoys similar to the Goose vehicles to fool our DEW Line and other radar fences in Canada,while vehicles similar to Quail and Duck vehicles could be designed to fool the local radar fences of the Air Defense Direction Centers and the Control Centers within the interior of the United States. 1 X Z77

U N I VE RS ITY OF M I CH I GAN 2260-29-F The role of The University of Michigan was to investigate the overall electromagnetic properties required for these vehicles and suggest passive means for obtaining these properties. The first input in such a study was a priority of the distribution of the Russian radar frequencies. The United States Air Force under this contract stated that the priorities in our investigation should be (1) S-band, 2600 - 3300 Mc, and (2) 65 - 300 Mc. I They suggested the third priority be L-band. Since it became desirable, and possible, to consider the problem for all frequencies higher than S-band, all at once, we concentrated on S-band and higher band radiations first. If time had permitted we would also have made a precise study of L-band, when we began concentrating on Goose. We agree with The Johns Hopkins University that for long range search radars affecting Goose, L-band is probably much more important than X-band. On the other hand for Quail it was felt that the third priority frequency for local Russian defense radars should be X-band. Since the effort on decoys for the B-36 had already started and since it was felt that the B-36 bomber should assume lower priority in the study than the B-47 and B-52, these latter two bombers were considered the prime ones upon which The University of Michigan should focus its attention. The first thing needed was the electromagnetic scattering properties of the B-47 and B-52 for monostatic linearly - polarized Russian radars at the above frequencies. This information was obtained and reported in one of our radar cross-section series (Ref. 2). We then focussed our attention on the design of corner reflectors and similar devices to go into the decoys. We found that it was quite easy to design decoys which had the reflection characteristics of the B-47 and B-52 at S-band (Sec. II). When we found that this design problem was an easy one, we questioned ourselves as to what 'For the reasons given in Section II passive devices like corner reflectors could not be used for this range. It was agreed almost at the start of the study that The Johns Hopkins University would be responsible for advising the USAF on active equipment for the 65 - 300 Mc range. 1 ~2_ ~7 ~

UNIVERS ITY OF MICHIGAN - 2260-29-F defenses we in the United States could and should use against similar devices. As a result, we designed possible defenses (Sec. III) against our offensive decoys. In Section IV, we make use of our study in a defense against decoys to again re-design the passive reflectors of the decoys, so that they will have a better chance to be interpreted as bombers by the Russian radars. Many aspects of the above study are of course not completed,but we do feel that the framework exists so that the Department of Defense should be able to make significant use of our investigations to design useful decoys on the one handand to have a practical defense against Russian decoys on the other hand. N Mm 3 I'-r=- I r F-\.

UNIVERSITY OF MICHIGAN 2260-29-F II OFFENSE WITH DECOYS 2. 1 OFFENSIVE DECOYS FOR A B-36, B-47, AND B-52 Initial investigations by others reveal that there are many types of vehicles that could fit into the B-47 and B-52 which could have the flight characteristics of a B-47 and B-52 for one flight of 200 mile range capability. The only questions to be asked in this section are associated with what are the best passive devices' to be put into decoys in order to fool Russian S-band monostatic linearly-polarized radars. It was foreseen at the start that decoys which work at S-band would probably work equally well or better at X-band against the above radars, and that passive devices would be of no use in decoys against radars in the 65 - 300 Mc ball park. In Figure 1, we present a decoy with appropriate corner reflectors such that the scattering pattern of the decoy simulates that of the B-47 at S-band, except primarily broadside, as shown. Considerable effort was made to design radar reflectors to be used by Convair on Duck. A quick and dirty tabulation of the B-36 crosssection obtained is given in Table 1. In Figure 2a, a comparison is made between the Duck cross-section and the B-36 cross-section. In order 'By a passive device is meant a device whose source of energy is furnished by the enemy, whose reflection characteristics are dependent upon the wavelength of the enemy's sources and the polarization of the enemy's sources and antennas, and whose reflection properties are dependent solely upon the characteristics of its geometry and conductivity. In other words we do not include devices such that the enemy's radiation is used to pulse our equipment which then uses its own source to blanket, either geographically or frequency-band-wise, the enemy's receiver or receivers. 4 I',-=i7K

- UNIVERSITY U N I VE RS ITY I OF M OF M I CH I GAN 2260- 29-F CO ILu LU a e) Y (IN DEGREES) FIG. 1 CROSS-SECTION CURVE OF COMPOSITE (db AVERAGE) B-47, B-52 AS COMPARED WITH CROSS-SECTION CURVE OF TYPICAL DECOY FOR 0~ ELEVATION AT S-BAND 5 - r-rv I, LrL z -\) \r \ 77

0 = 0~ C) b - I * a(JK) is defined in Section III -A Y IN DEGREES w te 1) IX 1* Y IN DEGREES GN 0 N) wO *o I 100 Y IN DEGREES FIG. 2a CROSS-SECTION OF DUCK AS COMPARED WITH THEORETICAL ANDEXPERIMENTAL CROSS-SECTION OF B-36

I_- r- r-. 77 UNIVERSITY OF MICHIGAN _____ 2260- 29-F FIG. 2b SUGGESTED NEW ARRANGEMENT FOR NOSE REFLECTORS IN DUCK (CF. FIG. A -2) 7 - r _r 1 L=^ U- I \v \ 77

I TABLE I [l#1 CONTRIBUTORS TO THE B-36 CROSS-SECTION (numbers in contributing parts columns are cross-sections in sq. meters; angle values are in degrees) Recip. Jet Jet Fuselage Vert. Hor. Pro- Prolate Tail Tail 3 Wing Engines Eng. Supp. Cylinder Tail Tail pellers Spheroid Cone Spheroid 0 0 1.75 - - - 21.2 Negl 0.0131 Negl 2.40 1.94 0 - - - 0 10 1.90 - - - 21.2.00704 Negl.0097 Negl 2.40 2.06 Negl - - - 0 30 3.67 Negl Negl.00011 Negl 965 Negl Negl 3.19 Negl - - - 0 60 400 Negl Negl.206 Negl.0131 Negl Negl 16. 1 Negl - - - 0 90 3720 105 m2 Negl Negl 1.35x105 0.0275 Negl Negl 53.0 - - - 90 0 0.184 Negl 83.6 695 5.0x104 2690m2 Negl Negl 53.0 0.54 0.63 90 10 0.289 Negl 83.6 695 5.0x104 Negl Negl Negl 53.0 0.76 0.63 90 30 2.14 Negl 83.6 695 5.0x104 Negl Negl Negl 53.0 1.81 0.63 90 60 33.8 Negl 83.6 695 5.0x104 Negl Negl Negl 53.0 11.4 0.63 120 0.000458 Negl Negl Negl Negl Negl Negl Negl Negl 0. 051 1.26 120 10.000519 Negl Negl Negl Negl Negl 0.00255 Negl Negl.00431 1.26 120 30.000996 Negl Negl Negl Negl Negl.00157 Negl Negl.0211 1.26 120 60.00736 0.0054 Negl Negl Negl Negl.00322 Negl Negl.0265 1.26 180 0 2160 Negl 21.2 Negl Negl.0256.0344 2.40 Negl Negl 1.26 180 10 2160 Negl 21.2 Negl 0.2742.0454 2.40 0 Negl 1.26 180 30 40 Negl Negl Negl 0.1239.0980 Negl 0.008 - - - 180 60 500 Negl Negl Negl 0.0009.155 Negl 0.0377 - - Z O-' C >. I r Hr 2Z y p Total 0 ' 0 25.55 0 10 25.57 0 30 971. 0 60 416. 1 0 90 1.388x105 90 '0 53521 90 10 53521 90 30 53521 90 60 53521 y p Total 120 0 1.31 120 10 1.30 120 30 1.28 120 60 1.29 180 0 2196 180 10 2196 180 30 40 180 60 500 I

U N IVERSITY OF M ICH IGAN 2260-29-F to illustrate the method used to compute the cross-section of Duck, we present in Appendix A the breakdown used for the Duck vehicle as originally designed and the associated computation. On the basis of this analysis a suggested new arrangement for the Duck corner reflectors is given (Fig. 2b) and in Figure 2a we also present the essential contributions of our suggested new arrangement. In Reference 2 we presented the cross-section of the B-47 and B-52. Since that investigation was completed, new experimental checks have been obtained and one of these is a comparison for low frequencies (Fig. 3). The total experimental data are presented in Appendix B. In Appendix C we present the experimental results obtained by a subcontract to the Microwave Radiation Company, Inc., on the parts of the B-47 needed for checks of theoretical work. Since the comparisons in Figures 1 and 2a are considered by us to be excellent when one considers the properties of present-day radars and their display systems, it was foreseen that most decoys to which a little thought has been given would be successful in fooling Russian S-band linearly-polarized monostatic radars. It was thus foreseen that a study should be started to determine what were the best means of defending against decoys. It also seemed reasonable to assume that the United States was doing the defending,so the outputs of our study can become the inputs of our United States Air Defense programs. In the course of our study on decoys, it became necessary to obtain the properties of elliptical and circular corner reflectors. In Appendix D we present the theoretical characteristics of elliptical and circular corner reflectors. In many of our investigations we have found that the work required to check the computations is of a greater order of magnitude than the work required to do the computations the first time. Thus, if we were going to save money and time, it became expedient to design a method of obtaining order-of-magnitude checks on computations involving corner reflectors. In Appendix E we present such a method. It was also foreseen that if fuel tanks could become efficient 9 C [I,- __r_

U N I VE RS ITY I - N IVE RS ITYI OF MICHIGAN OF M ICH IGAN I_____ 2260 -29- F 00 CO CO W. LI LU I) tA v Y (DEGREES) FIG. 3 CROSS-SECTIONS ( a(HH)) OF THE B-47 AIRCRAFT AT 0~ ELEVATION Theoretical: The University of Michigan Experimental: The Ohio State University & Evans Signal Laboratory 10 7K 10

UNIVE R S I TY OF MICHIGAN 2260-29-F reflectors, a good deal of space could be saved in the decoy. In Appendix F it is shown that this, in fact, is the case and a comparison between theoretical and experimental results for the fuel tank is discussed. Considerable work has been done both theoretically and experimentally on the bistatic cross-sections of corner reflectors and other multiple scatterers (Ref. 3). Theoretical and some experimental results of this kind of work are given in this reference. The Armed Forces have similarly carried through the analysis of corner reflectors, and military specifications now exist (Ref. 4). Considerable work has been done in the decoy area associated with making smaller aircraft look like larger aircraft. For example, attempts have been made to simulate B-17 characteristics by the mounting of corner reflectors on a F-4U. The results are quite good. However, the F-4U is too small an aircraft to do a really excellent job (Ref. 5). Reference 5 concerns considerable work and measurements on angular noise and it seems feasible, if one deemed it necessary, that angular noise could have been duplicated. Many means have been devised and investigated to make objects like decoys with no attempt to duplicate the flight characteristics of the aircraft. The best known of these is chaff (Sec. 2. 2). Other types of radar reflectors have been designed for similar purposes. For example, the United States Air Force let a contract to develop eight-pound, 10 -foot-diameter spherical reflectors to be attached to a balloon and borne aloft in a collapsed condition with the ability to automatically become corner reflectors after a certain amount of time had elapsed. Four hours was the time used in the study by the Fairchild Engine and Airplane Corporation (Ref. 6). The Air Defense Command has analyzed the offensive potentiality of electronic countermeasures carried by meteorological-type balloons borne by the wind into the radar net. Some thought has been given to offensive problems by the defense and some recommendations are given in Reference 7. The offensive problem has been analyzed and a discussion 11 C[ I[.,

- UNIVERS ITY OF MICHIGAN 2260-29-F has been made on using ground-launched balloon reflectors drifting east into enemy dominated areas for use as decoys against enemy tracking and gun laying radars. Preliminary thinking involves the location of 40 sites about 15 miles apart from southern England to northern Scotland and about 20 more sites in central western Norway. These sites, it is believed, could maintain 200 targets on most surveillance radars in the potentially enemy-dominated areas between 50 and 63 degrees north latitude (Ref. 8). 2.2 CHAFF John Hult of the Rand Corporation and others (Refs. 1 and 9) have suggested that an investigation should be made of the possibility of having the B-47 and the decoy both drop chaff. Assumed in the study is the fact that the cross-section of the chaff will dominate the return and as a result the two vehicles will look alike. Another idea involving chaff was the seeding or laying of chaff corridors which aircraft could fly through undetected. Many analyses have been made of chaff since and during World War II. However, there have been some recent studies which may have bearing upon the use of chaff in the bomberdecoy program. The tactical employment of chaff from 860 to 3000 Mc has been tested at Eglin Air Force Base (Ref. 10), especially towards obtaining optimum dispensing techniques. At Radiation, Incorporated (Ref. 11 ),echo amplitudes of chaff were analyzed for three different experimental chaff types. Recent theoretical investigations at The Johns Hopkins University (Ref. 12) indicate that the amount of chaff necessary to confuse the enemy is approximately equal to that necessary to hide both bomber and decoy (a lesser quantity obscures only the decoy). Their study yields numbers of units of chaff necessary to sow a trail 50 to 225 miles in length against radars of 1 to 10 pLsec pulse durations for aircraft with radar crosssection areas of 100 to 1200 square feet. In particular,for the B-47 their estimated sowing rate compares favorably with the 30 units per minute obtained in recent field tests at Eglin Air Force Base for a B-47 dropping chaff at the rate of 10 ft/min. Reference 12 also contains a 12 r ---ir7

U N I VERSITY OF M ICH IGAN 2260-29-F discussion of investigations of active equipment which would work in the 50 to 300 Mc frequency range. The second priority frequency range (Sec. I) can be covered with a pulse barrage simulator which would weigh about 100 pounds. This seems to be the most important device yet considered for the low frequency range. As this report was being written, information was received concerning a General Electric device to be used for the same range being built at Utica, New York. Considerable analysis would probably be required to decide what the right characteristics should be for either a barrage jammer or an amplifier with its own power supply which would respond only to the frequency that excited it. It is obvious that important future work in the offensive problem must take place in the low frequency range. Passive devices cannot be used in lower frequency ranges because it has been found that passive devices under consideration which would fit into small vehicles are usually highly wavelength dependent. In fact in most cases their cross-sections are proportional to 1/x2. We find that aircraft cross-sections are not significantly frequency dependent (see Figure 3 for the B-47 and Figure 4 for the F-86). As a result, since the cross-section of the corner reflector decreases with an increase in wavelength and since the bomber cross-section is a slowly varying function of wavelength above 75 Mc, it becomes clear that if we can obtain a good matching cross-section at high frequencies L- through X-band, this same collection of corner reflector-like devices will be of no use at much lower frequencies. In this neighborhood active devices must be used. Chu (Ref. 13) analyzed the question of when to use corner reflectors and when to use half-wave dipoles to simulate radar echoes for jamming. He found that at X = 10 cm, the corner reflector is best; at \ = 53 cm, half-wave dipoles are superior; and at 300 cm, half-wave dipoles are the only means to simulate echoes by passive devices. We find Chu's conclusions are equally valid today. 13 I r

FIF F 77 U N I VERSITY OF MICHIGAN 2260-29-F IUJ UJ O b ASPECT ANGLE FROM NOSE-ON (IN DEGREES) FIG. 4 CROSS-SECTION OF THE F-86 AIRCRAFT (Experimental - Horizontal Polarization) 14 I I II

UNIVERSITY OF MICHIGAN 2260-29-F III DEFENSE AGAINST DECOYS Five methods of defense against decoys have suggested themselves to us: A. The Circular Polarization Method B. The Bistatic Radar Method C. The Frequency Comparison Method D. The Broadside Discrimination Method E. The Scintillation and Glint Method Each one of these methods is worthy of a separate investigation in a separate report. However, since the amount of work we have done on each one of these methods is sufficient only to prove whether the method would or would not work (because this was the only type of effort justified in this regard under the present contract), we limit ourselves to approximate numbers and general discussions. 3.1 THE CIRCULAR POLARIZATION METHOD It was believed that major complex reflectors with wing-like structures might reflect as much energy in single and triple reflections as in even multiple reflections. Of course it was recognized that at some aspects, double reflections could dominate and at other aspects, single or triple reflections could dominate. Thus it was believed that if we took an average over a few seconds of time, equivalent in a typical case to an average over 100 - 20 in aspect, and if we transmitted rightcircularly-polarized energy and received with two receivers (one receiving energy polarized to the right, the other receiving energy polarized to the left), we would find the ratio of energy for aircraft from the two receivers would be between 1/2 and 2. Corner reflectors, on the other hand, have the property, even when edge effects and multiple reflection -15.. C C@X\ Fr

UNIVE RS ITY OF MICHIGAN 2260-29-F between edges and other corners and other gadgets in the decoy are included, that the reflection is either primarily odd or primarily even reflection at any particular aspect. After averaging over 100 - 200 in aspect we find that the energy ratio for decoys from the two receivers would be between 1/20 and 20. The instantaneous decoy returns would be at the extremities of this ratio (App. G), while it is expected that the aircraft instantaneous cross-sections would be near the middle of the range of ratios, with a slight preference towards single reflections. Thus it becomes obvious that we may use two receivers and one transmitter at one radar site to distinguish the difference between aircraft and corner reflector. It has been pointed out that if a corner reflector mounted on an aircraft is presented to a casual radar operator, this method of detection might be defeated. However, to an experienced operator, the tremendous increase in energy observed would clearly indicate that the cross-section was that of an aircraft plus a corner reflector. This is because, although the ratios might be in the wrong ball park, the level of energy in both receivers would be sufficiently high to guarantee the vehicle being seen as an aircraft. In order to prove these points, a study was made to determine the reflection characteristics of a B-47 at all polarizations for a monostatic probing radar at S-band (Ref. 14). In Reference 14 we discussed the experimental results of Raytheon, Hughes and others which showed that our theoretical conclusions are in the right ball park. We have determined in Appendix G the radar reflection properties of a corner reflector for circular polarization. This information, although not complete in the corner reflector case, does exhibit that the above method of detection of decoys will work. In our analysis on the cross-section of aircraft for different combinations of monostatic polarizations (Ref. 14) only experimental data of a confidential and unclassified nature were discussed. Of importance in cross-polarization radar problems is the considerable work of the British (Refs. 15 and 16) concerning the Lincoln, Wayfarer, and Canberra type aircraft. Some comparisons of results for these three aircraft (linear polarization results from Ref. 15 and circular polarization results 16 I,- r=-r

r I -J r L~. I \\ ) U N_ I V E R S I T Y OF MI CHI GAN A N 2260-29-F from Ref. 16) are made below with theoretical results obtained by us for the B-47 in Reference 14. For approximately nose-on incidence o- (HV) is down' from o- (HH) by 7.7 db 9.8 db 8.8 db from a- (VV) by 7.9 db 9.7 db 10.9 db 5 to 6 db for Lincoln, for Wayfarer, for Canberra, 5 to 6 db for B-47; r-(RR) is down from ar(LR) by 3.1 db 2.9 db 3 db for Lincoln, for Canberra, for B-47. For approximately broadside incidence o (HV) is down from C (HH) by 7.9 db 8. 1 db from C- (VV) by 9.9 db 7.0 db for Lincoln, for Wayfarer, 7 to 15 db 7 to 15 db for B-47; a (RR) is down from - (LR) by 2. 1 db 0 db for Lincoln, for B-47. 1The letters, H, V, R, L indicate horizontal, vertical, right circular, and left circular polarizations. In C (JK), J indicates transmitter polarization, K indicates receiver polarization. For the B-47, the numbers are obtained for an elevation of 40~. 17 F \ 77

UNIVERSITY OF MICHIGAN 2260-29-F 3.2 BISTATIC RADAR METHOD We are able in the case of decoys at S-band to duplicate the reflection characteristics of much larger vehicles by passive devices at most aspects. This is because of the nature of the passive device being used. That is, the aircraft was not designed to be an efficient scatterer in the direction from whence the incident radiation came. Since the passive device being used, namely a corner reflector, is an extremely efficient scatterer in the direction from whence the radiation came, we can use the high efficiency of a small device (corner reflector) to duplicate the inefficiency of a large device (bomber). If we use this very property of the corner reflector, that is its high efficiency to concentrate its energy in the forward quadrants, to detect it, we find that the method to be employed is to use bistatic radars. In other words, if a transmitter-receiver looks at a decoy and finds the energy primarily reflected in the forward quadrants, then the amount of energy which goes off into the backward quadrants is negligible. As a result, if we have a transmitter-receiver and a remote receiver, we would find the cross-section of the decoy to be very much larger in the transmitterreceiver site than in the remote receiver site for all aspects. However, for the bomber,the cross-section at the remote site compared with the cross-section at the transmitter-receiver site would for some aspects be larger, oth aspects equivalent, and still other aspects smaller. Thus a comparison of the energy at the two receivers would show, when corner reflectors had allowed the decoy to have a cross-section equivalent to the bomber cross-section at the transmitting site, that the ratio of the bomber cross-section to the corner reflector cross-section at the remote receiver site would be extremely high. A direct comparison over several degrees in aspect would always show whether the crosssection of the vehicle was coming primarily from corner reflectors or primarily from a bomber-like vehicle. Corner reflectors might be added to the aircraft to attempt to fool the casual observer, but again the level of energy in the remote receiver should clearly indicate that the vehicle is a bomber. In Appendix H the bistatic radar crosssections of a B-47 at S-band have been obtained. Since it has been found that the scattering from the edges of the corner reflector is negligible (Refs. 17 and 18), it is clear that the above method of 18 I r-E - ( M

UU N I V E R S I T Y r OF MI CH I GAN -1 2260-29-F detection of decoys will work. Similar analysis has been made for the bistatic cross-sections of an F-84 and the data is presented in the table of Figure 5. Forward Scatter and Back Scatter from a F-84F (Modified) Airplane1 20,000 feet 28,000 feet 36,000 feet Miles from Back Forward Back Forward Back Forward Base Line Scatter Scatter Scatter Scatter Scatter Scatter 1.9 10 7 12 14 0 17 3.8 6 3 5 -3 0 - 6 5.8 0 - 6 -3 1/2 noise -10 - 7 7.7 - 6 noise (-15) - 1 noise - 4 - 4 9.6 0 - 3 - 5 noise - 5 -10 11.5 - 9 noise - 9 - 8 -1 1/2 - 6 All values are in db. Reference level at 0 db is the back scatter from a 1 1/2" sphere, "noise" is in each case at least 15 db. True frequency is of the order of 330 Mc. Target ~ Transmitter Base Line Receiver 44 1 -411-.- 50 Mi.. FIGURE 5 'Personal correspondence, Nelson Logan, Air Force Cambridge Research Center. 19 BILZt -\< -

UNIVERSITY OF MICHIGAN_ 2260-29-F 3.3 THE FREQUENCY COMPARISON METHOD Since the cross-sections of bombers are slowly varying' functions of frequency in the high frequency range, and since corner reflectors vary rapidly (as 1/X2), two radars operating at a factor of 10 separation in frequency would obtain cross-sections differing by a factor of 100. As a result, a frequency comparison method, where the radars are close together and the antennas have overlapping patterns, should indicate the difference between decoys and bombers. The difficulty arising from this method is simply that this is the only method which requires two transmitters. It also requires a good deal more power than the other methods. 3.4 THE BROADSIDE DISCRIMINATION METHOD The Johns Hopkins University has recommended that the United States Air Force investigate the possibility of having a system which looks at the broadside returns of both bomber and decoy. The difficulty of matching large broadside radar cross-section returns with a small vehicle is obvious. However, the problem has been recently studied by The Johns Hopkins University (Ref. 12). They have been successful to the extent that, with a small increase in decoy diameter, the broadside bomber return (for X- and S-bands) can be simulated reasonably well by using a double corner (dihedral) reflector in a decoy. 3.5 SCINTILLATION AND GLINT METHOD The scintillation and glint method is based on the fact that there are other observables in the radar returns from a scatterer in flight which the aforementioned decoys have not been designed to duplicate. A method may be proposed which is based on rapid fluctuation in the echo of the 'By slowly varying is meant that the amplitude of the return signal, although it fluctuates rapidly with frequency, remains within a small variation in amplitude. In other words, with a particular aspect average the cross-section of a B-47 in the high frequency range is not expected to vary over 10 db. Despite the fact that it might fluctuate rapidly with frequency anywhere between these limits, we call radar cross-section a slowly varying function of frequency. 20. i

I UN I VE RUS ITY OF M I C H I GAN 2260-29-F aircraft which might be considerably different from the rapid fluctuation to be obtained from the decoy. For example, the return of a propeller-driven decoy would have frequencies (of the number of propeller blades times the number of engine revolutions per second divided by gear ratio between blades and engine) not present in a jet bomber return. If the bomber is propeller-driven and the decoy is not, the same conclusion exists. One of the difficulties in analyzing scintillation and glint effects for propeller-driven aircraft in the United States occurs in the fact that we use 60 cycle per second power sources in this country. Since the frequency in cycles per second is equal to the revolutions per second times the number of blades divided by the gear ratio from engine to propeller, we find that typical aircraft, i. e., the F -4U, the F -8U, the SNB, and the DC-3, would yield frequencies within one cycle of 60 cycles per second. Thus it is clear that if we are trying to detect propeller-driven aircraft we must think very carefully of the expected modulation frequency and choose the source accordingly. Examples of the above numbers for other propeller-driven aircraft are given in Reference 19. A great deal of work was done at the Radiation Laboratory of Massachusetts Institute of Technology (Ref. 20) on the detection of propeller modulation and the effect of trying to camouflage propeller modulation by adding layers of special material to the props. It was found that one could actually display prop modulations at ranges up to 2/3 of the normal tracking range of an aircraft. It is believed that the important conclusion reached as far as this study is concerned is that, in generalthe patterns of received echo intensity as a function of targetaircraft propeller-rotation angle are extremely complex. Again, however, the analyses of that reference show that it would be difficult to design a system which determined the difference between flying vehicles, i. e. difference between a B-36 and a decoyby angular or amplitude noise (scintillation and glint). This is especially true if we make attempts in the designing of the decoy to have motion in the decoy which is close in frequency to the modulation frequency of the propellers of the B-36. 2 1 L- i7K

U N I VE RS ITY OF M I CH I GAN_ 2260-29-F Since bombers are subject to vibration and strain, and since a decoy is a much smaller vehicle, there is a possibility that the low frequency vibration of the two vehicles might be quite different, expecially since the bomber is made of a metal and the decoy is probably made of a plastic material. If these vibrations result in perceptible changes in the frequency distribution of the returned echo, then again it would be possible to distinguish between the bomber and the decoy. Although the authors believe that there could easily be large differences between the two devices if acoustical means of detection are used, the authors do not feel this strongly about present day devices used to measure the frequency spectra of radar returns. Power spectra of aircraft in radar experiments (when the method of propulsion is the same) are so similar that it would at this time be difficult to design equipment to measure differences. The one third scale model of a V2 missile which was dropped from a B-29 at the Holloman Air Development Center showed a power spectrum not much different from those obtained from aircraft'. Since a larger difference is expected between a missile and an aircraft than between a decoy and an aircraft (because of the difference in wings), it is felt that this is a very difficult means of discrimination to instrument. The authors are thoroughly familiar with the tremendous differences in patterns obtained for the same aircraft and with the tremendous fluctuations present over relatively small changes in aspect. However, the experiments made on spheres indicate that the source of this fluctuation is often in the ground equipment itself and is more a property of the ground equipment than of the vehicle. Many measurements of the scintillation and glint of the target have been attempted. Despite our experiences concerning spheres we wish to point out some counter experiences of others, e. g., Hughes Aircraft Company, (Ref. 21). The results of scintillation measurements for a B-47 are given in this reference. Since the results the Hughes Aircraft Company obtained for scintillation noise from a corner reflector were 'The experiments and their results are described in Studies in Radar Cross-Sections XIII and XIV. (See list of Studies at front of this report.) 22 I i7K

UNIVERSITY OF MICHIGAN 2260-29-F found to be a negligible amount at all frequencies, it was concluded by Hughes that their experimental equipment was such that the noise obtained from the aircraft target was a function of the target only. Although we feel that the data obtained by Hughes on scintillation for a B-47 is not the type for which it would be easy to instrument a means of detection of aircraft versus decoys, we feel that the above reference is a significant starting point for future analyses. Analysis has been made of scintillation and glint of the B-47 aircraft as well as the effect of adding fuel additives to the exhaust of the B-47 so that this exhaust may serve as a radar countermeasure similar to chaff. The results of these type studies have been pretty much negative. An excellent source of the available information is Reference 22. The University of Texas under Air Force Contract AF 33(616)-2842 is doing some research on the characteristics of gases which cause reflections. They may be able some time in the future to develop gases which can be used for chaff (Ref. 23). Theoretical analyses have been made by the Rand Corporation (Ref. 24) for fluctuating targets and conclusions have been drawn from four cases. Two specific probability densities were assumed for each of the following: (1) pulse-to-pulse type fluctuations and (2) scan-toscan type fluctuations. Further analysis of experimental data should be made to investigate the physical meaning of the above models. However, preliminary results certainly show that the above models warrant further study. 3.6 CONCLUSIONS The conclusions reached here are that the circular polarization method, the bistatic radar method, and the frequency comparison method are worthy of further investigation. As pointed out in Section 3.4, extensive work on the broadside echo method has been done recently by The Johns Hopkins University. Their recommendations for handling this method appear in Reference 12. The difficulty with the scintillation I 23 XSC [C\

c=i UNIVE RS ITY OF MICHIGAN 2260-29-F and glint method is the lack of existing equipment to take care of spectral identification. Too much time and expense are required to design new equipment and too much time is required to operate present day equipment (Ref. 25) during a raid,even if the idea turned out to be feasible enough to warrant further work at the present time. The methods deemed worthy of further study have been investigated a little further in order to suggest methods of varying the offense to counter these expected possible defenses. These investigations are described in the next section. 24 7 r --- r — r11 j

U NI VE R S ITY OF MI CH I GAN 2260-29-F IV COUNTERMEASURES TO THE ENEMY'S DEFENSE 4.1 CIRCULAR POLARIZATION METHOD Since it has been found that,in decoys of feasible size, it is possible to place corner reflectors which will give echoes at most aspects of interest larger than those needed at the same aspect from the aircraft, two methods suggest themselves for countering the circular polarization detection scheme. The first is the use of 1/2 wavelength protuberances on one surface of the decoy corner reflector. This would allow for the scattering from one face to be almost randomly polarized and as a result it would reduce the return from the 95 percent - 5 percent energy ratio in the two receivers to possibly a 70 percent - 30 percent or a 60 percent - 40 percent relationship. A better scheme for doing this has been suggested by the Ohio State University (App. I). A study of the Poincare sphere indicates that a double layer of dielectric material can be placed over one of the faces of the corner reflector so that the ray picture remains unchanged but the polarization picture changes in such a way as to return to the 60 percent - 40 percent energy relationship. This method looks better than the protuberance one because it does not reduce the efficiency of the corner reflector. 4.2 BISTATIC RADAR CROSS-SECTION METHOD The bistatic radar cross-section method is the more difficult to counter; it requires the defense to have data processing equipment of sufficient magnitude in remote regions so that they can tie together the return from the receivers at the transmitter site to the returns at the remote receiver site. There is a possibility that the bistatic offensive situation could be improved and at the same time the circular polarization method countered. This would be possible if a face of the corner reflector, instead of having protuberances, were made from wire mesh with the spacings such as to change the polarization picture more towards the 60 percent - 40 percent ball park, yet at the same time 25 X~~eS[

---- UNIVERSITY OF MICHIGAN 2260-29-F improve the bistatic return. Possibly a loaded dielectric material could be used as the third face so that, by compromising slightly the efficiency of the corner reflector, the bistatic return could be improved. This is not as impossible as it might seem on first sight for the following reason. Since the decoy is smaller than the bomber, it intercepts less radiation and as a result scatters less energy. The bomber scatters this energy into all quadrants by the nature of its geometry. The requirement on the decoy is to scatter the energy in the downward quadrants and there is no necessity of any energy in the quadrants above the decoy. As a result, although it seems impossible to match the bistatic returns at all the lower aspects, it may be possible to scatter enough energy bistatically to confuse the enemy. Another possibility is the reflector shown in the sketch below. This reflector is a biconical reflector with added flat plates. An analysis has not been carried out, but it appears as if this reflector would concentrate the reflected energy in a fanshaped beam. A dielectric lens could be added for further control of the reflected energy. 4.3 THE FREQUENCY COMPARATOR METHOD The difficulty with the frequency comparator method is the need for two transmitters and receivers with frequency separation of the order of magnitude of at least 3 to 1. The enemy's distribution of radars 26 i (CWr_

UNIVE R S ITY OF M I CHIGAN2260-29-F suggests their use of S- and X-band as the two logical frequency bands in a frequency comparator mechanism (Sec. I). Since corner reflectors which easily match (except at broadside) the return of the B-47 can be used at S-band, it is clear that at X-band these corner reflectors will give radar cross-sections a factor of 10 larger than the bomber. It then seems possible to introduce holes in the corner reflector of circumference of 18 cm which have insulation material around the inner edge of the circular aperture and have a metallic material on the outer (back) edge of the circular aperture'. This then would allow for transmission of the X-band radiation through the aperture and at the same time would allow for reflection of the S-band radiation. In this way it is possible to make the returns to a monostatic radar equivalent at Sand X-band. Thus, as the quality and quantity of Russian radars are primarily in the S-, L-, and X-band range for those frequencies above 300 Me, it seems clear that this method might be successful in overcoming the frequency comparison method, might help in overcoming the circular polarization method, and would also help out in the bistatic X-band radar return. Another and probably better method to overcome the frequency comparison method is given in the next section. 4. 3.1 Use of Corner Reflectors With Curved Faces to Obtain Frequency Independent Cross-Section Let us suppose that we desire a scatterer with the following properties: 1. The scatterer is to be small enough to fit into a sphere of a given radius. 2. At some fixed frequency it is to have as large a monostatic cross-section as is feasible over a fairly large solid angle. 'This scheme would have been analyzed further if time had been available. 27 S[C=~lr

UNIVERSITY OF MICHIGAN 2260-29-F 3. At frequencies higher than that given in requirement 2, it is to have a reasonably constant cross-section. The first two requirements are well met by a corner reflector, but the third is not. In order to keep the cross-section from increasing rapidly at higher frequencies, we can curve the faces of the corner reflector. If the faces are made of pieces of a sphere, then, for very high frequencies, the cross-section approaches some constant multiplied by the square of the radius of the sphere. If this limiting crosssection is chosen to be about the same as the cross-section of the corner reflector with flat faces at the fixed frequency mentioned in the second requirement, then the cross-section will be relatively independent of frequency above this fixed frequency. Actually it is probably desirable to make the limiting cross-section somewhat larger than (say twice as large as) the corner reflector cross-section at the fixed frequency in order not to degrade the cross-section at the fixed frequency. No calculations have been made for the cross-section of the corner reflector with three curved faces. However, calculations have been made for some simpler but similar cases. For the bispherical reflector of Figure 6 where the faces meet at 90 degrees the crosssection in the plane perpendicular to the axis of rotation approaches ra 2/3, where a is the radius of the spheres, for high frequencies. For the bispherical reflector of Figure 7 where the faces meet at an angle of less than 90 degrees, the limiting cross-section is ra 2/4. If the faces were to meet at an angle greater than 90 degrees, then the limiting cross-section would be zero. From the slight difference between the cross-sections of the reflectors of Figure 6 and 7 we see that an error in the angle at which the faces meet is not as critical as it is for reflectors with plane faces. 1It is clear that if the decoy has a high enough cross-section at L-band, then everything said previously would hold for all higher frequencies than L-band. As a result, the following method might easily apply to Project Goose as well as Project Quail. 28 r- - r r

11 L-, Lr- I i r UNIVERSITY 2260 OF MICHIGAN FIG. 6 BISPHERICAL REFLECTOR FIG. 7 BISPHERICAL REFLECTOR An-D - - - r FIG. 8 SPHERICAL CAP 29 -- DI r L ---

UNIVE RS ITY OF MI CHIGAN__ 2260-29-F Numerical results are also available for the single scattering case. Figure 9 gives the cross-sections for a sphere of radius a and for a disk of radius a (at normal incidence). Also given are the high frequency limits as given by physical optics for the disk and by geometric optics for the sphere and a spherical cap (Fig. 8). It is reasonable to assume that the cross-section of a spherical cap with fairly large a/D would roughly follow the disk curve up to the geometric optics value, at which point the curve would level off. A similar conclusion would hold for the corner reflector with curved faces. The cross-section of the shape in Figure 6 was calculated using the method outlined in Section 3. 2 of Reference 3. For Figure 7 the results are given in Section 3. 2 of Reference 3. The disk cross - section of Figure 9 was taken from Reference 26. It should be noted that though we have been talking of spherical faces the corner could be constructed with either three cylindrical faces or with two cylindrical and one flat face provided the axes of the cylinders are not parallel. In fact, these latter arrangements might well be more efficient than spherical faces. An approach similar to that discussed above is considered in Reference 27. There the suggestion is to use deliberate errors in the angles at which the faces of the corners meet,instead of curved faces. With three equal errors they obtain a curve for the cross-section which rises to a maximum and then decreases to zero with increasing frequency, rather than leveling off at a limiting value as the curved face reflector does (see Fig. V-7 of Ref. 27). Also, the angles between the faces would be more critical in the deliberate error approach than in the curved face approach. On the other hand, the curved faces would be more difficult to fabricate than flat faces. 4.4 CONCLUSIONS If intelligence analysis concludes that the three major defensive methods are 4. 1, 4. Z, and 4.3 above, and if the conclusions bear out that 30 r- S r

Lr-.%., i 107 I I II 77 UNIVERS I TY OF MICHIGAN I. 2260 - 29- F 100 Ka FIG. 9 CROSS-SECTIONS FOR A SPHERE OF RADIUS a AND FOR A DISK OF RADIUS a (AT NORMAL INCIDENCE) 31. FrF I 1 I \ 77

L ~~~ — -- U NIVERSITY OF MICHIGAN. 2260-29-F the primary Russian radars are at S-band and the secondary high frequency (above 300 mc/s) radars are at X-band, then it seems that the offense may counter the circular polarization method and the frequency comparison method and improve its bistatic capability somewhat. Nevertheless, bistatic detection looks like the best method for the defense to use. This assumes they have sufficient data gathering and processing equipment at their disposal. 32 I r-tl

~E7LF~~i UNI VERSITY OF 2260-29-F MICHIGAN I v CONCLUSION This analysis shows that decoys can be made to duplicate the electromagnetic properties of B-47 and B-52 aircraft. This report further suggests to the Air Defense Command three methods which it is felt the United States should investigate to augment our defense against Russian decoys. This report further discusses means of countering Russian defenses specifically designed for decoy discrimination. In no way is the solution of the problem complete, but sufficient analysis has been made to permit those in charge of our offense and defense to make adequate decisions and to put into practice those requirements of this report deemed worth augmenting. 33 EX J F-\

. UNIVERSITY OF MIC HIGAN 2260-29-F APPENDIX A MONOSTATIC RADAR CROSS-SECTIONS FOR THE B-36 AND THE DUCK VEHICLE The monostatic radar cross-sections of the original Duck vehicle (Ref. 28) are presented in this appendix for the S-band wavelength X = 10 cm. These results have been extrapolated to X-band so that comparisons could be made with X-band B-36 data of the Hughes Aircraft Co. (Ref. 29) and the Naval Research Laboratory. The results of these comparisons are very unsatisfactory especially in the range of broadside azimuths. However, it must be pointed out that the experiments of the Hughes Aircraft Co. are not very reliable at X-band for the B-36 and can be shown to be inconsistent. (These inconsistencies, with the exception of one point, do not occur for the Hughes Aircraft Co. B-47 data. ) In addition, the Naval Research Laboratory (Ref. 30) experimental data for the B-36 are known to be very unreliable. We have, however, computed a few values of cross-section for the B-36 at a few aspects for comparison purposes with the Duck. The results verified our feeling that the comparison between the Duck and B-36 is not very good at certain frequency ranges and aspects. The Duck cross-section is definitely too small at azimuth angles of 90~ and 180~. In this light,a final section has been included in this appendix to indicate a possible nose corner reflector arrangement that would augment the cross-section of Duck. In the following we outline the computations which we did on Duck and on the B-36 and then present graphically the results of this computation. A. 1 DUCK For the Duck the cross-sections1 o-(HH) and -(VV) were computed 'The letters in parentheses refer respectively to the polarization of transmitted and received energy.,- 34 I [ Ir

, _U N I VE RS ITY OF M I CHI GAN — 2260-29-F for azimuths Y = 0~, 5~, 10~, 20~, 30~, 40~, 50~, 60~, 70~, 80~, 90~, 100~, 110~, 120~, 130~, 140~, 150~, 160~, 170~, 1800 and elevations 3 = - 4~, 0, 4~, 10~, 30~, 60~, 90~. We thus obtain cross-sections for a large range of aspects. Comparisons with rough theoretical computations for the B-36 have been made for the aspects V = 0, 90~, 120~, 180~ and 3 = 0~, 10~, 30~, 60~, 90~. Comparison with dynamic experimental data from the Naval Research Laboratory will be limited to elevations 3~0< 120 for azimuths Y = 0~, 5~, 10~, 900. For computational purposes, the Duck was approximated by the following simple contributing shapes: 1. Two circular corner reflectors in transparent housing were oriented as in the specificationsI. 2. The fuselage was considered to be a circular cylinder. 3. The wings were replaced by truncated elliptic cones, with a thin-wire trailing edge. 4. The top section of the vertical tail was considered an elliptic cylinder. It was faired into a rear wedge. The lower section of the vertical tail was simulated in the same manner. 5. The horizontal tail was considered an elliptic cone. 6. The fences were considered semi-circular flat plates. 7. The rear of the fuselage, with the -exhaust opening, was considered an annulus. The rear of the fuselage-cylinder was treated as a wire loop. For the autopilot, a rectangular parallelepiped was used. 'The front reflector consisted of eight corners oriented with one lobe pointing directly forward; the rear reflector consisted of four corners oriented so its reflection pattern to the rear was symmetric relative to the horizontal and vertical planes. - - 35 r- r-~ 7 7

U N I VE RS ITY OF M I CH I GAN __ 2260-29-F 8. The shell around the rocket motor was taken to be a truncated circular cone. The following approximations were employed: a. The circular cylinder was considered only at r = 90~. b. Flat plates were considered only at normal incidence. Their edges are in reality rounded, so that edge contributions were neglected. c. For wedges and elliptic cones, the contribution near normal was obtained until aspects were reached at which it became negligible. For off-normal, bodies of this type could be neglected. d. The effect of shadowing was determined from the plan views. This determination was necessarily crude. The list of cross-section expressions used in computation for the Duck are: I. The triple-reflection cross-section of the circular reflector was obtained from the relation 4w A2 0r = X2 where X is wavelength and A is given as a function of the direction cosines I, m, and n of the direction of incidence with the edges of the reflector, by Equations (D. 4-1) and (D. 4-2) in Appendix D. The values of A were obtained from Figure D. 4-1 in Appendix D. II. The circular cylinder which represents the central portion of the fuselage has a cross-section at normal incidence given by 2-rrL2 b r- = - X --- —- I, (C-C —

UN I VE RS ITY OF M I CH I GAN 2260-29-F where L is the length and b the radius of the cylinder. For peak widths, the sum of the two off-normal components becomes equal to a fraction p of the peak height for an angle 0, given by sin /L\ 2 = -x~8 -~ f cos 9 \ \2 where O is measured from the cylinder axis. It followed from this that the circular cylinder could be neglected for off-normal aspects. III. The wings were considered to be truncated elliptic cones except from the rear. For such a shape the cross-section at normal incidence is 8 w(2 - L1) tan4 a 9X a2 Icos01 3 where a is the half cone angle, n is a/b for the ellipse, and where the cone is truncated by the planes z = L1 and z = L2, z = 0 being its vertex. 0 is the angle between the direction of incidence and the z-axis. Off-normal, there are contributions for z = LI and z = L2 given by sin 0 2 - - cos 0 tan a x z _7 3 tana Vsin2 ~+,72 cos 2 X 8w1sin 0 /sin2&+i72 cos2~ sin 0 tan a /sin2+727cos2+?7 cos 0 Here the x-axis is the semi-major axis of the ellipse. < is the usual spherical coordinate. The horizontal tail was also considered an elliptic cone when viewed from below. -— 37 I, = ' r- F-\ r

- UN IVERS ITY OF MICH I GAN 2260-29-F IV. Wedges were used for the rear edges of the vertical and horizontal tails. Let the edge-length be L, the half-angle be a, and the z-axis be perpendicular to the edge, but in the plane which contains the edge and bisects the angle. For incidence in the normal plane, where 0 is the angle with the z-axis, 0< 0 < a, rL2 L2 2 irL2 L sin 2a C = --- for p) + -- - - --- --- - (7r-a)2 4 rrcos2(a - 0) cos2(a + 0) Here f(p) = 1 for polarization parallel to the edge of the wedge and = 0 for perpendicular polarization. For incidence in the normal plane, and for a <_ < Trr/2 - a, the cross-section is r L2 L2 = - f() + -- tan2 (a+ 0). (ir- a) 4'r The wedge contributions were not significant enough to necessitate employment of a peak-width formula for offnormal incidence. V. The top half of the vertical tail was taken to be an elliptic cylinder except from the rear. For such a body, of length L with semi-axis a, the cross-section at normal incidence is L 2 2 2 3/2 0' = --------— / X (a2 cos2 0 + b2 sin2 )3/2 ' where < is measured from the major axis. The cross-section of such a body was negligible, as expected, except near broadside. _________________________38 L -,

UNIVERSITY OF MICHIGAN 2260-29-F VI. The fences were represented by flat plates. The crosssection at normal incidence was,therefore, 4 A2 2 where A is the area of the plate. Since the edges of the fences are not too sharp, off-normal contributions were neglected. The battery and autopilot boxes have flat sides which were treated similarly as flat plates. Likewise, the corner reflectors presented flat plates at some aspects. VII. The rear edge of the cylindrical fuselage was taken as a wire loop, visible only directly tail-on. Its cross-section, which is small,is Co = nra2 (a is the cylinder radius). VIII. A small annulus is formed by the exhaust nozzle of the rear of the fuselage. Its flat-plate contribution at normal (tailon) incidence was computed as =r [r (R2 - R1 ) X2 where R1 and R2 are the inner and outer radii. It was found to be negligible. IX. Dihedral contributions were present at aspects for the corner reflectors for which one direction cosine vanishes. In this case, if m is intermediate in value of the three cosines the contribution is 4 rA2 cos 2 r x2 39 00,::T

FIr rarL-i UNIVER SITY OF 2260-29-F MICHIGAN __ where A is (ir/2)a2 m N, where N is the number of quadrants of the circle visible. Here a is the radius, and Y the angle between the polarization vector and the edge of the dihedral. X. The shell.housing the rocket motor was represented by a truncated circular cone. The formulas for this may be obtained by setting n = 1 in those for the truncated elliptic cone. A. 2 B-36 RADAR CROSS-SECTION COMPUTATION Rough computations of the monostatic radar cross-section of the B-36 bomber are herein presented for some aspects. The assumed configuration was that of the B-36H, gun turrets retracted. No account was taken of interior cross-sections of the objects visible to the radar through the transparent nose or through radome material. The formulas used were taken exclusively from References 2 and 31 and the configuration was simulated as follows: Fuselage- - - - - - - - - - Wing and Horizontal Tail - Vertical Tail - - - Reciprocating Engines - - (nacelles) Jet Engines (nacelles)- - - Vertical Jet Support- - - - Inclined Jet Support - - - - half of a prolate spheroid, a cylinder, and a truncated cone capped by a hemisphere - a truncated elliptic cone and a wedge - a cylinder, a flat plate, and a wedge - ogives faired into the "wing wedges" - two tori and a cylinder for each engine - an inclined cylinder and a wedge - a thin wire. 40 I I rrF mr r-_ I- A a 7r

Cha) r UNIVERSITY OF MICHIGAN I 2260 - 29-F I, Y / FIG. A-1 ELLIPTIC CONE GEOMETRY - 41 -H

I,I j I r — I= i U N I VE RS ITY OF M I CHI GAN 2260-29-F Throughout the above, the wedge contributions were modeled by a thin wire when the radar illumination was incident in or near the plane of the wedge. The prolate spheroid contribution was calculated from Formula A. 3-2 of Reference 2 by replacing 0 by Y and X by w/2 - p. At the broadside and vertical aspects the value used was one-half the value predicted by A. 3-2 (Ref. 2), i. e., TT b c2 of = -, (b2 sin2 y + c2 cos2 y )2 where b = 7. 0, c = 20, since the "stationary phase point" may be considered as "split" between the two halves of the prolate spheroid. Estimation of the cylinder contribution was obtained from the formula R sinO 21L o ro= e sin L- cos O 2 fr cos2 9 where R = 7 ft and L = 60 ft,which may be derived from Formula A. 1-11 of Reference 2. At broadside this gives 2 r R L2 At the vertical aspect, L was taken as 100 ft. Tail cone contributions were obtained from Formula A. 3-8 of Reference 2. X L tan a C = ~ ---- tan (e - a) 8 rr sin 0 1 42 L-LDF E\r

E_- 7 r — r- - U N I VE RS ITY OF 2260-29-F MICHIGAN I where L = 40 ft and a = 5. 5~. The geometry appears in Figure A-1. For aspects between broadside and tail-on the hemisphere contribution is given by Formula A. 3-3 of Reference 2 as C = Tra. For the B-36, it was assumed that a = 2 ft. Estimated cross-section for the truncated elliptic cone used to simulate the wing leading edge was obtained from A. 3-6 of Reference 2 using the following dimensions (in the terminology of Reference 2): L = 132 feet = a/b = 3. 67 a = semi-major axis b = semi-minor axis tan a = 5/33, and X L n 3tan a 8 s = 8 rrB sin O sin 0 1 2 F s - -cos 0 tan a B tan a + cos B sin 0 tan a + 7 cos 0 B2 = sin2 0 + r 2 cos2s, where 0 and < are again as defined in Figure A-1. The thin wire formula is Formula (5) of Reference 31 after averaging over all polarizations and defining L = 2 I. Since the precision of the calculations for our purposes need not be as great as for Reference 31, the objections to the thin wire formula are not serious, so that 43 - rr, ra~ 7r

E _- ' r- Lr- r- - UNIVERSITY OF MIC 2260-29-F Lsin 27rL cos O 6 rL2 sin2 0 - Cos 0 H I G A N ___ 1.78 a sin0 The dimensions used were L = 110 ft and a = 1/40 ft. the horizontal tail, L = 35 ft and a = 1/40 ft. In the case of The dominant contributions of the vertical tail were due to a cylinder 10 in. long corresponding to the essentially straight section of the leading edge, the trailing wedge 20 ft long and modeled by a wire 1/40 ft in radius and a flat plate 30 ft long and 1/2 ft wide. The flat plate contribution was assumed to be given by 4 rrA2 0 =2. 2 The jet engines were modeled by tori in the nose-on and tail-on regions and by a cylinder at broadside, for which R = 1. 2 ft and L = 6 ft. The torus cross-section is given by 8 rr3 ab2 0 = X where a = 0. 001 ft and b = 1 ft. The jet engine support and brace were found to have negligible cross-sections at the aspects herein considered. All of the above dimensions are approximate, so that while the computed cross-section is not exact, it is of the right order of magnitude. 44 r [C (CC [S -\

r 1 I1 UNI VERSITY OF M I CH I GAN 2260-29-F It was noted in the rough computations that for the B-36 a peak of = 2. 3 x 104 m2 from the leading edge of the wing occured for azimuth 15. 50 and elevation 0~. There was no matching peak for Duck since a peak of cr = 1. 5 m2 from the leading edge of the wing occured at azimuth 4~ and elevation 0~. A. 3 EXPERIMENTAL DATA The Naval Research Laboratory (NRL) S-band results shown in Figure 2a of the main text are taken from the data of the Naval Research Laboratory report previously referenced. Since this data covers only elevations from 3~ to 12~, a comparison is made only at the 10~ elevation for each azimuth except 30~. Due to the saturation effects (Ref. 30) this data is somewhat scattered and fragmentary. The medians were not measured directly but were determined from the measured 75th percentile and the characteristics of the distribution of amplitudes. No NRL values are shown in Figure 2. 2 for an azimuth of 300 because of the wide disagreement of experimental data in this region. A. 4 NEW ARRANGEMENT OF NOSE REFLECTORS FOR DUCK A possible new arrangement for the corner reflectors for Duck is as follows: In the nose of Duck place a circular corner reflector C of edge a = 18 in. with vertex abutting on battery installation 2-1/2 in. above longitudinal axis of Duck and with symmetry axis of C pointing forward at an elevation p = 10~. Let 1, j, k be unit vectors in the directions of the usual righthanded xyz-aircraft-coordinate system (x-axis forward out of the nose, z-axis upward). Take e1, e2, e3 to be a right-handed system describing the edges of C with ei in the vertical plane of symmetry of Duck. Put 1 45 I,- [ r

UNIVERSITY OF 2260-29-F LzIMICHrGAN MCHIGA NM I H IG A a = 10~ + cos -1 1= 64. 74~ y3 Then C AC AC Then e, are given in the i, j, k system by A C A A e = cos a i - sin a k, 1 AC 1 A A. A e3 = (sinai - j + cos a k). V2 3 n To the right and leftlof C place two circular corner reflectors, each of edge 14.4 in., with vertices coincident on the lC - axis 3. 6 in. from the vertex of C (Fig. A-2). AR AR AR Describe the right reflector R with the system e1,, e 3 and the left reflector L with the system 91L z2L, e3L. Then 1R = A1C L C 1 1 AR -A C AL 3C, e2 =e3 AR = C, AL Ce3 =-e2. and In the direction of the axis of symmetry of the forward-looking corner reflector C(0~ azimuth, 10~ elevation), 15.61 a4 (15.61)(18)4(2.54)4 aC = (10) (10=) \x2 (102) (104) = 68.2 m2 2 'Considered while facing C. 2This is -(HH) or o(VV). r(RR) = 27. 8 m2; o(HV) = 16. 55 m2 I 46 -I \\ L

I=1- r=-,) I I 77 UNIVERSITY OF MI CH IGAN 2260- 29- F x FIG. A-2 SUGGESTED NEW ARRANGEMENT FOR NOSE REFLECTORS IN DUCK 47. rWrCF <=- Ii-' -i

U N J VE RS ITY OF M I CH I GAN ___ 2260-29-F A A Broadside (direction of incidence r = j) a dihedral contribution is obtained from reflector R. The cross-section is a(mR)2 a4 - 1 m2 sinz 9 j2 R AR A AC A 1 where mR = e2R. r= - e3. -, R A R A el =e * k = - sin a, * = 90~; hence, o- = 11.25 sq. m For nose-on incidence (0~ azimuth, 0~ elevation), the crosssection is computed by 2 4Tr A here2 A =.202 sq. m and X =. 1 m; so that 'This is o-(HH) or o-(VV). o-(RR) = 27.8 sq. m; -r(HV) = 16.55 sq. m. 2The expression for A for a circular corner reflector of edge r with edges making direction cosines I, m, n with the direction of incidence is given by A 1 1-2 f2 -1 1-g m2 1 1-2 n2 1 - tan- 1 m tan + n tan - n for 2I < r2 4 12mn 4 2mn 42-mn A 21 2n -1 2 f r 1 A2 =m m ntan + n tan 2 for 1 2 > 1r -2 n2 1-2m2 2 For a more detailed discussion, see Appendix D...., 48 WC Ir

1= Lr- r U N I VE RS ITY 2260 - OF MICHIGAN 29-F o-= 51.3 sq. m. For 0~ azimuth, 30~ elevation, the cross-section has dropped off to a- = 21.6 sq. m. TABLE A-I COMPARATIVE CROSS-SECTION, OLD AND NEW ARRANGEMENTS FOR DUCK a- (new arrangement) o- (original arrangement) - - Y =, 3 = 10 Y = 90, P = 0 r = 0, p3 = 30 68. 2 sq. m 11.25 sq. m 21.6 sq. m 25. 9 sq. m 11.1 sq. m 94. 6 sq. m An alternative possibility might be to place a circular flat plate forward of the battery and auto-pilot with its normal having 0~ azimuth and 10~ elevation. Place another flat plate perpendicular to the first. This yields a cluster of four corner reflectors (Fig. A-3). The 0~ azimuth, 10~ elevation contribution would of course be from the circular flat plate and would be a- = 169 sq. m. The broadside contribution would be due to an almost semi-circular flat plate and would be a-. 50 sq. m. The situation here of course is that the desired large contribution is obtained in exactly two particular directions with rapid drop-offs near these directions. 49

c00~-r ----- UNIVE RS ITY 22 OF MICHIGAN 60 - 29- F Front View Side View FIG. A-3 AN ALTERNATIVE REFLECTOR ARRANGEMENT 50 W7 lr.

S) = 1n r - ___ \ Lr UNIVERSITY OF MICHIGAN 2260-29-F APPENDIX B EVANS SIGNAL LABORATORIES EXPERIMENTAL DATA ON THE RADAR CROSS-SECTION OF THE B-47 AIRCRAFT The Antenna and Microwave Circuitry Branch of the Evans Signal Laboratories conducted a series of radar back-scattering crosssection measurements from a model of the B-47. The measurements were performed at an actual frequency of 3000 Mc which corresponded to a "full-scale" frequency of 150 Mc. Figure B-i shows the coordinate system used in the measurements and gives meaning to the 0 and 0 which appear in later figures. Figures B-2a through f are graphs of cross-section o- vs. 0. 51

00 I 7r UNIVERSITY OF MICHIGAN 2260- 29-F FIG. B-1 COORDINATE SYSTEM FOR AIRPLANE REFLECTION COEFFICIENT PATTERNS (as used by the Evans Signal Laboratory) 52 - [- l, r -. r-l

I Ir r-! i r- - \ I UUNI VE RS ITY OF MICHIGAN 2260- 29-F I I I I I. I11. I i I I 8 ~ I I i i i -I V) I — LU.I OL L/) 6 4 2 Max. and Min. values over 5~ intervals; points are plotted at left ends of intervals. 102 8 6 4 c - - - [ --- - -. I - 8 - - L - | _.= 10 11 I I 4 t I V \ 21 I: U Ii III II 2 I& I i: '4U!II I [ 11 \ I I 1.0 -I I I I E I I I I II 0 40 80 120 160 200 240 280 320 360 0 (DEGREES) FIG. B-2a CROSS-SECTION OF THE B-47 AIRCRAFT AT 150 MC. - EVANS SIGNAL LABORATORY DATA (O = 90~; Ee) 53 - - r- 1 i F 77

WfcrF"r L: -In\<~ 77 UNIVERSITY OF M ICH IGAN _ 2260- 29-F Lu I — LU LU C (I) I b, 8 6 2 Max. and Min. values over 5~ intervals; points are plotted at left ends of intervals. 102 8 6 4 10, 4 1.0 4 -------- --- - ------------— /_ --- —--- V f g l I - 0 40 80 120 160 200 240 280 320 360 0 (DEGREES) FIG. B-2b CROSS-SECTION OF THE B-47 AIRCRAFT AT 150 MC. - EVANS SIGNAL LABORATORY DATA (0 = 0~; Eq) 54 --- II I I Ir! I lF\r Fr-i

C — r-. i 2 -- UNIVE RS ITY OF MICHIGAN N 2260 - 29- F I I I I U jr i i i a ^ I i i t I B. LUJ LUJ LUJ 0 Cn 102 I 4/ Max. and Min. values over 5~ intervals; points are plotted at left ends of intervals. II I ILI= I 1. II I 1 It 4,,,,, ~,,,,,,! 2 Ii 1I I T I I II 1 II III III\. - ~l I 1 N 1( 1.1 0 40 80 120 160 200 240 280 320 360 o (DEGREES) FIG. B-2c CROSS-SECTION OF THE B-47 AIRCRAFT AT 150 MC. - EVANS SIGNAL LABORATORY DATA ( = 0~; E ) 55 00, L- a i I., Ir

---- UN IVERSITY 2260 - I --- OF MICHIGAN OF M I C H I GAN so 29-F (n LU I — LU I LU a b 103 8 2 Max. and Min. values over 5~ intervals; points are plotted at left ends of intervals. 102 8 6.. / h! I 40 u8 120 160 200 240 280 320 360 0 (DEGREES) FIG. B-2d CROSS- SECTION OF THE B-47 AIRCRAFT AT 150 MC. - EVANS SIGNAL LABORATORY DATA ( =45~; E~) 56 -~ r 1r0 r Ir

I" r-, I I \ -H UNIVERSITY OF M ICH IGAN 2260- 29- F tt) uLI ILLU I b 8 6 4 2 Max. and Min. values over 5~ intervals; points are plotted at left ends of intervals. 102 I 8 6 -- 2 10 4 ' 1.08 on - 6 -/11 It!! U 4U oU IZU IOU 2UU 240 280 320 360 0 (DEGREES) -2e CROSS-SECTION OF THE B-47 AIRCRAFT 0O MC. - EVANS SIGNAL LABORATORY DATA ( =45~; EE) 57! I? f J i I r-\ - I

E_- I,r I 1 II \\ 77 U UNIVERSITY OF MICHIGAN 2260 - 29-F oI) JL:D UJ ul b I U'II L 6 4 2 Max. and Min. values over 5~ intervals; points are plotted at left ends of intervals. 102 8 6 4 2 10 6 4 29 __ _ _ __ _ _,L I 1,,/!) 'v/v V U 1.0 I - - \ V 4 0 40 80 120 160 200 240 280 320 360 0 (DEGREES) FIG. B-2f CROSS-SECTION OF THE B-47 AIRCRAFT AT 150 MC. - EVANS SIGNAL LABORATORY DATA (O = 900; E,) 58 -~ rr Lr~ lr\ 77

I U N I. V E R S I T Y 7 r OF MICHIGAN 2260-29 F APPENDIX C EXPERIMENTAL SCATTERING DATA OBTAINED BY MICROWAVE RADIATION COMPANY, INC. In order to set a foundation for the theoretical discussion of repolarization we have had performed a number of radar scattering experiments. Under subcontract to the Microwave Radiation Company, Inc., the back scattering cross-sections of various geometrical configurations were to be measured for a range of linear polarizations. The combinations are as follows: Transmit 1. vertical 2. horizontal 3. horizontal 4. horizontal 5. +45~ 6. +45~ 7. vertical Receive vertical horizontal +45 -450 -450 +450 +450 In addition, the back-scattering cross-sections were to be measured for various geometrical configurations when circular polarization combinations are used. The combinations are as follows: Transmit 1. right hand 2. right hand Receive right hand left hand 59 r ==-, 7 r- E r1. i

UNIVE R S ITY OF M I C H I GA N 2260-29-F The geometrical configurations to be measured are as follows: 1. Ten elliptic cylinders whose semi-major axes are equal and of 5 X magnitude and whose semi-minor axes are 0. 15 X, 0.30 X, 0.45k, 0.60k, 0.75k, 1.10k, 1.45k, 1.80k, 2.15k, and 2.5 \. The length of the elliptic cylinders is primarily determined by far zone considerations of phase front uniformity. It is assumed that an aspect ratio comparable to that of the B-47 or B-52 wing would be a reasonable value. The length, L, would then be approximately 30 k to 40 \. The cylinders are fitted with smooth end caps. 2. Three ogival cylinders whose semi-major axes are 5 X and whose semi-minor axes have the values 0.30 X, 0.45 X, and 1.0 \. The ogival cylinders are fitted with smooth end caps. 3. A wing and body scatterer simulated by a right circular cylinder fuselage and two sets of wings. The diameter of the right circular cylinder is 10 X. The first set of wings are elliptic cylinders of semi-minor axis 0.45 k. The second set are ogival cylinders of semi-minor axis 0.45 X. Both sets of wings are to be fitted in two positions, high wing and intermediate wing, and for two sweep-back angles of 30~ and 45~. 4. Two rectangular plates whose center lines are separated by a spacing "d" and which are inclined at an angle, 0, with respect to each other (used as a model for diffraction repolarization studies). The three values of d to be used are 10k, 15k, and 20 k, and 0 has values 0~, 15~, 30~, 450, 60~, 75~, and 90~. Measurements to be made on the configurations are as follows: 1. Elliptic Cylinder. The back-scattering cross-section is measured at intervals of 5~ from 0~ to 50~ and at intervals of 10~ from 50~ to 90 in the principal plane for each of the nine polarization combinations. The major axis defines the zero angle of incidence, and the plane of rotation is the plane transverse to the cylinder axis. 1 ----60__ _ SS7

UNIVERSITY OF MICHIGAN 2260-29-F 2. Ogival Cylinder. Measurements are made at the same points as for the elliptic cylinder. 3. Wing-body Assembly. Measurements are made to furnish the back-scattering cross-section of the right circular cylinder fuselage alone for the points specified by the conical cuts 0 = 30~, 45~, 70~, and 90~, where 0 is measured with respect to the vertical z-axis of the cylinder. The cylinder axis is aligned along the x-direction. Measurements are made at 10~ intervals in from 0~ to 90~. When 0 = 90~, the values of r are determined for which the back-scattering cross-section is 1/3 and 1/10 the peak value. The "fuselage" is fitted with "wings", and backscattering cross-section is determined for 0 = 700, 90~, 1100~, 135~, and 150~ in 100 steps for = 0 to 180. The measurements are repeated for the two wing positions. For the high and intermediate vertical positioning of the wings for both wing sets and both sweep-backs 0 = 70~, 90~, 110~, 135~, and 150~, and for each 0, 0 < s 180~ in steps of 10~. For the intermediate vertical positioning of the wings for both wing sets and both sweep-backs 0 = 30~, 45~, 70~, 90~, 110~, 135~, 150~, and for each 0,0 < 0 < 180~ in steps of 10~. A polar coordinate system is defined in which the polar angle a is measured from the x-axis and the azimuthal angle P is measured from the z-axis in the yz-plane. For both wing sets, vertical positioning, and both sweep-backs a = 900, 900 - 1/3, 90~ #1/10, and for each c,O00< ( < 180~ in steps of 10~. 4. Parallel Planes. Measurements are made at 15~ intervals from 0~ to 360~ for all values of spacing and plate angle for the nine polarization combinations. 5. Single Plane. Measurements are made at 15~ intervals from 0~ to 360~. At the completion date of the subcontract only the results for the elliptic and ogival cylinders and the flat plates had been received and these only for the polarization combinations: 61 I,- L i

UNIVERSITY OF MICHIGAN 2260-29-F Transmitted Received 1. vertical vertical 2. horizontal horizontal 3. +45O +450 4. +45~ -45~ 5. right hand left hand 6. right hand right hand. In order to interpret the scattering data from the various cylinders we consider the formulation of the back-scattering problem in terms of the scattering matrix (Ref. 14, Sec. II) notation. Since the backscattering properties of a given object are specified to within an arbitrary phase degeneracy by five independent cross-sections (Ref. 14, Sec. II), the six polarization experiments should specify the scattering matrix and in addition give a consistency check among the various quantities. In the notations of Reference 14,the S-matrix for a scatterer with cylindrical symmetry is of the form (S(hh) 0 S= (C-1) \0 S(vv)/ where the polarization directions are along the cylinder axis (S (hh))and perpendicular to the cylinder axis (S (vv)). The transformation to other polarization bases is of the form S' = Ut S V (C-2) where Ut is the transpose of U, U and V are unitary, V is the transformation from the hv system to the new incident system, and U is the transformation from the hv system to the new emergent system. From this we see that, for example, in the circular polarization basis where -" Ti c; 62 IErLDF~Elr

j I [C i UNIVERSITY OF MICHIGAN 2260-29-F (r 1 2 <(rl)-a(=r)~~ S1 +Sz (C-3) a(rr) =:(li)^-T S1 - S2 where we write Si = S (hh), S2 = S (vv). In an orthogonal linear basis inclined at an angle of 45~ with the hvbasis, U =V (1 1) o(++) = ( —)~- S +S (C-4) 1 2 o(+-) = o(-+)~4 S - 2 As we noted above the scattering matrix is specified by a knowledge of any five independent cross-sections a(hh), a(vv), a(re), a(rr), a(++), a (+-). Since these six were measured in the course of the experiments we can, in principle, specify the S-matrix as well as check the consistency of the results. In particular, if 4 is the phase difference between the horizontal and vertical fields, a(ri) = o(++) =- [a(hh) + a(vv)+2 (hh) o(vv) cosj], (C-5) o(rr) = a(+-) = a[(hh) + a (vv) -2 (hh) o(vv) cos ], etc. From the results it was hoped that an approach to the problem might be found in terms of a phenomenological theory. This theory would be expected to predict the repolarization effects or, what is the same thing in the S-matrix notation, the behavior of the phase difference 4 above as well as the magnitudes of say a(hh) and a(vv). However, the experimental results are inconsistent to such an extent (ranging upward to 30 db) that it must be concluded that to base any theory or even supposition of repolarization results on these experimental data would be untoward. 63 L- I, -X

5I1 db 20 Physical Optics 15 00' II 15 -^> -Derived from (hh), -(vv), llll- l -l nlUo \./ Ma / o 5 II 0 \ - ' \, ' i \ /,, \\ \ / ' Derived from a (hh), 7(vv), /% and r(++)..-" -5 ---- Derived from a (hh), 7(vv), and a (r]) --- Measured Value of a (+-). --- —-- Measured Value of a (rr) io I --- o 0\ I i til Cni O H P1 I 07, 4^ 0 Z (7 0 10 20 30 40 50 60 DEGREES FROM NOSE-ON FIG. C-1 ELLIPTIC CYLINDER NO. 10, b=2.5X 70 80 90

I I I 20 --- The derived value from a(hh), a(vv) and a(r.) becomes negative at angles < 45~ except for 35~ i r - Physical Optics I -I I I K '001 ** 15 Mn 1 i I I. IV db 7,- ' -M OO. / // -\ / \ \ / /. I;,7T i " I, ipP \ /,.. \ / ~ "_/ _ i_ \i___. W ON 10!r 0" Un 5 0 z >Z Ct 0 ^e ili Lzj 511 ^nf -j tt - Derived from a (hh), a (vv) and a(++) ---- Derived from a (hh), a (vv) and a(rP) V V V 60 0.0 '4 do- '. % U % 46 mo -0 I% I I 11 I I IL % % 10.-.- Measured Value of a(+-) --—.. Measured Value of a (rr) I -- _ -, 40 50 60 DEGREES FROM NOSE - ON 70 - 80 90 % g I-9 I I I %,,/- 9.8 FIG. C-2 ELLIPTIC CYLINDER NO. 9, b= 2.15X

UNI VE RS ITY OF MICHIGAN 2260-29-F An immediate check on the consistency is available from the comparison of the measured value of a(rl) vs. a(++) and a(rr) vs. a(+-). Since we found large discrepancies we considered the possibility that the errors might have arisen from the departures of the polarization sense from strict circularity in the measurements of a(rr) and a(rl). For this reason the measured values of a(+-) and a(rr) are compared with the corresponding values derived from a(hh), a(vv), and a(++) or a (r ). These four quantities should be identical. This follows from (C-5) on eliminating the angle: r(+-) = a(rr) =- -(a(hh) + a(vv)) - r(++) (C-6) =2 (o(hh) + a(vv)) - a(r). To illustrate that the departure from circularity is not the source of error, these four quantities will be shown graphically for the two best results, those for the elliptic cylinders of semi-minor axis 2. 5 X and 2. 15 X. The graphs of these four quantities appear in Figures C-1 and C-2. The various cross-sections are normalized by a factor proportional to the physical optics result and appear plotted against the angle of incidence as measured from the semi-major axis of the elliptic cylinders. The values used in Figures C-1 and C-2 are the average cross-sections as determined from the measured noise level under the assumption that the phase difference between the target return and all extraneous signals be random (Ref. 35, App. 2). The curves of Figure C-2 indicate a greater degree of consistency at the smaller angles, i.e., for aspects at which the return is smallest, since the radius of curvature at the specular reflection point is smaller for a smaller angle. For this reason the apparent consistency may be spurious since the background discrimination would of course be less at the smaller angles. In the flat plate experiments the radar cross-section was found to be very small except in the regions of specular reflection. Because of this we present the cases of largest return, namely, those in which the 66 C= - r

U N I VERS ITY OF M ICHIGAN 2260-29-F two flat plates are perpendicular and their centers separated by a distance of 10k. In particular, since the same symmetry obtains as for the cylinders, i.e., the vertical polarization direction lies along axes of the flat plates so that in the horizontal-vertical polarization basis the S-matrix is of the form S S (hh) 0 \ 0 ( S (vv) as in Equation (C-l) above, we can again make use of the relationships (C-6). However,in this case we exhibit the cross-sections a(r ) = o(++) = 2 (a(hh) + a(vv)) - o(rr) (C-7) -= (c(hh) + a(vv)) - o(+-) in Figure C-3, as well as the same set of cross-sections obtained for the cylinders in Figure C-4. We include both sets in this case to illustrate a point in the consistency test. We note that in the side-lobe regions, about 90~ 30~, -r(++) and a(rl ) are much smaller than a(hh) and a(vv). Hence, in the derived values of a(rr) or a(+-) there is actually no critical check on the consistency of either a(++) or a(rl ) since the process involves subtracting these small values from the average of a(hh) and a(vv). For this reason a more apt set to use in the consistency check is the set a(+-), a(rl). This does involve a subtraction of numbers of the same order of magnitude and hence a more critical measure of the consistency. Figures C-3 and C-4 indicate that the flat plate results are also inconsistent to a considerable degree. In fact, derived values of ((+-) and a (rr) are found to be negative in the angular range 0~ to 450, and those of a(rQ) are found to be negative over most of the range 00 to 1500. No 67 I [7

UN I VERSITY OF MICHIGAN P 2260- 29-F 60~ 70~ 80~ 90~ 100~ 1100 120~ 50~ 130~ 40~ 30~ 20~ 10~ 360~ 350~ 340~ 330~ 320~ 310~ 140~ 150~ 160~ 170~ 180~ 190~ 200~ 210~ 220~ 230~ 300~ 290~ 280~ 270~ 260~ 250~ 240~ FIG. C-3 POLAR PLOT OF CROSS-SECTION OF PERPENDICULAR FLAT PLATES 68 ~mll~mmlmlmll~mmmlI immmmmmlmm~m L-. 107 I 1 77

- I I k [C r` 77 ----- UNIVE RS ITY OF 2260- 29-F MICHIGAN G A N_ 600 700 80~ 90' 1000 110~ 120~ 500 130" 40' 30' 20" 100 0 350~ 340~ 330~ 3200 310" 140~ 150~ 160~ 170~ 180~ 1900 200~ 2100 220" 230' 300' 290' 280~ 2700 260" 250' 240' FIG. C-4 POLAR PLOT OF CROSS-SECTION OF PERPENDICULAR FLAT PLATES 69.,wmmm~ r F r -

00, 11 L- Lr - UNIVERSITY OF 2260-29-F MICHIGAN ____ __ experimental error analysis was available for the flat plate results at this writing. The experimental procedure used is similar to that described in Reference 35. The equipment there described, however, has been modified to obtain the various transmitter and receiver polarizations. A diagram of the experimental arrangement appears in Figure C-5. An analysis of the source of errors in terms of the experimental equipment lies beyond the scope of this report. In conclusion, we wish to emphasize the importance of such polarization experiments despite the present inconsistent results. For such relatively complex scatterers (complex in the sense that the exact theoretical solution of the scattering problem is extremely difficult) as elliptic cylinders, the available theoretical check on the experimental results is very crude. However, a polarization experiment in which enough independent cross-sections are measured so that the S-matrix is specified and, in addition, there is a consistency check, i.e., at least six independent cross-sections are known, will furnish an excellent measure of the validity of the experimental results. 70 -I

I I VERSITY OF 2260- 29- F MICI M I C H I U NI GA N I -- HJ I RCVR I RCVR V FIG. C-5a Tuners in FIG. C-5a Variable Polarization Angle Obtained by Rotation of Antenna Receiving Antenna Transmit Only FIG. C-5b -5 EXPERIMENTAL ARRANGEM 71 - [ C I I_ I.

UN I VE RS ITY OF M I CH I GAN 2260-29-F APPENDIX D MONOSTATIC RADAR CROSS-SECTION OF THE ELLIPTICAL CORNER REFLECTOR D. 1 INTRODUCTION As discussed in Reference 3 the monostatic radar cross-section of a corner reflector is given by 4Tr A2 f 2 v (D. 1-1) in which A is the area of the projection of an equivalent aperture on a plane normal to the direction of incidence. A convenient aperture, as described in Reference 3, may be constructed by cutting out of each of the four quadrants of each coordinate plane an aperture of the same shape as the leaf of the corner reflector associated with that plane. This A will be determined here for the elliptical corner reflector, a shape frequently employed in asymmetric and limited volumes; as a special case, the area A will also be given for the circular corner reflector. Only triply-reflected radiation will be considered. D. 2 PROJECTION OF THE EQUIVALENT APERTURE The area A will be a function of I /a, m/b, and n/c, where I, m, and n are the direction cosines of the line-of-sight with the three coordinate axes, and a, b, c the edge-lengths of the ellipses along these axes. Because of the symmetry of the optical model, it is necessary to consider only the range of parameters I/a > m/b > n/c, (D. 2 -1) where 1>., m, n > 0. (D. 2-2) The coordinate system may then be chosen in accordance with 72,I-rZ17

=r I I UNIVE R S I TY OF MICHIGAN 2260-29-F Equation (D. 2-1). Because of the invariance of the optical model under reflections in the coordinate planes, a right-handed system may always be chosen. Consider the corner reflector of Figure D. 2-1. z y x FIG. D.2 - 1 ORIENTATION OF CORNER REFLECTOR The equations of the three ellipses are x2/a2 + y2/b2 = 1 x2/a2 + z2/c2 = 1 (D. 2-3) y2/b2 + z2/c2 = 1 Project these curves onto the X-Y plane along the line-of-sight, or (I, m, n) direction. The equations of these projected curves are 73 mmmmmmmw

UNIVERSITY OF MICHIGAN 2260-29-F x2/a2 + y2/b2 = 1 ( 2 c2 + n2a2) 2 2/ 2 x - -xy + y2 a (D. 2-4) m 2 2 m c m2c2 + n2b2 2 2m y2 b2 x2 - xy + yZ = b. 2 2 I c The area commontothe three curves is to be determined, and then projected onto the plane normal to the line-of-sight. A is therefore the common area in the X-Y plane multiplied by n, the cosine of the angle between the normals to the two planes. The procedure is simplified by an additional projection which transforms the first ellipse into a circle. If b < a, the projection introduces the transformation x' = x cos = x, (D.2-5) a where P is the projecting angle. If b > a, use y' = ycosx = y. (D. 2-6) Either of these will lead to the same final result for A. The first is employed. Equation (D. 2-4) then becomes (dropping the primes on x and y) 2 + y2 = b 2 21 b y 2 x xyy b2 ma m2 2 a2 2 (D. 2 -7 (D. 2-7) 74 -^ W^I 1-* Ir-\ =^ 1

UN IVERSITY OF MICHIGAN 2260-29-F m2 a2 2 + n2 a2 b2 2 2ma 2 2 - x2 - xy + y2 = b2 2 b c2 i The area common to these three curves must be found, and multiplied by na/b to yield A. D. 3 THE INTERSECTIONS, SEMI-AXES, AND ORIENTATIONS OF THE CURVES Using the condensation symbols L =2 b2 c2 M = m2 a2 c2 N = n2 b.0.1 J (D. 3-1) Equations (D. 2-7) become (a) x2 + y2 = b2 (b) x2 -2 / xy LN y2 = b (D. 3-2) ( ) M+N _ =.2 (c) MN x 2 -2 xy + y2=b The intersection points of these three curves are displayed in Table D. 3-2, the key to which is Table D. 3-1. In each block, the upper intersection is encountered first in a counter-clockwise circuit. TABLE D. 3-1 NOMENCLATURE FOR INTERSECTION POINTS 1 2 3 1 2 3 P E B F C I D J G K H L mmld~ m 7 I I c~7 ==C: / - - 77

I,C —, r=ll r 7r U N I VE RS ITY OF MICHIGAN 2260-29-F TABLE D. 3-2 LOCATION OF INTERSECTION POINTS e =o Zt = 2 p=b p= b tan9 a= L-MLN tane = "M/L tan = L-(MN) LL-M+N 2 L 2b_2 (L+M)(L-M)2+2N(L-M)2+N2(L+M) (LM)+2N (L-+M)+N2 It follows from the inequality[Equation (D. 2-1 )]which may be written L>M>N (D. 3-3) that the intersection points are ordered in the following fashion: TABLE D. 3-3 ORDERING OF INTERSECTION POINTS Case 1 L<M +N Quadrant 1 2 3 4...... - Poir at: P G I C E K B p: b a >b b <b b la= H J b >b D F b b L <b 76... L-L t rz-\ 7r

I- n1 r I I \ r UN I VERSITY OF 2260-29-F MICH I GAN _ TABLE D. 3-3 (Continued) Case 2 L>M+ N Quadrant Point: P p: b K I b >Pk C b B b L J >b >PL D b F b H b The curves may, therefore, be drawn as shown in Figures D. 3-1 and D. 3-2. Now the area of a sector of an ellipse of semi-major axis r and semi-minor axis s between the angles a and 3 is given by Area = - arctan (- tan 0) ] 2 s (a (D. 3-4) The semi-axes and orientation of the semi-major axes in our coordinate system must therefore be obtained. For the circle, of course, r = s =b; (D. 3-5) for ellipse (b) of Equation (D. 3-2) r2 s2 2 b2 M L+N+M T (L+N-M)2 + 4LM (D. 3-6) for ellipse (c) 2 r s2 S 2 2b L L+N+M + /L-M-N)2 + 4ML (D. 3-7) The angle between the semi-major axes of ellipse (b) and the xaxis is the first quadrant root of 1 - 2 1 2 jML 02 = - tan L 2 L~N-M (D. 3-8) mwmftm II. 77 ^D j\ 1r

-S T EI -I SITY OF MICHIGAN U N I VE R 2260- 29- F.3-1 SIX-SIDED AREA FOR L < M + N 78 r i I I_ F E ir

L[-.L rD r UNIVERSITY OF MICH 2260 - 29- F IGAN 123.3-2 FOUR-SIDED AREA FOR L, 79 -I 1 C X - I \ L

C _- ' r - r UNIVERSITY OF 2260-29-F MICHIGAN The similar quantity for ellipse (c) is given by the first quadrant root of 1 -1 2 /ML 03 = - tan L-M-N 2 L -M-N (D. 3-9) The final expressions for A, the shaded areas in Figures D. 3-1 and D. 3-2,may also be given. They are, for L < M+N: A = nab (C-G) + nab arctan 2 /MN tan ' L+M+N - /(L-M+N) +4LM K-02 C-02 + nab /I arctan Y N 2 VLN tan 4 L+M+N - /(L-M-N) + 4LM H-03 K-03 (D. 3-10); for L > M+N: A = nab (C-P) +nab V/M/N arctan KM 2 MIN tan 4 L+M+N - /(L-M+N)2 + 4 LM (D. 3-11) When the values of P, B, C, G, H, and K from Tables D. 3-1 and D. 3-2 and the expressions for 02 and 03 from Equations (D. 3-8) and (D. 3-9) are utilized in Equations (D. 3-10) and (D. 3-11), these expressions for the common area become: L > M+N, A i tan-1 (2LN L>M+N, abc L+M-N + V-tan1 2 /LM L+N-M 1 (D. 3-12) - - - 80 I77 r - I I r -

LrL lr i UNIVERSITY 226 OF MICHIGAN ___ 0-29-F L < M+N, A = }/i tan-1 ((M+N)2_L2 4 L VMN + J/Mtan-1 (L+N)2 -M2 \4 M YL NV + -Rtan-1 L+M)2 -N2 4 N L~-M M/ (D. 3-13) We may simplify the form of these equations by making use of the symmetric functions S = 1 (L+M+N) T= LMN. Then we have L > M+Nj abc = VMtan-l ) abc \ S-/ + [/N tan -1(N (D. 3-14) L < M+N, c = vLtan 1 abc (S- L)) \VLT + /-M tan-l S(S-M) + J'N tan-1 S(S-NN) I / \JN ^ (D. 3-15) This form is the easiest for numerical computation. D. 4 DISCUSSION OF RESULTS It is to be noted that for the transition point L = M+N, G = P = 0 and E = B = H = Tr, so that Equations (D. 3-12) and (D. 3-13) become identical, as they should. Further, the transition point corresponds to that of - 2 = 1/2 for a circular reflector. For a circular corner reflector of edge length R, 81 iL- 3 rz-\ 7r

r r LI r UNIVERSITY OF MICHIGAN 2260-29-F Equations (D. 3-12) and (D. 3-13) reduce to 2 1 A -1 1, 2 = m tan " R2 2( +n -a1 2 m + n tan 2 4 m R -2 ( 4 _)m (12mn + m tan ( n 2 1 2 2 = tan-1 R (D. 4-1) (D. 4-2) -1 _ 1 -2n2 n tan - (4 1mn2) The values of A/R2 for a circular corner reflector of unit radius have been computed from Equations (D. 4-1) and D. 4-2). A is plotted as a function of m2 (or n2) for fixed values of - 2 from 0. 01 to 0. 99 in steps of 0. 01 (Figs. D.4-1 ff). Of course, -2, m2, and n2 = 1 - - 2 - m2 may be permuted in any convenient way in using these graphs. o is determined from the graphs as 4 TrA2 0r = X2 (D. 4-3).M 82 r I Z17 L — II\ L

,-j A 00 wJ ON 0 T1 0 -0 -z -Jo 0.01.02.03.04.05 m2 or n2 FIG. D.4- 1 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. M2or n2 FOR J2=.99(01).95

.20.16 0.01.02.03.04.05.06.07.08.09.10 vs. m2 or n2 FOR 2=95(.01)90 VS. M2 or n2 FOR A2 =.95(.01).90 d,-L] *-O cio r) o I 0 z >1 Z

.24 0 000.8.048 000 0.02.04.06.08.10.12.14.16.18.20 m 2or n2 FIG. D.4 - 3 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, z~ ILe] tFfllf P~N/I II 0 F 1 VS. m2 or n2 FOR ~I2=.90(.01).85

An nrl -Ji A.32__ _ _ _.04.16 _ _ _ _____ ___________ 0 T1 0 -0 z 5110 crx 0.02.04.06.0.10.12.14.16.18.20.22 m2 or n FIG. D.4 - 4 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. M2or n2 FOR R2=85(O01).80

L h1 Uil Un) -j A ha CN GO!Tr z 0-i ^ r) -i I m2 or n2 FIG. D.4 -5 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, vs. m2or n2 FOR ~2=.80(.01).75

.48 LiffE].40 tinrH.32 J A ~o.24 fl.16 ____74 71 ___ 2=.73 =.72 ].08 O ----— i --- —-i --- —i______iii _______ 0.04.08.12.16.20.24.28.32.36 m2 or n2 FIG. D.4-6 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, vs. m2 or n2 FOR 2=.75(.01).70 i-o OA O r 1 I j O" t ) I ^0

I "'Oo - z 14 Uirfl A.04.56.48.40.32.16 __ __ _ 08 ______.66 =.65 0 ___ _____ ________ 0* -00 ON 0 -J 0 z I 0.04.08.12.16.20.24.28.32.34 2or n2 FIG. D.4 - 7 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. M2or n2 FOR g2'=70(o01)65

-j A 0 T1 C) Cf, 0 *0 z -J m2 or n FIG. D.4 - 8 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. M2or n2 FOR 92 =.65(.O1).60

1.0 LiFH -0 A 0 T1 z~ H2~ 0 -0 -ji m2 or n FIG. D.4 - 9 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. M2or n2 FOR 92=60(01).55

1 I -J A.8 ___________________.6 \\\ 1.4 4 ~2 / l I I '. l l.54.53.5 2.51.50 n [ i ONi 0 CIA C m C/),-. 0 rtj rlrl -1 --j 0 5 10 15 20 25 30 35 40 45 m2 or n2 FIG. D.4-10 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, vs. m2 or n2 FOR (2 =.55(.01).50 50 n 0 z

.50 =t 49 9246 0.10.20.30.40.50 m 2or n2 FIG. D.4 -11 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. M2or n2 FOR j2=. 5O0(.01).45 z~ IL-1 0 -z

.6 _ 5I~~J.4__.2 ~~1 2=44 k2 =.42 ~2=A4 0.05.10.15.20.25.30.35.40.45.50.55.60 m 2or n FIG. D.4 -12 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, vs. m2or n2 FOR 92 =45(01).40 1Le1 *0 z — I'J.

I 77 UNIVERSITY OF MICHIGAN - 2260- 29- F 1. mlo I - i I I I \ A.00.90.80.70__.60.50.40.30.20 3 2=.39 2=.36 2 2 =.38 =.37___.10 0 - 0.10.20.30.40.50.60.70 m2 or n2 FIG. D.4 -13 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, vs. m2 or n2 FOR 2=.40(.01).35 I 95 III I,-r= Lr- ri

1.21 1 -J0 A 0 z~ 0 0 z -j0 I'D a, m2 or n2 FIG. D.4 -14 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. M2or n2 FOR ~2=.35(.01).30

nrl -jl A 0 T1 z~ 0 0 z LTh1 F1 iJ nrfl -j mor n FIG. D.4-15 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. M2or n2FOR,Q2=30(01).25

I,- 7 -1 I r UNIVE RS ITY OF MICHIGAN 2260- 29- F 1 A R2=.2O?2=.21.2.22 m2 or n2 FIG. D.4-16 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, vs. m2 or n2 FOR Q2 =.25(.01).20 98

L- r= \\ L UNIVERSITY 22 1.0.80 //.60 A / OF MICHIGAN!60 - 29 - F m2 or n2 FIG: D.4-17 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, vs. m2 or n2FOR 92.20(.01).15 99 I I E 1

lifT]-0 ci 41 0-4 m Pd Cl) ) —O -i 0 Tl A 0.0 OIN 0 ND L —Th10 U-irf 0 z m 2 or n2 FIG. D.4'-1 8 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, VS. m 2 or n2 FOR ~2 =.15 (.O 1).1O0

51 -j — I A.60 1.09 I.......10, w- - - -------—. ---------------- /..../.06.60 or - ol:~ I ~.20 / /// __z~zN S^ --- "N I //// -\[ - - - --- I 0 0 T1 z 0 0 zrl 0 ^,tl 4 r)z *-4 07 >P — i 'I 0.20.40.60.80 1.0 m2 or n2 FIG. D.4-19 A, FOR UNIT EDGE CIRCULAR CORNER REFLECTOR, vs. m2 or n2 FOR 2=.10 (.01).05

.200 _ i _= _ 2 22 mAr FIG D42 A FR UITEDE IRULR CRNR=EFECOR vs.~~m or n2FO 20(0)0 z~ -o?0 z I

-UNIVERSITY OF MICHIGAN 2260-29-F APPENDIX E GRAPHICAL TECHNIQUES FOR RADAR CROSS-SECTIONS To present the cross-sections of aircraft, or of corner reflectors in vehicles, in specified coordinate systems, it is advantageous to make use of certain graphical techniques stemming from stereographic projection methods. In the following sections the stereographic projection and the resulting graphical technique are discussed briefly with an application to triple reflections of a circular corner reflector oriented in a particular manner. E. 1 STEREOGRAPHIC PROJECTION Let S denote the sphere x +y + (z - 1/2)2 = 1/4. The stereographic projection onto the xy-plane is defined as follows: If (x, y, z) is a point on the sphere then the corresponding point (x', y') in the plane is given by - x (1-z) y= ( +y2 + (z - 1/2) = 1/4 The projection can be interpreted geometrically as follows: let N denote the point (0,0,1). Given any point p on S, except N, the projected point p' is the intersection of the line through N and p with the xy-plane. This projection has strong geometrical invariants; namely, it is a conformal mapping of the sphere into the plane and furthermore it projects circles on the sphere into circles or straight lines on the plane. - 103 I i~l

-UNIVE R S ITY OF M I CHIGANN 2260-29-F Introduce the complex variable z = x + iy. As is well known, the linear fractional transformations ct z + P3 w = Z +, a6 d - 3Y / 0 where a, y, y, 6 are complex numbers, give all conformal mappings of the complex plane onto itself which carry circles onto circles and which can be continuously deformed into the identity transformation. A sub-group of this group of transformations which is of primary interest here is w az + P aa + I3 = 1 (E. - 1) -3z + These transformations correspond, by the stereographic projection, in a 1-to-l way with the group of proper rotations on the sphere. These transformations, of course, carry circles into circles but also carry circles which correspond to great circles on the sphere into circles which also correspond to great circles on the sphere. E. 2 APPLICATION TO CHANGE OF COORDINATES The only changes of coordinates of concern here are those in which the new x', y', z' system is positively oriented,rectangular, and has the same origin as the old. Such a change of coordinates can be completely described by three points p, q, r on the sphere S. If the origin of the sphere is s the point p is chosen so that the direction s`p is the same as the direction of the new positive x'-axis; q and r are chosen in a similar fashion. The points p, q, and r are, of course, not arbitrary. Let wl, w2, and W3 be the points in the plane which correspond to p, q, and r respectively. The points which correspond to the positive x, y, and z directions are 1, i, and oorespectively. Thus, the mapping in Equation (E. 1-1) which corresponds to the change in coordinates must carry 1, i and oo into wl, w2, and W3 respectively. - 104 I [g ma [C r

UNIVERSITY OF MICHIGAN 2260-29-F The mapping in Equation (E. 1-1) which satisfies these conditions can be written w3(1 +wlw3)z - (w3-w1) w = - - _ _ __ -- - -.(E.2-1) (1 + w lW-) z 3 (w3 -W ) Example: Consider the change of coordinates x' = -z, y' = -y, and z' = -x. The points in the plane, w1, w2, and w3 which correspond to the positive x', y', and z' directions are respectively 0, -i, and -1. Thus, 1-z =+z The old and new coordinates of any point on the sphere have then the stereographic projections z and 1-z/l+z respectively. E. 3 APPLICATION TO POLARIZATION-INDEPENDENT CROSS-SECTIONS The monostatic cross-section of a closed surface in space can be completely described by a real valued, non-negative function on the sphere S where at each point of S the function has the value which is the cross-section of the surface for the direction corresponding to the point on S. In order to describe this function one could make contour plots on the surface of the sphere, the cross-section constant on each contour. In order to represent these contours more conveniently consider the stereographic projection of the contours into the z-plane. For those cross-sections which are polarization independent a rotation of the sphere takes contours on the sphere into contours with the same constant cross-section. Therefore, the transformations of Equation (E.2-1) will take the projected contours into the projected contours on which the cross-section has the same constant value. Thus, given the cross-section of a surface with respect to a convenient coordinate system, let its contours be projected into the z-plane. Then the contours can be transformed into the contours with respect to any other coordinate system; i.e., the contours are invariant with respect to the group of transformations of Equation (E. 2-1). 105

I',-r= —, r- N- i L-7 UNIVERSITY OF MICHIGAN 2260-29-F E. 4 GRAPHICAL TRANSFORMATION OF COORDINATES A A A Given a right-handed triad of orthogonal unit vectors i, j, k. Given also an arbitrary direction. Let 0 be the angle between k and A the direction. Leto be the angle between i and the projection of the A A A direction in the plane spanned by i and j. Given a second system i, J, ks 09,<. The problem is to graphically relate 0, 0 to 09, As a preliminary step let us calculate the Euler angles for the A A A A. A* transformation from i, j, k to i, j, k since our graphical technique A A A A will be given in terms of them. Let il, jil kl be obtained from i, j, k by a rotation through an angle a about the k axis. Then A 1 i cos a +j sin a A A. = - i sina + j cos a (E.4-1) A A k - k 1 Now let i2, J2,2 2 be obtained from i, jl, kl by a rotation through an angle p about the j1 axis. Then A A A A A A iz = i1 cosP - k1 sinp = i cosa cosp + j sina cosp - k sinp A A A A J = i = - i sina + j cosC (E. 4-2) A A A A A A k2 = i1 sinP + k1 cosf = i cosa sin3 + j sina sinp + k cosp. Finally let i, j*, k be obtained from 2, J2, k2 by rotation about the k2 axis through an angle Y. Thus i = i2 cosY + j sinv = (cosa cosp cosY -sina siny )i A A + (sina cosp cosY + cosa sinz )j-sinp cosy k 106 L- I t r - I F r-7

I',-r= —, Lr- r- - U N I V E R S I T Y OF MICHIGAN N 2260-29-F A A ^ ^ j = - i2 sin + j2 cosY = (-cosac cosp sinY -sina cosy)i A + (-sina cosr siny + cosa cosy) j + sinp sin- k A A A A A k = k2 = cosa sin3 i + sina sin j + cosp k. (E.4-3) We will require 0'o 3 rso that sin p > 0. We can obtain cos p from k' k, and then compute sin = + 1 - cos2 P. We can then obtain sina, cosa, siny, and cosy from k4.j, ki.i, kj4, and k-" respectively. Now the angles 01, <1 and 02,02 are related to 0,o and 0*, as follows: O = 01 02 = 0 (E.4-4) < - a = O1 -2 - y = 0 Thus if we get the relation between 01, 4 1 and 02, 02 we can obtain the relation between 0, and 0", 0readily from Equation (E.4-4). If we draw the lines of constant 01 and 01 on a sphere and make the stereographic projection of the sphere into a plane we get Figure A A A AA E^.4-1. The positions of il, jl, i2, J2i k2 are marked for ( = 60~ (kl lies at infinity). The distance from the point 01 = 180~ to the circle of constant 01 is proportional to cot (01/2). The stereographic projection of the curves of constant 02 and 02 can be drawn easily. Due to the properties of the stereographic projection these curves are all circles or straight lines. Due to the symmetry about the (x1 - z1) (x2 - z2) plane, the centers of the constant 02 circles will lie on the 01 = 0~, 180~ line. These circles will cut the =1 = 0~ line at 01 = (3 02 if these numbers lie in the interval 0~ to 180~. 107 l r-, L — i ir

UNIVERSITY OF MICHIGAN_ 2260-29-F They will cut the line 1 = 180~ at 02 - 3 and 2rr - (P + 02) if these numbers lie in the interval 0~ to 180~. The curve 02 = 3 is a straight line perpendicular to the line 01 = 0~, 180~, and is the perpendicular bisector of the segment 02 = 00, 02 = 180~. Since all of the curves of constant <2 go through the points 02 = 00, 02 = 180~ the centers of the constant O2 curves must lie on the line 02 = p. Since the '2 = constant curves must go through the points 02 = 0~, 1800 at the same angle which the 01 = constant curves go through 01 = 180~, the centers of theo2 = constant curves lie on a line parallel to the 1 = 2 + 90~ lines and passing through one of the points 02 = 0~, 180~. The curves of constant 022, 2 are shown in Figure E.4-2 for 3 = 600. The positions of i1, j1, i2, J2, and k2 are also located on Figure E.4-2. If Figures E.4-1 and E.4-2 are superimposed, then 02, '2 can be read off in terms of 01, 1 and vice versa. The superimposition is best done in two colors to avoid confusion. This transformation technique is designed for application to obtaining radar cross-sections of complicated shapes. The approximation methods which are used for obtaining such cross-sections involve breaking the complicated shape down into simply shaped pieces and getting the cross-sections of the pieces. The coordinate systems appropriate to each of the pieces and to the total object are generally different. With this technique one can plot the cross-section of the simple shape in a standard orientation on a coordinate system like that in Figure E.4-1 and then make the appropriate coordinate transformation graphically. This procedure is illustrated with the constant crosssection curves for a circular corner reflector in a coordinate system whose axes correspond to edges of the reflector (Fig.E.4-3a) and in a transformed coordinate system (Fig. E.4-3b). (The transformation consisted of a rotation of 45~ about the z-axis followed by a rotation of 300 about the new y-axis.) 108 Lr- I \ L

E IN rI r r - UNIVERSITY OF MICHIGAN2260- 29- F FIG. E.4-1 STEREOGRAPHIC PROJECTION OF SPHERE I - 109 L- \\ Fr-i L~I

UNIVERSITY FMCirOF M ICH IGAN _____ 2260 - 29-F 02 =180~ FIG. E.4-2 STEREOGRAPHIC PROJECTION OF ROTATED SPHERE - 110.L-... \. r - B e mal I _ i i _ /

PI I 0.___ N c? - 1 t-i fi Gj t^ \0 IT 0 17f t~l e I- I CO,)? * (n -4?'1-.0 FIG. E i TI NIT EDGE CIRCULARp CORNER REFLECTOR. (so PRotiN Po negative z-ax itie x Psitv -axes)Y-, and

-j z7 He 0 - 0 T1,.Ml-, N 0 z FIG. E.4-3b STEREOGRAPHIC PROJECTION OF CORNER REFLECTOR IN TRANSFORMED COORDINATE SYSTEM

I UNIVERSITY OF MICHIGAN 2260-29-F APPENDIX F EFFECT OF FUEL ON THE RADAR CROSS-SECTION OF CORNER REFLECTORS The problem of finding the effect on radar cross-section of fuel of different types at various levels in differently shaped corner reflectors with many sorts of coverings is in general difficult. An approach to the problem has been made by finding the radar cross-section for a circular corner reflector covered with a spherical cap and filled with fuel of index of refraction n < 2. These results are compared to certain experimental data (Ref. 33). F. 1 RADAR CROSS-SECTION OF FUEL-FILLED CIRCULAR CORNER REFLECTOR The simplest approach is to let the circular corner reflector of edge R be an octant of a sphere of radius R. With this arrangement incident rays may be traced through the sphere as through it were a lens since the action of the corner reflector would simply reverse the directions of the traced rays. Thus for a cylindrical tube of rays of given crosssectional area incident on the sphere the cross-sectional area of the emitted tube (or cone) of rays may be calculated at some distance r from the sphere. Under the assumption that there is no absorption in the fuel, the amount of energy in the incident and emitted tubes must be the same, and since the square of the field is proportional to this energy, the transmitted field (or at least its magnitude) may be obtained. Let the radius of the cylinder of incident rays be a. The crosssectional area of the emitted cone of rays must be found at large distance r from the sphere. This is the problem of finding b in Figure F-la. To do this consider the simplified two-dimensional picture of Figure F-lb. From Snell's law, sin9 9 = n, or, 'o - sin 9' n I 113 ELDFEi ---r

cr- o 77 U N I V E R S I T Y OF MICHIGAN 2260- 29- F FIG. F-la RAY PATHS THROUGH A SPHERICAL LENS F-lb SECTIONAL VIEW OF RAY PATHS THROUGH A SPHERICAL LENS 114 LrL —r\ 77

rUNIVERSITY I 2260-2 OF MCH-rGANOF MICHIGAN I for small angles 9 and 9'. The geometry of triangle AGO indicates that angle ABD is approximately, ( n 1 From this the distance a' is found to be (again making use of the fact that the angles involved are small) I 2 - n\ whence angle DBO is given approximately by, a' R (2 - n) this is also the value of angle EBF. Now using the value 9/n for angle ABO and reapplying Snell's law, angle EBH is found to be 9. Finally angle FBH is 9 (2 - n - 2ar(n - 1) Rn za(n - 1) Rn so that, The cross-sectional area of the the sphere is approximately, cone of rays at a large distance r from Area = r L2ar(n - 1)] 2 Rn. 115 L_ \L

UNIVERSITY OF L-I Ir-NMIICHIGAN 2260-29-F Since the cross-sectional area of the incident tube of rays is ira2, the transmitted field has the form,. eikr Rn iY Field = Eo r n- e r 2(n- 1) where Eo is the incident field and eiY is some undetermined phase factor. Consequently the radar cross-section a- of the fuel-filled corner reflector being considered is', 7rR2n2 (n- 1)2 F. 2 COMPARISON OF RESULTS WITH EXPERIMENT As an example consider a circular corner reflector (empty) whose radar cross-section along the axis of symmetry is 35 sq. m for a frequency of 9375 Mc (\ = 3.2 cm). From the formula (D. 1-1, App. D), R4 - = 15.61 the edge of this reflector will be 4 (35) (. 032)2 15. 61 'Reflections from the spherical face of the fuel have been neglected since the reflection coefficient is about 0. 03. Moreover, the covering of the fuel has been neglected entirely. This formula is not valid if it predicts a cross-section greater than that given by the corner reflector formula. 116 I (C r - FIE17K

c- -F Eir U UNIVE RS ITY OF MICHIGAN N 2260-29-F Thus for such a reflector full of fuel of index of refraction n N" bT' the radar cross-section will be 7rR2n2 (n-1 = (n - 1)2 /15.61 (. 032) (2) (4J - 1)2 = 1.76 sq.m. This example was chosen in order to be able to effect a comparison with experiment. In experiments of the Microwave Radiation Company, Inc. of Gardena, California (Ref. 33), the 35 sq. m nose-on cross-section (along its symmetry axis) of an empty reflector (or pod of reflectors) dropped to 1. 1 sq. m for the reflector 2/3 full of fuel and to 3. 3 sq. m for the reflector 5/6 full. 2 Although the levels of fuel considered in the experiment differ somewhat from that considered theoretically, the above example seems to indicate good agreement between theory and experiment. A fairly simple discussion may also be given for a diheral partially covered by fuel (see sketch below) when the direction of incident rays is perpendicular to the edge of the dihedral. Let a be that fraction of the length of the dihedral edge not covered by fuel. 'This is a realistic number for 91 and 100 octane gas, kerosene, JP-1, and JP-3 fuels. 2In these cases the corner of the reflector was completely covered by fuel. -- 117 I7 r_ r-\ I Ir

I 7 1 r I__ r UNIVERSITY OF MI CHI GAN I G A 2260-29-F Then the emitted field is given by an expression of the form, - aat + (1l- a) Aa ei E= --- ^ ^- --- ^ where 4 is some phase difference depending on the index of refraction of the fuel and the wavelength of the incident radiation, and r-0 is the radar cross-section of the empty dihedral. The radar cross-section is then, - = oo[a2 +(1 -a)2 + 2a(1- )cos ] = o [ 1 -2a( )(11 - cos )] In the graph below C is plotted vs. a for certain fixed values of 4. a=ao for 0 =0, 27r, 47r,.... In 77r.... 7r 37r.. 37 5r.... 4' 4 1 a (et) for e = r', 3r, 57r,. 118 FLr F~r

UNIVERS ITY OF MICHIGAN 2260-29-F F. 3 RESUME OF EXPERIMENTAL RESULTS FOR RADAR CROSSSECTION OF CORNER REFLECTORS AS A FUNCTION OF FUEL LEVEL' In Reference 33 a description was given of experimental results for the radar back-scattering cross-section of the XQ-4 reflector assembly measured at a frequency of 9375 Mc as a function of JP-4 fuel level in the. 080 inch fiberglas-laminated pod housing the reflector assembly. The following six paragraphs are direct quotes from Reference 33: "The work was performed several months ago as a portion of our development of the passive reflector system for the XQ-4. The reflector assembly used was the final model of the reflector assembly delivered to Radioplane for the XQ-4 program. "In Figure 1, the change in back-scattering cross-section for the nose reflector assembly is given in increments of liquid level where the total capacity of the tank was 60 gallons and fuel was added in 10 gallon increments. "In Figure 2, the change in the return of the broad side reflector assembly was measured simultaneously with that of the nose reflector under the same conditions. (The modulation present in the back-scattering return of the broad side reflector was a specific feature of the design of the reflector assembly. A more detailed discussion of the reflector assembly design, as such, is given in the XQ-4 report.) "The last series of measurements on each of the two figures represents the change in the back-scattering cross-section when the pod was drained, five gallons of fuel put in, the tank vigorusly agitated as to thoroughly wet all surfaces, the fuel drained and the back-scattering cross-section measured in the next few moments. Microwave Radiation Company, Inc. This section gives a resume of Reference 33. 119

=- I r-< _ 11 U N I V E R S I T Y OF MICHIGAN_ 2260-29-F "There are two striking features in Figures 1 and 2 [Figs. F-2a and F-2b]. First, the marked reduction in cross-section as the fuel level approached the 1/3 full mark and, second, the minor change in back-scattering cross-section for the wetted but empty tank. "These data are more than adequate to provide a semiquantitative measure of the effects of the JP-4 fuel on the backscattering cross-section of the reflector assembly at X-band. If a more general picture were desired, a further systematic study would have to be made. " It was pointed out in Reference 33 that the graphically presented measurements were made in the plane of maximum return, which here was the azimuthal plane, for azimuths 0~ 5~, 100, and 850, 90~, 95~ for each indicated fuel level. Since the corner of the reflector was covered for levels of 2/3 full and 5/6 full it was felt that it would be feasible to compare these experimental curves with a curve (which happens to be a constant) determined theoretically for a full reflector. This theoretical value is indicated on the Figure 1 graph of Reference 33 (Fig. F-2a) in the 5/6 full column. 120 4 1 r - _ r -

I,C=, r 77 UNIVERSITY OF MICHIGAN 2260- 29- F A A i,.,,,,,,, 1 i 1 -I I I I I I LU In w 0 z cO 0 u I-I n L) L) 0 u 8 ----— = --- —------------------------- Empty 1/6 Full 1/3 Full 1/2 Full 2/3 Full 5/6 Full Vapor Filled 1000 8 6 4 8 — -- - ----- --- ---- --- 2 100 8 6 4.0 8 6 8 -- ---- -- --- --- * -- -- --- --- A.l { Theoretical Value for Completely Filled Reflector i i i i I~~t i i ii I 2 -, ---,-, 4 2, i I I I I I I I I I I I I I I I U 5 U 5 0 5 0 5 0 5 0 5 0 5 o * Nose Aspect Reflector DEGREES * Fig. 1 of Reference 33 FIG. F-2a RADAR BACK SCATTERING CROSS - SECTION OF XQ-4 REFLECTOR ASSEMBLY AS A FUNCTION OF AMOUNT OF JP-4 FUEL IN REFLECTOR POD* - 121 I I77 - -.

i. i UNIVERSITY OF MICHIGAN 2260- 29- F (A ui Le ILU VI) z 0 u [LU I,. (I O 0 u ea ev 85 90 85 90 85 90 85 90 85 90 85 90 85 90 *Broadside Aspect Reflector DEGREES * Fig. 2 of Reference 33 FIG. F-2b RADAR BACK SCATTERING CROSS - SECTION OF XQ-4 REFLECTOR ASSEMBLY AS A FUNCTION OF AMOUNT OF JP-4 FUEL IN REFLECTOR POD* 122 E L D F ir r- r -l -..

0r'1 -UNIVERSITY OF MICHIGAN 2260-29-F APPENDIX G CIRCULAR POLARIZATION ANALYSIS FOR A SQUARE CORNER REFLECTOR A corner reflector was chosen to match the theoretical nose-on value of r (RL) for a B-47 (12 sq. m). Since the theoretical value of o-(RL) is sharply peaked near nose-on, a square corner reflector was chosen (the square corner reflector has a sharper peak than the triangular or the circular corner reflector). The wavelength of interest was 12 cm and the edge length of the corner reflector was taken to be 26 cm. The axis of symmetry of the corner reflector was taken to point straight ahead. More details of the orientation of the corner reflector appear below. A right-handed x, y, z coordinate system was used with the xyplane horizontal, and the x-axis the axis of the B-47. The edges of the corner reflector were taken to have the directions A 1 A I f~ A el = - i k, 1 A 1 ^ 1 A e2 = i + k, A 1A 1 A 1 ^ e3:= 1 — 3 +k The direction to the radar was taken to be A A, ^ d = sini + sin sin +cos k. The vectors specifying horizontal and vertical polarization were taken to be p(H) = - sin 4 i + cosj^ p (V) = -cos cost 1 - cos sing j + sin 0 k, 123 W[ol[Slr

"I,7 r --- Lr r i UNIVERSITY OF 2260-29-F MICHIGAN while those specifying right and left-hand circular polarization were taken to be p(R) = - (H) + P(V) ^A 1^i p(L) -- p(H) + P(V) The cross-sections were computed by physical optics (Ref. 2). Flat plate, dihedral, and trihedral contributions were taken into account. The cross-sections of the various contributions were added, thus obtaining phase-averaged cross-sections. In order to compute the flat plate contributions,the faces were approximated by circular flat plates having the same area as the faces. The flat plate contribution is then o-v) (RR) = 0 T(1) (RL) = (T(1)(HH) = (1) (VV) bX 4Tr 3/2 r 2 2 2 - I n m I _(2+m2)3/2 +n2) 3/2 +(m2+n2) 3/2 (G. 1-1) where any of the terms in the square brackets that exceed 1 6ir5/2b3 >3 are to be replaced by this value. Her the corner reflector, X = 0. 12 m is t magnitude) of L, M, and N, m is the: largest. 124 L - - ', e b = 0. 26 m is the side length of he wavelength, I is the smallest (in next in magnitude, and n is the [ )'rnF

U NIVE R S ITY OF M I CHIGAN 2260-29-F L, M, and N are given by A A 1 L = el. d = sinO cos4 - cos 1 ] 3cos A A 1. ^ A 1. i*. 1 M= e2 = sin cos + sin c sin s + cos 0 N ' d =-sin cos - sin sine + cos. The three terms of Equation (G. 1-1) in square brackets represent the three flat plates and the limiting value is the normal incidence value. The trihedral contribution is zero if any of L, M, and N are negative. When L, M, and N are all positive the trihedral contribution is o(3) (RR) = 0 4 A2 a(3) (RL) = 0(3)(HH) = r(3)(VV):. where 4m 2 (4 b n A = n(4 n)b2 m (m< i) n (* * 5 The dihedral contribution is a-(2)(RL) = 0 (2) (RR) 2 m2b2 rrl 2 21 2b2 2 rm 2, 2bn arn2 I 125 I -. LC 77

! I r C I UNIVERSITY OF MICHIGAN 2260-29-F where the first term is replaced by 16irr m2b4/X2 if it gets bigger than this, and the second and third terms are limited by 16-r 2b4/k2. r(2) (HH) and (2) (VV) are obtained by multiplying one of the terms in the formula for (2) (RR) by (3 24 )z \3sin~ J and multiplying the other two terms by 3sin204 The factor 4 3sin2O goes with first, second, or third term as L = I, m, or n respectively. The total effective cross-sections are: o-(RL) = -(1)(RL) + o-(3)(RL), o(RR) = r(2) (RR), o (HH)= -(VV) = -(1) (HH) + 0(2)(HH) + -(3)(HH) Comparisons of the cross-sections of the square corner reflectors described above and the theoretically determined cross-sections of the B-47 at S-band (X = 12 cm) are given in Figures G-2 ff. The geometry defining the parameters 04 and 4 used in these figures is given in Figure G-1. 126 X [a CX [Sir

t=- (l-1 m r- I I r —rFrJ 77 ______ UNI VERSITY OF MICHIGAN 2260- 29-F Y x /, Direction to Radar FIG. G-1 BASIC COORDINATE SYSTEM USED IN DETERMINING THE CROSS-SECTIONS 127 E01 F ^== fi *'1I [=n l- = r\ L- I r

I',L- r —-, 7 r- r UNIVE RS ITY OF MICHIGAN 2260- 29 - F 0*=86~ -e- (HH) - Corner Reflector e (VV) - Corner Reflector - (HH) - B-47 —.-(VV) - B-47 0*= 90~ e0 (HH) - Corner Reflector - Oe- (VV) - Corner Reflector (HH) - B-47 ---- (VV)- B-47 1( I.LU LU (I b cO LU ILU I — 0 20 40 60 0* 40 k* FIG. G-2 FIG. G-3 COMPARISON OF CROSS -SECTIONS OF THE B-47 AND SQUARE CORNER REFLECTORS AT S-BAND Linear Polarization __ --- - 128 -- - -- - - - EWcDF F7F

L - 0, - L I N. - - UNIVERSITY OF MICHIGAN 2260- 29- F 8* =94~ -'0 - (HH) - Corner Reflector - 0" (VV) - Corner Reflector ---- (HH) - B-47 ---- (VV)- B-47 8* =980 -..-.- (HH) - Corner Reflector 0- -- (VV) - Corner Reflector (HH) - B-47 —.- (VV)- B-47 i i 4 ~ i I I —' ILI I (/ I — 103 8 6 4- - 102 8 6 4 2 10 8 6 4 2 8 6 0-1 'fcS ~ ~~ i-:== UIV) LU I' i I 1 0 20 40 60 FIG. G- 4 Linear Polarization FIG. -5 Linear Polarization* FIG. G-5 Linear Polarization COMPARISON OF CROSS -SECTIONS OF THE B-47 AND SQUARE CORNER REFLECTORS AT S-BAND 129 fL I A [ i 77

Flo 7 -- UNIVE RS ITY OF 2260- 29- F 0*=1020 -- 0- (HH) - Corner Reflector 0- (VV)- Corner Reflector (HH)- B-47 --- (VV)- B-47 MICHIGAN 0*=120~ - -- (HH) - Corner Reflector - e (VV)- Corner Reflector (HH)- B-47 - -.(VV)- B-47 LU I — v) O - b t — LU LU I 0 20 40 60 0 20 40 60 * FIG. G- 6 Linear Polarization FIG. G- 7 Linear Polariztion FIG. G- 7 Linear Polarization COMPARISON OF CROSS-SECTIONS OF THE B-47 AND SQUARE CORNER REFLECTORS AT S-BAND 130 r I Lr [' J FIE17K

- i Ir U N I VE R S IT O*= 86~ -- -'(RR) - Corner Reflector -- 0- (RL) - Corner Reflector --— (RR) - B-47 (RL) - B-47 Y OF 2260- 29- F MICHIGAN i*= 90~ -- -e (RR) - Corner Reflector -G — (RL) - Corner Reflector --— (RR) - B-47 - (RL) - B-47 I — VU I — LUJ LU w LV) t ILU LU C 1) FIG. G-8 Circular Polarization FIG. G-8 Circular Polarization FIG.G-9 Circular FIG. G-9 Circular Polarization COMPARISON OF CROSS-SECTIONS OF THE B-47 AND SQUARE CORNER REFLECTORS AT S-BAND 131 E L I \ - i

Fr 77 U N I VE R S IT O*= 94~ ~g — (RR) - Corner Reflector -— e- (RL) - Corner Reflector ---- (RR) - B-47 (RL) - B-47 *- (RR) - B-47 Est. Y OF 2260- 29- F M I C H I G A N! 8* = 98~ -e.e- (RR) - Corner Reflector -0 — (RL) - Corner Reflector —.- (RR) - B-47 (RL) - B-47 -- (RR) - B-47 Est. LU ILU v) b t~ I-s /) 11U LU a LI) 0 20 40 60 FIG. GFIG. G-10 * COMPARISON OF CROSS-SECTIONS REFLECTORS AT S-BAND FIG. G-11 OF THE B-47 AND SQUARE CORNER Circular Polarization 132 M f [ I i 77

Icr I r r UNIVE R S IT Y OF 2260- 29- F MICHIGAN O*= 1020 -e- -"- (RR) - Corner Reflector -- -- (RL) - Corner Reflector ---- (RR) - B-47 - -- (RR) - B-47 Est. (RL) - B-47 O*= 120~ -- -e- (RR) - Corner Reflector -e- - (RL) - Corner Reflector -. --- (RR) - B-47 - - (RR) - B-47 Est. (RL) - B-47 LL ILLJ cY 0 - I — LU ILU LU LI b 11 0 on Afn 60 z FIG. G-12 FIG. G-12 / 40 ^* FIG. G-13 COMPARISON OF CROSS-SECTIONS OF THE B-47 AND SQUARE CORNER REFLECTORS AT S-BAND Circular Polarization 133 r Ir, r 77

U N I VERSITY OF MICHIGAN 2260-29-F APPENDIX H BISTATIC RADAR CROSS-SECTION OF THE B-47 AIRCRAFT AT S-BAND The dimensions of the fuselage, nacelles, and wing tanks are such that geometrical optics gives a good estimate of their cross-section for many aspects. With the exception of their trailing edges, the wing and the horizontal and vertical tail are amenable to the physical optics approximation. The contributions from the trailing edge of the wing, horizontal and vertical tail, engine and wing-tank supports, and jet intake and exhaust can be better approximated by formulas based on thinwire theory. The actual estimation of the radar cross-section is predicated upon the assumption that the aircraft may be replaced by a configuration of simple geometrical shapes with only a negligible change in cross-section. Two such substitute configurations may be found in Reference 2. The geometric optics cross-sections, where applicable,were computed from the relation ra = rr R1R2 for all but the forward, and nearforward, scattering. In this formula, R1 and R2 represent the principle radii of curvature at the specular reflection point. In particular, for the ogive the value of a- is given by u=,a2 (1- c os \ Icosn y where a is the radius of curvature of the generating arc, 3 is the halfangle corresponding to the generating arc, and w7 is the angle between the equatorial plane and the line OS to the specular reflection point as shown in Figure H-l. In terms of the incident and reflecting directions, 1 (sin OT+sin OR)2 +(cos 8T sinT +cos ORsin R)2 2 cosn = --- —----— R --- —---- 2 [ +sin OeT sin OR+c os OTcos ORcos (b s t R) where the transmitter and receiver positions must be such that 1 >cos,l > cos 3. 134 ELD7r

C- I —i L-.. UNIVERSITY OF MICHIGAN 2260-29-F a 0 x FIG. H -1 COORDINATE SYSTEM FOR THE OGIVE The prolate spheroid cross-section is given by 2 0- = -ra2; 7 = a/b, where a is the semi-major axis and b the semi-minor axis. terms of transmitter and receiver directions, Again in tan2 e = 1 - cos2 OA cos2 A cos2 OA cs2 A where cos2 OA = 2cos TosR cos( O Rcos (+T)+ c2 T+cos2 OR 2 1 +cosTcos Rcos (mT + R)+ sin OT sin R] I 135 |. \< r

_______ UNIVERSITY OF MI C H I GAN 2260-29-F (cos TR cos T + cos OR cos OR) and cos2 A = 2 cos OT cos OR cos (OT+OR)+ cos20T+cos20R In these expression's OR, OR, and OT, OT denote the receiver and transmitter directions respectively. A physical-optics approximation to the cross-section of a truncated elliptic cone is given by X L2 tang Kg(no,) n L1 i r = ----- 1 + — +2 cos k(ytana+v)(Lz-L)j, wr tana Y3 (y tana+ v)2 L L2 1 L x2 y2 where + z2 tan2 a tan2 is the equation of the elliptic cone; (09T, T) and no(0R, R) are unit vectors directed toward the transmitter and receiver respectively; K(no,) = [(7 tan a + v) sin (T+6)-sinR sin0T -(1 + cos cos T - OR)]; Y = sin cos (T + 6 ) +sin R cos(R + ) tan2g3 2'> 1 + (cos OT + cos OR) } 2; tan a v = sin0T sin({kT + 6) +sin R sin(~R + 6); 6 is the angle between aircraft y-axis and wing-axis; and L1 and L2 are respectively the smaller and greater truncation distances measured from the tip of the full cone. The above is for the starboard wing. For the port wing, let 6-.-r - 6. The port wing is in the positive y-direction. 136 r[C r

EcDrrr UNIVERSITY OF 2260- 29- F M I C H I GAN Y. x FIG. H-2 COORDINATE SYSTEM FOR THE B-47 AIRCRAFT 137 W_[I Lri

I,I_- r - r L-i U N I VER S ITY OF 2260-29-F M I C H I GAN The cylinder cross-section was calculated from the formula (Ref. 34, p. 1381) 2rrL2 T+ \ 0 in, 2 +T 2 i =g x a t s+ ct [ka (0R+ T) 2 22 2 2 which is valid for the broadside case and which contains a forward scattering term, unlike the preceeding formulas (Fig. H-l). In fact the forward scattering term here and the forward scattering as given in the exact solution to the sphere problem were used to approximate the beam width of the forward lobe of similar geometrical shapes. The straight thin wire cross-section was obtained from the current distribution suggested in Reference 31, that is, iwEo cos 4 I(z) = - k2 Q sin T - + i coski + A S2 sinq z sinki - sink z sin qf 1 -----—: ---, sinki + Q B where S = 2 [in k + Ci(2k)] C = kc, k = 2rr/X, c = velocity of light, q = k cos OT, 138 EE= I7 r

_____ UNIVE RS ITY OF M ICH IGAN 2260-29-F 1 + F~ A coski + -fCin(4k1)cos2 ql - L cos2ki cos 2qi 2 COS os -sin2kl inq F(l o i2kI( o 2TT (I1~Co 0T ) sin2ki (1~+ cos OT)] cos 2kl}I 41=sin2 OT ki+ 2cose 0 cos k- -i((1+coseT)sinkle(1- coseOT)+ (I - COS eT) sink I(I1 -icos eT)} eos qI [2k(1co+C]oCs k(1coeT (in -cosOT) - Ci 2k 1+cs0T i2lT(4cs Fl +$COS28T B= sink I+ Ltin(4k1) sin2 qI-i- 2 L sin2 kICos 2q I 2- sin Zki sin 2qi] [(1+CoseT0sin2ki(1-coseT)+ (1 - Cos 0T) sin2k I (1 + cos eT)] sin k I =sin2eT LkI -si 2coeT sinki - {)1~coseT) sin Lki(l-esTj (1csT) sin k(10+COSeOT)]}.in 9 - - 139 I ~ 7 L

UNIVERSITY OF 2260-29-F Mir MICHIGAN C_____ _: = Si [2k (1 + cos OT)] + Si [2k (1 - cos T)], and a y Eo OT OR Si(3 = radius of wire, = 1.781072 (Euler's number), = length of the wire, = angle between | Eo and plane defined by the wire and the direction of incidence, = the incident electric field, = angle defined by the wire and the direction of incidence, = angle defined by the wire and the direction of reflection, c) and Ci(x) are the sine and cosine integrals, respectively, of x as defined in Jahnke and Emde (Ref. 32) and Cin(x) = In x + 0. 577 - Ci(x). The scattered field is given by ik sin OR Es c R JI( z eikzcos ORd I (z) e dz, J I from which the value of a- is obtained through lim 4rR2 Es = R-~4rR Eo 4 \2 cos2o p2 + 1-L2 that is, a- = rr sin2 Rsin2 T L2 + B2 140 c r^r I

UNIVERSITY OF 2260-29-F Lz CHIGAN M I C H GA N where, cos (kQ cos OT) cos (ki cos OR) p = A Q, 1 2 = {cos OT sin2 R cos (k cos OT)sin(k cos OR) - cos2 OT - cos2 OR cos OR sin20T cos (k cos OR) sin(k cos OT) 1 - B cos (kicos 0T) cos (k I cos OR) A which applies when OR / OT. For the case where OR = OT = O the crosssection is given by o- = ----------- (r/2)2 + n (ra sin 2 yrra sin i. In this report the average value of o- over the polarization angle is used, i. e., 1 r 2 - r., o- d The wire loop cross-section may be estimated as in Reference 2, ignoring the current induced in the wire by the scattered field from all other segments of the wire. Consider the loop to lie in the xy-plane and the transmitter and 141 C [g [C ["").

I J EII r\\ L- 1 UNIVERSITY OF MICHIGAN 2260-29-F receiver directions to be indicated by the unit vectors PT and PR as shown in Figure H-3a. By rotating the coordinate system about the z-axis through the angle P given by cos 3 = sin 8R + sin OT /(sin R + sin T)2 + (cos OR sin'R - cos OT sin T) we may express the scattered field by the integral 2r (ika (PT + PR) ' r) = A [(PRx t)PR (b * t) e 0 where b is a unit vector in the direction of the incident electric vector, and t = dr/da,where r is a unit vector in the direction of the integration element, and a is measured as in Figure H-3a. The complex constant is easily evaluated by referring to Reference 2. y 7 PR PT O, 619 L —^^!^V^"^x I I/ FIG. H - 3a COORDINATE SYSTEM FOR THE LOOP 142 I ' \ L - c _ r

I - C: 7K U N I VE R S ITY OF MICHIGAN 2260-29-F Carrying out the integration, one finds that = Tra2 C12 + C22 + C32 where C1 = b2 P1 P2 [Jo(p)+J2() ] C = bl P2 Pl Jo(P)- J2(p) -bl(1-pl2) -b2(1-p22) +b2 P2 P3 Jo(P) - J2() ] 1Jo(P)+J2(P) ] I C3 = bl Pl P3 Jo(p) - J(p) ] [Jo(pl~J2 (P] and P1 = cos OR sin R cos P - sin OR sin, P2 = cos OR in in sin sin sinR cos, P3 = cos OR cos R, bl = -sin Y cos T cos T +cosy [(sinZT sin2 T - 2cos 20T)sin 2p q 2 -1 ) + cos 213 sin 20T sin Tj b2 = q cosy b3 = - cos v (sin 20T cos0 T cos P - cos20T sinp sin20T) - 3 q i2 L1 sin y (sin OT sin + cos OT cos sin*T) }, p = ka (cos OR sin OR -cos 0T sin )T)sin +(sin R +sin OT)cos 3, q2 = 1 - (sin T cos - cos T sin P sin 4T) 143 L[Liz l-\ 77

C= - \ L-! UNIVERSITY OF 2260-29-F M ICHIGAN This formula reduces to that of the monostatic case when OR = XT = 0, and OT = OR = 0, since then cos P = 1 and q = cos 0, to give P1 = 0, P2 = sin, P3 = cos 0, bl = sin, b2 = cosY cos 0, b3 = cosy sin. Using AA* = a2/4Tr2 R2 (A* is the complex conjugate of A) where a is the radius of the loop, and R the distance to the observation point, and the "effective radar cross-section" is proportional to b Es, the formula of Reference 2 is obtained exactly. As in the case of the straight wire, the average value of cr over the polarization angle is used. Thus, 2 2 [ C2 + C 32] d 0 1 f2 r ( 2 +j (1-p l) (Jo J2)2 + q (1-p)2 (Jo + J 2 q f P P (Jo2 -2 J)} where the quantities are defined as above, except for f and g, which are f = (sin OT- cos2OT sin2 pT) sin 23 + sin 20T sinXT cos 2, g = cos 8T cos T. The forward scattering cross-section was computed from the relation 4 7A2 0' =, X2 where A is the area projected upon a plane perpendicular to the direction of propagation. These areas were computed from the following formulas. 144 X ' [ X 1 r =D - ^!=i r\ ^ I

C_- - 7 r-_ r- - U N I VE RS ITY OF 2260-29-F MICHIGAN ---- For 4 = 0, 180 degrees the projected area of the airplane is given by 2 2 2 tanw sinew A' = r(2ae +afbf+2ade bde+2ap2)+Za tanw sin + 3a2 tann sin 1HT IHT HT where af, bf = semi-axes of fuselage ellipse, ade, bde = semi-axes of dual nacelles, ae = radius of single engine nacelle, ap = radius of fuel pod, alw, alHT = 7w' "HT = /w' 'HT = "exposed" length of maximum-area plane (Fig. H-3b) of the wing and horizontal tail respectively, half angle of maximum-area plane of wing and horizontal tail respectively, sweep angle of maximum-area plane for wing and horizontal tail respectively. (The "exposed" section of the maximum-area plane for the wing has the same projected area as the wing when the airplane is viewed noseon. ) The projected area for aspects other than those above is the sum of the projected areas of the components given below. The component cross-sections may be added directly, as pointed out in Reference 2, to obtain the total cross-section for the composite shape. The formulas for the projected area of these components are given below. II _ I I 145

I -.UN IVE RSITY OF MI CH IGAN 2260-29-F Maximum Area Plane: '7HT 77W FIG. H - 3b DEFINITION OF PARAM __ _ __ _ __ _ __ _ __ _ _146 I,L- r- r-, 77

r I 1 r LH I M- I M I CH I __ U N I VER S ITY OF 2260-29-F G A N ----- Starboard wing, W1 [aosin(T - 'w) - Ilw sinT Wl A IL tani (15~TT) sin (T + Ow) ao sin4T1 1 sin(T1 + Ow) [a sin(Ow+ T) + 2w sin 'T] 2 stan,? (r-T2 <)1650) sin(Owy + OT) Alwi Wl ao sinOT2 2 sin(w - T2 ) Port wing, W2 I [a0 sin(w - T) 12w sin- T] sin(Ow - 'T) ao sin( T- Pw) - lw sinT] 2 sin (T -Ow) 2 tannw (15~ 0< 4T<T2). tan w (ir-4Tl<- T<165t). A = W2 Port and starboard horizontal tail projected areas are given by these formulas after replacing Iw, I i, 1 2 and n w by their counterparts. The fuselage and vertical tail projected area is: A'f+vt = Af+vt sin The formula for the engine supports is of the same form, namely, AlS = Aes sin iT (H. 1-1) 147 3E=- I r -

UNIVERSITY OF MICHIGAN 2260-29-F By modeling the fuel pods and engine nacelles with cylinders, we may approximate their projected areas by A' = 2RL sinXT + wR2 cos T (H. 1-2) e T The constants are given below: lw = 27 ft. 1H = 3 ft. HT i2 = 65 ft. HT 20,7HT = 20 HT 1210 w = 125~ ao =66 ft. a = 1.75 ft. a t. e OHT af,bf = (5. 5)(5) ft.2 a = 17.5 ft. ade,bde = (4)(2) ft. 2 L= 20 ft. a = 2.5 ft. Le = 13 ft. P al = 66 ft. Rp =2 ft. Afvt = 1122 ft. 2 Re 1.75 ft. 1HT = 3 ft. Equation (H. 1-1) is to be used as follows: For = 150 Al' = (26 + 16) sin 15~; T s 30 A' = (16) sin 300; T 300' es 148

C_r L-I U N I VE RS ITY OF M I CH I GAN 2260-29-F XT = 150~, T = 165~, A' = (16) sin 30~; es Al = (42) sin 15~; es Equation (H. 1 -2) should be applied to the two engine nacelles (the dual and the single) and one fuel pod at XT = 15~; to the fuel pod and single nacelle at 30~; to the single nacelle at 135~; to the single nacelle and fuel pod at 150~; and to two engine nacelles and one fuel pod at 165~ (same as 15~). The total area A appearing in the cross-section formula is simply the sum of the projected areas corresponding to the particular aspect. In adding the component cross-section to obtain the total, the effects of "shadowing" of some components by others were considered in a manner similar to that of Reference 2. Approximate values of or were computed for the transmitter in the lower port quadrants and the receiver in the lower starboard quadrants. Transmitter and receiver positions, denoted by (OT, 'T) and (OR, #R), were chosen such that ST and OR ranged from 0 to ir/2 in 15 degree intervals and XT and OR ranged from 0 to ir in 15 degree intervals; the angle measured as in Figure H-3a (Fig. H-3a is drawn after a rotation of 7r radians about the z-axis). For each transmitter position the estimated o- is presented in Tables H-1 through H-7. A graphical representation of o- vs. XT and OR for 9T = 15 0 is given in Figure H-4. 149 EcCFlrir

[C Xf Iz Lhi lr 77 U N I V E R S I T Y OF MICHIGAN 2260- 29- F 104 103 102 10 1.0 10-1 10-2 FIG. H-4 BISTATIC RADAR CROSS-SECTION (o IN m2) FOR THE B-47 AIRCRAFT FOR OT = OR =15~ 150 r- rF i I i 77

2260 - 29 - F TABLE H - '9R OR OT=00 OT'15 0 OT=3 00 OT=4O T6 0 ~=50 T OT OT=900 6-1 T I..! ~ I 0 0 0 0 0 0 0 0 0 0 0 0 0 30 30 30 30 30 30 30 30 30 30 30 30 30 45 455 45 45 45 45; 45 45 60 60 60 60 60 60 60 60 60 60 60 60 60 75 75 75 75 75 75 75 75 75 75 75 75 0 15 30 115 60 75 90 105 120 135 150 165 180 0 15 30 45 60 75 90 105 120 135 150 165 180 0 15 30 60 75 90 105 120 135 150 165 0)3 15 30 45 60 75 90 105 120 135 150 165 180 0 15 30 60 90 105 120 135 150 165 180 0 15 30 45 60 75 90 105 12n 135 150 165 190 3.84s 0 1.40O, 0 2.15, 0 3.6o., o 8.6o, o 5.30s 0 B. 00" o 1. 00 1 1.60,, 1 3.30., 1 7o5os 1 2.410, 6 9.800-1 1.082 0 1.362 o 1.80, 0 2,~70, 0 3.47o, 0 5.30, 0 7.50, 0 1.002 1 1.50, 1 2.6o, 1 4-40o, 1 2.622 2 1.27, 0 1.35, 0 1.622 0 2.10., 0 2.902 0 4.50, 0 5.50, 0 7-00s 0 9.30, 0 1.41., 1 2-15s 1 3.63, 1 Ir.e59 1 1.779 0 1.85, 0 2.11, 0 2.57, 0 3.25, 0 4.19, 0 7.26, o 6.923 0 7 o4, o 1: o6, 1 1.38., 1 2.100 1 9.912 0 2.57, 0 2 63, 0 2:85v 0 3.220 0 3.75., 0 5,25s 0 6.16s, o 7.17s 0 8.480 0 9.6o, o 1.079 1 1.9is 0 3.360 0 3.89s 0 4.129 0 4.899 o 5,23 v 0 -5.68. 0 6 189 0 7:65s 0 7 lo't 0 7:360 0 1.4o,, o 9.15,-l 9.812-1 1.27i 0 1.58s 0 2.63 v 0 1.01, 1 7.419, 0 1.75., 1 3.21v 5 4.85,-l 9.000-2 1.01, 0 1.10., 0 1.36" 0 1.87, 0 2.70, 0 2.81., 1 5.40s 0 6.4o., o 2.60, 1 4.30, 2 1.853, 3 1.38s 0 1.30., 0 1.39., 0 1.662 o 2.16, o 1.982 0 2.1TP 0 8.20, 0 7.40s 0 1. o6, 1 6-70s 0 6.40e, 1 7.210 1 1.92, 0 1.84l, O 1.91rS o 2.912 0 3.99s 0 6.9o, o 4. go,, 0 7.90, 0 6.1o, o 7.80p 0 1.0op 1 1.64, 1 1.77 9 1 4 002 0 3:50, 0 4.30.9 0 3.709 0 4.07s 0 5.50, 0 4.20, 0 5.00, 0 5-90P 0 6. go, o 7.90s.0 8.001, 0 6. 02 s 0 7.401-1 8.30,-l 1.39, 0 2.70., 0 3.4o, o 3.29j, 0 4;629 0 6.172 0 5.652 6 2 93., 0 3:34., 0 1.6o, o 1.022 0 9.201-1 1.092 0 1.70, 0 3.00., 0 4.309 0 3.61, o 5.20, 0 7.90i 0 1.74., 3 5.64, 0 6.811-2 2.802 0 2.00, 0 1.6o,, o 2.30, 0 3.00, 0 3 60, 0 3 -00.p0 4-30t, 0 6.1o, o 8.902 O 1.51, 2 2.30, 2 3.18., 3 3.702 0 3.30) 0 3.30.. 0 3.00s 0 4.509 0 2. go. 3.809 0 5.00., 0 6.6o,, o 8.70" 0 3.07s 1 6.20, 1 6.oo, 1 3 12, 0 3:460 0 3.80s 0 3.00s 0 3.4o, o 3 got 0 4:6o, o 5.6o, o 6.70t 0 8.00't 0 1.239 1 1.282 1 9.4o0, o L.5o. o 4.4o, o 4.40s 0 4.5ox 0o 4.,70s 0 5. oo, o 5.40, 0 6.oo, o 6.5o, o 7.30s 0 A-A7- n 2.30s, 1 6.20s, 0 3.702-1. 5-los-1 2.30, 0 9.100-1 1.6o, o 7.23.9 6 1.93, 0 2.44, 0 2.93s 0 1.40, 0 1.70, 0 6*70p-1 5;.70x-1 9.00.1-1 1.4o, o 2.000 0 2.90,0_1 4.,63 o 3 4.83s 0 8986,9-2 2.871-2 1.37, 0 1.03, 0 9.902-1 1.13: 0 1.38, 0 1.982 0 6.8o,-l 2.802 0 1.50, 2 7.722-2 4.00.,-4 1.96s 0 1.64, 0 1.50P 0 1.50s 0 2.12,9 0 3.00., 0 1.25s 0 4-,70j 0 2.800 1 7.25s 1 3.00., 2 5-30,9 3 2 73 x 0 2.35., 0 2.57s 0 2.720 0 3.17s 0 5.000 0 6.6o, o 1.06., 1 1-59o 1 6~Coo, 1 4.40s, 1 3.90s 0 3,890 0 3.99, 0 4.10s 0 4 20,, 0 5:6o, o 2.010 1 6.8o, o 4 8 7,* 0.5:62., 0 7.13 x 0 8.14, 0 5.421-1 1.702-1 1.80.,-l 2.3 Ot-1 1 - o4, 7 1 03.9 0 1 93s 0 2:44, o 1.63 s 0 1-15s 0 7-30s -1 7.20s-1 1-38s 0 5.132 2 7.Olj,-l 6.3 j,-1 4.,080-2 2.102 0 1.64, o 1.28$ 0 1.17s 0 1.85s 0 3. o4, o 2.90$ 0 1 33, 2 7:56,, 1 2.933 o 5.14,0-1 1.12$-2 7.35s 0 2.48, 0 1.65s o 2.15, 0 2-53s 0 3.28.$ 0 5.503, 0 9.4o, 0 5.203, 1 4.90s 3 1.180-1 1.701-1 1.70s-1 1.29i 7 4.79,9-1 7.089-1 1.03.9 0 1.44, 0 1.93, 0 3.57, 0 1.73s 0 1.26, 0 1.02s 0 9.702-1 1t,28, 0 3.322 0 3.66., 2 1.59s 0 1.52P-1 5.199-2 3.61,9-2 7.240-2 3.17s 0 2.97s 0 2.10, 0 1.1-9., 0 2.25s 0 3.28, 0 8.30, 0 2.37., 2 1-34s 0 2.50P -1 3c78c, 0 3.802 0 4.13, 0 7.6o, o 2.002 1 1.73, 2 4.17s 0 2.180 0 7.23p-1 9.730-2 6.30s, 0 5,10s 0 5.10, 0 6.5o, o 8.5o, o 3.00j. 1 1,169 2 3.230 2 5.70s-l 3.46,-l 1.35arl 3.171-2 1,320 1 1:34s, 1 10409 1 1.800 1 2-70a 1 4.6o, i 7 7 2p 1 1:55V 2 3.35,p 2 3.00., 2 3.220 2 6.82s 3 1-38s 7 2.55,-l 3.33j-1 7:08.,-l 1 03., 0 1:44, 0 7.12, —1 6.4c,-l 4.25,-l 1. o6~, o7 1.79, 3 8.361-1 6.81s-2 1.739-2 7.5ox-3 4.70,,-3 8.802-1 2.74, o 9.70o-1 1.17, 0 2.56., 2 2.78s 3 5.23v 0 3.38s-1 7.54j-2 3.130-2 2.091-2 2.379-2 2.50, 0 1.800 0 2.51, 0 5.50s 0 3-19s 1 4. o5, 3 1.29, 1 3.25, 0 7.420-1 3.09o-l 2.241-1 2.44s-l1 8.200 0 7,30v 0 8.00,0 0 1.280 1 2.92j, 1 1.219 2 5.30s 3 2.31, 0 3.57s 0 3.18p 0 1.859 o 8.21p-1 5.50s, 1 5-50,9 1 6.58, 1 1.59., 2 2.579 2 6,l45, 3 4r.99*:-l 5.23v-1 1.77s 0 4.13p-l 1.890-1 2.31,-l 2.55;,-l 3.331-1 4.79,-l 7.08.,-l 1.03, 0 1.302 0 8.6o.,-1 6.45.,-l 1.48, 0 4.46., 2 1.98, 0 6.43j-1 5.93.,-l 1.121 0 2.78, 0 1.76, 0 1.63, 0 2.55, 0 3.20, 1 4-55v 1 5 -o3.,o 1-71s 0 1.090 0 9.260-1 9.58,-l 1.12, 0 1.39, 0 6 90, 8:6., 1.07., 1.13., 3.22$ 2 *06,9 1.69s, 1*59P 1.66. 0 0 0 1, 2 1 1 0 0 0 0 0 0 2.3lo-1 2.55o-1 3.33x-l 4.79,-l 7.09,-l 3.30o o 1.800 0 1.320 0 2.90s 0 4.87.9 2 6.802-1 3.31.,-l 3.33j-1 4.03 t-1 7.71 s-1 9.00, 0 6.51o o 8.322 0 4.722 1 i.57, 0 3.34., 1 9.08.9-1 6.67,-l 5.98s-l 6.34o-1 7.58o-1 5.86.* o 5.5o, 1 -5.50, 1 1. 10., 2 2.18, 1 2.849 0 5.36., 1 3.78, 1 2 -35, 1 1.44.. 1 1-31m 1 2.76s 1 6.46,o 3 1.92,,-l 7.02t-l 3.28, 0 1-15s 1 5.03 s 0 6.27, 1 4.,83, 1 4.,36, 1 4.1S6, 1 4.39v-l 1-17s 0 2.262 o 5.02 t 0 8.00, 0 7.25, 0 6 99., 1 6:52, 1 6.20, 1 5 98,9 1 5:86., 1 5.84p 1 5.91, 1 2.31,-l 2.55,-l 3.33,-l 4.79.,-l 2*80p 2 5-70s 0 8.~o 0 2~, 1.2CI-3 2.00,-h 6.17,c~-l 3.15,-l 2.80,3.011-1 3.78.,-l 5. 24, -I 3.58, 2 5.60, 1 2.11t 2 9.04, 1 7.oo,-4 7.290 0 6.72t-l 5.11,-l 4.52.,-l.24,, - 6.66.0-1 5 62, 3 5.12p-2 1.00,9-3 3.33., 1 1.439 1 7 61,-l 7:43 s -1 7.98t-l 2.030 0 3.021, 2 7.37s,-l 1.179-2 2.70,0-2 2.909-3 4-70o 1 3.78s 1 2.95, 1 2.36., 1 2 30,9 1 2:760 1 2.5ol, 2 1.5ox-3 1.13.,-2 6.30.,-3 1.OOP-3 1.30.9-3 5.47 p 1 5.13, 1 4.82P 1 4 6o., 1 4:49o, 1 4.50,0 1 4.62, 1 3.423 2 5.,6o., 1 '7-70,3.71,2 *00, -4 7.69,,-l 3.731-1 2.902-1 2.88,-l 3.50, 3 3.28, 2 3. o6 3 3.20,-3 4.00, —4 6.70o-1 4-0.99-1 3-.71~,-l 3.93,-l 4.72,-l 3.02p 2 8.70s-2 6. o6., - 1.90,,-3 1.201-3 5.00,-4 2.06., 1 go6,,-l 7.23.,-l 6.171-1 5.752-1 5.920-1 2.522 2 2.5oo-3 5 o00.9-3 5.00.,-4 1.40,-3 4.00.,-4, 3.33s 1 2.259 1 1.222 1 4.079, 0 9.020-1 9.091-1 5*86P 0 1.902 2 1. 90s-3 1.40.,-3r 39009-4 y.oo,-4 3 78.,p - 3:39, 1 3.109 1 2.95t 1 2.94, 1 3.099 1 2.311-1 2.55,-l 2.3lo-1 3.331-1 2.55..-l 2.3li-1 2 8s~, 3 6 1C~-2 2r. C-0~-t 7.34, l 5.0-71-1?..61 u 2,l~c R2 2,5 -it,.04,0 2 7.11, 1 3.63,-2 4.50,,-3 2 *00, -4 3.00.,-4 1.66$ 1 8.13;-l 5.93,-l 3.67,-l 3.66.,-l 2.6oo 2 30,-2 1101,),-3 4.63, 1 1, oo., - 2.22.. 1 3.69, o 7.431-1 5:26,9-1 5.00,-l 5.242,-1 2.04., 2 4.201-3 2.00,,-4 2. 00,9 -r 3" 62, 1 2.800 1 1.68,, 5.03, 0 8.44p-1 7.759-1 7.51,9-1 7.71s-1 1.472 2 8:oo.,-4 2. oo,, -4 1.00,-4) 3.33,9 1. Z.84L, 1 2.37s 1 1.982 1 1.71t 1 1.680 1 2,18s 2 9,282-1 4.,03.,-2 r5 90,-3 3.33, Ix 2.801-1 2.551-1i 2.82; 2 7.82)-l 1.00.,-3 1.001 —4 3.33s 1 7.911-1 5.78x-1 3.58,-l 2.372 2 1.60,9-3 1.20.,-3 3.33t 1 1.84, 1 9.001-1 7.08s-1 5.78s-1 5. o3..-1 4.79t-1 1.84r, 2 2*00s-4 1.90s-3 15.112 1 4.00,-4r 3.33, 1 2.33, 1 1-17v 1 9.00.1-1 7-91s -1 7.29s-1 7.08.,-l 1.310 2 8.00, —4 3 - o.,-4 5.43. 1 2.001,-4 3.009-4 3.33 o 1 2.84, 1 2.33P 1 1.17, 1 1.08, 1 4.oo, 1,31,o 3.84,, 3.90,p 5-70.* 9 50,9 2:563, 9.319 3 210 6,o3O, 5 30.9 7 -00.t 7.70,9 1.35s, 2,31 0 3.41, 4.8o., 6.203, 0 2 0 0 0 0 2 0 1 1 2 2 3 0 0 0 0 0 0 1 0 1 1 1 1 1 5.50, 1 5 50., i 8:61s 1 1 859 2 9:80p-1 3.65s 0 1.269 1 7.94., o 4.io, o 2.96$ 0 2.58S 0 2.49s 6 2.55, o 6 82, 3 9:359-2 2.03s-1 8.30s,-l 9.59s 0 6.12$ 0 6.990 0 6.79v 0 5.83 s 0 4.74o, 0 3.88, 0 3.37s 0 3 o6op 3.55., 3 *64p 3 66, 3:96: 4.26s 4 63v, 5:05s, 5.52,0 6 009 6,l469 6.17 j 3.20p 0 0 0 0 0 0 0 0 0 0 0 0 0 90 P0 1 5.20., 0 5.10, 0 6.00, o 6.30,, 0 1.34s 1 6.30, 1 7.50v 3 1.84s 0 7.11s 1 5.70s I 4.63s 1 3.620 1 3.19, 1 BISTATIC CROSS-SECTION (Cr IN rn2) FOR THE B-47 AIRCRAFT U n (The~~~Th numbers following comma indicate multiplication by that power of 10) ~~r Revisadt. 1; June 1956 0,T,= tj

TABLE H - 2 2260 - 29 - F 15 15 15 15 15 15 15 15 15 15 15 15 15 30 30 30 30 30 30 30 30 30 30 30 30 30 t 0 15 30 45 60 75 90 105 320 135 150 165 180 0 15 30 45 6o 75 90 105 120 135 150 165 180 Jr 00 1.26.9 0 1.36.9 0 1.589 0 2 269 0 3:24p 0 9. 77,v 0 5.761 0 9.60) 0 1.28.9 1 2.309 1 4.70i 1 3 o 13,9 2 8.53p 3 1. 83 j, 0 1. 84 p 0 2.25P 0 2.829 0 3.58.9 0 6.62i 0 7.86.9 0 8.601 0 1.25P 1 1-95P 1 3.209 1 6.20j 1 1. 23.p 2 ) —150 lly —300 OT —450 Jf=6011 P —750 OT — 90 11 OT —1050 $T —1200 OT —1350 OT —1500 $T —1650 OT —1800 45 0 2.49, 0 45 15 2.60i 0 45 30 2.73 s 0 45 45 3.489 0 45 6o 4.07, 0.45 75 5.52.9 0 45 90 2.6011 1 45 105 8.60.9 0 45 120 1.17, 1 45 135 1.51.0 1 45 150 2.25, 1 45 165 3.1op 1 45 18o 1.81.9 1 6o 0 3*69y 0 60 15 3.80, 0 60 30 4.03, 0 6o 45 4 48.9 0 6o 6o 5:18P 0 6o 75 6,o 73, 0 60 90 6.981 0 60 105 8.509 0 6o 32o 1.01P 1 6o 135 1.31.9 1 6o 150 1.43, 1 60 165 1.54.9 1 6o 18o 6.57, 0 75 0 5.301P 0 75 15 5.32.9 0 75 30 5 o 54,9 0 75 45 5.68P 0 75 6o 6. 76.9 0 75 75 6.89j 0 75 90 7.10$ 0 75 105 7.30.9 0 75 120 8.50P 0 75 135 8.701 0 75 150 1. ols 1 75 165 1. 03.t 1 75 180 2.53 j 0 90 a3l 8.20P 0 I 281f 0 1:41p 0 10 80.1 0 2.489 0 3.47p 0 1.09P 1 6.95p 0 1. 54,p 1 1. 93 j, 1 5.70P 1 8.37.9 3 2.86.9 0 1-97p 0 1.83., 0 1.94.2 o 2.38.9 0 3.13 p 0 4 * 04.9 0 5. fl4,t 0 8.202 0 1.07., 1 1.781 1 4. go, 1 1. 94,p 2 1. 21P 2 2. 72 p 0 2.70.9 0 2 81.9 0 3:261 0 3.92 3 0 4.94, o 5.78P 0 8 30Y 0 1: 06 p 1 1.72.9 1 2.44 p 1 2.62.1 1 3.0211 1 3.92.0 0 3. 92 It 0 4 * IL4., 0 4 37.9 0 5:06.9 0 6.18P 0 6.99p 0 8.40.9 0 9. lop 0 1.23, 1 1.48.9 1 8 01.9 0 2:86.* 1 5. 55 p 0 5-55P 0 5.67, 0 5. 7211 0 6.77p 0 7.94, o 7.10.9 0 7-30j 0 8.60i 0 1. 01.9 1 1. o4. 1 7* 94, 0 3.14., 0 1. 39, 0 1 56.1 0 2:04.9- 0 2. 91 It 0 7. 26P 0 1.982 1 1. 24,P 1 3.072 2 6.96.9 3 1. 2 7.t 0 4.272-1 2.362 0 2. o4,, o 2.14., 0 2. 26.0 0 2.92.9 0 3.91.9 0 1.10$ 1 8. 20.0 0 1.45, 1 5.10.1 1 5.001 2 5.78, 3 3.82,P-2 3.36.1 0 3-03, 0 3 14, 0 3:461 0 4*04p 0 5.07, 0 6. 84,t o 8.60P 0 1. 26P 1 2.4olf 1 9. oov 1 4.29, 1 8.01) 1 4.72P 0 4-58P 0 4.6o, 0 4 9 5, 0 5:432 0 6.81.9 0 8. 001 0 2.30Y 1 1. 21P 1 1*64p 1 2.19, 1 1 9 8P 1 1:64,0 1 6.85, 0 4 9 84, 0 6.85, 0 1.97, 0 7.109 0 8.20.9 0 8.501 0 1. 00,9 1 1. 14 p 1 1.34.9 1 7.172 0 5.24.9 1 1.40P 1 1.62.9 0 2. 04.9 0 2-30P 0 4.36.9 0 7.30.9 0 4.17p 2 1.69., 4 7-45P 1 6.60.9 1 6.861 1 3.13 p 0 2.69p 0 2.47p 0 2-59P 0 3 a 14, 0 4.261 0 6.77, 0 1.01.9 1 2.80.4 1 1.43p 3 7.929 1 7.10.1 1 7. o4. -1 4.26P 0 3.97p 0 3 91.9 0 4: IL4., 0 4 73p 0 5: 74 p 0 8.30.1 0 1 24 p 1 2:40P 1 1.07p 2 2. 18Y 2 6.94, 3 7.19p 2 6.72.9 0 6.69 p 0 5-,69;p- 0 6.763 0 6.97p 0 7.301P 0 9.10.1 0 1.28.9 1 2.4 7j, 1 3.05, 1 3.412 1 4.1210 1 7.40.1 1 300.9 0 9.50) 0 8.501) 0 8.960.0 0 8.90.9 0 1 - 03, 1 1.29Y 1 3.52.9 1 2.97.9 1 1.28.1 1 1-56P 1 1. 33, 1 1. 511 1 2 3 7.t 0 3:47, 0 6 o 73.1 0 1.621 1 1.689 4 7.35, 1 5.821 1 5* 74.% 1 6.09, 1 4.35,t 0 3.58.$ 0 3. 26.0 0 3.37, 0 4.15, 0 5.69, 0 8.70.0 0 2.501 1 4.392 2 8o34, 1 7.00.$ 1 6.64, 1 6.66.0 1 8-36P 0 5.29, 0 5.181 0 5. h4s 0 5. 85.s 0 8.50J 0 1.369 1 2 56.9 1 1: 061 2 7.79, 1 I7.27., 1 7. o8J. 1 7.05, 1 9.301 0 3.32.1 1 8,20- 0 8-50P 0 1. COP 1 1.33.9 1 4.12.t 1 3.5op 1 4. ol, 1 1.342 2 3. 11Y 2 7..86.t 3 7.20.1 1 1.16p 1 1.15, 1 1.26.9 1 1.309 1 1. h 71 1 1. 73 j, 1 2.321 1 2.90P 1 2.90P 2 2.99, 2 3 * 04.p 2 3.011 2 3.09, 2 5. 63, 0 1. 4 o., 1 1.66.9 4 6. 98.9 1 4.781% 1 4 *15.9 1 4.50.9 1 5.22 1..9 5.78.1 0 5-38P 0 4.61.9 0 4.98P 0 6.79, 0 9. 901p- 0 2.40P 1 h. 55 p 2 8. 4 8P 1 6.45 p 1 5.86.9 1 5.78.9 1 6.01p 1 8-30P 0 8.10P 0 7. 10i 0 8-30P 0 9. 80P 0 1. 72P 1 8.00P 1 2. 709 2 8.01.9 1 7.35j, 1 6.88.9 1 6.67p 1 6.66.9 1 1. 19 p 1 i.hol 1 1.73 2 1 3 OOP 1 5:30.9 1 1.55, 2 6. 52.9 3 7.30$ 1 7-17p 1 7 08.9 i 7: o6., 1 2. 10.9 1 2.10.9 1 2.30P 1 2.70.4 1 3.00.0 1 4. go., 1 5.009 1 8. 2 l.? 1 2.11.9 2 3.10.9 2 3.22P 2 8.46,p 3 7.203 1 1. 95,v, 4 6.3 2.1 1 3. 83.9 1 2.09, 1 2.50.9 1 2. 8C.9 1 3.97, 1 1.69-j, 0 1.011 0 2. 73, 0 1.33, 0 9.521 0 2.90.0 1 4.56, 3 7.68.1 2 6.011 1 4. gip 1 4.01 1 4.55, 1 5.03, 1 3.423 0 7.17, 0 2.97, 0 6-70P 0 1. 72P 1 4. o4., 1 5. 73.9 3 8.34, 1 0.97, 1 6. 27, 1 5. 92P 1 5.85, 1 5-98J 1 1.12.4 1 1. 16P 1 7.13, 1 1.5 1 P. 8 2 7.81.9 1 6. go, 3 7.55, 1 7-56P 1 7.09, 1 6. 83,p 1 6.69, 1 6.67, 1 4.11) 1 4.12P 1 5* 74.s 1 7. 883 1 8.315 1 3.019 2 8. 03,p 3 7.30i 1 7. 25., 1 7.19, 1 7*27y 1 7.4o, 1 7.4 Tp 1 3.58.9 1 3,85, 0 8.bij, -1 1.011 0 4.7?9 0 2.32.9 1 3-15p 0 2. 73p 0 3.08.9 0 7.25, 0 3.48Y 1 1.28$ 2 8.31$ 1 5.75, 1 4. 19 p 1 8.07, 1 2. 66P 1 3. OOP 1 3 9 83, 1 1. 21P 1 9.64, o 1.17, 0 2.52Y 1 1. 29p 2 1.739, 1 8-59P 1 1.48.9 2 6. 05 p 1 5. 26.9 1 b. 89., 1 4.89, 1 5-19P 1 4. 21P 1 4. 22J 1 3.11.9 2 1 213 2 3: 2 5, 2 6. c2 j, 3 8.30.9 1 7.48.9 1 6. 86P 1 6.47, 1 6. 25, 1 6 19.9 1 6: 26.9 1 3.23p 2 1.889 1 4.27p-1 8.081-1 1.39, 0 2.20.1 0 7.93 p 1 7*63,1 1 7-h8l 1 7.28.9 1 7. 13 1 7.03 1 7.011 1 6.671-1 5.66$-l 6.071-1 6.691-1 8.761-1 1. UP 1 9-79, 0 1.57, 1 5-48Y 1 1-48P 2 6.111 0 5.65, 1 3.80) 1 1.889 1 4.44, 0 1. o6, 0 6.87, 0 1.913% 1 It. 01.9 1 4.74, 1 7.95, 1 3.29, 2 2-48Y 1 2 3 OP 2 6:45, 1 5.39, 1 4.39, 1 3.62.9 1 3. 25, 1 3.33, 1 3. 80P 1 3. 23, 2 7.9 86, 3 1. 261 0 4 29.1 0 1: 14, 1 6.35.9 0 7.11.9 1 8.34, 1 6.40, 1 5.4 5 5. 161 1 5. UP 1 5-26,9 1 4. go., -1 2.05, 0 5-08P 0 4.53, 0 6.19.9 0 5*672 0 7. 25, 1 6.90.9 1 6.63, 1 6.45, 1 6.339 1 6. 29.1 1 6.32.9 1 4.52.9 -1 4.40.1-1 4.839-1 6.203-1 3.71.$ 1 4.273 1 3.081 2 2.03 2 1.561 1 1.20.$ 0 4.183 1 2.08.1 1 8.94.9-1 7. 40.1 -1 7.00"-l 7. 18 J, -1 8.42.1-1 3. 22 2..9 6.94, 3 7 72.9 0 2: 86.9 1 7 81) 0 5: 883-1 5.24, 1 4. o4. 1 2.83., 1 1. 853 1 1.35,9 1 1.44, 1 2. o6.V 1 8.811-1 5-181 0 9.62 3 0 8 C21 0 2: 82.9 2 2 50.9 2 5: 860 1 5.21.9 1 4.6o 1 4.13 1 3.93., 1 3.813 1 4.02 1 3.26 0 4 44, 0 4:41.$ 0 3.4o., 0 2.52 3 0 2.39, 0 6.451 1 6*733 1 5.903 1 5.693 1 5.509 1 5.383 1 5oh33 1 3.79) -1 3.80$-l 4. 55 J, -1 3. 221 2 5.78,p 3 6. 16.9 3 6.49, 2 5. 66.p -1 3. 56.1-1 3.45, 1 1-37, 1 8.173,-l 6.50.0 -1 5.761-1 5.653-1 6.34 5 -1 2.06.1 0 1.179 1 1 59.9 3 5:15, 0 1 29, -0 1:46J-1 4-39j, 1 3.09, 1 1.71) 1 4.49, o 8. 83 j -1 8.55,-l 9. 13 lp -1 4 - 74,; 0 5.66.1 0 4.095 2 4.26.9 0 6. go., -1 1.635-1 5. Oll 1 4.295 1 3.57, 1 2.97, 1 2. EM 1 1 Y 2 47., 1 2:67, 1 1.62P 0 3.33) 0 1.311 2 5.55, 0 2. o6., 3 6 12.9 -1 5:441 1 5-131 1 L. 84) 1 49621 1 4.50 1 4.41 1 4.461 1 6.79j, I 3.44,-l 3.64.,-l 8. 96.) 0 3.58.2 3 8.39, 0 9.381-1 7.6h.1-2 4.681-2 3o67y 1 1. 88P 1 9.57, 0 6. 81.1-1 5. 5 5,p -1 5.012-1 5.19,-l 1.025 1 4.92.9 1 4 34., 1 7:58P 1 3.04,9 -1 5.51$-l 4.213 1 3 02.9 1 1: 52.9 1 9.26.9-1 8. 07, -1 7.482-1 7.62.9 -1 2.78.9 2 6.66Y 0 1. 84, 0 8*73p-l 3.23.9 -1 4 389 -2 4:6o, 1 3.85, 1 3. o6, 1 2.33, 1 1.761 1 48.9 1 54 j, 1 2.981 2 1.64, 0 8.011-1 h. 26.1 -1 1.96.1-1 6. 931-2 4. go.) 1 4.56 1 4.23 1 3o953 1 3.75, 1 3.64 y 1 3 o 65.9 1 4.92i 1 3.38.1-1 2-37y 2 1. ill% 1 2. h 1.T 0 9. 09 y -1 2. 191-1 2.32.1-2 4.42Y 1 2. 96P 1 1.361 1 1-57y 0 6.36 IV -1 5.19.9 -1 4.85y-l 1. 73 j, 1 4*74y 1 1 97.9 0 5: 67 y -1 1. 04.,-1 3.57,-2 4.63, 1 3 74,p 1 2: 252 1 7.65Y 0 8.631-1 7.51.9-1 7-a6$-i 2.775 0 4.4o.f 0 6.66,9 0 1.98P 1 2. 00- I -1 9 64 5, -i 4: 84.9 1 4.07y 1 3*h5j 1 2.489 1 1. 77.9 1 1. 262 1 1.08.9 1 7.20.9 -1 6.68.1-1 5. 24.9 -1 3. 241-1 1.291-1 1. 94.1-2 4. 84P 1 It - 50.9 1 4.15, 1 3.83 j, 1 3.57.9 1 3.39-9 1 3.33 p 1 4.68.9 1 7.30,0 0 1.10.0 1 1.50.9 1 2.70.9 1 9.30.9 1 8.98p 3 7.77p 1 7.13, 1 6.27p 1 I-.Ln N BISTATIC CROSS-SECTION (a IN M2) FOR THE B-47 AIRCRAFT (The numbers following comma indicate multiplication by that power of 10) Ot = 15'

2260 - 29 - F TABLE H - 3 OR OR OTU00 OT=150 OT=300 OTw450 OTz6oO OT=750 OT=900 OT=1050 OT=1200 OT=1350 OT=150'D OT=1650 OT=1800 30 30 30 30 30 30 30 30 30 30 30 30 30 45 45 45 45 45 45 45 45 45 45 45 45 45 60 60 60 60 60 60 60 60 60 60 60 60 60 0 15 30 45 60 75 90 105 120 135 150 165 180 0 15 30 45 60 75 90 105 120 135 150 165 180 0 15 30 45 60 75 90 105 120 135 150 165 180 0 15 30 45 60 75 90 105 120 135 150 165 180 2.50 s 0 2-71s 0 3.159 0 3.94.9 o 5.082 0 1.50s 1 8.312 0 2.22, 1 2-03,9 1 3 2 8.p1 1:36, 2 2.70, 2 4.33, 3 3.69.9 0 3.44, 0 4.27, 0 4.95, 0 6. ol,,o 7.79s 0 1.020 1 1.23, 1 1.68, 1 2-78s 1 4.25, 1 7.89, 1 1.13, 2 5.24s 0 5,379 0 5*69p 0 6.26, o 7.13 s 0 8.372 0 9.800 0 1,17s 1 1,719 1 3.36,9 1 3.27s 1 2.87, 1 2.520 1 7.24, 0 7.352 o 7.56,o o 7.92.9 0 8.482 0 9.2o,, 0 1.01, 1 1.102 1 1.23s 1 1.38s, 1 1.63, 1 1.67, 1 6.92, 0 2.69, o 2.67s 0 2.929 0 3 o 54,v0 4*50P 0 5.99, 0 1.27v 1 1.13.91 1 - 93,v1 3.522 1 4.28, 3 5915P 0 3.89o 0 3.88s 0 4.712 0 4.74, o 5.65,po 6o98s 0 8090, 0 1 o 26,1 2.28, 1 9oO3s 1 1.37, 2 6 o 84,1 lo25, 1 5o482 0 5.5o, o 5.73, 0 6.02, 0 7. o5,o 8 o 16.90 9.64, o 1*220 1 10102 1 2 * 08,p1 2o962 1 5 o 66,0 1.102 2 6.66,po 6 o68,0 6o779 0 8.,15,po 8o67o 0 9o45s 0 1.010 1 1-14s 1 lo27o 1 1.46,p1 lo59o 1 9.73p-l lo4ls 0 3.08, 0 3.5o, o 4.47 s 0 5 92,9 0 7: o6., o 2.62 x 1 9.54, 1 8.58i 3 8.63, 3 7.96.9 o 4.9is-1 4.45,, o 4.31.9 0 4*47p 0 5.01.9 0 5.90, 0 7.30o 0 9*56p 0 1.30, 1 2.88, 1 5.26, 1 1.143, 2 7.88, 0 1.989 o 6.23, 0 6.14, o 6*37P 0 6*95P 0 1.65, 0 8.90,0 0 1.08, 1 1.49s 1 1.95, 1 3.03s 1 4.77 o 1 1.U., 1 9.880-1 8.800 0 8.722 0 8.87o 0 9.182 0 9,86', 0 1,08, 1 1.23, 1 1.39, 1 1 - 74,p1 1.95s 1 8.93, 0 6.362 1 8.91,9 0 4 9 01, 0 5 * 04, 0 6.70 0 1 2. o6., 1 6.04.9 5 8*67p 3 9.41P 1 7.23p 1 7-00p I 5.44,v 0 5.17p 0 4.9is 0 5.82, 0 6.92p 0 8 o 74p 0 1.192 1 2.14,p 1 4.68, 1 7.952 1 8.42 p 3 7.30, 1 7.19, 1 7.72 p 0 7.44p 0 7.57, 0 8-17p 0 9.28p 0 1.08P 1 1.4op 1 1.96., 1 4,31p 1 4-88p 1 1. o6., 1 7.77Y-1 2.90p-l 2.03 v 1 1.17, 1 1 * 12,P 1 1.13,v 1 1.24P 1 1.43 p 1 1.74p 1 3.74P 1 1.09s 2 9.54P 0 6.20p 0 6.78p-1 2.36p-l 6.23o 0 8.77, 0 1*50,v 1 6.37s 1 8.63 s 3 1.402 2 7.o4,, 1 6.662 1 6.65., 1 7.62, 0 6.59s o 6,682 o 7.32, 0 8.90, 0 1.172 1 1.77, 1 5.07 s 1 1.3 2,p2 8.980 1 8 * 94.p1 7.323, 1 7.17, 1 1.229 1 1.072 1 1.21, 1 1.07, 1 1.26, 1 1.54, 1 3.112 1 1,20, 2 1.663 1 7.49P 0 9.18 o 3 7.23, 1 7.19s 1 1.52, 1 1.522 1 1,562 1 1.712 1 2.03 s 1 2.71, 1 3,13 s 1 3.822 1 6.55, o 4*87P 0 2.85, 0 2.282-1 1. 71i -1 1. 43,p 1 4.66, 1 8.589 3 2.33, 2 1.81, 2 6.14,p 1 5,97s 1 6. og, 1 9.30.9 0 1.43, 1 8.99.9 o 1.01,0 1 1.312 1 2.34s 1 1.32.9 2 8.Ul 1 9.41, 1 7.5o, 1 7.50, 1 6.72.9 1 6.70, 1 1.38.9 1 1.38,p 1 1.49, 1 1.712 1 2.742 1 4 012 1 5:86,9 1 1.182 1 7.85.0 1 7.49s 1 7.252 1 7.65s 1 7.4o, 1 2.66s 1 2.6gs 1 2 9 94.p1 2.25, 1 3.695, 1 4.452 1 7.18, 1 3.769 0 2 *51# 0 1,610 0 9.362 3 8.17, 1 7.20, 1 1.422 4 9.4o, 1 6*482 5.64, 5.20.* 1 5-04, 1 5.312 1 4.36, o 3.81o 0 4.58 o 0 7.572 1 2.13,0 2 2. 06,v 2 6.96o 3 1. 06.t 2 7.87, 1 6.59t 1 6.93,P 1 6.09s 1 6.16,9 1 1.512 1 1.47, 1 1.91, 1 3.07, 1 6.88, 1 1.79, 2 8.03,p 3 8.032 1 7.911 1 7.182 1 6.920 1 6.78s 1 6.75.9 1 8.812 1 9.03, 1 1.09, 2 1.399 2 2.020 2 2.82, 2 8.98.9 3 7.422 1 7-35s 1 7.26.9 1 8.772 1 7.30, 1 7.76, 1 6.62.1 1 5.53, 1 4-56t 1 4.ol, 1 3.98s 1 4.43 o 1 1.3 7.1 1.26, 1 1.812 4.56o 1.810 2 6.94,v 1 1.80o 3 1-34s 2 6.760 1 5-95s 1 6.212 1 5.49s 1 5.64.9 1 6.51o 1 7.15, 1 1.01, 2 1.732 2 3.25, 2 1. 16 j1 9.01, 1 7.79o 1 7-18o 1 6,8o, 1 6.59.9 1 6-51s 1 6.53, 1 3.13.9 2 3.210 2 9.36,p 3 1.51, 0 2.53, 0 3.65, 0 7-89o 1 7.84, 1 7.592 1 7.39j, 1 7.25s 1 7.16.9 1 7.142 1 4.24, 1 3*08, 1 2.42, 1 2.44.0 1 3.05, 1 5.022 1 5.6o, 1 1.02, 2 2.77, 2 8.212 1 8.54, 1 7 - Uv 1 6.30.v 1 5.57, 1 4.93.9 1 5.80, 1 4.43, 1 4.65s 1 2.8o, 2 2.96, 2 9.182 3 7.53 s 0 1.48, 1 1 53 s, 1 3:590 2 7.25, 1 6.432 1 6,07i 1 6.34,p 1 5,77, 1 6.12.v 1 5.98,p -1 1,38s 0 2.84, 0 6.46,p o 7.97, 0 5. go, o 7.55,p 1 7.23, 1 6. 98,p 1 6.81, 1 6.71, 1 6.66.9 1 6,672 1 1*68p 1 7.85P 0 7 07 s, 0 1:41p 1 2.20p 2 2.53 p2 8.42 p3 1.46.92 2.49, 1 2.73 p0 6.322 1 5.512 1 4.66,t1 3-90p 1 4-76P 1 3.25o 1 3-51P 1 i.o5, o 3.61P o 1.02p 1 2.18p 1 2.02p 2 5 12,t0 6:62, 1 6.14,p1 5.69.v1 5 30, 1 5:12, 1 4-94, 1 5-ols 1 2.92p 0 4-54P o 5.49joo 5 949p0 5.47 p0 9.02p 0 1.43 p2 8.23p 1 6.43, 1 6*50p 1 7.22, 1 6-07p 1 6.09p 1 8.712-1 8.192-1 8.712-1 2.49, o 1.75, 1 3.86, 3 9.152 1 1.94i,1 1.35, 0 6.05, 1 5.001 i 3.99s 1 3-09p 1 3.39,t1 2,152 1 2.35, 1 5*352 0 1.39j,1 1,12.*3 1.08, 1 2. llj0 5. ogs -1 6.100 1 5.592 1 5 '- 08,1 4.62 -1 4,29,91 4.14, 1 4.20, 1 3.05, 0 7.18, 0 3 13.92 1:36,p1 1.412 1 1.102 0 6.31, 1 6.07, 1 4.86.v1 5.69.91 5.59, 1 5.49, 1 5.502 1 7.47j-1 7.52 s -1 1. 96,P 1 2.242 3 1.67s, 3 4-19s 0 4.321-1 2.341-2 5.83, 1 4.75, 1 3-77s 1 2.77, 1 2.42 x 1 1.432 1 1.43, 1 5.21, 1 3.40s 1 7.27, 0 5.45, 0 5.79, 1 9.78s 3 5.823, 1 5-30s 1 4.75,9 1 4 23, 1 3:82.v 1 3*58P 1 3.57x 1 2.88, 1 4e94s 0 2.12 J, 0 1.09, 0 4,91P-1 1.161-1 5.98,p 1 5 74,p 1 5.5o, 1 5.30, 1 5.15, 1 5.05p 1 5 * 04, 1 7.161-1 1.642 2 2.72, 1 5, 9 9,p 0 1.3 5.v 0 2.76,-l 3078.9-2 5.73, 1 4998, 1 4.11o 1 5.24, 1 1.92.9 1 1.3 5, 1 1.08, 1 1.15, 1 2.64, 2 2.81x 2 2.29s 0 2.6 7 j, -1 4*09.9-2 6.37s 1 5.4is 1 4.98.9 1 4.27o 1 3.782 1 3.45, 1 3.33, 1 1.99, 0 1. 02 s 0 1.599 o 1-13s 0 5.46 s -1 7.141-2 5.92, 1 5.682 1 5.44, 1 5.222 1 5.o4, 1 4.912 1 4.87, 1 90 all l.o5, 1 1.18, 1 1.610 1 2.13, 1 4.00, 1 1.22, 2 9-80s 3 7.262 1 7.26, 1 6.68, 1 1.07, 2 5.87, 1 5.72, 1 I.Un W BISTATIC CROSS-SECTION (aIN M2) FOR THE B-47 AIRCRAFT (The numbers following comma indicate multiplication by that power of 1 0) a - =,zno

SECRET 2260 - 29 - F TABLE H - 4 @R t T2=0o~ T=15~ 0T=30~ 0T=45~ 0T=~0 T=T15~ $T=90~ T=105o OT=120~ F1350 00o~ 165' 0r=180o 45 45 45 45 45 45 45 45 45 45 45 45 45 60 60 60 60 60 60 60 60 60 60 60 6o 60 60 60 60 60 60 60 60 60 60 75 75 75 0 15 30 45 60 75 90 105 120 135 150 165 180 0 15 30 45 60 75 90 105 120 135 150 165 180 0 15 30 45 60 75 90 105 120 135 150 165 180 5.24, 0 5.39, 0 5.94, 0 6.93, 0 8.50, 0 2.59, 1 1.39, 1 2.12, 1 3.31, 1 7.26, 1 1.58, 2 3.52, 2 3.0U4, 3 7.31, 0 7.44, 0 7.88, 0 8.78, 0 1.01, 1 1.19, 1 1.66, 1 1.96, 1 2.71, 1 3.98, 1 1.37, 2 7.04, 1 8.43, 1 1.02, 1 1.04, 1 1.08, 1 1.12, 1 1.24, 1 1.36, 1 1.49, 1 1.71, 1 2.12, 1 2.56, 1 2.89, 1 2.95, 1 2.00, 1 5.47, 0 5.90, 0 6.77, 0 8.08, 0 1.01, 1 1.51, 1 2.14, 1 3.46, 1 8.16, 1 2.28, 2 3.02, 3 2.06, 1 7.50, o 8.6o, o 8.07, 0 8.75, 0 9.98, o 1.18, 1 1.47, 1 2.08, 1 3.55, 1 5.95, 1 8.64, 1 1.14, 2 3.15, 2 1.07p 1 1.08, 1 1.10, 1 1.16, 1 1.26, 1 1.37, 1 1.44, 1 1.86, 1 2.25, 1 2.72, 1 3.19, 1 2.22, 1 2.63, 1 6.25, 0 7.08, 0 8.48, 0 1.07, 1 1.52, 1 4.80, 2 6.91, 1 2.92, 2 6.07, 3 2.14, 1 2.76, 0 8.36, 0 8.33, 0 8.62, 0 9.48, 0 1.07, 1 1.28, 1 1.67, 1 2.54, 1 3.98, 1 7.4O, 1 4.21, 2 1.36, 2 1.30, 2 1.21, 1 1.20, 1 1.24, 1 1.29, 1 1.41, 1 1.56, 1 1.87, 1 2.29, 1 2.91, 1 3.81, 1 6.03, 1 1.38, 3 3.71, 1 8.07, O0 9.62, 0 1.27, 1 2.o5, 1 6.68, 1 1.67, 4 6.13, 3 1.45, 2 7.54, 1 7.19, 1 9.82, 0 9.62, 0 9.99, 0 1.09, 1 1.27, 1 1.62, 1 2.33, 1 3.81, 1 8.31, 1 8.80, 2 3.41, 2 3.25, 2 7.50, 3 1.97, 1 1.53, 1 1.51, 1 1.60, 1 1.79, 1 2.18, 1 2.87, 1 4.71, 1 5.17, 3 6.85, 1 5.09, 1 5.64, 1 5.76, 1 1.21, 1 1.76, 1 3.42, 1 9.86, 1 6.11, 3 3.32, 2 8.60, 1 7.11, 1 6.99, 1 3.07, 1 1.27, 1 1.26, 1 1.40, 1 1.74, 1 3.17, 1 4.12, 1 2.40, 2 2.77, 2 8.42, 3 7.96, 1 7.31, 1 7.19, 1 2.08, 1 2.09. 1 2.16, 1 2.66, 1 5.37, 1 5.71, 1 5.31, 1 6.51, 1 7.12, 1 7.73, 1 1.34, 2 2.45, 2 2.94, 2 4.%, 1 3.77, 2 6.09, 3 1.21, 3 7.42, 2 7.09, 1 6.71, 1 6.69, 1 1.62, 1 1.66, 1 1.73, 1 2.29, 1 3.46, 1 1.26, 2 3.54, 2 3.78, 2 9.88, 1 8.14, 1 7.48, 1 7.16, 1 7.06, 1 2.96, 1 2.99, 1 3.32, 1 3.55, 1 4.74, 1 7.28, 1 9.93, 1 1.48, 2 3.27, 2 8.42, 3 7.39, 1 7.24, 1 7.209 1 1.4o, 4 2.25, 2 8.84, 1 7.14, 1 7.17, 1 6.25, 1 6.27, 1 1.50, 1 l.$57 1 1.92, 1 3.07, 1 6.99, 1 1.63, 2 9.02, 3 1.04, 2 9.43, 1 7.37, 1 6.98, 1 6.83, 1 6.80, 1 5.47, 1 6.09, 1 6.52, 1 8.17, 1 1.24, 2 2.26, 2 9.80, 3 7.86, 1 7.66, 1 7.44, 1 7.26, 1 7.67, 1 7.65, 1 7.87, 1 6.90, 1 6.43, 1 6.10, 1 5.94, 1 5.99, 1 3.05, 1 3.73, 1 4.53, 1 8.00, 1 3.4i, 2 5.01, 1 1.32, 2 1.90, 2 2.86, 2 7.58, 1 6.85, 1 6.75, 1 6.75, 1 3.11, 2 3.21, 2 3.24, 2 8.42, 3 6.61, o 8.71, 0 8.39, 1 9.96, 1 7.81, 1 7.52, 1 7.36, 1 7.27, 1 7.25, 1 6.33, 1 5.82, X 5.44, 1 5.26, 1 5.34, 1 1.05, 2 1.20, 2 3.20, 2 8.42, 3 5.99, 1 2.13, 3 2.32, 2 7.52, 1 6.90, 1 7.34, 1 6.41, 1 6.28, 1 6.29, 1 9.46,-1 2.37, 0 5.00, 0 8.56, o 1.11, 1 1.80, 1 8.13, 1 7.71, 1 7.34, 1 7.11, 1 7.00, 1 6.95, 1 6.95, 1 5.23, 1 4.78, 1 4.56, 1 4.63, 1 7.50, 3 1.30, 1 2.61, 1 1.09, 2 2.89, 2 1.03, 1 7.22, 1 6.78, 1 6.43, 1 6.13, 1 5.91, 1 5.78, 1 5.79, 1 3.55, 0 2.49, 1 1.10, 1 1.43, 1 2.66, 1 4.90, 2 1.03, 2 7.38, 1 6.90, 1 6.76, 1 7.15, 1 6.61, 1 6.61, 1 4.24, 1 3.95, 1 3.98, 1 8.26, 0 3.01, 1 2.97, 3 5.27, 1 1.97, 1 4.98, 0 6.85, 1 6.466, 1 6.0o, 1 5.75, 1 5.49, 1 5.33, 1 5.33, 1 7.24, o 1.97, 1 9.15, 2 6.77, 1 1.18, 1 2.59, 0 6.994,1 6.74, 1 6.58, 1 6.45, 1 6.38, 1 6.29, 1 6.28, 1 3.57, 1 3.51, 1 5.07, 1 1.71, 3 2.96, 2 1.37, 3 2.06, 2 1.20, 2 6.65, 1 9.10, 1 5.91, 1 5.53, 1 5.23, 1 5.03, 1 4.99, 1 6.26, 1 2.73, 1 8.64, 0 4.30, 0 1.93, 0 6.21,-1 6.73, 1 6.55, 1 6.39, 1 6.25, 1 6.14, 1 6.06, 1 6.0o, 1 3.33, 1 1.23, 2 2.10, 3 1.-92, 1 2.83, 0 6.12,-1 7.92.-2 6.65, 1 8.02, 1 5.99, 1 5.64, 1 5.19, 1 4.96, 1 4.87, 1 9.09, 0 9.52, 0 1.21, 1 2.37, 2 7.10, 0 6.92,-1 9.09, 1 6.58, 1 6.38, 1 6.22, 1 6.0o, 1 5.99, 1 5.96, 1 90 all 1.54, 1 1.67, 1 2.56, l 2.86, 1 3.93, 1 9.32, 1 1.o4, 4 7.42, 1 7.44, 1 7.07, 1 2.69, 2 6.62, 1 6.48, 1 eJl BISTATIC CROSS-SECTION (a IN m2) FOR THE B-47 AIRCRAFT (The numbers following comma indicate multiplication by that power of 10) $ @ SM t OT=5

TABLE H- 5 R OR 0T0 T150 T=30~ 0T=45~ Po=60~ 0T=750 T=90~ 0T1O0~ 4-120~ 0T135~ Tl5Oo 0t=165~ 4;=180~ 1I 1 - 60 60 60 60 60 60 60 60 60 60 60 60 60 0 15 30 45 6o 75 90 105 120 135 150 165 180 0 15 30 45 60 75 90 105 120 135 150 165 180 1.00, 1 1.04, 1 1.17, 1 1.38, 1 1.56, 1 9.60, 1 2.60, 1 3.50, 1 7.10, 1 9.30, 1 2.83, 2 3.76, 2 2.47, 3 1.10, 1 1.10, 1 1.30, 1 1.58, 1 2.00, 1 7.20, 1 4.10, 1 8.30, 1 1.77, 2 5.75, 2 2.47, 3 7.77, 1 1.30, 1 1.40, 1 1.70, 1 2.30, 1 3.60, 1 5.70, 5 3.24, 2 1.35, 3 4.94, 3 6.52, 1 1.01, 1 1.50, 1 2.00, 1 2.90, 1 4.30, 1 2.38, 2 6.49, 3 5.01, 3 2.84, 2 8.30, 1 7.146, 1 - 75 n 75 75 75 75 75 75 75 75 75 75 75 75 1.70, 1.70, 1.80, 2.00, 2.10, 2.10, 2.15, 3.40, 5.00, 9.00, 1.19, 8.10, 7.60, 1 1 1 1 1 1 1 1 1 1 2 1 1 1.70, 1.70, 1.80, 1.90, 2.05, 2.50, 2.80, 5.20, 7.20, 1.10, 1.87, 9.43, 2.42, 1 1 1 1 1 1 1 1 1 2 2 1 2 1.80, 1.80, 1.90, 2.20, 2.35, 2.75, 3.30, 4.20, 6.80, 1.14, 8.70, 2.20, 8.50, 1 1 1 1 1 1 1 1 1 2 1 2 1 2.70, 2.50, 2.30, 2.55, 2.80, 3.50, 5.45, 7.90, 3.15, 4.64, 6.10, 9.21, 8.140, 1 1 1 1 1 1 1 1 2 2 1 1 1 3.20, 3.80, 8.70, 4.77, 4.99, 7.32, 1.22, 7.48, 7.21, 4.00, 3.50, 2.90, 3.20, 4.50, 8.80, 7.65, 5.69, 2.03, 2.07, 2.02, 1.05, 2.46, 1 1 1 2 3 2 2 1 1 1 1 1 1 1 1 2 2 2 2 2 4 2 1.13, 2 2.93, 2 4.98, 3 2.40, 4 1.73, 3 9.84, 1 7.12, 1 7.03, 1 4.10, 1 4.20, 1 4.40, 1 6.50, 1 1.25, 2 1.59, 2 1.95, 2 1.69, 2 1.05, 4 9.26, 1 7.95, 1 7.35, 1 7.22, 1 1.47, 4 1.94, 3 4.23, 2 1.24, 2 1.82, 2 6.87, 1 6.83, 1 5.20, 1 5.30, 1 6.80, 1 8.80, 1 1.56, 2 1.68, 2 1.05, 4 1.05, 2 9.18, 1 8.09, 1 7.48, 1 7.18, 1 7.12, 1 1.36, 2 8.12, 1 7.42, 1 7.07, 1 6.94, 1 6.93, 1 1.16, 2 1.23, 2 1.38, 2 1.78, 2 1.04, 4 4.18, 1 1.15, 2 1.04, 2 8.93, 1 8.65, 1 7.49, 1 7.36, 1 7.35, 1 7.23, 1 6.95, 1 6.79, 1 6.68, 1 6.67, 1 2.45, 0 -1.05, 4 2.29, 1 3.27, 1 5.02, 1 7.28, 1 2.21, 2 7.67, 2 5.12, 3 1.03, 2 7.25, 1 7.19, 1 7.19, 1 6.72, 1 6.54, 1 6.42, 1 6.40, 1 7.57, 0 1.81, 1 3.86, 1 9.27, 1 2.22, 3 3.68, 2 1.16, 2 7.95, 1 7.30, 1 7.14, 1 7.54, 1 7.02, 1 7.02, 1 6.34, 1 6.19, 1 6.17, 1 2.23y 6.97, 2.55, 7.07, 4.66, 1.14, 7.56, 7.22, 7.07, 7.00, 6.98, 6.87, 6.87, 1 1 3 2 1 1 1 1 1 1 1 1 1 6.05, 1 6.01, 1 2.20, 3 1.47, 3 7.63, 1 6.76, 1 4.45, 1 1.44, 1 7.31, 1 7.10, 1 7.01, 1 6.93, 1 6.87, 1 6.78, 1 6.76. 1 5.96, 1 1.05, 2 7.12, 2 8.85, 2 6.79, 2 6.75, 1 2.86, 1 7.42, 1 7.35, 1 5.92, 2 7.09, 1 6.90, 1 6.78, 1 6.74, 1 0 T1 z H I? -0 tt Po 0 *-a ) —O Cn UiH 5IJ ifl -J 90 all 3.00, 1 3.50, 1 6.80, 1 8.10, 1 1.05, 2 1.69, 2 1.09, 4 7.88, 1 7.87, 1 7.70, 1 8.21, 2 7.96, 1 7.31, 1 BISTATIC CROSS-SECTION (,o IN m2) FOR THE B-47 AIRCRAFT (The numbers following comma indicate multiplication by that power of 10) I

TABLE H- 6 % OR 0Tf 00 4Tj.50 4P~-300O 4=450 $f=600 4~-750 OT4900OT4j1050 %qf1200 4T-1350 4T150 0 Or-165' $vr-1800 1 --- IInn-.1 75 75 75 75 75 75 75 75 75 75 75 75 75 0 15 30 45 60 75 90 105 120 135 150 165 180 2.30,p 3.20,p 3.60., 3.80,9 4.*70,9 2.02,9 4.70, 9.50,, 1. 27, 2.18,9 4.93, 4.64, 2.223, 1 1 1 1 1 6 1 1 2 2 2 2 3 3.30,9 3.30,9 3.50,9 3.*50,v 5.o00,9 1.71,9 2.*18,9 2 * 72,v 5.85, 1.53,p 2.20, 6.35, 1 1 1 1 1 3 2 2 2 4 3 2 3.40,, 3.40,, 4.10, 5.40, 1.o52,1 4.31,o 3.07, 8.38,v 4.43,s 5.o03, 6.68, 1 1 1 1 2 3 3 4 3 2 1 3.90, 1 5.10, 3. 9.50, 1 1.81, 2 7.75, 2 3.89s,3 4.49, 3 9.97, 2 1.32,02 8.*76, 1 9.00,9 1 1.32, 2 2.76, 2 1.21, 3 4.48, 3 1.87, 3 3.44,9 2 8.84, 1 7.66,p 1 2.22,o 8.*53., 4.47,9 1.35, 2.39,v 2.51, 7.68,t 7.27, 2 2 3 4 3 2 1 1 1.53,p 1.*45,p 1.87,9 1.48,0 6.79,9 7.24,9 7.12, 4 6 3 3 2 1 1:'l a'% 7.80,9 2.36, 3.32,0 9.65, 8.50, 7.90,p 2 2 2 1 1 1 9.5 9, 1 8. 96, 1 7.43,p 1 7.37, 1 7.40, 3. 0 T10 7.39,9 1 7.49, 1 7.36, 1 7.40, 1 z~ I*r.h mLJ 0 7.56, 7.*38,p 7.38,p 1 1 7.46, 1 1 7.40, 1 7.49, 1 90 all 1.25, 2 1.44, 2 3.80, 2 7.41, 2 3.39, 2 3.79, 2 1.13, 4 1.80, 2 1.07, 2 1.16, 2 2.37, 3 1.37, 3 1.36, 2 BISTATIC CROSS-SECTION (or IN in2) FOR THE B-47 AIRCRAFT (The numbers following comma indicate multiplication by that power of 1 0) T-= 750 z

_ __ z a~ ) — LITflI Hirfl -I0J prfl #1ii TABLE H-7 GR 0R=0o~ 0R=15~ 0R30~ H-450~ 0R=60o~ $R75~0 0R900 0R=105~ R=-120~ 0R*135~ 0R=150~ PR-165~ 0R=180~ 90 1.55, 4 1.55, 4 1.55, 4 1.55, 4 1.55, 4 1.55,, h 1.55, 4 1.55, 4 1, 1.55, 4 1.55, 4 1.55, 4 1.55, 4 BISTATIC CROSS-SECTION (a IN m2) FOR THE B-47 AIRCRAFT (The numbers following comma indicate multiplication by that power of 10) T= 90~ and ALL XT The values omitted from the preceding tables can be obtained by reading the entries corresponding to an interchange of the subscripts R and T rsj 0-< o 'O ' L=T1 Hifl -j (n ) _I 0 z.2 -

U NIVERSITY OF MICHIGAN 2260-29-F APPENDIX I CORNER REFLECTOR EXPERIMENTS AT OHIO STATE UNIVERSITY Under Contract AF 30(635)-2811 the Antenna Laboratory of the Ohio State University Research Foundation is investigating the design of reflectors suitable for use with cross-linear and circularly polarized radar systems where maximum discrimination against rain clutter is desired. In their Quarterly Progress Report for the period ending 31 March 1955 (Ref. 17) some of the results obtained for modified corner reflectors are reported. As of that date all of the patterns of reflectors investigated were measured using linear polarization; in that report (i. e., Ref. 17) it is stated that analysis and measurement of circularly polarized return from modified corner reflectors was planned for the next reporting interval. 1 Of the modifications on corner reflectors being studied at Ohio State the one which is of interest in this paper is the one in which one or more of the surfaces of the corner is lined with a layer of dielectric. This modification is examined in Reference 17 for two types of corners: a "double-double bounce" corner (Fig. I-1) and a triangular corner reflector. Reflection patterns were obtained for two double-double bounce corners using horizontal polarization at K-band (X=1/2 inch). Both doubledouble bounce corners had four-inch square apertures and the "modified corner" differed from the "standard" one only in that the upper and lower surfaces were lined with 1/16-inch thickness lucite sheets. The reflection patterns obtained are reproduced in Figure 1-2. It will be observed that the null obtained along the axis of the "standard" corner is completely eliminated by using the indicated modification with little change in the remainder of the pattern being obtained. 'At the time of the writing of this report the 0. S. U. Progress Report dated 16 June 1955 was being bound and thus no copies were available. Information received in a letter from the Antenna Laboratory of O. S. U. indicates that they are preparing a technical report on the subject which will be completed in the near future. 158 E c r'r-L-r

LLIr 77 UNIVERSITY OF MICHIGAN - 2260- 29- F I I I I I I N N ' N I FIG. 1-1 DOUBLE - DOUBLE BOUNCE CORNER USED IN OHIO STATE UNIVERSITY MEASUREMENTS 159 l - ol, r- I i 77

to upper and lower surfaces) L f 28.4 uj 18.5 0 > 9 9.5 -' ' _ LLL _ _ I_ I____ I 60 40 20 0 20 40 60 DEGREES OFF AXIS FIG. 1-2 REFLECTION PATTERNS OF "DOUBLE - DOUBLE BOUNCE" CORNERS (four-inch square aperture, horizontal polarization, measured at K-band (X=Y2 inch)) -i P N z G I r InI II O". I 0 I

I U NIVE RS ITY OF MI CHIGAN 2260-29-F For the triangular corner reflector, only theoretical considerations are reported in Reference 17. A brief resume of these theoretical considerations is as follows: For an unmodified corner reflector the S-matrix, referred to a linear polarization basis, is of the form 1 0) 0 1 i.e., there is no cross-polarization return and the phase difference between the orthogonal components is not changed. However, on introducing a dielectric coating on one or more of the faces, in general there will be a change in the phase difference of the two components while there still will be no cross-polarization return. The S-matrix then will be of the form ig e 0 0 e-i where 2G is the change in phase difference between the two components and 0 will depend upon the dielectric constant, the thickness of the coating, and the angle of incidence. It is to be noted that the ray picture is unaltered by the introduction of the dielectric coating, that is, the effect of the dielectric on the ray picture is a parallel displacement of the rays. Referred to a circular polarization basis, the S-matrix in the unmodified corner reflector in triple reflections is of the form (: 1) i.e., for right-circular incident radiation, left-circular emerges and vice versa. Upon modification, however, the S-matrix takes the form (sin G cos 0\ (cos 9 -sin 0 which, for sin 90 0, indicates a non-vanishing return for the same emergent and incident circular polarization. Since the latter form of the S 1........ 161_______.. L- Lr

UNIVERSITY OF MICHIGAN 2260-29-F matrix was obtained by a coordinate transformation of the linear basis S-matrixit is again noted that the ray pictures remain the same. Coverage diagrams were computed for a triangular corner reflector for linear polarization and for a triangular corner reflector with a sheet of polystyrene of thickness (X/16) on one face for circular polarization. These coverage diagrams are repeated, in part, in Figure I-3a, and the coordinate system involved is shown in Figure I-3b. 1 With reference to these coverage diagrams, it is stated in Reference 17 that: "The echo contours are drawn for 1 db variations in echo area relative to the maximum obtained with the unmodified triple-bounce corner. It is seen that the peak return for circularly polarized waves is about 5 db below that for linear polarizations. The 3-db down points for the circularly polarized return enclose a region approximately 40 degrees wide in azimuth and 20 degrees in climb angle. The center of this region is 15 degrees below the symmetry axis of the corner. The improvements to be obtained by use of coatings on more than one face, or several layers of different dielectric material in each coating, are under study. A special report on the polarization properties of a corner with such modifications is in preparation. " 'In Reference 17 the coverage diagrams are drawn for 1 db variations in echo area; only "odd-numbered" db variations are shown in Figure I-3a. 1162

L-, r I r- I I i 7r - UNIVE RS ITY OF MICHIGAN - 2260- 29- F 300 20~ 10~ 10~ 20~ 30~ FIG. I-3a COVERAGE DIAGRAM -TRIANGULAR CORNER REFLECTOR FIG. I-3b COORDINATE SYSTEM FOR COVERAGE DIAGRAMS OF FIG. I-3a 163 LI' 7r

-— UI NIVERSITY OF MICHIGAN 2 260-29-F REFERENCES Number 1. (a) RM-1080, Research Memorandum, "Electronic Countermeasures Against U. S. Air Defense: 1953-1960, " Barlow, E. J., Rand Corporation (1 May 1953). SECRET (b) RM-1090, Research Memorandum, "Electronic Countermeasures Against Air Defense Systems, " Hult, J. L., Rand Corporation (1 June 1953). SECRET (c) RM-1144, Research Memorandum, "Some Promising Counter - measures Against Enemy Air Defense Systems, " Hult, J. L., and Graham, W. B., Rand Corporation (14 September 1953). SECRET (d) RM-1176, Research Memorandum, "The Detection of Aerial Decoys by Air Defense Radars, " Hult, J. L., Rand Corporation (20 December 1953). SECRET (e) RM-1295, Research Memorandum, "Influence of Certain Offense Countermeasures on the Comparison of High and Low Altitude Capabilities of Strategic Bombers, " Schamberg, R., Rand Corporation (23 April 1954). SECRET 2. 2260-1-T, "Studies in Radar Cross-Sections XV —Radar CrossSections of B-47 and B-52 Aircraft, " Schensted, C. E., Crispin, J. W., and Siegel, K. M., University of Michigan, Engineering Research Institute (August 1954). CONFIDENTIAL 3. UMM-106, "Studies in Radar Cross-Sections VI- Cross-Sections of Corner Reflectors and Other Multiple Scatterers at Microwave Frequencies," Bonkowski, R. R., Lubitz, C. R., and Schensted, C. E., University of Michigan, Engineering Research Institute, AF 30(602)-9 (October 1953). SECRET (UNCLASSIFIED when Appendix is removed. ) 164 ~ - rr

UNIVERSITY OF MICHIGAN _ 2260-29-F REFERENCES (Continued) 4. NADC-EL-5340, "Proposed Military Specification for Triangular Corner Reflectors for Drone Aircraft, " U. S. Naval Air Development Center, Bureau of Aeronautics (29 April 1953). CONFIDENTIAL 5. NRL-MR-148, "Target Drone Reflectivity Radar Characteristics Measurement and Simulation Studies, " Lewis, B. L., Naval Research Laboratory Radio Division III, (13 March 1953). CONFIDENTIAL 6. 35M-967, "Monthly Progress Report for May 1954, Contract AF 30(602)-978, Lightweight Collapsible Spherical Radar Reflector, " Fairchild Aircraft Corporation (10 June 1954). CONFIDENTIAL 7. "Balloon-Borne ECM, " Memorandum, Headquarters Air Defense Command, Ent Air Force Base (11 April 1952). SECRET 8. ADC-SAB-52-C1, "Military Characteristics for Balloon Radar Reflectors, " Department of the Air Force, Deputy Chief of Staff, Development Directorate of Requirements, (11 March 1952). SECRET 9. RM-1436, Research Memorandum, "Strategic Bombardment Campaigns and the Effects of Some Electronic Countermeasures - Abridged Edition;" Rand Corporation (15 March 1955). SECRET 10. APG-SAB-28-A, "Tactical Employment of Chaff-Phase I, Eglin Air Force Base (10 July 1952). SECRET 11. 1044-1, Interim Engineering Report, "Echo Amplitude Comparisons of Chaff at 200 MC -Radar Reflectivity Measurement," Radiation, Incorporated, Contract AF 33(616)-2577 (27 April 1955). SECRET 165

UNIVE RS ITY OF M ICHIGAN 2260-29-F REFERENCES (Continued) 12. AF-15, "MX-2223 Simulation Studies - Part Two," Brodwin M. E., Frey, G. W., Glaser, E. M., Smith, C. W., The Johns Hopkins University Radiation Laboratory (September 1955). SECRET 13. Project A-400, Report 4, "Analysis of Window and Related Matters, Chu, L. J., Radio Research Laboratory, Harvard University (22 October 1952). UNCLASSIFIED 14. 2260-6-T, "Studies in Radar Cross-Sections XVII- Complete Scattering Matrices and Circular Polarization Cross-Sections for the B-47 Aircraft at S-Band," Maffett, A. L., Barasch, M. L., Burdick, W. E., Goodrich, R. F., Orthwein, W. C., Schensted, C. E., and Siegel, K. M., University of Michigan, Engineering Research Institute (June 1955). CONFIDENTIAL 15. TRE-TN-170, Technical Note, "The Effect of Cross-Polarization on Radar Echoes From Aircraft, Precipitation and Land Targets at 8mms Wavelengths," Robinson, N. P., Telecommunications Research Establishment (September 1952). SECRET 16. TRE-TN-183, Technical Note, "Radar Echoes From Aircraft, Precipitation and Land Targets Illuminated by Circularly Polarized Radiation at 8mms Wavelength," Robinson, N. P., Telecommunications Research Establishment (April 1953). SECRET 17. 612-2, "Quarterly Progress Report-Polarization Dependence of Radar Echoes, Contract AF 30(635)-2811, Period ending 31 March 1955," Antenna Laboratory, The Ohio State University Research Foundation (16 March 1955). UNCLASSIFIED 18. Informal Communication, Ehrlich, Morris J., President, Microwave Radiation Company, Inc., to K. M. Siegel. UNCLASSIFIED ______ 166 I LZ

UNIVERSITY OF MICHIGAN__ ___ 2260-29-F REFERENCES (Continued) 19. NRL-4258, "The Coherence of Radar Echoes," Boyd, F. E., Special Research Branch, Radio Division III, Naval Research Laboratory (8 December 1953). CONFIDENTIAL 20. S-10, "Detection of Propeller and Sambo Modulations, " MingChen, W., Uhlenbeck, G. E., Allred, C. M., et al, Massachusetts Institute of Technology (16 May 1944). 21. Hughes TM-377, "Amplitude Scintillation Spectra of Aircraft Targets," Jackob, D. M., Muchmore, R. B., and Wanlass S. D., Hughes Aircraft Company (1 August 1954). CONFIDENTIAL 22. "Radar Characteristics of Jet Exhaust Gases," Lewis B. L., Tracking Branch, Radar Division of the Naval Research Laboratory (2 December 1954). 23. Report No. 1, "Quarterly Engineering Report, " Electrical Engineering Research Laboratory, The University of Texas (15 May 1955). UNCLASSIFIED 24. RM-1217, Research Memorandum, "Probability of Detection for Fluctuating Targets, " Swerling, P., Rand Corporation (17 March 1954). UNCLASSIFIED 25. P-2186-12, "Fourth Quarterly Engineering Report on Research on Radar Terrain Return Theory, Instrumentation, and Techniques, " The Franklin Institute (June 1951). CONFIDENTIAL 26. "The Calculation of the Echo Area of Several Scatterers of Simple Geometry by the Variational Method, " Kouyoumjian, R. G., Symposium on Microwave Optics, McGill University (22-25 June 1953). 167 LD F I-\ ir

U N IVERS ITY OF MICHI GAN 2260-29-F REFERENCES (Continued) 27. TR-AF-15, "MX-2223 Simulation Studies, Part One," Thomas, R. K., Smith, C., Glaser, E., Brodwin, M., Johns Hopkins University Radiation Laboratory (March 1955). SECRET 28. FZM-377, "MX-2224A Flight Test Program Report," Convair Division, General Dynamics, Contract AF33(600)-27337 (1 February 1955). SECRET 29. TM-341, Technical Memorandum, "X-band Radar Cross-Section Measurements," Wanlass, S. D., Muchmore, R. B., Jacob, D. M., Hughes Aircraft Company (1 March 1954). CONFIDENTIAL 30. C-3460-94A/51, "Quantitative Measurements of Radar Echoes From Aircraft III-B-36 Amplitude Distributions and Aspect Dependence," Naval Research Laboratory (19 June 1951). CONFIDENTIAL 31. "Theory of Radar Reflection From Wires or Thin Metallic Strips," Van Vleck, J. H., Bloch, F., Hamermesh, M., JournalofApplied Physics, Volume 18, No. 3, pp. 274-294 (March 1947). 32. Tables of Functions, Jahnke and Emde, Dover Publishing Company (1945). 33. Informal Communication, Ehrlich, Morris J., President, Microwave Radiation Company, Inc., to K. M. Siegel (3 May 1955). SECRET 34. Methods of Theoretical Physics, Part II, Morse, P. M., Feshbach, H., McGraw-Hill Book Company, Inc. (1953). 35. UMM-134, "Studies in Radar Cross-Section XIV-Radar CrossSection of a Ballistic Missile," Siegel, K. M., Barasch, M. L., Crispin, J. W., Schensted, C. E., Orthwein, W. C., Weil, H., University of Michigan (September 1954). SECRET 168 c _-. F\ r

UNIVERSITY OF MICHIGAN 2260-29-F DISTRIBUTION LIST COPY NO. 1-2 Commander, Wright Air Development Center ATTN: WCLRE-5, R. Rawhouser Wright-Patterson Air Force Base, Ohio 3 Commander, Wright Air Development Center ATTN: WCSG, Major F. Porter Wright-Patterson Air Force Base, Ohio 4 Rheem Manufacturing Company Research and Development Laboratories ATTN: J. Joerger Downey, California 5 McDonnell Aircraft Company ATTN: G. G. McKee St. Louis, Missouri 6 Fairchild Aircraft Division ATTN: Walter Tydon Hagerstown, Maryland 7-12 Armed Services Technical Information Agency Document Service Center Knott Building Dayton 2, Ohio 13 Commander, Wright Air Development Center ATTN: WCLRC-1, G. W. Schivley Wright-Patterson Air Force Base, Ohio 14 Commander, Wright Air Development Center ATTN: WCLGB, A. L. Brothers Wright-Patterson Air Force Base, Ohio 15 Commander, Wright Air Development Center ATTN: WCOSI Wright-Patterson Air Force Base, Ohio 16 Commander, Wright Air Development Center ATTN: WCSB, J. S. McCollom Wright-Patterson Air Force Base, Ohio 17 Commander, Wright Air Development Center ATTN: WCSM, P. R. Doty Wright-Patterson Air Force Base, Ohio 1 169 W-II ) [CC I

UNIVERSITY OF MICHIGAN 2260-29-F DISTRIBUTION LIST (Continued) COPY NO. 18 Commander, Wright Air Development Center ATTN: WCSM, J. A. Walker Wright-Patterson Air Force Base, Ohio 19 Commander, Wright Air Development Center ATTN: WCSM, J. R. Korosei Wright-Patterson Air Force Base, Ohio 20 Commander, Wright Air Development Center ATTN: WCSP, E. B. Bell Wright-Patterson Air Force Base, Ohio 21 Commander, Air Materiel Command ATTN: ATIAE, R. L. James Wright-Patterson Air Force Base, Ohio 22 Commander, Wright Air Development Center ATTN: WCLRO, Major G. J. Akerland Aircraft Radiation Laboratory Wright-Patterson Air Force Base, Ohio 23 Commander, Wright Air Development Center ATTN: WCLRD, G. B. Fanning Wright-Patterson Air Force Base, Ohio 24 Director of Research and Development Headquarters, USAF ATTN: AF-DRD-EL Washington 25, D. C. 25 Commander, Air Research and Development Command ATTN: RDDE, Major D. L. Deal P.O. Box 1395, Baltimore 3, Maryland 26 Commander Rome Air Development Center ATTN: Research Library, RCRES-4C Griffiss Air Force Base, Rome, New York 27 Commander, U. S. Naval Air Missile Test Center ATTN: L. S. Marquardt Point Mugu, California 28 Commander, Air Force Cambridge Research Center ATTN: CRRDG, Ralph Hiatt L. G. Hanscom Field, Bedford, Massachusetts 29 Commander, Air Force Cambridge Research Center ATTN: Electronics Research Library L. G. Hanscom Field, Bedford, Massachusetts 170 EcDr7 r

UNIVE RS ITY OF MICHIGAN 2260-29-F DISTRIBUTION LIST (Continued) COPY NO. 30 Commander, U. S. Naval Air Missile Test Center ATTN: Stanley R. Radom Point Mugu, California 31 Commander, Air Force Cambridge Research Center ATTN: CRRDG, Nelson A. Logan L. G. Hanscom Field, Bedford, Massachusetts 32 Commander, Air Force Cambridge Research Center ATTN: CRRDG, C. J. Sletten L. G. Hanscom Field, Bedford, Massachusetts 33 Commander, Air Force Cambridge Research Center ATTN: CRRDA, R. M. Barrett L. G. Hanscom Field, Bedford, Massachusetts 34 Commander, Air Force Missile Test Center ATTN: A. R. Beach Patrick Air Force Base, Cocoa, Florida 35 Commander, Holloman Air Development Center ATTN: Operation and Project Center Alamogordo, New Mexico 36 Research and Development Board, Library Branch Information Offices ATTN: W. H. Plant RE. E1065, The Pentagon Washington 25, D. C. 37 Commander, Rome Air Development Center ATTN: RCECC-1, Louis F. Moses Griffiss Air Force Base, Rome, New York 38 Commander, Air Force Armament Center ATTN: A. J. Wilde Eglin Air Force Base, Florida 39 Commander, Air Proving Ground Command ATTN: Class. Tech. Data Br. D/01 Eglin Air Force Base, Florida 40 Commander, Strategic Air Command ATTN: Operations Analysis Office Offutt Air Force Base, Nebraska 41 Commander, Headquarters Central Air Defense Force Post Office Box 528 Kansas City, Missouri 171 I',- C r

UNIVERS ITY OF MICHIGAN 2260-29-F DISTRIBUTION LIST (Continued) COPY NO. 42 Director, Air University Req. CR-3998 Maxwell Air Force Base, Alabama 43 Commander, Rome Air Development Center ATTN: RCER, Morris Handlesman Griffiss Air Force Base, Rome, New York 44 Commander, Rome Air Development Center ATTN: RCDE, Joseph Vogelman Griffiss Air Force Base, Rome, New York 45 Dr. George Adomian, Member Special Studies Group Analysis and Planning Section, Systems Laboratories Hughes Aircraft Company, Culver City, California 46 Director, Naval Research Laboratory ATTN: John E. Meade, Code 5340 Washington 25, D. C. 47 Director, Naval Research Laboratory ATTN: W. S. Ament, Code 5278 Washington 25, D. C. 48 Chief, Bureau of Ships, Department of the Navy ATTN: Code 816 Washington 25, D. C. 49 Chief, Bureau of Aeronautics, Department of the Navy ATTN: Electronics Division Washington 25, D. C. 50 Bureau of Aeronautics, Central District ATTN: Electronics Division Wright-Patterson Air Force Base, Ohio 51 Chief, Bureau of Ordnance, Department of the Navy ATTN: Code AD-3 Washington 25, D. C. 52 Chief of Naval Operations, Department of the Navy ATTN: OP-42-B2 Washington 25, D. C. 53 Commanding Officer and Director U. S. Navy Electronics Laboratory San Diego 52, California 54 Commander, U. S. Naval Air Development Center ATTN: Electronics Laboratory Johnsville, Pennsylvania 172 XrrcDF\EIir

UNIVERS ITY OF MICHIGAN 2260-29-F DISTRIBUTION LIST (Continued) COPY NO. 55 Commander, U. S. Naval Ordnance Laboratory Silver Spring 19, Maryland 56 Commander, U. S. Naval Ordnance Test Station, Inyokern China Lake, California 57 Commander, Rome Air Development Center ATTN: Harry Davis, Technical Director - RCT Griffiss Air Force Base, Rome, New York 58 Chief Signal Officer, Department of the Army A TTN: Engineering Technical Division Washington 25, D. C. 59 Department of the Army, Office of Chief of Ordnance ATTN: ORDTU, Capt. W. 0. Fuller Washington 25, D. C. 60 Massachusetts Institute of Technology Project Lincoln, Lincoln Laboratory ATTN: V. A. Nedzel Post Office Box 73, Lexington 73, Massachusetts 61 Hughes Aircraft Company Research and Development Laboratories ATTN: C. H. Wilcox Culver City, California 62 Cornell Aeronautical Laboratory, Incorporated ATTN: R. Kell Buffalo, New York 63 Commander, Signal Engineering Laboratory ATTN: Technical Documents Center Fort Monmouth, New Jersey 64 Cornell Aeronautical Laboratory, Incorporated ATTN: George Richmond Buffalo, New York 65 Document Room, Project Lincoln Massachusetts Institute of Technology ATTN: Ethel R. Brans P. 0. Box 390, Cambridge 39, Massachusetts 66 Massachusetts Institute of Technology ATTN: Dr. Dan Dustin, Lincoln Laboratory P. 0. Box 73, Lexington 73, Massachusetts 173 r~ e:

UNIVE RS ITY OF MI CHIGAN 2260-29-F DISTRIBUTION LIST (Continued) COPY NO. 67 Massachusetts Institute of Technology ATTN: I. Shapiro, Lincoln Laboratory P. O. Box 73, Lexington 73, Massachusetts 68 Commander, Air Defense Command ATTN: Major Richard J. Lloyd Colorado Springs, Colorado 69 Ohio State University Research Foundation ATTN: Dr. A. Fouty 310 Administration Building, Ohio State University Columbus 10, Ohio 70 Radiation, Incorporated ATTN: M. Cox Melbourne, Florida 71 The University of Texas Electrical Engineering Research Laboratory ATTN: Dr. A. W. Straiton Box 8026, University Station, Austin 12, Texas 72 Franklin Institute Laboratories 20th St. Benjamin Franklin Parkway ATTN: Dr. S. Charp Philadelphia 3, Pennsylvania 73 Boeing Airplane Company ATTN: R. H. Jewett Seattle 14, Washington 74 Hughes Aircraft Company Research and Development Laboratories ATTN: M. D. Adcock Culver City, California 75 Hughes Aircraft Company Research and Development Laboratories ATTN: Dr. L. L. Bailin Culver City, California 76 Hughes Aircraft Company Research and Development Laboratories ATTN: Dr. N. Begovich Culver City, California 77 Hughes Aircraft Company Research and Development Laboratories ATTN: R. S. Wehmer Culver City, California 174 I,[ a7 r- - r - 11 I

UNIVERSITY OF MICHIGAN 2260-29-F DISTRIBUTION LIST (Continued) I I! I COPY NO. 78 79 80 81 82 83 84 85 86 87 88 89 The Rand Corporation ATTN: Dr. John L. Hult 1500 4th Street, Santa Monica, California The Rand Corporation ATTN: Dr. Sidney Bertram, Electronics Division 1500 4th Street, Santa Monica, California Ramo-Wooldridge Corporation ATTN: Dr. F. S. Manov 8820 Bellanca Ave., Los Angeles 45, California Stanford University ATTN: Professor L. I. Schiff, Physics Department Palo Alto, California University of Tennessee ATTN: Professor F. V. Schultz Knoxville 16, Tennessee University of California ATTN: Professor Samuel Silver Electrical Engineering Department Berkeley 4, California Philco Radio Corporation ATTN: B. D. Steinberg —Project Engineer Philadelphia 34, Pennsylvania Electronics Defense Laboratory ATTN: Dr. V. Twersky P. 0. Box 205, Mountain View, California Bell Telephone Laboratory ATTN: Dr. Allen B. Currie Whippany, New Jersey Ramo-Wooldridge Corporation ATTN: Dr. S. Ramo 8820 Bellanca Ave., Los Angeles 45, California Ramo-Wooldridge Corporation ATTN: Dr. A. D. Wheelon 8820 Bellanca Ave., Los Angeles 45, California Cornell Aeronautical Laboratory, Incorporated ATTN: Dr. Robert A. Wolf Buffalo, New York 175.EcrE7

UNIVE RS ITY OF MICHIGA N 2260-29-F DISTRIBUTION LIST (Continued) COPY NO. 90 Georgia Institute of Technology State Engineering Experimental Station Atlanta, Georgia 91 Standard Rolling Mills, Incorporated ATTN: Vincent Lane 196 Diamond Street, Brooklyn 22, New York 92 The Johns Hopkins University ATTN: Dr. D. D. King —Radiation Laboratory 1315 St. Paul Street, Baltimore, Maryland 93 The Johns Hopkins University ATTN: E. M. Glaser —Radiation Laboratory 1315 St. Paul Street, Baltimore, Maryland 94 Massachusetts Institute of Technology Research Laboratory of Electronics ATTN: Dr. L. J. Chu Cambridge, Massachusetts 95 Lockheed Missile System Division, Dept. 75-31 7701 Woodley Ave., Van Nuys, California 96 Ryan Aeronautical Company ATTN: J. R. Giantvalley Lindbergh Field, San Diego 12, California 97 Convair, A Division of General Dynamics Corporation ATTN: Orison Wade —Engineering Department San Diego, California 98 Operational Research Group ATTN: G. R. Lindsay Defense Research Board Ottawa, Ontario, Canada 99 McGill University ATTN: Professor G. A. Woonton Eaton Electronics Laboratory Montreal, Quebec, Canada 100 Sylvania Engineering Laboratory ATTN: Dr. L. S. Scheingold 70 Forsythe Street, Boston, Massachusetts 101 William R. Hutchins Raytheon Manufacturing Company Missile and Radar Division Hartwell Road Bedford, Massachusetts 176 _ _ _L-_ r - -

C _- I r-. r- L UNIVERSITY OF MICHIGAN 2260-29-F DISTRIBUTION LIST (Continued) COPY NO. 102 Dr. R. S. Elliott Research and Development Laboratories Hughes Aircraft Company Culver City, California. 177 rIr r lr

I