UMM-127 -RL-20i7 Sudisin Rdr Coss - ections-XI Summaryv of Radar C ross-Section Studies undfer ~Project MIRO by K. Ml. Siegel, M. F. Anderson, R. R. Bonkow ski, and WV. C. Orthwein Poect MIR C1ontract N'\o. AF30(602)9 Wlow Rin Research Center It Ths do-ur- t C. r'n 0`40o mg 1,p "o?, tes within I,,* L r " I 5 (7 Se, 'Qs o,,d 79-d Its u -I )r -ed,,error,!i pro-b ted by low.

FOR INTRA-L' 'VElISrTY CORiFSPONDENCE UNIVERSITY OF MICHIGAN lENGITERING RESEARCH INSTIlTTE 21 February 1958 MEMO TO: Prof. K. M. Siegel FROM: Security Office SUBJECT: Project 2015 This is to advise you that all reports and Project 2015 (AF30(602)9 are unclassified. memos generated on Please see that all documents in your possession are marked in the manner illustrated below. Regrading markings should appear on front and back covers, t iCle, first and last pages, with the previous classification lined through. CL aC";-7-!C T';ON,- i F;-,U AU.F- CCITY I le.L -*rev;A 4 UF, sTy l II...".,- ItV -$,.n_. C,,= -VA f, 44 -a gf4 yp Bulk files of aforementioned reports need not be so marked immediately. Regrading markings can be affixed when the documents are being used or charged out or transmitted. However, if bulk files are in your possession, the change of classification should be indicated inside the file drawer or storage container. v. J. SCO \ Security Officer fg c.c.: J. H. Richter

I N I VT E R S I T Y () F NI I C H I G A N UI'M 1Z7 Studies in Radar Cross-Sections - XII: Summary of Radar Cross-Section Studies Under Project MIRO, by K. M. Siegel, M. E. Anderson, R. R. Bonkowski, and W. C. Orthwein (UMM-127,December 1953). Contract No. AF 30(602)-9. SECRET. Errata Pg. 47, 1st col., 6th row Pg. 53, Ref. A. 10 Pg. 89, 4th col., 2nd row Replace 4" sq. 1/8" thick) by 4" sq., 0. 8" thick) Replace 308-23 by 302-23 Replace.12 by.02 Addenda None -

WILLOW' RUN RESEARCH. CENTER -UNIVERSITY OF MICHIGAN UMM-127 TABLE OF CONTENTS Section Page List of Figures ii List of Tables iv Preface v Summary of Radar Cross-Section Studies 1 References for the Text 5 Appendix A - Compendium of Experimental Cross-Section Data 6 References for Appendix A 52 Appendix B - The Theoretical Approximation of the Radar Cross-Section of Various Missiles and Manned Aircraft 62 References for Appendix B 90 Appendix C - Exact Solution to Electromagnetic Scattering Problems 92 References for Appendix C 96 Distribution 98. i.......... I.... I ]

WILLOW RUN RESEARCH CENTER - UNIVERSITY OF MICHIGAN UMM- 127 LIST OF FIGURES Number Title Page B-1 Radar Performance Survey, July 1945. 66 B-2 Basic Geometry Used in Determining Theoretical Cross-Sections of Aircraft. 68 B-3 Comparison of Theoretical and Experimental CrossSections of the B-29 at Essentially Nose-on Aspect. 69 B-4 Comparison of Theoretical and Experimental CrossSections of the B-29 at the Aspect Defined by Azimuth 30~ and Elevation 0 0- 4~. 69 B-5 Comparison of Theoretical and Experimental CrossSections of the B-29 at the Aspect Defined by Azimuth 60~ and Elevation 0 - 4~. 70 B-6 Comparison of Theoretical and Experimental CrossSections of the B-29 at the Aspect Defined by Azimuth:- 90~ and Elevation 4 4~. 70 B-7 Basic Geometry Used in the Determination of the Bistatic Cross-Section of the TU-4 (B-29). 71 B-8 Comparison of Theoretical IL-28 Cross-Section and Experimental B-45 Cross-Section at the Aspect Defined by Azimuth ~ 0~ and Elevation. 4~. 74 B-9 Comparison of Theoretical IL-28 Cross-Section and Experimental B-45 Cross-Sectio at the Aspect Defined by Azimuth $ 30~ and Elevation - 4~. 74 i ii iiii I t i i __ II

WILLOW RUN RESEARCH CENTER - UNIVERSITY OF MICHIGAN UMM- 127 Number Title Page B-10 Comparison of Theoretical IL-28 Cross-Section and Experimental B-45 Cross-Section at the Aspect Defined by Azimuth ' 60~ and Elevation ~ 4~. 75 B-ll Comparison of Theoretical IL-28 Cross-Section and Experimental B-45 Cross-Section at the Aspect Defined by Azimuth ~ 90~ and Elevation ^; 4~. 75 B-12 Comparison of Theoretical IL-28 Cross-Section and Experimental B-45 Cross-Section at the Aspect Defined by Azimuth r 120~ and Elevation 4~. 76 \ B-13 The MX-2091 77 B-14 The Martin 286-12 78 C-1 Cross-Section of a Paraboloid as a Function of/. 95 E I I I III ~ I IIII.... iii

WILLOW RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN I UMM-127 1 LIST OF TABLES N Tumber Title A-1 Missile Cross-Sections A-2 Shell Cross-Sections A-3 Aircraft Cross-Sections A-4 Cross-Sections of Simple Geometrical Shapes B-1 (J for the TU-4(B-29) B-2 3 for the IL-28 B-3 Radar Cross-Section of the 286-12 in Square 1 B-4 Radar Cross-Section of the 286-12 Bomb in Sc Meters B-5 Radar Cross-Section of the 286-12 and Bomb Square Meters B-6 Radar Cross-Section of the MX-2091 in Squar B-7 Radar Cross-Section of the MX-2091 Bomb in Meters B-8 Radar Cross-Section of the MX-2091 and Bor Square Meters B-9 (J for the Loon Missile B-10 ( for the Regulus Missile B-l11 3 for the Snark Missile B-12 ( for Other Missiles Page 7-16 17-24 25-45 46-51 71 73 79 Meters quare 80 in 81 82 e Meters Square lb in 83 84 86 87 88 89 - iv

WILLOW RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN UMM-127 PREFACE This paper is the twelfth in a series of reports growing out of studies of radar cross-sections at the University of Michigan's Willow Run Research Center. 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 boundary-value problems arising from the electromagnetic vector wave equation. (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 inside of the front cover. K. M. Siegel _............ J.......... v

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN UMM-127 SUMMARY OF RADAR CROSS-SECTION STUDIES The need for work in the radar cross-section field has been well expressed in a recent USAF report (Ref. 1), as follows: "During World War II, many measurements of aircraft radar reflection characteristics were made but unfortunately almost none were made with sufficient accuracy and uniformity of measurement technique that they can be considered meaningful. "As a result of these measurements, contractors and components of the Air Force are using values of echo area that vary in value and are insufficient in detail to allow proper calculations of factors vital in the research and development of radar equipment." The Willow Run Research Center, because of its interest in parameters which are vital in Air Defense system problems, started an analysis of the radar cross-section field in 1949. It is believed that the capability now exists at the Willow Run research Center to determine the radar cross-section of any target of military importance to within a factor of 10. Radar cross-sections may be determined either theoretically or experimentally. In either case great difficulties are encountered. In the precise theoretical determination of cross-sections the mathematical complexity is so great that the analytical problem can be solved only for the simplest shapes, and even then the computational procedures in obtaining numerical answers are forbiddingly difficult. To date the analytical problem has been solved only for five shapes: sphere, prolate spheroid, oblate spheroid, semi-infinite cone, and semi-infinite paraboloid. However, approximations are known for a great many other shapes, including the following: finite cone, finite paraboloid, ogive, circular cylinder, elliptical cylinder, wire, thick dipole, wedge, circular disk, rectangular flat plate, various corners, hyperboloid of one sheet, hyperboloid of two sheets, and torus. Furthermore composite bodies composed of mixtures of these simple shapes are also subject to approximate analytic methods, which yield -- I!~I 1

WVILLOWV RUN RESEARCH CENTER - UNIVERSITY OF MICHIGAN UMM- 127 appropriate solutions. Finally, real objects, such as aircraft, may be approximated by composites groups of such simple shapes, again within the limits of the necessary accuracy of the approximation. These methods of approximation are discussed in some detail in other papers of this series, notably References 2 and 3. The over-all results of any such approximation method should be accurate within a factor of 10. It is of course hoped that the approximations will be better in many cases, but this maximum error is tolerable because the range of detection varies as the fourth root of the cross-section. In other words, if the radar cross-section is known within a factor of 10, the range performance of the radar system is known within a factor of 1.78. The other method of determining radar cross-sections is by experimental measurements. These measurements may be made on full-size objects or on scale models, and they may be either static or dynamic in nature. Many difficulties plague each of these types- of experiments, and again it is difficult to be certain that answers obtained are reliable within a factor of 10. In static experiments the model or full-scale object must be suspended in some way away from the earth, and it is difficult to eliminate reflections from the supports. Furthermore there are likely to be reflections from the ground. It is often difficult to guarantee that the radar and the scatterer are sufficiently far apart so that the results can be truly' said to represent a far-zone (as distinguished from a near-zone) cross-section. In dynamic experiments it is difficult to measure the exact aspect and range of the object at the instant the measurement is made, and furthermore calibration difficulties are frequently involved because of the difficulty of getting a comparison object at the same range within a reasonable time. In all cases there are difficulties in eliminating reflections from spurious targets in side lobes, and numerous other instrumentation difficulties. Measurement of crosssection of full sized objects presents obvious difficulties connected with the expense of the experiments, whereas the use of scale models brings into question the appropriate modeling theory and also leads to questions of the accuracy of the models. For all of these reasons, a particular number which is produced as representing the cross-section of any particular object is not likely to - 2

WILLOWV RUN RE~SEARCIH CENTER - UNIVERSITY OF MICHIGAN U NM 1O - 1 2 7 be reliable unless this number has been verified both by several different types of experimental measurements and by theoretical calculations. The only cross-section values which could probably be relied on to within an accuracy of a few per cent are those of the simple shapes mentioned above for which exact electromagnetic solutions are availalble. In some cases, however, numerous static and dynamic experiments on both full-scale objects and scale models have given answers all in the same neighborhood, and when these answers are further corroborated by theoretical evidence there can be considerable confidence in the results, and also in the approximation technique used. In general, then, an approximation method can be considered reliable and physically significant if it satisfies the following tests: a) A collection of sim-ple shapes (such as those listed above) can be substituted for the actual object in question (for example, an aircraft) without appreciably changing the scattering effect on electromragnetic radiation. b) A suitable numerical solution is available for the resulting collection of simple shapes, which is a good approximation for the exact answer to this collection of simple shapes. c) Some member of the class or kind of composite configuration (like fighters with swept-back fins) should have had its cross-section measured in a laboratory and the approximation method when applied to that configuration must have yielded results which were within a factor of 10 of the measured results averaged over some suitable range in angle (usually determined by expected accuracy of the experimental equipment). Many of the approximation techniques which lead to the numerical results mentioned in Appendix B, and which will be analyzed in another paper of this series, have met all of these tests. 9 This report, the final radar cross-section report sponsored under Project MIRO, summarizes many parts of the radar cross-section field. In particular it brings up to date all knowledge available to us on the radar cross-section of aircraft and other airborne military vehicles 3 II......II II I III I I IIII

WILLOW RUN RESEARCH CENTER- UNIVERSITY OF MICHIGAN UMM-127 (such as guided missiles). In Appendix A is presented an up-to-date summary of all known experimental values of radar cross-sections of aircraft, missiles, and artillery and mortar projectiles. This summary includes both dynamic and static measurements on both full-scale targets and on models. This table replaces the corresponding portions of the similar tabulation in Reference 4. In Appendix B are tabulated all of the theoretical values of radar cross-sections of aircraft and airborne missiles which have been computed by the Willow Run Research Center. (The corresponding theoretical calculations for ballistic missiles will be published separately later.) In three cases these theoretical results are compared with experimental results. In Appendix C are discussed all the exact values of radar cross-sections presently known for three-dimensional configurations. The radar cross-section field, and the series of papers of which this is a part, must be viewed as a whole. It is of interest to note, for example, that the cross-section of a prolate spheroid which was anallyzed at Willow Run Research Center under Project Wizard has been of value because the fuselage of many aircraft can be approximated by a prolate spheroid. Also the cross-section of a cone, which was analyzed under Project MIRO, has been of value because the cone (and the closely related configuration known as the ogive) are important in computing the cross-section of ballistic missiles. The work on the radar crosssection of the sphere has been applied to the scattering of light by air molecules, water droplets, and dust. It appears that there is considerable utility in theoretical radar cross-section studies of the type which are reported in this series, and that the fundamental theoretical work has now proceeded to the point where a maximum of pay-off can be obtained with a minimum of effort. It is therefore recommended that this type of effort be maintained. In particular, it is recommended that continuing surveys be made of the theoretical work being done and the experimental results reported in the radar cross-section field, and that these results be tabulated and circulated periodically. It is also recommended that a continuing study be made of new and old methods of obtaining radar cross-sections of composite shapes (missiles and aircraft) to determine the best methods available for radar cross-section determinations. Finally it is recommended that such a group be maintained so that it is available to supply particular radar cross-section estimates in accordance with requests for such data from appropriate authorities in the Department of Defense. - - ----- 4 -- ' ' J L J

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN I UMM-127 REFERENCES FOR THE TEXT 1. Wm. F. Bahret, "Dynamic Measurements of Aircraft Radar Reflection Characteristics, Part 1: Measurement Equipment and Techniques", Wright Air Development Center Technical Report 53-148 (April 1953) UNCLASSIFIED. 2. R. R. Bonkowski, C. R. Lubitz, and C. E. Schensted, "Studies In Radar Cross-Sections VI: Cross-Sections of Corner Reflectors and Other Multiple Scatterers at Microwave Frequencies", Willow Run Research Center, University of Michigan, External Report No. UMM-106 (October 1953) SECRET (UNCLASSIFIED when appendix is removed). 3. K. M. Siegel, H. A. Alperin, R. R. Bonkowski, J. W. Crispin, A. L. Maffett, C. E. Schensted, and I. V. Schensted, "Studies in Radar Cross-Sections VIII: Theoretical Cross-Sections as a Function of Separation Angle Between Transmitter and Receiver at Small Wavelengths", Willow Run Research Center, University of Michigan, External Report No. UMM-115 (October, 1953) UNCLASSIFIED. 4. K. M. Siegel, J. W. Crispin, and R. E. Kleinman, "Studies in Radar Cross-Sections VII: Summary of Radar Cross-Section Studies Under Project Wizard", Willow Run Research Center, University of Michigan, External Report No. UMM-108 (November, 1952) SECRET. a 5

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN UMM-127 APPENDIX A COMPENDIUM OF EXPERIMENTAL CROSS-SECTION DATA The Willow Run Research Center has continued collecting and tabulating cross-section data. The results of this tabulation are presented in this appendix. For the sake of unity this present survey embraces all of the material previously presented [Ref. Al], with occasional corrections and the deletion of some retracted data. In addition, a considerable amount of new data is presented. These tables thus represent all published experimental data known* to the authors. However, it is to be stressed that the following tables are neither presumed nor intended to be exhaustive, but rather representative. Frequently, the data given for sample aspects is taken from a more complete tabulation or from entire polar diagrams of cross-section. Hence, the original references should be consulted if more specific and detailed information is desired. Attention is called to the fact that a very exhaustive bibliography of research on radar reflections has appeared recently [Refs. A2, A3, A4]. This bibliography contains abstracts and comments on over 1000 published articles. While very little numerical cross-section data is included, these three volumes are an invaluable reference and catalog aid to researchers in this field. *If the reader knows of any data not covered herein, the authors would appreciate obtaining references to them. 6 I I I I I[ II...... II I -- ~ I I I.,

Table A-i: Missile Cross-Sections Static CW Radar CrossFrequency Body Equipment Polarization or Aspect Section Ref (in me/ s),.?i Dynamic Pulse (in m2 Corporal E Nose-on 0.78 (model) Hybrid T Horizontal Static 20 CW Broadside 79 A5 Tail -on ( 0.09 Nose-on 23 Verticai " 50 " Broadside 26 A6 _____________ __ Tail - on 25 Nose-on 1.5, Horizontal " 100 " Broadside 133 A7 _____________ __ Tail-on. 2.7 Nose-on 3.6 Vertical " 300 " Broadside 137 A8 __________________ _ _______ ______ Tail-on 2.2 Nose-on 0.35 Horizontal ' 600 " Broadside 137 A9 __ _________ Tail-on 7 Nose-on 0.61 Vertical " 600 " Broadside 91 A9 __ Tail -on 8.6 Nose-on 0.012 Horizontal " 1200 " Broadside 16 A10.......________ Tail-on 3.3 Nose-on 0.012 Vertical " 1200 " Broadside 11 A10 Tail-on 2.4 Hermes A Underwater (model) Sound Method - -- 1666 -- Nose-on 0.0078 All,,,~.......,.... I b-a r r o O z tI m 0p;d O PI O.7 -3 C) Iz C/i 0-) t ZS 2^) - ----

Table A-1: Missile Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or (in mc/s) or Aspect Section Ref _______ ___ Dynamic Pulse (in m2) ___ Underwater Equivalent to Nike (model) Sound -- Static x-band -- Nose-on 0.064 All _, Method Equivalent to -- k-band -- Nose-on 0.013 All Rocket model Perpendicu(without fins) Hybrid T lar to axis " 9375 CW Nose-on 8.2 A12 length = 3.8 X of rotation diameter = 0.6 A 30~ ogive nose Rocket model (with fins)...9375 " Nose-on 0.2 A12 length = 3.8 A diameter = 0.6 A 30~ ogive nose UMA. with fins (model) H" orizontal " 568 " Nose-on 1.25 A13 " " Vertical " 568 " Nose-on 0.56 A13 UMA-1 without fins (model) " Horizontal " 568 " Nose-on 0.45 A13 I-4 0 r o,C) z z 0 C) I 0 -3:z h^

Table A-1: Missile Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or Frequency or Aspect Section Ref (in Mic/s) 2 _____ Dynamic (in c/s Pulse (in mn2) UMA-1 without fins (model) Hybrid T Vertical Static 568 CW Nose-on 0.45 A13 V-2 Nose-on 9.7 (model) " Horizontal 2' 0 " Broadside 128 A14 _____________ _____ ____________ _______ Tail-on 6.5 Nose-on 6.6 Vertical 2" 0 " Broadside 30 A14 Tail-on 8.5 _ Nose-on 29 Horizontal ' 50 ' Broadside 200 A14.___.......__ __-_......__ Tail-on 17 ___ Nose-on 25 Vertical "50 " Broadside 241 A14 ______________ Tail-on 14 _ AN/TPQ-2 Horizontal 50 Pulse Nose-on 30 A15 Vertical " 50 " Nose-on 25 A15 Nose-on 3.3 Hybrid T Horizontal " 100 CW Broadside 400 A7 __________________Tail-on 5.7__ AN/TPQ-2 2. 100 Pulse Nose-on 11 A15.. I...............,.0 r 0 r o z z m Ci 0 i CM I 0 0 >i

Table A-1: Missile Cross-Sections (Cont.) Static CW Radar CrossFrequency Body Equipment Polarization or reqeor Aspect Section Ref Dynamic Pulse (in m2) V-2 (model) AN/TPQ-2 Vertical Static 100 Pulse Nose-on 6 A15 Peak radar area V-2 SCR-270 -- Dynamic 109 -- 147 (before fuel A16 cut-off), 0.3- 3 (after fuel cut- off) V-2 (model) AN/TPQ-2 Horizontal Static 110 " Nose-on 9 A15. Vertical " 110 Nose-on 6.5 A15 Horizontal " 200 Nose-on 2.8 A15, Vertical 200 " Nose-on 2 A15 Horizontal " 250 Nose-on 2 A15 Vertical 250 Nose-on 0.85 A15 -.............,....... I. r C. z z (A) lil;d C,) rl H 0 -C') m z Cl) )-O - --

_ __ Table A-1: Missile Cross-Sections (Cont.) Static CW Radar CrossFrequency Body Equipment Polarization or or Aspect Section Ref.......... (in mc/s) Dynamic ) Pulse _______ (in m") V-2 (model) AN/TPQ-2 Horizontal Static 300 Pulse Nose-on 0.46 A15. Vertical " 300 " Nose-on 1 A15 Nose-on 7.4 Hybrid T Horizontal " 300 CW Broadside 73 A8 _____________ T_ ail-on r 14 30~ off nose 2.5 AN/TPQ-2 I, 500 Pulse 600 off nose 0.26 A15 Nose-on 1.3 500 ' Broadside 197 A15 ___________ __ __ Tail-on 3.2 Vertical " 500 " Nose-on 0.5 A15 Nose-on 2.6 Hybrid T Horizontal " 600 CW Broadside 166 A9 ____ Tail-on 73 30~ off nose 0.61 600 ~ 60~ off nose 0.97 A9 Nose-on 0.19 AN/TPQ-2. 750 Pulse Broadside 994 Al 5 Tail-on 5.1 C:. 0 --— j 0 r r 50 o c z;d t 0 t?fl;4 2; (1< 11 I M 1 - - ---

Ta-ble A-I:- Missile Cross- Sections WCont.) SttcCWA Radar CrossBody E~quiprnent Pola ir iza tioun o)r o r A s pc t Se ti on Ref D v.I c (in mc/s) P-Ise(I n M 2) V -2 300 oft, nose 0.19 (mnod el) AN/ TPQO - Horizontal Static 7 50 Pul s c 000 off n os e 0. A 1 Nose-on 0.24 V er t ical 7 50 Broadsidie 994 Al1 5 T__ _ _ _I_ _ _ _ _ _ ___ _ _ _ _ __r i -o n 11 30~' off nose 1.1 75-)0 60'~ off nose 1 Nose-on 0.12 Hc —rl zontdl 1 00u0 Broadside 47 80 AI5 -__ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _Tail-on 5 6_ _ _ 300- off nose 0.5 It00 0 600 off nose 4 A15 Nosec- on 0.18 Vertical 1 0 00 Broads ide 6 50 A15 Tal -o 26I i00 off nose 04 1000 (5u"'O off nest. 2.6 A15 Nos e- on 0.27 Hybrid T Horizontal 120 CW Broa~-dside 35 AlO ________ TailI-on 4 __ 0 30 off nose 0.27 1200 60 0 off nose 0.14 AIO r 0 z z C)) 0 C) z

Table A-1: Missile Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or or Aspect Section Ref (in rr}c/s) Pulse ______________ ______________ __________ Dvnamic Pulse (in m2) V-2 Nose-on 0.11 (model) Hybrid T Vertical Static 1200 CW Broadside 30 A0l Tail-on 30 30C off nose 0.11 1200 " 600 off nose 0.14 A10 V-2 Radar(type unknown) -- Dynamic 1250 Pulse Various aspects 1 A17 3000 " Tail-on 10-300 A17 Nose-on < 0.01 AN/MPS-3 -- -- -- -- Broadside 16 A18 30~ off nose 0.09..,, - 600 off nose 0.3 A18 V-2 Bistatic radar (model) (45~ between Horizontal Static 20 CW Rec. nose-on 0.23 A19 trans. and rec.) Trans. nose-on 6.6 Vertical 20 Rec. nose-on 4.9 A19 Trans. nose-on 4.2 Horizontal 50 " Rec. nose-on 2.8 A19 Trans. nose-on 3.3 0 r o z -3 z I 0 0 0 cn o-0 (.#

_ _ Table A-1: Missile Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or Frequenc or Aspect Section Ref (in mc/s), Dynamic P(n rs) Plse (in mZ) V-2 Bistatic radar Rec. nose-on 15 (model) (45~ between Vertical Static 50 CW Trans. nose-on 12 A19 trans. and rec.) Rec. nose-on 0.11 Horizontal 100 Trans. nose-on 0.19 A19 Rec. nose-on 0.038 Vertical 100 Trans. nose-on 0.061 A19 Bistatic radar Rec. nose-on 2.2 (300 between Horizontal 300 Trans. nose-on 2 A19 trans. and rec.) Rec. nose-on 2 Vertical 300 Trans. nose-on 1.6 A19 Rec. nose-on 0.77 Horizontal 600 Trans. nose-on 0.97 A19 Rec. nose-on 0.47 Vertical 600 Trans. nose-on 0.14 A19 WAC Nose-on 0.002 (model) Hybrid T Horizontal " 0 Broadside 32 A5 Tail - on < 0.04 Nose-on 0.19, I 50 " Broadside 13 A6 Tail - on 0.27 Cd K~ I, - r 7 z - Cv 4 cn c3 z 0-i PI r PI ---- --

- Table A-1: Missile Cross-Sections (Cont.) IL Static CW Radar CrossBody Equipment Polarization or q / | or Aspect Section Ref Dynamic (in cs) Pulse (in mn2) WAC Nose-on 3.6 (model) Hybrid T Horizontal Static 100 CW Broadside 16 A7 Tail-on 4.9 Nose-on 0.53 " " " " 300 " Broadside 22 A8 _________ ____________ ______ Tail-on 0.41 Nose-on 0.18 " " " ft 600 " Broadside 19 A9 ____________ ___ Tail-on 2.5 Nose-on 0.19 " " Vertical " 600 " Broadside 20 A9 ________ __ Tail-on 1.2 Nose-on 0.35 H " orizontal " 1200 " Broadside 20 A0l Tail-on 0.8 Nose-on 0.2 Vertical | 1200 Broadside 20 A10 ________ ____________ Tail-on 0.74 Nose-on 0.093 Horizontal 2900 Broadside 24 AZ0 Tail-on 1.8 Nose-on 0.0058, Vertical | 2900 Broadside 6.4 AZ0 Tail-on 1.3 L..... z C m m td 0 Z CP b N < r t 1-4 0 C) z

__ IIC_ Tiible A-I: M issilIe Cross- Setntr irs (Corit.) StatiC CW Radar CrossBoy I'Pla' —'FrequencL e Body Equipment Polari ition or F r n or Aspect Section Ref ncnar/iic Puls (in t2) Bistatic radar WAC (model) ( 30 between Horizontal Static 12001 C W Rec nrose-on 0.012 Al( trans. and rec.) r rans. nose-on 0.008 Vertical 1200 Rec. nose-on 0.1 A19 Trans. nose-on 0.1 Horizontal 29 0 0 Rec. nose-on 0.00 3 A19 Trans. nose-on 0.061 Vertical 2 900 Rec. nose-on 0.048 A19 Trans. nose-on 0.048 C: I 1 — p.14 Z r" z Yll I IT1 C) zl z; Ic:4 0 -Z-I --

WVILLOWV RUN RE —SEA-RCH — CENTER- UNIVERSITY OF MICHIGAN I UNIMM-127I I I I I I I I I I T CD N. CD Nj N3 N'l 0 Nl N0 rn i 0 0-.0 N, -,.0 r-1- N N.0j CI-!P O CD C)'l ( z N 0. C0D CN C0, N 0 OrCc f C0 00 O COD C). 90) 0.00 000 ID CO(0) 00)( CQO0)0.( C. II Ij (n10 -0 9D ) N2 0DI -a2 cn, '1"I 0) -ue 0) 0 E u 00 01 - 0 `0 i I__ _ _ _ LI__ _ _ _ I _ _ _ _ _ I... _ _ _ _ I _ _ _ _ 1 7

_ _ __ _____ Table A-2: Shell Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or requency or Aspect Section Rf Dynamic (in nc/s) Pulse (in m2) 60 mm Mortar Shell (model) Hybrid T Horizontal Static 600 CW Broadside 0.19 A24 Vertical ' 600 " Broadside 0.0034 A24 Tail-on 0.0019 " Horizontal " 1200 " Nose-on 0.01 A25 ". 2900 " Nose-on 0.0002 A26 Vertical 2900 " Nose-on 0.00093 A26 " 9000 " Nose-on 0.017 A27 Nose-on 0.0097 Horizontal " 16,000 " Broadside 0.092 A28 Tail-on 0.012 Nose-on 0.018 Vertical " 16,000 " Broadside 0.092 A28 Tail-on 0.015 Doppler radar Static 23,700 -- Nose-on 0.0024 A21 Doppler l-4 -J r 0 r o Cz I) m;d > ri C1 Z;o 0 I

Table A-2: Shell Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or Frequency or Aspect Section Ref Dynamrnic ( c/) Pulse (in mn2) 60 mm Mortar Nose-on 0.029 Shell (model) Hybrid T Horizontal Static 24,000 CW Broadside 0.13 A29 Tail-on 0.015 Nose-on 0.0038 " " Vertical " 24,000 " Broadside 0.034 A29 Tail-on 0.012 81 mm (large) Mortar Shell " Horizontal " 200 " Broadside 1.4 A23 (model) _ _____ Tail-on 0.018 Nose-on 0.00065 Vertical |200 Broadside 0.0079 A23 Tail-on 0.0021 81 nmm (small) Mortar Shenl " Horizontal " 200 " Broadside 0.016 A23 (model) Nose-on 0.0013 " U Vertical | 200 " Broadside 0.0026 AZ3 __________ Tail-on 0.0021 81 rrm (large) Mortar Shell " Horizontal " 600. Broadside 0.21 A24 (model) Nose-on < 0.005 Vertical 600 Broadside 0.05b A24 _______________ _____ _____________ _______ Tail-on < 0.02 ____ 81 mm (small) Mortar Shell " Horizontal " 600 ' Broadside 0.13 A24 (model) Tail-on 0.0035 C rl -j so r r 0 Xo C) Z t ni < I H 0 C

'WILL-OWV fZUN RESE.ARCH CENTER -UNIVERSITY OF MICHIGAN I _UMM- 127 I r I i I I l N N fN 0 N1 U: 0 C-j N -- C) O C 0tT -U0. CC- C, 5 C C CCC C x0 CF I: z = " I.., j -L: Z I lp, L I 1 1-4. -- -I E -t - - 0 cr,.4 Ct.-.A N~o' -c E NO - N - 0 -it a., -a LO 't El 0) IC -I I4. I_________ I__ A5 ______.5. C ______ I5 I... LI Z 0

_ ___ Table A-2: Shell Cross-Sections (Cont.) Static CW Radar CrossFrequency Body Equipment Polarization or or Aspe ct Section Ref in me/s) Dynamic Pulse (in m?) 81 mm (small) Mortar Shell Hybrid T Vertical Static 2900 CW Nose-on 0.018 AZ6 (model) 81 mm (large) Mortar Shell.,. 9000 Nose-on 0.0049 A27 (model) 81 mm (small) Mortar Shell 9000 Nose-on 0.0068 A27 (model).].. 81 mm Mortar Nose-on 0.016 Shell (model) " Horizontal l" b,000 ' Broadside 0.11 A28.____._________ ________ Tail-on 0.046 Nose-on 0.012 '' Vertical " 16,00) " Broadside 0.06 AZ8 Tail-on 0.031 81 imm (heavy) ' Nose-on 0.015 Mortar Shell " Horizontal " 16,000 " Broadside 0.47 A28 (model)_____ Tail-on 0.038 Nose-on 0.025 Vertical r " 6,00' Broadside 0.432 A28 Tail-on 0.064 81 mm (large) M1ortar Shell Doppler Radar " Static 23,700 -- Nose- on 0.0064 A21 (model) __ Doppler _ 81 mm (small) Mortar Shell " 23,7)0 -- Nose-on 0.0071 A21 ( model)... _ C" ci 0-.4 r O o (? C) z z z C) 0 > 0 -m I0.4 < O I.4 - -- -

'able A-2: Shell Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or Fequcy or Aspect Section Ref Dynamic (mc/s) Pulse (in m) 81 mm (large) Nose-on 0.0091 Mortar Shell Hybrid T Horizontal Static 24,000 CW Broadside 0.24 A29 (model) ______Tail-on 0.027 Nose-on 0.0079 " " Vertical " 24,000 " Broadside 0.16 A29 Tail-on 0.022 81 mm (medium) Nose-on 0.0029 Mortar Shell Horizontal 24,000 " Broadside 0.23 A29 (model) _______ ___Tail- on 0.089 Nose-on 0.016. Vertical " 24,000 " Broadside 0.04 A29 Tail-on 0.12 4.2. Mortar Nose-on 0.017 Shell without " Horizontal " 16,000 " Broadside 0.47 A28 fins (model) ______Tail-on 0.075 Nose-on 0.017 " " Vertical " 16,000 " Broadside 0.36 A28 Tail-on 0.053 t S and L-bands Rifle Shells 2xl1-0''>a>2x 10~I 5, 6, 8, Radar (type Horizontal Dynamic S, L, X-bands 18~ - 40 off no return at A31 12, 18. unknown)______ __ __ nose X-band 40 mm Shell Doppler Radar Vertical Static 23,700 -- Nose-on 0.012 A21 ____________ __ Doppl e r ______ _ 90 mm Shell Hybrid T Horizontal Static 1200 CW Nose-on 0.0056 A22 (model) r 0 Z M z ni C,) 0 c - s z H 0 0 M O^

_ __ Table A-2: Shell Cross-Sec tions (Ceont.) Static r CW Radlar CrossFr e~q~eriv I Body Equipment Polarization or (n nAspect Section Ref (in inc/ -) (in i2) Dv nami c Puls 0(in 90 m, m Shell Hybrid r Vertcal Stati c, 1 CW Nose-on 0. 0056 AZZ (model) Duppler Rladar StatiC 2 13,70 -7 Ns c-on 0. 008 AZ I 105 mm Shell Hybrid T Hor zont! -Static 1 200 CN' A' No. 0.1 5 AZ (m odel) _ _ _ _ _ __ ____ 120 mm Shell Irti 1 1zo INoSc- on 0.022 A 22 (n od ei -- -1 ai -oin (nose~ up 1200 1 50) 0. 0.003 AZ2 155 rem Shell Horizontal 1200 1 Nu st —,rOn 0.028 AZ U (model) Doppler Radar Vertical Static 2894 -- Nose-on 0. 00025 AZ 1 Nose-on 0.0038 Hybrid T Static 2900 CW Broadside 0.27 A30 'Fal _ l-on 0. 16 Doppler Radar -- Static 9883 -- Nose-on 0.0027 A21 C: I I — r r 0;o z C) ni H 0 "1 M Sd Or r "I C) z rl z (A 10. H

Nr NA Table A-2: Shell Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or Frequency or Aspect Section Ref (in Vc/s) _______________ _____ Dynamic (in -c/s) Pulse (in m) _____ 155 mm Shell Doppler Radar Vertical Static 23,700 -- Nose-on 0.057 A21 (model) Doppler 240 mm Shell " -- " 9883 -- Nose-on 0.0096 A21 (model)___ ____ 240 mm Shell " Vertical " 23,700 -- Nose-on 0.0064 AZ1......... -I, I III.... _ _... I.....I. I............... I................ I.. ' '-.............. I N 0 — rlj -4 {-4 r 0 z z m ri - 3 0 0-4

__ Table A-3: Aircraft Cross-Sections J1 Static CW Radar CrossBody Equipment Polarization or quenc or Aspect Section Ref (in mic/s) Dynamic Pulse (in m2) Aircraft (fighters and Modified 80 -- Dynamic 22.7 -- -- 2 - 80 A32 bombers, CH Radar including iets) Nose-on (approx) 4.4 A-20 APG-16 Circular " X-band -- Broadside (approx) 5.2 (mean) A33 Nose-on (approx) 7.2 (mean) Horizontal -- Broadside (approx) 86 (mean) A33 T________ __ ail-on (approx) 2.4 (mean) Vertical -- Nose-on (approx) 8 A33 AT-11 Radar (type -- -- -- All* 19 A34 unknown),. - Approaching and 11 A35, Receding A36 B-17 (model) Hybrid T Horizontal Static 100 CW Nose-on 9.3 A37 Nose-on 115 100 -- Broadside 740 A38 Tail-on 16 Nose-on 5 Vertical 100 -- Broadside 180 A38 ________________________ __________ _ Tail-on 7 *"All" indicates an average over several aspects. - -, ~r C);0 r z n ~ o r2; I?C Z t!;0 0-4 0 2T ~)

Table A- 3: Airc raft Cross-Sections (CGnt.) SaIC C Radar CrossBody Equipment Polarization or or Aspect Section Ref _______Dynamic (in rnc/s) Pul Se (in in2 B-i?7 (model) Hybrid T Horizontal Sta-tic 450 CW App roac hin g 70 A36, _ _ _ _ _ _ _ _ _ _ _ _ _ _Receding 9.3 A39 1 ~ Vertical 450 Approaching 8.5 A36, _ _ _ _ _ __ _ _ _ _ _ _ __ _Receding 6.1 A39 — Hrzna 5 - Approaching 23 A36, ___ ___ __ ___n____ __ 450__ Re cedi ng 1 2 A40 — Vertical 450 -- Approaching 16 A36, __ _ _ _ __ _ _ _ _ _ _ _ _ _ _ Receding 8 A40 B-i? APG- 33 - Dy namic IC Puls e Tail-on 1 76 A41 Radar (type - -- All 74 A34 un-known) ------ Approachinig and 45 A 3, __ _ __ _ __ _ _ _ _ __ _ __ _ __ _ __ _ _ __ _ _ _ __ _ _R ec e ding _ _ _ _ __A 36 - -8 — -Approaching and 3 6 A _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _R e c e d in g _ _ _ _ _ _ _ 3 Radar (type - - All.60 A34 ______ _____ _____unkntown) _ _ _ _ _ -J (N C: z ('I ni 0-4 ni (fl C1) S z I

Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or reqc or Aspect Section Ref Dynamic P(ulse (in m) Advanced B-18 Development -- Dynamic 10,000 -- All 65 (av) A42 System D2-1 Advanced Development -- " 3000 -- All 65 (av) A43 System JIl-I B-24 (model) Hybrid T Horizontal Static 100 CW Nose-on 93 A44 Nose-on 50 100 -- Broadside 1000 A38 __ail-on 30 No s e- on 40 " - Vertical 100 -- Broadside 800 A38 Tail-on 20 H- orizontal 450 -- Approaching 150 A36, Receding 3 A40 -Vertical 450 -- Approaching 20 A36, Receding 5 A40 B-24 Radar (type -- Dynamic -- -- All 60 (av) A34 unknown) Nose-on 22 B-25 APG- 33 -- -- Pulse Broadside 46 A41 _Tail-on 5.7 rxj -,4 -4 r 0 o Z 73 z Xr] C) > r? 0 2: I ( C 0 I., Pi n. x/ bh4 C)

0 Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or or Aspect Section Ref (in mnc/s) -> Dynamic Pulse (in mi2) B-25 APG- 36 -- Dynamic -- Pulse Nose-on 93 + 28 A41 Tail-on 10.2 + 4.6 Radar (type -- - -- All 30 (av) A34 unknown) TS-35A* -- " - Pulse -- 9.6 A45 B-29 APG-36 1- -- Front 59 - 69 A41 I1 II II t! Tail-on 69 + 22 A41 TPS-IB Horizontal " 1250 Az. l2~ 27~ 80 A46 Elev. 2o~- 100 1250 All 103 A47 SPM Horizontal 2810 Az. 2- 27 250 A46 Elev. 2o- 100~ Actually consisted of the TS-35A test set (used both as a power meter and a signal generator), antenna, directional coupler, waveguide, receiver, and 'A' scope. C I — rj Pi (I Z ni I 0 t) C 0 1 -^4 - --- -- --

Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or requency or Aspect Section Ref Dynamic P(Pulse (in m2) B-29 SP-IM -- Dynamic 2810 Pulse All 370 A47 MK-33 -- 9380 " All 75 A47 -- -- " - -- Approaching and 67 A35, __________ __ __ Receding____ A36 Nose-on 3.4 B-36 (model) Hybrid T Horizontal Static 73 CW Broadside 2600 A48 Tail-on 86 Nose-on 1.7 " Vertical " 73 " Broadside 1700 A48 _ _ _ Tail-on 1.9 B-36 TPS- I 1B Horizontal Dynamic 1250 Pulse All 21 (mean) A49 " " " " 1250 " Az. 359~ 6.3 A50 __Elev. 40- 100 " SP-1M 2" " 810 " All 44 (mean) A49 " 2810 " Az. 31~0 - 56 25 A50......._____________ ______________________ ____Elev. 4~-6~0_____________ I — 4 0 r 0 Z IC z z ni 0 0 r. Pi CA 2:

J.3 D Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossFreque~ncy etu f Body Equipment Polarization or or Aspect Section Ref Dynamic (in mc/s) Puls e (in n2) B-36 MK-33 Horizontal Dynamic 9380 Pulse All 8.75 A49, A511 ItI9380 Az. 3590 4.5 A49, Elev. 40 - 100 A51 B-45 TPS- IlB 1250 Az. 1 0 6 A50 _El ev._20- 80 1250 All >31 A52 1250 All (except 12 A52 Az. 850 - 950) SP-IM. 2810 Az. 110 14 A5O Elev. 20 - 80 2810 ' All 28 A52 2810 All (except 11 A52 Az. 850 - 950 MK- 33 " 9380 All 53 A52 I 1 —) r 0;o z ni C):t, C) O r. 0ni z -4 r. 0 --4 z U) H 0 - -- -- -- --- -- L

_1_ _ OJ Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or re ncor Aspect Section Ref (in me/ s) 2 Dynamic Pulse (in m2) B-45 MK-33 Horizontal Dynamic 9380 Pulse All (except 11 A52 Az. 85 - 950)___ Nose-on 11 B-47 (model) Hybrid T I Static 73 CW Broadside 780 A53 Tail - on 2 Nose-on 37 " Vertical " 73 " Broadside 1100 A53 Tail-on 25 Nose-on 24 B-47 SHF Radar -- Dynamic 9375 Pulse Broadside 178 A54 T ail-on 12_ Nose-on 100 B-50 (model) Hybrid T Horizontal Static 73 CW Broadside 1090 A55 Tail-on 225,,,,,,, Nose-on 64 Vertical 73 Broadside 900 A55.. ______________ ail-on 40 ___ Advanced Cessna Development -- Dynamic 10,000 -- -- 14 (av) A42 | System D2- 1.. " — --. — -- Approaching and 9.5 A35, R___eceding _ A36 Curtiss-Wright -- -- " - -- Approaching and. 23 A35, 15-D____ __ __ Receding ___ A36........................................ ___....... C cl I txa. b-d r C o I'T z m (P;d n > I C Z O z -

Table A-3: Aircraft Cross-Sections (Cont.) N ttcCW Radar CrossStaticmet Poaizton o Frequency or Aspect Section Ref BoyyqupenaPlaiaton o (in mncfs) (inlsin2)i_____ AdvancedAUZA4 Curtiss-Wright Development -- Dynamic 10,000 Al2 4 15-D System D2-1 ____________ AdvancedAU1A4 Development — 3000 -Al1A4 ____ ____ ____ System JI-l _ _ _ __ _ _ _ F-51 TPS- IB Horizontal 1250 Puls e Az. 16o -20o 0.13 A50 Elev. 30 -60 it it it 1250 Az. 22 0- 32 0 0.5 A50 _______ ____ __ ______Elev._70 11II0 _ _ _ _ _ _ fit1250 AU1 > 1.3 A56 All (except TII T I 1250 Az. 85 0 90o 0.9 A56 _____________ and 950~ 1I000) _ _ _ _ _ _ _ Nose-on 35 F-1(oe) —"Static 2600 ffBroadside 380 A5 7 F_51_(odel)Tail-on 0.14 Nose-on 60 it VrtcaZ600 itBroadside 560 A57 Vertical_ _____Tail-on 0. 16 F-51 SP-lM Horizontal Dynamic 2810 Az. 16o~0 -?o. 6 ASO _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ E le v. _3 0 -6 0 C K I 0 —a tl%) — j 0 z C,) z z Cl) 0 -C)

_ ___ Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or re ncor Aspect Section Ref Dynamic (in mc/s) Pulse (in m2) F-51 SP- M Horizontal Dynamic 2810 Pulse Az. 22~ - 320 0.5 A50 Elev. 7~- 11~0 t 2810 " All 4.8 A56 All (except 2.3 A56 2810 " Az.85- 90~ ____________and 95~- 100~)___ " MK-33 " " 9380 " All 8.3 A56 All (except 4.6 A56 " " " " 9380 " Az. 85~- 90~ and 950- 1000) TS-35A* _ -- " -- 1 1.8 A45 F-80 (with TPS-IB Horizontal l 1250 " Az. 349 - 359~ 1 A46 wing tanks) ____ Elev. 1 - 7 SP-IM " 2810 Az. 3490- 3590 1.6 A46 ______Elev. 10 - 7~_ F-80 (without, TPS-1B " " 1250 " Az. 333- 356~ 1.3 A46 wing tanks) ________Elev. 3~ - 12~___ *Actually consisted of the TS-35A test set (used both as a power meter and a signal generator), antenna, directional coupler, waveguide, receiver, and "A" scope. C I -3 0 z 0;o 0 z tTI z rl;d C H:tf 0 0 -z II c4 rl zl cn Hd -

Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or or Aspect Section Ref Dynamic (in rnc/Ps) ulse (in m2) F-80 (without SP-IM Horizontal Dynamic 2810 Pulse Az. 333~- 356~ 1.5 A46 wing tanks).____________ ______. Elev. 3o~ 12~ O___ F-80 APG-33 -- " -- " Nose-on 0.19 A41 Nose-on 4 F-80 (model) -- Horizontal Static 2600 Broadside 50 A58 _______ __ __ Tail-on 1.8 Nose-on 3.2 " -- Vertical " 2600 " Broadside 100 A58 ______ Tail-on 1.4 Nose-on 5.6 F-84 (model) AN/TPQ-2 Horizontal 2" 600 " Broadside 225 A59 ____ _____ __ Tail-on 16 _ Nose-on 10 Vertical, 2600 Broadside 100 A59 ____ ____ __________ _____________ _____ Tail-on 17 Nose-on 49 " Hybrid T Horizontal " 73 CW Broadside 156 A60 ___~________ ______________ __ Tail-on 36 Nose-on 1.4 " " Vertical " 73 " Broadside 144 A60 ____ ____________ ________ __ Tail-on 5.8 Nose-on 42 " Horizontal " 73 " Broadside 240 A60 Tail-on 42 ____... C K I P —A t'll-i -j r r 0 o z x C) -1 z IC) 0 '11 0-4

_ __ ___ __ __ Table A-3: Aircraft Cross-Sections Cont.) - -.. I... I I I._ Body Equipment Polari zation Static or Dynam ic Frequency (in mnc/s) C;W or Pulse As pe c t Radar CrossSection (in m2) Ref LNose-on 0.64 F-84 (model) Hybrid T Vertical Static 73 CW Broadside 196 A60 Tail -on 1.6 Nos e- on 0.1 F-86 (model) -- Horizontal ' 73 Broadside 130 A61 T_ ail-on 0.9 Nose-on 1.4 Hybrid T ' ZO0 Broadside 55 A62, 'F ail-on 3.8 A6b3 Nose-on 4.4 Vertical " 00Z " Broadside 100 A62, Tail-on 0.3 A63 Nose-on 12 Horizontal " 54S Broadside 300 A62, Tail-on 36 A63 Nose-on 9.8 Vertical 545 Broadside 500 A62, A63 Nose-on 1.8 Horizontal 1200 Broadside 300 A6Z, Tail-on 4 A63 Nose-on 13 Vertical 1200 Broadside 300 A62, Ab3 F-86 TPS- B Horizontal Dynamic 1 5 0 Pulse All 6.7 A64............... C, IS r-, -s r o r0 z Ct;d C) z ~-1 Cl) -4 z 11 2 / -- - --

Table A-3: Aircraft Cross-Sections (Cont.) Stati c Feuny C W Radar CrossBody Equipment Polarization o r (nm/ or Aspect Section Ref _________Dy namnic (i n/) Pul se (in in2) ___ Nose-on 0. 2 F-86 (rnodel) AN/TPQ-Z Ho r Izontal Static 2600 Puls e Broadside 210 A65 Tail-on 1.4 __ Nose-on 0.23 Vertical it2600 Broadside 130 A65 Tail-on 1___ F-86 SP-IM Horizontal Dynarmic 2810 All 12 A64 Nose-on 3 -— 9375 Broadside 31 A66 __ __ __ _ __ _ _ __ __ _ _ __ _ __ __ _T ail-on 20_ _ _ VIMK-33 Hori zontal 9380 All 5.7 A64 F-86 (with TPS-lIB Horizontal 1250 Az 3570 -30 1.6 A50 wing tanks) __ _ _ _ _ _ _ _ _ _ _Elev. 2o0 - Q 100__ _ __ _ SP-IM 2810 Az. 3570 -30 2. 3 A50 Elev. 2o - 100 _ _ _ _ _ _ _ V-formation of three TPS-IB Hori zontal 11250 Az. 3590 -60 1 A46 IF-86's El~v. 2o~ 1I00 __________ I t1250 All 10 A67 C-14 I 0-..rl —) -j 0 z xT C!:tI z m z I

__ Table A-3: Aircraft Cross-Sections (Cont.) Static GCW Radar CrossBody Equipment Polarization or (in m s or Aspect Section Ref (in mc/s) 2v Dynamic Pulse (in m) V-formation of three F-86's SP-IM Horizontal Dynamic 2810 Pulse Az. 359~- 6~ 16 A46 Elev. 2~- 10~ ", " 2810 " All 50 A67 M" MK-33 " " 9380 " All 9.2 A67 Havoc (A-20) Hybrid T Static 600 CW Approaching 3.2 A36, (model) ______ __ Receding 0.03 A39 " " Vertical r 600 " Approaching. 1.9 A36, Receding 0.02 A39 -- Horizontal " 600 - - Approaching 2.8 A36, _Receding 0.092 A40 -- Vertical " 600 1 - Approaching 0.84 A36, ___ ___ Receding 1 0.009 A40 Radar AA no. 3 - Dynamic S-band Pulse Approaching 33 A68 _Mk 2 | M Receding 15 Advanced J2F Development -- " 3000 -- All 32 A43 ___ _System Jl-1 ~~~~~~~.............. C t-sj r 0 Cr z m PI ca 0 3 o -) c3 0 z C -- -- -- --

Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or Fre ncy or Aspect Section Ref -2 Dynamic Pulse (in rn Advanced J2F Development -- Dynamic 10,000 -- All 39 A42 System D2-1 _ " Radar (type -- " - - All 41 A34 unknown) ___ _ - - -- -- Approaching and 25 A35,....____________ ___ Receding | A36 JRF -- - -- | -- Approaching and 30 A35, _ __ _ Receding A36 Lancaster -- 45 " 1200 -- Approaching 265 A69 Receding 127 Radar AA No. 3 -- " S-band Pulse Approaching 147 A68 Mk 2..... Receding 1 70 450 S-band -- Approaching 234 A69 _Receding | 102 Radar Nose-on 172 AA No. 3 -- -- X-band -- Broadside 930 A70 Mk 7 T _ _ _ Tail-on 64 Lincoln -- Dynarric X-band -- Nose-on 380 A70 ________Tail-on 44 I -j r r 0 o z i< m 0 -a t) (P 1Z $ —g -.I

Te(xt A -: Aircraft Cross-Sections (Cont.) V v I I T Body Equi pme nt Polarization Static,or Dy rarnic Fr equenc y (in nc/ s ) cw or Pul s e Aspect Radar CrossSection (in m2) Ref i - f. -, i. i i Meteor Dyna rrn. Approac hing R ec eding 6.1 4.5 A69. -. t 4:-> S- bIti. Approaching Rec eding 7. 1 4.4 A69 i i i Radar R ad a r AA No. i iMk Z R.idar A, A No. lMb '7 S-barnd i ul s Ap p roaching Recedirn 10 A71; - -, i. X - band Nos e- on Tail-on 7 2.5 A70 I'_ 1 1 I -. -—. —4 - - i i Mosquito 45.J 4i 0 - fl',, aarroic I 2UO ci K I Nj -j r F' r o z z 0 0 Tz O* x "I x z 0 -"d Approac hing Receding 18 14 A69 — 4 i 1 S - b- nd Approaching Rec edi ng 15 9.6 A69 Radar AA No. 3 -- ' S-band Pulse Approaching 19 A68 Mk Z ___e c edi ng __ Radar Nose-on 15 F AA No. 3 - X-band Broadside 88 A70 Mk 7 ____ _'___rail-on 8 ' _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ [ _ _ _ _ _ _ _ _ _ _ _

Tabi e A - A: Aircraft Cross- Sc,. tiens (Cont.) 0 Static' e n Cw Radar CrossF` requnc v~ Body Flq u i p m n t P o ila r i z ation or or Aspect Se c ti on Ref Pu Via ry i Cc Pilse (in tn2) MX- 1626 Nose-on 115 (with pod) Hybrid T Hori zontal Stati.c 75 CWNV Broadside 485 A72 (model) __ _________ Tail-on 9_ Nose-on 12 Verticala 75 Broadside 2100 A72 Tail-on 1 MX-1626 Nose-on 100 (without pod) Hcorizontal 75 Broadside 196 A72 (model) _ _ _____ Tail-on 25 Nuse-on 4 Vertical 75 Broadside 575 A72 _ __A__T ailI-on 0.25 __ Nose-cn MIX-1626 pod Horizontal 75 Brocadside 250 A72 (model) J ail —un 2. 3 ',No~s e`- on 0.25 Verti cal 75 B roadsid e 272 A72 _laii-on 0.25 Advanc ed 0-47 Devel opment -- Dynamic 10,000 -- -- 12 (av) A42 System D2-1 -Approaiching andI 10 A35, R c C C d I r1 1 A If,Ardvanc ed 0S-2U Development 0 - 1000 - - Al 13 A43 System Jl - I Cd K: r r t.4 0 C) (.) z U) ttf O C) z m z _ ~ _ I

Table A-3: Aircraft Cross-Sections (Cont.) Static C U Radar CrossBody Equipment Polarization or or Aspect Section Ref (in rnc/s)in m2) Dynamic Pulse (in m2) Advanced OS-2U Development - - Dvna-ict 10,000 -- All 12 A42 Svystem D2-1 _ A... pproaching and 9.5 A35, { Receding A36 OS-2V Radar (type -- - - -- All 16 A34 unknown) P-38 Radar (type -- - - - All 5.4 A34 _______unknown)... u no w n Advanced P-47 Development -- " ),000 -- -- 16 A42 System D2-1 __. _.. Radar (type -- -- - All 8 A34 unknown) TS-35A* -- " - Pulse - 1 3 A45 P-61 -- -- -- 26 A45 r 0 o z r Cf Z ct n C) rl -4 Z I 0 z (P 2; C) O.,6 0 -z/ a1 I - I I I I a *Actually consisted of the TS-35A test set (used both as a power meter and a signal generator), antenna, directional coupler, waveguide, receiver, and "A" scope. --

__ __ __ _ Table A-3: Airc-raft Cross-Sectionrs (Cont.) - -- Body Equi pment Polarization Stati c or Dvna v i C F r q ie nc v (in n-cC/s) ew or Pul s e Aspecc t Radar CrossSection (in in2) Ref N") P-So (photo A PG-16 Horizontal Dyn.Am X-hand - j Approaching 0. 1 3 (mean) A33 equipped) P-80 (with X - bai -- Approaching 0.28 (mean) A33 wing tanks) Approaching J 006 P-80 Circ ular X — bandBroadsidIe (approx) 0.92 (mean) A33 R edi ng i (mean) Horizontal X-band Broadside (approxj 10 A33 R ec e ding 1.7 (mean) Appr udic hiing 0.24 Isi. appox I0 (mean) A Vertical) X - )and Broadside (dApprox)33 Rece.ding 2.3 (mean) C -ircle at one to Horizontal I I I - two i e s with- 1.5 (mean) A33 steep bank TS- 35A* - -- se 0.19 A45 PBY Radar itype1 A I I - A34 unklrown) Approa ching and 31 A35, 9 R L.c in, _ _ _ A36 I -4 rs t4 z r") m c) tj1 z ti) C) zl C: z r *Actuially consisted of the TS-!5.A test s-t (tesced both as a powe r meter.!nd.i.;ignaJ generator), ontenna, directional coupler, waveguide, receiver, and "A" scope. I — -- - - -- - - -- - - I- -- I -- - -- --- ---- ------- - - -- -

_ _ __ I__ _ _ 1 Ta blke A-3: Aircraft Cross-Sections (Cont.) Static Fe CW Radar CrossBody Equipment P —lolarization or Frqecy or As pe r t Section Ref IRDynarmic __ _ Pulse (in n2) R..T.VA RE~adar or AA No. 4 -- Dynamic 212 Puls e All.1.5 (mnean) A73 Lop/Gap MkA SNB Radar (type -- -- — 21 unknown) A dvanc ed SNC Deviopr ent I -- 10,000 -- All 6.2 A42 System 1)D2-1 Approaching and 3.9 A3h C Rec edin_ Ath36 SNJ Approaching and 5 A35, Receding _ _ _ A36 Rad(a r Spitfire AA No. i- P S-band Pulse Appr oac hing 13 A68 _M k 2 _ _ ______ Receding 5 _ SWB Approaching and 13 A35, Receding _ A36 Adv anc cd Taylorcraft Development -- 10,000 -- All 19 A42 Systern DZ- I Radar (type All 16 A34 unknown _ Z r" 0 -z tTI z;o C,) CI) ri 1-1 C: z

I _ Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossFreque'ncy Body Equipment Polarization or ( or Aspect Section Ref (in mc/s ), Dyna rric Pulse (in mr) Taylorcraft -- -- Dynamic -- - Approaching and 9.5 A35, Receding A36 Tempest -- 45~ " 1200 -- Approaching 5.7 A69 Receding 4 4.2 _ — 45~ S-band -- Approaching 5.8 A69 _____________.._ Receding 3. 5 Radar Valiant AA No. 3 -- - - X-band -- Nose-on 98 A70 Mk 7 _______ Tail-on 196 _ Nose-on 5 Vampire Hybrid T Horizontal Static 400 CW Broadside 100 A62, (model) _______ _ Tail-on 7.5 A63 Nose-on 3.1 Vertical 400 Broadside 80 A62, Tail-on 2 A6 3 Nose-on 1.4 Horizontal 1090 Broadside 60 A62, Tail-on 1 1 A63 Nose-on 1 6 " " Vertical " 1090 " Broadside 60 Ab 2, _________Tail-on 2.5 A6 3 Nose-on, 4.. Horizontal " 2400 " Broadside 60 A62, _____T ail-on 3 A63....J................. 4 4 Cz I —, r 0 tr z x;L cn Z r3 Z C PI C0 r 0-~ t r, a --- -- ~~ ---- -

_f _ _ _ U4 <Ji Table A-3: Aircraft Cross-Sections (Cont.) Static CW Radar CrossBody Equipment Polarization or or Aspect Section Ref Dynamiic ( c/s) Pulse (in m2) Nose-on 1.5 Vampire Hybrid T Vertical Static 2400 CW Broadside 50 A62, (model) ____ ___ Tail-on 4 A6 3 Vampire -- 450 Dynamic 1200 -- Approaching 6.6 A69 Receding 4.3 " - - 45 0 S-band - - Approaching 8 A69 R eceding 3.3 -45~ S-band -- Approaching 6.6 A69 __________ __ _ _ Receding 4.1 Radar Wellington AA No. 3 -- " S-band Pulse Approaching 110 A68 Mk 2 ____Receding 79 IT l )! I t l n - l S-band Approac hing 122 A68 __________ _ ______ Receding 75 r r 0 IC) - C) c z 3 I: n O/ I

Table A-4: Cross-Sections of Simple Geometrical Shapes Static Frqec CW Radar CrossBody Equipment Polarization or i icor Aspect Section Ref __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _D y na ini c (i m /s) P ulse _ _ _ _ _ _ _ _ _ _ _ (in in2) C one (Alt. z6 AN/TPQ-2 Horizontal Stati c 2 3,870 Pulse Nose-on 3 x lO0 A15 dia. of base 311_____ Cone Pulse-d (AlIt. 6 Radar — Nosk-on 2.54 \2A15 di.o ba e 2 2 M ethod__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~Cone (Alt. 6 ' Nsec-uc)n 0.57 'k A15 dia. of base 13_ _ _ __ _ _ _ _ __ _ _ _ _ _ __ _ _ _ _ __ _ _ __2_ _ _ _ _ _ 40 0 Cone* Standing Wave No ---s e- n 1.1I 10 Io \3k A74 500 Cone* Nos — on1.6 l-3 'Z A74 650 Cone* - -- Nosev-uon 4.8 10 12A2 A74 65 0 Cone4 (large wooden --- -— Nos (-on 0.5 kV (av) iA75 trietalized surface Cone 058 ~Doppler Radar Vertical Stati c 2 3,700 — Nose-on8. l0Al L D oppler __ _ _ _ _ _ __ _ _ _ _ _ _ _ _ - _ __ _ _ _ _ _ Cylinder I- oeu. ~l ~ A> (length = 1.51 Nose__-______ ______ _ I___-__ 3_A______ I d ilam ete r = 0. 58 8 ) __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ c I b..tl%) — j C rr z x, H cr 0 z" *Angle represents 1/2 cone angle.

WILLOW RUN RESEA.RCH CENTER -UNIVERSITY OF MICHIGAN UMM- 127 7 ___I____ I I I I I I I' < 0...-,, a. 3 4 -1 -0 (9,I T.. c c u - - o, -r 'F —, ~ I I I 2.. -,, - -. -.0 03 0 - 01.x. ^ 0^ 0 0 0 0 0 1 -o -e 0 2 I I -I I *..... - t |, >.r,' 0 z c3 I.. ^ 0 -.. - - A. d- I L 0 -^, 3 j ________^ 'p iy):i ___________ ____ ____________ LI-~ o >} a-r;> a c - Q ~ 0 _ _ __ _ __ __.__._ __ _ _ 0^ O C N N - ~ a a,e. -e -, 0 Z 0 a cc I~ - * I I,0o 1~ I I ': 0: 0 i C- I N1 - 0 0 -, n ~ -I 0 06J - rt 0 K I00 0 60 ~cO T Ir > 0 0,1 E 4 a X,-,, 0c ' CL~:I I L I I...,. I I I I - I - I I 47 C( c7

WILLOWX PlUN RESEARCH CENTER -UNIVERSITY OF MICHIGAIN IIUMM- 127 1 I I I r I> -1 r u r.f iU pC1, C>. -C C C -D Q -0 r. ~:J I-1 C: CLO-I - UL C C) I-~ a>.4 -c I I_ _- I t. I_ _ _ _ I I_ _ J1 *- * C j _ _ I ', 48

WVILLOW RUN RESE.ARCHI CENTER -UNIVERSITY OF MIC'HIGAN UMM- 127 I I I I I I 0' Dx ecc 0:0 rU -C 0f tN LI 11 U1) r0 I Hr IC.0 rN 0 or D-.o-r- - C -Dcc C - -n r '-~ & Cc p c / -t 0 ) -' - CT U - - - 0 0 0 0C0O U). I 0A 0j NC 0 -C E CC cc I 0J- 1 Il N;- U: _C: cc U) 0: la N -O 0 Cl: 'A-, 2 -Ul) C-' N I-O cc I I 10 N4 0 U1) -0 I I _ _ I _ _ _ I I__ _ I _ _ _ I _ _ _ _ I _ _ _ I I_ _ 49

un 0 Table A-4: Cross-Sections of Simnple Geometrical Shapes (Cont.) Static CW Radar CrossF requency Body Equipment Polarization or Frequeor As pect Section Ref Dy nami c (in mc/s) Pulse (in in) Sphere (polystyrene Hybrid T -- Static 3000 CW -- 7.17 x 10- 5 A84 radius - 1/2 _ Sphere (polystyrene -- 3000 - - 1.3 10A84 radius = I Sphere (polystyrene N - - 3000 - - 1.52 10-4 A84 radius =-1/4") Sphere (polystyrene 3000(). - - Z.0 10o A84 radius = 1-1/2 Sphere (polystyrene - - 3000 -- 1.25, 10 A84 radius= 2 Wedge* Parallel Plates Parallel to Perpendicalar to 1.04 x 10 -3 (included (standing wave axis of -- edge andinplaneof 1.02 i1-3 A78 angle Q 200m rnethod) wedge _______symmetry of wedg 8.7 Iji-4 __ 1.17 1O` Wedge* 1.12 i O 43 A74i (included ' N N N 1.18 I A3 angle = 300) _ _ _ _ _ 128 Io -3 r 0-3 Wedgc* 1.75 5 io- A78 (included 1.61 1 I Iangle - 45 0 1.7 I 0 1-3 1.1 8 O~1 -3 (included I 42 -3 A78 ang~le -:: 000' I 1 i1 26 *1 -3 *Radar cross-section given as cross-section per unit length of wedge (square meters per meter). c2 NJ C z 9 r r4 z z vl r(I) I11;o OTi zo crj z (A )W4 H _ -— LL~I

\WILLO'X' RUIN RESFZtXRCLi CENTER UNIVERSITY OF MICHIGAN UMM- 127 r r-co ~iY e-4 fl-1

WILLOW RIUN RESEA-RCH CENTER - UNIVERSITY OF MICHIGAN UMM- 127 REFERENCES FOR. APPENDIX A Al Siegel, K. M., Crispin, J. W., and Kleinman, R. E., "Studies In Radar Cross-Section VII, Summary of Radar Cross-Section Studies Under Project Wizard," Willow Run Research Center, University of Michigan, Report UMM-108, November 1952. SECRET. A2 Meeks, M. L., Logan, N. A., Brewer, H. R., and Wilcox, C. H., "A Bibliography of Radar Reflection Characteristics Vol. I," State Engineering Experiment Station, Georgia Institute of Technology, 1952. RESTRICTED. A3 Meeks, M. L., Logan, N. A., Brewer, H. R., and Wilcox, C. H., "A Bibliography of Radar Reflection Characteristics Vol. II," State Engineering Experiment Station, Georgia Institute of Technology, 1952. CONFIDENTIAL. A4 Meeks, M. L., Logan, N. A., Brewer, H. R., and Wilcox, C. H., "A Bibliography of Radar Reflection Characteristics Vol. III," State Engineering Experiment Station, Georgia Institute of Technology, 1952. SECRET. A5 "Back Scattering Coefficient Patterns of Rocket Shells for 20 MC," Ohio State University Research Foundation, Report302-15, (ATI-49022), August 1948. CONFIDENTIAL. A6 "Back Scattering Coefficient Patterns of Rocket Shells for 50 MC," Ohio State University Research Foundation, Report302-16, (ATI-48939), August 1948. CONFIDENTIAL. A7 "Back Scattering Coefficient Patterns of Rocket Shells for 100 MC," Ohio State University Research Foundation, Report302-17, September 1948. CONFIDENTIAL. 52 - --

WILLOWV RUtN RESEARCH CENT'R - UNIVERSITY OF MICHIGAN UMM- 127 A8 "Back Scattering Coefficient Patterns of Rocket Shells for 300 MC," Ohio State University Research Foundation, Report302-18, (ATI-40573), September 1948. CONFIDENTIAL. A9 "Echo Patterns of Rocket Shells for 600 MC," Ohio State University Research Foundation, Report-302-20, (ATI-42137), October 1948. CONFIDENTIAL. A10 "Echo Patterns of Rocket Shells for 1200 MC," Ohio State University Research Foundation, Report-308-23, (ATI-49037), November 1948. CONFIDENTIAL. All Linderman, O. E., "Project Thumper: Missile Echoing Area," General Electric Company, Report GE-TR-55408, June 1948. SECRET. A12 "Radar System Analysis Comparative-Performance Study of Pulse, F-M and Doppler Techniques for Ground-Based LongRange Search and M.T.I. Radar Systems," Sperry Gyroscope Co., Report Sperry-5223-1109, (ATI-52865), June 1948. SECRET. A13 "Determination of Echoing Area Characteristics of Various Objects Fourteenth Quarterly Progress Report," Ohio State University Research Foundation, Report-302-36, August 1950. CONFIDENTIAL. A14 "Determination of Back Scattering Coefficients of Various Objects," Ohio State University Research Foundation, Report302-10, (ATI-28341), May 1948. CONFIDENTIAL. A15 Sichak, W., "Missile Detection Final Report," Federal Telecommunications Laboratory, Report ATI-42811, August 1948. SECRET. A16 MacDonald, F. C., "Radar Area Measurements of V-2 Rockets," Naval Research Laboratory, NRL Report-3220, January 1948. RESTRICTED. 53 - - -- I

WILLOW' RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN I UMM- 127 A17 MacDonald, F. C., "Measurements of Radar Area of a V-2 Rocket," Naval Research Laboratory, Report NRL-C-3460 -52/48A. (ATI-105502), August 1948. CONFIDENTIAL. A18 General Electric Company, "The Thumper Project Final Report Phase I," Report ATI-57044, June 1949. SECRET. A19 "Echoing Areas of Objects Progress Report, 1 November 1948 to 31 December 1948," Ohio State University Research Foundation, Report-302-25, (ATI-68314), January 1949. CONFIDENTIAL. A20 "Echo Patterns of Tanks and Missiles," Ohio State University Research Foundation, Report-302-26, (ATI-71401), January 1949. CONFIDENTIAL. A21 "Research Investigation on Counter-Battery and Fire Control Radar," Belmont Radio Corporation, Final Report, May 1948. SECRET. A22 "Back Scattering Coefficient Patterns of Rifle Shells for 1200 MC," Ohio State University Research Foundation, Report-302-ll, (ATI-49021), January 1948. CONFIDENTIAL. A23 "Back Scattering Coefficient Patterns of Mortar Shells for 200 MC," Ohio State University Research Foundation, Report-302-8, (ATI-28359), November 1947. CONFIDENTIAL. A24 "Echo Patterns of Mortar Shells for 600 MC," Ohio State University Research Foundation, Report-302-6, (ATI-28358), September 1947. CONFIDENTIAL. A25 "Echo Patterns of Mortar Shells for 1200 MC," Ohio State University Research Foundation, Report-302-2, June 1947. CONFIDENTIAL. A26 'Echo Patterns of Mortar Shells for 2900 MC," Ohio State University Research Foundation, Report-302-1, May 1947. CONFIDENTIAL. i - - 54 - --

WILLOW RUN RESEARCH CENTER - UNIVERSITY OF MICHIGAN U MM NI- 127 A27 "Echo Patterns of Mortar Shells for 9000 MC," Ohio State University Research Foundation, Report-302-4, July 1947. CONFIDENTIAL. A28 "Back Scattering Coefficients of Mortar Shells for 16,000 MC," Ohio State University Research Foundation, Report-302-30, (ATI-64626). CONFIDENTIAL. A29 "Echo Patterns of Mortar Shells for 24,000 MC," Ohio State University Research Foundation, Report-302-21, (ATI-43506), October 1948. CONFIDENTIAL. A30 "Determination of Back-Scattering Coefficients of Various Objects," Ohio State University Research Foundation, Report-302-9, (ATI-23410), January 1948. CONFIDENTIAL. A31 MacDonald, F. C., "L, 5, and X Band Radar Echoes from Rifle Shells," Naval Research Laboratory, Report NRL-3720, August 1 50. UNCLASSIFIED. A32 "Quarterly Progress Report, Project Lincoln," Massachusetts Institute of Technology, Report MIT-LINCOLN-RLE-QPR-1, (ATI-123811), October 1951. SECRET. A33 Muchmore, R. B., and Wtiss, L. H., "Radar Echo Scintillation From P-80 and A-20 Airplanes," Hughes Aircraft Company, Report Hughes-TM-212, November 1948. SECRET. A34 "Pilotless Aircraft Guidance and Control System Design Handbook," Raytheon Manufacturing Company, Report Ray-172, November 1947. SECRET. A35 "Summary Technical Report of the Committee on Propagation," National Defense Research Committee, Summary Technical Report CP, Vol. 1, Ch. 10.2, 1946. UNCLASSIFIED. -. - --- 55 I

WILLOW RUN RESEARtc rL_ i ^1 R - UNIVERSITY OF MICHIGAN UMM-127 A36 "Equivalent Echoing Areas of Aircraft, and Characteristics of Aircraft Echoes: A Critical Survey of the Literature," Telecommunications Research Establishment, Report TRE-TN-47, (ATI-83160), October 1949. SECRET. A37 Jacques, R. B., "B-17E Bomber at 100 MC Reflection Patterns," Ohio State University Research Foundation, Report-759-22, (ATI-14551), March 1944. UNCLASSIFIED. A38 "Analysis and Application of Measurements of Radar CrossSection of Airplane Models," Harvard University Radio Research Laboratory, Report 411-157, February 1945. UNCLASSIFIED. A39 Yates, K. P., "A Continuous-Wave Method of Measuring Radar Cross-Sections and Reflection Patterns by Means of Models," Ohio State University Research Foundation, Report-759-33, (ATI-14550), October 1945. UNCLASSIFIED. A40 "Analysis and Application of Measurements of Radar CrossSections of Airplane Models - II," Harvard University, Radio Research Laboratory, Report-411-157A, September 1945. UNCLASSIFIED. A41 "Report on Trip to Hughes Aircraft and Rand Corporation,". Willow Run Research Center, University of Michigan, Internal Memorandum 59-D-10, December 1951. SECRET. A42 "Recent Performance of the 3 cm Advanced Development System," Massachusetts Institute of Technology, Report MIT-RL-72-7, June 1943. UNCLASSIFIED. A43 Linford, L. B., Williams, D., Josephson, V., and Woodcock, W., "A Definition of Maximum Range on Aircraft and Its Quantitative Determination," Massachusetts Institute of Technology, Report MIT-RL-353, (ATI-6010), December 1942. UNCLASSIFIED. A44 Jacques, R. B., "B-24 Bomber at 100 MC Reflection Patterns," Ohio State University Research Foundation, Report-579-21, (ATI-15557), March 1944. UNCLASSIFIED..... 56.

WILLOW' RUN RESEAiRCIH CINTER - UNIVERSITY OF MICHIGAN UMM- 127 A45 Winn, O. H., "Effective Radar Target Area of Various Types of Aircraft," General Electric Company, EMT-1010, December 1946. CONFIDENTIAL. A46 Ringwalt, D. L., MacDonald, F. C. and Katzin, M., "Quantitative Measurements of Radar Echoes from Aircraft II," Naval Research Laboratory, Report NRL-C3460-18A/51, March 1951. CONFIDENTIA. A47 Amntnt, W. S., MacDonald, F. C., and Passerini, H. J., "Quantitative Measurements of Radar Echoes from Aircraft XI. B-29," Naval Research Laboratories, NRL Memorandum Report No. 164, May 1953. CONFIDENTIAL. A48 "Echo Measurements of the B-36 Aircraft," Ohio State University Research Fculndiation, Data Set 5, June 1952. CONFIDENTIAL. A49 MacDonald, F. C., "Quantitative Measurements of Radar Echoes from Aircraft," Naval Research Laboratory, Report NRL-C34t-0-94A/51, June 1951. CONFIDENTIAL. AS0 Ringwalt, D. L., MacDonald, F. C., and Katzin, M., "Quantitative Measurements of Radar Echoes from Aircraft," Naval Research Laboratory, Report NRL-C-3460 —73A/50, (ATI-93449), October 1950. CONFIDENTIAL. A51 Ament, W. S.. Katzin, M., MacDonald, F. C., Passerini, H. J., and Watkins, P. 1.., "Quantitative Measurements of Radar Echoes from Aircraft V. Correction of X-band Values," Naval Research Laboratories, Report NRL-C-3460-132A/52, October 1 q5. CONFIDENTIAL. A52 Ament, W. S., MacDonald, F. C., and Passerini, H. J., "Quantitative Measurements of Radar Echoes from Aircraft VIII. B-45," Naval R,;oseaarch Laboratories, NRL MemoranduLr Report No. 116, Jantuary 1953. CONFIDENTIAL. A53 "Echo Measurements of the B-47 Aircraft," Ohio State University Research Foundation, Data Set 3, June 1952. CONFIDENTIAL. - 57.

WILLOXW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN UMM-127 A54 Schivley, George W., "Measurements of B-47 Aircraft Dynamic Reflection Characteristics," Wright Air Development Center, Report WADC-TN-WCER-52-1, (ATI-163743), June 1952. CONFIDENTIAL. A55 "Echo Measurements of the B-50 Aircraft," Ohio State University Research Foundation, Data Set 1, June 1952. CONFIDENTIAL. A56 Arnent, W. S., MacDonald, F. C., and Passerini, H. J., "Quantitative Measurements of Radar Echoes from Aircraft IX. F-51," Naval Research Laboratories, NRL Memorandumr Report No. 127, March 1953. CONFIDEN'TIAL. A57 "Echo Measurements of the F-51 Aircraft at 2600 MG," Ohio State University Research Foundation, Data Set 9, July 1952. CONFIDENTIAL. A58 "Echo Measurements of the F-80 Aircraft at 2600 MC," Ohio State University Research Foundation, Data Set 10, August 1952. CONFIDENTIAL. A59 "Echo Measurements of the F-84 Aircraft at 2600 MC,'" Ohio State University Research Foundation, Data Set 8, June 1952. CONFIDENTIAL. A60 "Echo Measurements of the F-84 Aircraft," Ohio State University Research Foundation, Data Set 2, May 1952. CONFIDENTIAL. A61 "Echo Measurements of the F-86 Aircraft," Ohio State University Research Foundation, Data Set 4, May 1952. CONFIDENTIAL. A62 Hay, D. R., "Radar Cross-Sections of Aircraft," Eaton Electronics Research Laboratory, McGill University, Report No. 3 on Contract DRB-X-27, June 1952. SECRET. - -- -~~....-cl

WILLOW RUN RE SEAR C H CLNI NR - UNIVERSITY OF MICHIGAN UMM- 127 A63 Woonton, G. A., Hay, D. R., and Hogg, D. C., 'Radar CrossSections of Aircraft," Eaton Electronics Research Laboratory, McGill University, Report No. 1 on Contract DRB-X-27, October 1951. SECRET. A64 Ament, W. S., MacDonald, F. C., and Passerini, H. J., "Quantitative Measurements of Radar Echoes from Aircraft VI. Corrected F-86 Amplitude Distribution and Aspect Dependence," Naval Research Laboratories, Report NRL-C-3460-143A/52, December 1952. CONFIDENTIAL. A65 "Echo Measurements of the F-86 Aircraft at 2600 MC," Ohio State University Research Foundation, Data Set 7, May 1952. CONFIDENTIAL. A66 Schivley, George W., "Measurements of F-86 Aircraft Dynamic Radar Reflection Characteristics," Aircraft Radiation Laboratory, Wright Air Development Center, Report TN-WCLR-52-2, September 1952. CONFIDENTIAL. A67 Ament, W. S., MacDonald, F. C., and Passerini, H. J., "Quantitative Measurements of Radar Echoes from Aircraft X. Three F-86 Aircraft in Formation," Naval Research Laboratories, NRL Memorandum Report No. 144, April 1953. CONFIDENTIAL. A68 Beeching, G. H., and Corcovan, N., "The Characteristics of S-Band Aircraft Echoes with Particular Reference to Radar A.A. No. 3 Mk. 2," Ministry of Supply, ADRDE-Research Report No. 253, (ATI-109830), August 1944. CONFIDENTIAL. A69 Tomlin, D. H., and Merrifield, C. V. F., "An Interin Report on Aircraft Echo Characteristics at L-Band," Radar Research and Development Establishment, Report RRDE-TN-34, (ATI-84621,), April 1949. CONFIDENTIAL. A70 Hutchinson, G. L., and Caswell, A. F., "Further Measurements of Radar Echoing Areas on X-Band," Royal Aircraft Establishment, Technical Note No. G.W. 175, (ATI-145917), February 1952. SECRET. - - 59 ~ I II III ---

WILLOW RUN RESEARCIH (C'NTER - UNIVERSITY OF MICHIGAN UMM- 127 A71 Beeching, G. H., "The Characteristics of the S-Band Radar Echoes II - The Jet-Propelled Meteor Aircraft," Radar Research and Development Establishment, Report RRDE-CR-326, (ATI61518), January 1947. CONFIDENTIAL. A72 "Echo Measurements of the MX-1626 Aircraft," Ohio State University Research Foundation, Data Set 6, December 1952. CONFIDENTIAL. A73 Bonelle, G. J., "A Velocity Measuring System for R.T.V. 1 and Similar Projectiles," Radar Research and Development Establishment, RRDE Report No. 358, (ATI-92241), September 1950. SECRET. A74 Sletten, C. J., "Electromagnetic Scattering from Wedges and Cones," Cambridge Research Center, Report CRC-E5090, July 1952. UNCLASSIFIED. A75 "Technical Progress Report No. 17 to the Steering Committee from the Antenna Laboratory," Carrmbridge Research Laboratories, CRL Report No. E3110, April 1951. CONFIDENTIAL. A76 "Quarterly Progress Report for Period April 1 to July 31, 1947," Ohio State University Research Foundation, Report-302-5, July 1947. CONFIDENTIAL. A77 "Determination of Echoing Area Characteristics of Various Objects," Ohio State University Research Foundation, Report-302-7,. October 1947. CONFIDENTIAL. A78 "Technical Progress Report No. 16 to the Steering Committee from the Antenna Laboratory," Cambridge Research Laboratories, CRL Report No. E3102, January 1951. CONFIDENTIAL. A79 "Echoing Area Characteristics of Various Objects: Ninth Quarterly Progress Report," Ohio State University Research Foundation, Report-302-29, May 1949. CONFIDENTIAL. 60 -

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN i UMM- 127 A80 Aden, A. L., "Electromagnetic Scattering From Metal and Water Spheres," Harvard University, Cruft Laboratories, Technical Report No. 106, (ATI-92016), August 1950. UNCLASSIFIED. A81 Ringwalt, D. L., "A Model Technique for the Measurement of the Radar Characteristics of Targets," Naval Research Laboratory, NRL Report 3800, (ATI-110653), June 1951. UNCLASSIFIED. A82 Hamren, S. D., "Scattering from Spheres," University of California, Antenna Laboratory, Report Univ-Calif-AL-171, (ATI83900), June 1950. UNCLASSIFIED. A83 "Project NIKE — Technical Report - 15 July 1947," Bell Telephone Laboratories, Inc., July 1947. CONFIDENTIAL. A84 "Determination of Back Scattering Coefficients of Various Objects," Ohio State University Research Foundation, Report302-14, (ATI-123923), August 1948. CONFIDENTIAL. -... 61

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN UMM-127 APPENDIX B THE THEORETICAL APPROXIMATION OF THE RADAR CROSS-SECTION OF VARIOUS MISSILES AND MANNED AIRCRAFT B.: Introduction In the work at the Willow Run Research Center it has been necessary on various occasions to estimate the radar cross-section of various aircraft and missiles. In this appendix the results obtained are summarized and, wherever possible, these theoretical results are compared with experiment. Much work has been done in connection with V-2 type and intercontinental ballistic missiles; it is planned to report this work in a future paper in this Radar Cross-Section series. The methods employed in finding theoretical values of cross-section are briefly discussed in Section B-2. Manned aircraft are considered in Section B-3, and Section B-4 contains the results obtained in the consideration of the cross-section of missiles (excluding ballistic types). B.2: The Methods Employed in Approximating the Cross-Section of a Missile or an Airplane The purpose of the following paragraphs is simply to place the theoretical values of radar cross-section which are tabulated below in their proper perspective with respect to experimental values of C, and to re-emphasize the need for the use of the concept of radar crosssection with appropriate regard for its relation to the properties of the radar system. In determining the cross-section of a composite body such as those under discussion here it has been assumed that components vibrate in such a manner that their fields can be added in random phase. This assumption leads to a simple addition of the radar cross-sections of the various parts of the body in finding the cross-section of the composite body itself. The following argument shows why "random phase" implies this process of simple addition. - 62 ---

WILLOW RUN RESEARCri ~r.~ I e - UNIVERSITY OF MICHIGAN UMM-127 The radar cross-section of an arbitrary surface is given by rlir 4rr2 [iH i-2 r.. co where r is the distance from the radar to the target and Hs and H1 are the scattered and incident magnetic field vectors respectively. For convenience we may write! it 2 = Ae A. Consider the radar cross-sections for two scatterers given by A 1 e A and sl 2l 2 andr Ae A 2 2 2 The radar cross-section of two scatterers, considered together, is given by i" 1 i~2 - = A e + Aze If the position of one of these scatterers is random relative to the other, the expected value of a, E (a), is given by E (c 2 r Ae) (A(Aee + Ae (Ae 4w 2 + A1 (27 0 O 2A2 A2 1 2 - - -- 63!.........

WILLOW RUN RESEARCH CENTER - UNIVERSITY OF MICHIGAN UMM- 127 The procedure used in finding these cross-sections involves considering a target as a combination of simple surfaces such as cylinders, flat plates, prolate spheroids, etc, and then adding the calculated return from each surface. The justification for a random phase addition of the radar crosssections of the component scatterers is based upon the fact that the relati-ve positions of the component scatterers (or at least the relative positions of the simple geometric configurations used to approximate them) cannot be precisely determined. In a more exact treatment, the relative positions of the component scatterers would be specified and an approach such as this would not be appropriate. But this approximate method has achieved a moderate degree of success (Ref. B-l) at large wavelengths (for example, greater than about 1 meter for manned aircraft); hence it is only natural to try to extend this technique into the microwave region. It is important to note that for the longer wavelengths the radar cross-section is dependent upon both wavelength and polarization. Resonance effects are probably always present in the consideration of conventional aircraft. Experimental values of U indicate that this quantity is less dependent on polarization and resonance phenomena as the wavelength decreases. Since the approximations of geometrical and physical optics are such that the back scattering 6( calculated by these methods does not depend upon either polarization or resonance effects, but does depend upon the relative magnitude of.\ and ( (where t is a characteristic dimension of the scattering surface), it is only reasonable to expect a moderate degree of success when extending the above technique into the microwave region (i.e., A < ). The advantage of this technique is the relative simplicity of the calculations employing physical and geometrical optics. It should be noted that, although the calculated values of radar cross-section presented herein in some cases seem high, they are really not incompatible with values encountered in the field. The problem of correlating the analytical and experimental values of radar crosssection fundamentally depends upon three factors: the condition of the 64 I1 I... II

WILLOW RUtN RE, SE,\RCH CL-.NTER - UNIVERS ITY OF MICHI-GAN UMM-127 equipment; the experimental -lmethod employed to observe the radar echo; and the validity of the theoretical results. During World War II a scientific teram from the Radiation laboratories rmade measurements ol the perforrmance of a number ol radar sets nd(l compared their range performiance with the laboratory or "ideally maintained and adjusted" value. These results are shown in Figure B.1 and discussed below. Fromn- this char't we see that; in practice a large percentage of radar systemns tested were not working at their calibrated efficiency, ',ut at 10 (lb or more below. Consequently, the values of G surmised from operational experience with these systems are too small. One of the attempts to assign causes for this performance degradation may be found in Reference B-2, wherfein the sources are taken to be assoc i:te w i th 1. receiver noiste figure, 2. S/N ratio. 3. coll.aping loss, 4. beamr shape loss, 5. plumrb)in tg losses,. op)e rator losses, aInd 7. ob-)sr. rver tac ttor. Though definitions of the above mi-ay %vary, depenrding on the facility to assign values for each error in a( particular radar, thel composite effect is observable and measurable. Losses of 2 to 530 db are not unheard of. and thus with a r)articil tr r; easuring ins trurent _ ui h as a usual field-type radar orne may be n-measulring the properties of instrument plus target, instead of the target alone, Linford (Ref. B-3) defines the effective radar cross-sectiton as that value of i obtained from the radar range equation which is exceeded during one-half of a series of measuring time intervals. In this way, as Kerr (Ref. B-1) points out, the essential feature of the probability of detecting the echo is introduced into the value of J. If desired, the required degree of probability could be modified, and the resulting value of J would be changed accordingly.

WILLOW RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN UMM-127 1 L0 I) LU zo CL: z 50 DECIBELS BELOW RATED PEPFORMANCE FIG. B-1 RADAR PERFORMANCE SURVEY JULY 1945 Taken from Radiatlon Laboratory Series No. 1, "RADAR SYSTEM ENGINEERING". Ridenour, McGraw-Hili, reproduced in Ref. B-2 e 66 II ~

WILLOW; RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN UMM-127 Another factor important in correlating analytical and experimental values of radar cross-section is the angular variation in target aspect that occurs during the time of observation. This variation may be due to surface vibrations of the scatterer, relative motion between target and radar, etc. As Barlow and Emnerson (Ref. B-2) point out, the probability of detection is dependent upon the nature of the fluctuations of the target signal:; from scan to scan. They say, "A large bomber viewed at the short wavelengths used for A.I. has an echoing area which is such a rapidly varying function of aspect that the inevitable smnall aspect changes from scan to scan are sufficient to cause considerable fluctuation." B.3: The Cross-Section of Manned Aircraft The results obtained for trhe radar cross-section of the TU-4 (B-29), the IL-28. and the B-47 are tabulated in this section. Throughout this section the aspect will be specified in terms of ( and 09 where ) is the azimuth angle measured from the nose in the plane of the wing, and 6 is the elevation angle measured from the nose in a plane perpendicular to the wing and containing the axis of the fuselage, as illustrated in Figure B-2. B.3.: The TU-4 (B-29) For the purposes of this work, the radar characteristics of the TU-4 are assumed to be esetntially the same as those of a B-29, (Ret. B-4). Applying the techniques briefly outlined in Section B.2 above, the following results were obtained for the aspects defined by & = 0~ and 4~ and Q 0~ to q - 180~ at 300 intervals at X-band, S-band, and L-band. The results so obtainedt are listed below in Table B-l. I ~7 - --

WILLO-C\X RIUN RESFARC(I C(.NTER -UNIVEIRSITY OF MICHIGAN UMM-127 FIG. B-2 BASIC GEOMETRY USED IN DETERMINING THEORETICAL CROSS- SECTIONS OF AIRCRAFT At the tine of the cornpultti on of the following data, experirnmental information cou'ld be obtained (-)1only for essentially nose-on and tail -on views S. Concui rrt nt with the co-,mputatiion of those values a report on the mrreasuremient of radar ec:hoes frorm a B-29 was published at the Nav;al Research Laboratories (Ref. B3-). A comparison of the theoretical values given hbelow and the NP.i experimental values, for comparable aspects. is pre(:;rnted in the following graphs. The graphical method of presentatL-io)n i-; tihe same as that Cappearing in the NRL report, with the theoretical values added. Holwever, in the following graphs the plotted NRL points are connected to forrn broken line graphs. Approximately nose-on aspects tare sho'Awn in Figure B-3, aspects near 300 in azimuth are given in Figure B-4, those near 6Oc' in azimuth are shown in Figure B-5, a.id Figure B-6 shows the comparisorr for approximately broadside aspects. Even though small differences exist between the theoretical and experimental aspects compared, examination of the following graphs shows that the predicted values are in general agreement with those obtained experimentally. (,t - - --

WILLOW RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN UMM- 127 30 CN Z S- Band Aspect A 20 - ----- --- -"" -. —... L - Band Aspect A 0 S - Band, Aspect B X,S- Bands L - Band Aspect B Theoretical Value (Az.: 0', El. 0' - 4' ) 0 L - Band, Aspect C 1 2 5 10 20 30 40 50 60 70 80 PERCENTAGE OF TIME THE VALUES EXCEED THE ORDINATE Aspect A: Azimuth 6.59' - 6.75' Flrvation 1.92~ - 2.00' Aspect B: A ' rrl.,h 356.08~ - 355.83';, Ie., i, 7.00' - 7,30~ Aspect C: Azimuth 6 17' - 6.25'; Eievation 1 50' - 1.59' FIG. B-3 COMPARISON OF THEORETICAL AND EXPERIMENTAL CROSS -SECTIONS OF THE B- 29 AT ESSENTIALLY NOSE -ON ASPECTS 0o - Band, Aspect D ' E 4 Band Aspect D 10o Il - - X Band, Aspect E 1 2 5 10 20 30 40 50 60 70 80 L - Band Aspect E PERCENTAGE OF TIME THE VALUES EXCEED THE (FORkNATE Aspect D: Azimuth 35.0' - 36.75'; Elevation 5.75' - 6.08~ Aspect E: Azimuth 27.0~ - 28.08~; Elevation 2.25 - 2.33~ FIG. B-4 COMPARISON OF THEORETICAL AND EXPERIMENTAL CROSS-SECTIONS OF THE B-29 AT THE ASPECT DEFINED BY AZIMUTH -30~ AND ELEVATION-00 -4~ - 69.

WILLOW RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN UMM-127 z I0 I: Theoretical Value-^ - u Pi.r r (Az.:60~, El.: ) e0 _ ~L- Baind Aspect F Theoretical Value (Az.:600, El.: 40) _ _ - F 1 2 5 10 20 30 40 50 60 70 80 90 PERCENTAGE OF TIME THE VALUES EXCEED THE ORDINATE Aspect F: Azimuth 67.50~ - 72.00~; Elevation 3.17' - 3.170 FIG. B-5 COMPARISON OF THEORETICAL AND EXPERIMENTAL CROSS-SECTIONS OF THE B-29 AT THE ASPECT DEFINED BY AZIMUTH-60~ AND ELEVATION-O0 -4~ 300 CN Theoretical Value Z 2 - (Az.:.90~ El.. 4' C 0 0 1 2 5 10 20 30 40 50 60 70 80 90 95 98 99 99.5 PERCENTAGE OF TIME THE VALUES EXCEED THE ORDINATE Aspect G: Azimuth 90.00~ - 93.08'; Elevation 3.67' - 3.75' FIG. B-6 COMPARISON OF THEORETICAL AND EXPERIMENTAL CROSS-SECTIONS OF THE B-29 AT THE ASPECT DEFINED BY AZIMUTH 90~ AND ELEVATION-O00 -4~ _ 70 II 7 - i1~............

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN i UMM-127 ASPECT 2 (in degrees) RADAR CROSS-SECTION IN m (in degrees) 6 X- Band S-Band L- Band 0 0 65.1 66.2 68.0 4 0 68. 69.1 70.9 0 30 9.8 9.8 9.8 4 30 6.9 6.9 6.9 0 60 38.4 38.4 38.4 4 60 12.8 12.8 12.8 0 90 2630. 1200. 1370. 4 90 2530. 843. 474. 0 120 32.3 32.3 32.3 4 120 6.7 6.7 6.7 0 150 8.7 8.7 8.7 4 150 5.8 5.8 5.8 0 180 62.6 62.6 62.6 4 180 62.6 62.6 62.6 G for the TU-4 (B-29) Table B-1 The monostatic and bistatic radar cross-sections at 600 mc for the TU-4 (B-29) were also computed and compared for one particular aspect. The monostatic radar cross-section, rmn, and the bistatic radar cross-section, Gb, were calculated by means of physical and geometrical optics. The target aspect is determined from the geometry in Figure B-7 where points P and Q are 30 miles apart and where the target is at an altitude of 500 feet directly above the midpoint of a straight line connecting P and Q. I I Dn r FIG. B-7 BASIC GEOMETRY USED IN THE DETERMINATION OF THE BISTATIC CROSS-SECTION OF THE TU-4 (B-29) 71

WILLOW RUN RESEARCH CENTER- UNIVERSITY OF MICHIGAN UMM- 127 The monostatic case analyzed is the case in which the transmitter and receiver are both at Point P in Figure B-7. The monostatic radar cross-section was found to be 316 square meters. The bistatic case analyzed is the case in which the transmitter is at P and the receiver at Q. The bistatic radar cross-section was found to be 55,300 square meters. It might be well to point out that to date there is, to the authors' knowledge, neither experimental bistatic cross-section data on a B-29 for comparison, nor a method of obtaining an exact solution to the bistatic radar cross-section problem for objects of this complexity. Although the value of 55,300 m2 may seem large. it should be noted that Canadian early warning radar experiments indicate that large increases in radar cross-sections do result from bistatic operation. B.3.2: The IL-28 (Type -27) The radar characteristics of the IL-28 are based upon configurations appearing in Ref. B-6. Since small changes in tile configuration of a scattering surface may produce significant changes in the scattered energy distribution, it is reasonable to exptct that the following values of radar cross-section for the various aspects may change as more detailed information becomes available regarding the configuration. The IL-28 results are collected in Table B-2.A Subsequent to the calculation of the radar cross-section for the IL-28, it was pointed out in Reference B-6 that a Russian L-28 (Type 27) has approximately the same reflection characteristics as a B-45. Consequently, the theoretical values of radar cross-section for the IL-28 and the experimental values for the B-45 should be of the same order of magnitude. This is found to be the case, as illustrated in the following graphs. The type of comparison and the method of presentation are the same as in Figures B-8 to B-12. *The meaning of the aspect angles 6 and ~ is indicated in Figure B-2.. 72

WILLOWX RIPN RKSEAXRCIH CFNTIER - UNIVEIRSITY OF MICHIGAN UMM- 127 ASPECT 2 (in degrees) RADAR CROSS-SECTION IN m (in degrees) 6'& X-Band S-Band L-Band 0 24.1 29.6 22.4 4 0 24.1 29.6 22.4 030 0.58 0.58 0.58 4 30 0.58 0.58 0.58 --- - 0 60 4.39 4.39 4.39 4 60 4.39 4.39 4.39 0 90( 21 000. 2090. 418. 4 90 1030. 453. 324. 0 i 120 4.36 4.36 4.36 4 - 1 —20 3 4.6.3 9 4 1 120 4.36 4.36 4.36 I f~ -- I —. 1 1 5 0 - - - T 0.38 I 0.38 0.38 - - 0 1 0 4 - 150 _ 0 1_____ 80 4 __ 180 j 4~wil~.. - 0.38 0.38 0.38 -- - i r — I 0.38 0.38 0.38 0.38 0. —1, 0.38 1 0.38 0.38 I - for the IL-28 T;Tble B-2 B.3.3: 1The MX- 2'091 and the 286-12 Bombers The- radar cross-sections of the MX-2091 and the 286-12 (see Fig's. B-13 and B-11) bombers have also been computed by these approximation technique s. The aspec(t angles shown in Figure B-2 were used. The results obtained for the 28- 12 are given in Tables B-3, B-4, and B-S. The results obtained for the MX-2091 are in Tables B-6, B-7, and B-8. R.3.4: The B-47A The theorettical phvsic(;l-optics nose-on radar cross-section for the B-47 A has be-en coirputed and previously reported in Reference B-7. The results obtained were as follows: (1) L-Band. ( 2.79 r2 (2) S-Band, "- - 7.44 ni - -- -- -

WNILLOWX PUN RESEA.,RCfi CENTER - UNIVERSITY OF MICHIGAN UMM- 127 -.______I_ z tZ 0 0. fP ~CE N -A GE OF T IME: TH E V 4W.)ES E XCE ED DI. GND'4A TE -250 Mc'1sec. Q380 Mc/,~ec. FIG. B 8 C2-."MPARISOIN OF IHEORETICAL IL -28 C ROSS - SFCT ION AND FXPERIMFNTrAL B-45 CROSS-SECTION AT ASPECT DEiFINED BY AZIMU'TH.,O'0 AND ELEVATION ~4O I i I i i I I I I i I iII I I I I i i i II I i i I.0 0 -0C I i I I i0 I5 L-. 90 ' 9 8 9-? 9(, 8 RCF~cNTAC~ OF TIME THE VALUL;E: EXCEED THE Ol'RDINATE 1 ',50 Mc,' sec. 28? m3 " M/ sec, ~V- %S MCI sec. FICG. - 9 COMPARISON OF THEQREBTCAL I L -28 CROSS- SEC-TION AND EXPeRIMENTAL B-45 CNOSS —SECTiON AT ASPECT DEFINED BY AZ!MurH -- 30'~ AND ELEVATION — 40 174

WILLOW\ RIUZN RESLEARCH CENTER- UNIVERSITY OF MICHIGAN U — UN1M-127 27 - L I t t2 4 *|-4 i I I i i. -.. Theoretical Curves.. z C) 0 0 90 95 98 99 99.5 99.8 PERCENTAGE OF TIME THE VA.UES EXCEED THE ORC)INATE 1250 M c/sec. - 2810 Mc/sec. - Q380 Mc/sec. FIG. B - 0 COMPARISON OF THEORETICAL I - 28 CROSS- SECTION AND EXPERIMENTAL B- 45 CROSS-SECTION AT ASPECT DEFINED BY AZIMUTH 60" AND ELEVATION - 4~ 7 0 0 Au 0 frCRCENTAGE OF TIME THE VALUES EXCEED THE ORDINATE 1250 Mc/sec. - 2810 Mc/sec. - 9380 Me/sec. FIG. B " 1 COMPARISON OF THEORETICAL I L - 28 CROSS - SECTION AND EXPERIMENTAL 3-45 CROSS-SECTION AT ASPECT DEFINED BY AZIMUTH -- 90~ AND ELEVATION — 4~ 75 - --- -- -- --

WILLOW RUN RESEARCH CENTER — UNIVERSITY OF MICHIGAN UMM-127 -- CM z 0 - 0 0 30 40 50 60 70 80 PERCENTAGE OF TIME THE VALUES EXCEED THE ORDINATE. - 1250 Mc/sec. K - 2810 Mc/sec. - 9380 Mc/sec. FIG. B-12 COMPARISON OF THEORETICAL IL- 28 CROSS - SECTION AND EXPERIMENTAL B-45 CROSS-SECTION AT ASPECT DEFINED BY AZIMUTH -1 20~ AND ELEVATION -4~ 7

WILLO'XV RUN RESEARCH CENTER UNIVERSITY OF MICHIGAN UMM-127 10 _ I ii i X I i KI _ --- — W 8'06 -W 00'6 - 77

5/ 17 Basic Dimensions in Inches Windows Omitted ' / 25% Chord Line t 33 8 2 5'*25% Chord Line -.-- J200 — --- 2i0 -.. 42 - 702 ------ --.934..............- 164 FIG. 14 THE MARTIN 286- 48812 FIG. B-14 THE MARTIN 286-12 r r 0. Z x! (A;o O M3 ).. C,

WV11 ILLO'X PUN PFSE- ARGl (I uNIVERSITY OF MICHIGAN UMM-127 TABLE B-3 RADAR Cf.OSS-SEGTION OF THE 286-12 IN SQUARE" METERS (Without the Bomnb) liL. L.. & O 0 L 0 Fr --- _ 15 I 4 h 0 K 30 4 i -— t~~~~-' --- — - - -._. __ii 4._L __~.O.__ WAVELENGTHS (in meters) = 0.03 A 0.10 A 0.25 87. 26. 19 _ II I i I 4.6 J 1.5.35.36.35.36.53.5 5.5 3 -.56 1.1 1.9 L_,,,I c. —L --------- ------,Ti I I ~ ---I --- — C~3 i 4 7. 3.1 ---- — K ---Yi — 75 0 19. B-. --- —-- --—.. ----~ ~ --- —-.4-.85 1 48. I 3 -90~ (1(j30 I () 0 1~ 9. 0 *~ --- ~-.- - ). ----.- ---------. — ~- ------- -. Li -. -- ----- -— ' — — I --- —- ~- — 4~ - - ~ i — 1-... -- 4 - --- - It-S i 1)3, 1.4 1- - -_ _ __ _ _ __ _ _ __ _ _ __ _ _ 3.2 - ~17.0O I 0 -16. 1-_IT ---Y-. -.- i. 940-. ---- -----— t 370 0. 1.3 __.37 -.37.60.62 - 2.1 3. 3 3.2 - -49. 5.3. 4300. 1 6 — 00. 3'. 49,. 0. _t )20. 21. -21 3.3 3.3 - - __ 1.4 2.0 1.4 2.0 - I.. —.6O0 12.70 -1o _.39___ I --- - --------- — ~- i F.-~ — ---- — l —cl180; 4 0S) tJ 3.0t".98 7 9

'WILLOW" PUN PEISELARCIIl CE1-NTER-, UNIVE1RSITY OF MICHIlGAN 1 UMM- 127 TABLE B-A RADAR CROSS-SECTION OF THE 286-12 BOMB IN SQUARE METERS ASP ECT WAVELENGTHS (in meters) &A 0.03 2% 0.10 A 0.25 5.6-1- 29. o1-6 1____ 1__ 4 I 1 0.018.018.018 t12 t.019 $7_________ 30 U04.08 3.086 301 4 0 -.091 __.10 45_.2 5.27 1 __ _ 60. 7 __ 2 0 72 76.83 60 4.7 2 4 -.76 ___ _ _3 75 0 3.5 3. 7 4____ 7_ 4 2 ~3.5 I 3.7 1 4. _ 854 0 Z. _9 3. 96. 85 4 92. 9 3 _ 196. - 90 0 100- 1 600. 240. __ 9 0 41 O 6 30. 470. _ 5 032. 33. 3_ _ _ _ _ _ 921. 4 32. 3 3. __3 L5 ___ I 5 0 3.5 3. 7 3.9 I i I I 1 120 4 K135 }0 1 50 4 165 4 1 80 1 35 3. 7 _ --.7 2.7 6.7 2.76.2 5.2 7.08 5.091.085.091 01 9.021.3 3.096 I I 3.9.81.81 _ _. 9 _ _ _.29 -4.. -t.102. 026.32 I!.0719 80

WILLOW, RUN RESEARCH CENTER- UNIVERSITY OF MICHIGAN UMM- 127 TABLE B-5 / RADAR CROSS-SECTION OF THE 286-12 AND BOMB IN SQUARE METERS ASPECT WAVELENGTHS (in meters) (in degrees). 0 9;, = 0.03 A= 0.10 k = 0.25 0 0 87. 26. 1.9 0 4 4.6 1.5 1.5 15 0.37.37.39 15 4.37.38.39 30 0.61.63.69 30 4.62.65.73 45 0 1.3 2.2 2.4 ~ 45. 4 1.3 1.7 2.4 60 0 3.9 4.0 4.1 60 4 ~ 3.9 4.0 4.0 75 0 22. 20. 24. 75 4 23. 20. 23. 85 0 140. 150. 140. 85 4 140. 140. 150. 90 0 46000. 11000. 4500. 90 4 13000. 43000. 2100. 95 0 80. 92. 84. 95 4 78. 83. 150. 105 0 22. 23. 25. 105 4 22. 23. ~'~ 24. 120 0 3.9 4.0 4.1 120 4 3.9 4.0 4.1 135 0 1.3 1.7 2.3, 135 4 1.3 1.7 2.3 150 0.62.64 ~.70 150 4.62.64.70 165 0.37.38.39 165 4.37.38.39 180 0 5.7 1.9.73 180 4 - 1.3.60 __.47. 81........ -- m I

WILLOW RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN UMM-127 TABLE B-6 RADAR CROSS-SECTION OF THE MX-2091 IN SQUARE METERS (Without the Bomb) ASPECT (in degrees) 0 0 30P_ 0 --- 3 0 4 15 0 45 4 30 __ _0 30 4-.. 45 4 ^ — - - - -4 -- WAVELENGTHS (in meters) X = 0.03 ---- = 0.10 A= 0.25 i,.37.37.02.37 --- -----— ~ —f.37.02.38.38.02 I I t.- i a.02.08.02.09.03.13.19 e I -+.08.14 - A4 I.20.22 -- 4- I.15.18.29.32.12 1.7.. A 60 0 i i 60 75 4 0.80.58 6.8.92.59 A - i 8.0 12. 75 4 6.4 6.6 12. 85 0 160. 250. 340. 85 4 160. 190. 250. 90 0 27000. 8300. 3400. 90 4 520. 600. 690. 95 0 160. 250. 350. 95 4 1000. 2100. 1000. 105 0 6.2 7.4 12.0 I.- - -~- - - 105 4 _ 6.3 8.3 9.0 120 0.90 1.1 1.4 120 4.86,91 1.3 135 0.31.34.37 135 4.31.33.40 150 0.02.03.10 150 4.02.03.09 165 0.06.39 3.2 165 4.03.05.19 180 0 6.3 1.9.88 180 4 31. 9.4.39 82

NWILLOW\ RUN RESEARCHi CENTER -UNILVERSITY OF MICHIGAN UMM- I Z( TABLE B-7 RADAR CROSS-SECTION OF THE MX-2091 BOMB IN SQUARE METERS ASPECT (in degrees) WAVELENGTHS (in meters) 0 A O.03 A= 0.10 A = 0.25.Q. 0 6.7*10-7 7.210-7 2.2.10-5 0 4 5.910' 3.2*l0' 2.8-10 -15 0.0074.0074.0074 15 4.0074.0074.0075 30 0.035.035.035 30 4.035.035.035 45 0.10.10.10 45 4.10.10.10 60 0.31.31.31 60 4.31.31 -31 75 0 1.7 1.6 1.5 75 4 1.7 1.6 1.5 85 0 130. 150. 150. 85 120. 130. 150. 90 0 59000. 5700. 1000. 90 4 1000. 1000. 1000. 95 0 120. 120. 120_ 95 4 120. 120. _ 120. 105 0 1.5 1.4 1.4 105 4 1.5 1.4 1.4 120 0.31.31.31 120 135 4 0.31.10.31.31 — 4 ---.10.10 i i -+ — ~ --- —------ -— ~ ---i 135 4.10 1_____1 0,.0 3 5 150 1 4 1.035 I _ _ _ _ _ _.0 3 5 - 165 165 180 0 4 0.0076.0076 1.5.10.10.035.035 _035.036 __.0082.0075.0081.0079.52.26 _.30 - 1.17 -- f i - --- - - - - -- --. 180 4.69 _ _ - I - t _, ------- ~ ---~I —~I --- —--— L _ __ __ 83

WILLOW R UN RESEARCHt CENTER -UNIVERSITY OF MICHIGAN UMM-127 TABLE B-8 RADAR CROSS-SECTION OF MX-2091 AND BOMB IN SQUARE METERS ASPECT WAVELENGTHS (in meters) (in degrees) = 0.03 A= 0.10 A= 0.25 0 0.37.37.38 0 4.37.37.38 15 0.023.028 -.25 15 4.023.025.034 30 0.12.12.16 30 4.12.17 '.26 45 0.30.32.40 45 4.26.29.42 60 0 1.1 1.2 1.5 60 4.89.90 2.0 75 0 8.5 9.6 13. 75 4 8.1 14. 13. 85 0 290. 400. 540. 85 4 290. 320. 400. 90 0 86000. 14000. 4500. 90 4 1500. 1600. 1700. 95 0 280. 380. 470. 95 4 1200. 2200. 1200. 105 0 7.6 8.8 13. 105 4 7.7 9.7 10. 120 0 1.2 1.4 1.7 ~ --- ~ -.- — ~ 120 4 1.2 1.2 1.6 135 0.42 _.45.47 135 4.42.43.50 150 0.059.065.13 150 4.057.069.13 165 0.066.40 3.2 165 4.038.057.20 180 0 34. 2.6 1.3 I I I i 180 4 42. 13. 4.3 I lI _ ___ 84

WILLOW RUN RFFiSEARCH CENTER - UNIVERSITY OF MICHIGAN UMM- 127 B.4: The Cross-Section of Missiles Using the aspect connotation given in Figure B-2, where the & and 0 aspect angles are defined, and employing the techniques briefly outa lined in Section B.2, the radar cross-section of the Loon, Regulus, and Snark Missiles were determined at various aspects and at the three frequencies denoted by X-band, S-band, and L-band. The configurations used were taken from References B-8, B-9, and B-10 respectively and the results of the computations are given in Tables B-9, 10, and 11. Other missiles have been considered but not in as great detail as those we have previously mentioned. All other theoretical missile cross-section determinations made at the Willow Run Research Center are listed in Table B-1Z, except ballistic missiles which will be analyzed separately in a future publication in this series... 85.

WILLOW RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN I UMM-127 1 ASPEC T RADAR CROSS-SECTION IN m2 (in degrees) ' X-Band S- Band L-Band 0 0 37.8 12.6 5.4 4 0 37.8 12.6 5.4 0 30 0.23 0.30 0.23 4 30 0.23 0.30 0.23 0 60 1.55 1.51 1.51 4 60 1.55 1.51 1.51 0 80 16.5 16.5 17.1 4 80 16.5 16.5 17.1 0 85 28.2 28.2 28.2 4 85 28.2 28.2 28.2 0 90 664. 227. 83.0 4 90 283. 143. 148. 0 100 21.6 21.6 22 1 4 100 21.6 21.6 22.1 0 105 34.8 34.8 35.4 4 105 34.8 34.8 35.4 0 120 2.63 2.63 2.58 4 120 2.63 2.63 2.58 0 150 0.45 0.52 0.45 4 150 0.45 0.52 0.45 0 180 4.11 2.02 1.15 4 180 4.11 2.02 1.15 =. _ _....H. Cy for the Loon Missile Table B-9 -- -- L... I.. I -- - I..... Il 86 I..

WILLOW RUN RESEARCH CENTER- UNIVERSITY OF MICHIGAN UMM-127 ASPECT RADAR CROSS-SECTION IN m2 (in degrees) & X-Band S-Band L- Band 0 0 21.7 6.5 2.6 4 0 21.7 6.5 2.6 0 30.060.60.060 4 30.060.060.060 0 60 0.486 0.486 0.486 4 60 0.486 0.486 0.486 0 90 4680. 1480. 640. 4 90 98. 150. 259. 0 120 0.486 0.486 0.48 4 120 0.486 0.486 0.486 0 150.060.060.060 4 150.060.060.060 0 180 745. 66.8 10.7 4 180 745. 66.8 10.7 C for the Regulus Missile Table B-10 - -— 87................ W

WILLOW RUN RESEARCH CENTER-UNIVERSITY OF MICHIGAN UMM-127 1 ASPECT RADAR CROSS-SECTION IN m2 (in degrees) 6 ~__ X-Band S-Band L-Band 0 0 0.13 0.13 0.13 4 0 0.13 0.13 0.13 0 30 0.21 0.22 0.22 4 30 0.21 0.22 0.22 0 60 1.51 1.54 1.59 4 60 1.51 1.54 1.59 0 80 13.4 13.58 14.08 4 80 13.4 13.58 14.08 0 85 19.4 19.6 19.83 4 85 19.4 19.6 " 19.83 0 90 14900. 4500. 1847. 4 90 14900. 4500. 1847. 0 95 19.4 19.6 19.83 4 95 19.4 19.6 19.83 0 100 13.4 13.58 14.08 4 100 13.4 13.58 14.08 0 120 1.51 1.54 1.59 4 120 1.51 1.54 1.59 - - -. - -.-. — - 0 150 0.21 0.22 0.22 4 150 0.21 0.22 0.22 - - - 0 4 180 1020. 91.8...... --- 180 8.87 ___8.87 14.7 8.87 - _______ __ _ J - - -.- - CJ for the Snark Missile Table B- 1. - 88...I

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN I mUMM- 127 1 WAVE U' REFERENCE FOR?hl.ISI I F ASPECT LENGTH IN mZn CONFIGURATION DATA Navaho Rascal Big Richard G-2 Bomarc Bomarc Bomarc Bornarc Bomarc Bomarc Boma r c Bornarc Bomarc Lockheed Ramjet (missile only) Lockheed Rarmjtt (missile 4 jetbrace) Lockht-t d Rain iiet (missile + jet) Redstone Missile Nike Md ta d o r Nose- on Nose-on Nose-on Nose-on Nose-on 30~ off nose-on 60~ off nose-on 80~ off nose-on Broadside 100~ off nose-on 120~ off nose-on 150~ off nose-on Tail - on A > A X A A. A -2 -=..Z ift. lft. 1ft. 1ft. ift. 1ft. lft..8.12.67.60.16.11.98 2.38 300. 2.2 94.1 2 14.2 B-11 B-12 B-13 B-13 B-14 B-14 B- 14 B-14 B- 14 B- 14 B- 14 B- 14 B- 14 Nos e- on Nos e- on Nos e- on Nos e- on Nose-on Nos e- on Nose- on Nose- on Nos e-on Broadside Broadside Broadside Nose- on Nose-on Nose-on ' X-!S-! LXI S-1 Li XS -I S-1 L1 XS-1 L = lft. -- 1ft. - Ift.: Ift. - lft. I lft. b.irnd band band band band band band band band band band band.04.057.17.04.17.057 7. 1 7 i.062.069.193 2000 < C < 12300 600 '! G < 1500 200 < ') " 310.18.07.22 B-15 B-15 B-I B-15 B-15 B-15 13- 15 B-15 B-15 B-15 B- 15 B-15 I I 6C for Other Missiles Table B- 12 89

9MISSIN

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN UMM-127 B9 XSSM-N-8 Regulus Progress Report #1 (covering review of progress through June 1951), Chance Vought Aircraft, Dallas, Texas. SECRET. B10 Project Snark, (A review intended to supplement lecture material scheduled for presentation for the USAF Institute of Technology Guided Missile Seminar & Wright Patterson AFB, May 1951), Northrup Aircraft, Hawthorne, California. SECRET. Bll "Standard Missile Characteristics", WADC Report. B12 "Bell Aircraft Quarterly Progress Report - Project Rascal - Project Shrike, BMPR-25, June 1951. SECRET. B13 "Surface to Surface Guided Missiles", Air Technical Intelligence Center, Study No. 120-AC-51/44-34, January 1952. SECRET. B14 "Bomarc Missile Design Data", Boeing Airplane Company, Document D-11550, Model MX1599, September 1951. SECRET. B15 Jenks, F. P. and Thoren, R. L., "Ram Jet Test Vehicle Report", Lockheed Aircraft Corporation, Progress Report No. 22, October 1951. CONFIDENTIAL. / 91 I II I i l I I I I I IIII

W'ILLO\W RUN RE-SEARCH CENTER -UNIVERSITY OF MICHIGAN UMM-127 APPENDIX C EXACT SOLUTION TO ELECTROMAGNETIC SCATTERING PROBLEMS Exact solutions of Maxwell's equations for boundary value problenis involving the scattering of electromagnetic waves by three - dimensional configurations are very few indeed. The few exact solutions which are known are discussed below. The Sphere The cross-section of a sphere was determined theoretically by Mie (Ref. C-l), Stratton (Ref. C-2), Kerr (Ref. C-3), Aden (Ref. C-4), Ohio State University (Ref. C-5), University of California (Ref. C-6), and Brillouin (Ref. C-7). The above papers involved spheres which are perfect conductors (Ref. C-l, 2, 3, 5, 6, 7) and also dielectric spheres (Ref. C-l, 2, 3, 4). Only in references C-5 and C-6 is found a comparison between theory and experiment for conducting spheres of a particular size, where the transmitter and the receiver are separated. Only reference C-4 compares theory and experiment for water spheres. Thus it is apparent that there is much to be done both theoretically and experimentally before the general electromagnetic scattering from even such a simple shape as a sphere is generally understood. The theoretical aspect involves such matters as summability techniques and the task of computing many more numerical values of cross-section. A parallel expansion of experimental data pertaining to the dielectric sphere is necessary for an evaluation of the theoretical results. The Prolate Spheroid The back-scattering cross-section of a conducting prolate spheroid has been determined exactly by Schultz when the incident Poynting Vector is on the axis of symmetry (Ref. C-8). Some of his results have been used in the computation of the prolate spheroid's cross-section by the i - - q2.... I

WrILLOW' RUIN RESIEARCIT CElN'TER - UNIV1RSITY OF MICHIGAN UMM- 127 Willow Run Rese-arch Center ori the Mai-rk III and his theoretical results have been extended to general receiver location in Reference C-9. Reference C-9 also solves several of the thef oretical questions involving the prolate spheroidal recllrsion formulas. No experinmental results have been published, to our knowledge, although sonme experirmental work on the prolate spheroid is b)eing conducted at the University of California under Prof. S. Silver. Again there is still nmuich numerical as well as theoretical work to be done, especially in the dielectric case, wVhich is practically untouched, as well as in thf general bistatic case. The C(one The work of Hansen and Schiff (Ret. C-10) Cand Willow Run Research Center (Refs. C- 11 & C-1Z) has resulted in the exact cross-section for axially symrnrnetric back-scattering fror-. semni-infinite conr-1ducting cone. It is shown that up to at least;a sece(ond ordtir approximation for both small aind large cone angles the exact result is in, agreement with the physical optics result j: 4 X lau (0 16CT I where is te cross-section,, isthewavelenth,and is i/ the cone a ngl e. Sletten (Ref. C-13) has done the (experimental work for the axially symmetric back-scattering problem. Work has been started on other theoretical cone problems and it is believed that beftoret too long a time the conducting cone problem will have been completely resolved. To our knowledge no work, either experimental or theoretical, has been conducted concerning the dielectric cone. 9 3 --

NWILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN UMM- 127 The Oblate Spheroid In the ninth paper in the series of studies on scattering crosssections, the exact solution of the radar cross-section of an oblate spheroid was obtained by the method due to Hansen (Ref. C- 14). The solution obtained was for the case in which the transmitter and receiver were both situated along the axis of symmetry for a perfectly conducting spheroid. As in the case of the sphere, for example, the radar crosssection has been obtained in the form of an infinite series. Unfortunately the defining relations for the coefficients in the series are quite complex and their values have not been tabulated very extensively. Consequently no numerical values of radar cross-sections exist as yet for the oblate spheroid. The Paraboloid A solution has been obtained at the Willow Run Research Center for a semi-infinite paraboloid. It has been found (Ref. C-15) for the case in which the transmitter is along the axis of symmetry of the paraboloid that the exact radar cross-section can be obtained by the LunebergKline method, based upon geometrical optics considerations. The exact bistatic radar cross-section of a paraboloid is plotted in Figure C-1. One can observe by substituting directly into Maxwell's equations and the boundary conditions that the geometric optics solution for the above case is the exact solution.. 94

WILLOW RUN RESEARCH CENTER- UNIVERSITY OF MICHIGAN UMM- 127 103 9 8 /26 Angle between Transmitter and Receiver 5 Vertical and Horizontal Polarization for Paraboloid of Focal Length F/2 / 4 l<[($) 16 r / F2 (I+CosS8)2 ' / 2 F2 102 9 8 6 5 4 3 2 10 1, ---- i.... ' -...................*i~,,/ 0 20 40 60 80 100 120 140 FIG. C-1 CROSS-SECTION OF A PARABOLOID AS A FUNCTION OF jA ^ P 95 J

WXXILl,()\X,' RtlN R.ISE;,ARC-! C.L NTER N - IJNIVLI.RSITY OF MICHIGAN r UMM-127 REFERENCES FOR APPENNDIX C C1 Mie, G., "Beitraege zur Optik trueber Medien, speziell Kolloidaler Metalloesllnge.n, ' Annalen der Physik, vol. 25. p. 377j 1908. C2 Stratton, J A., Flectroragnetic Theory, McGraw-Hill Book Co., New York, 1941. C3 Kerr, D. E., Propagation of Short Radio Waves, McGraw-Hill Book Co., New York, 951. C4 Aden, A. L., "Electronagnetic Scattering From Metal and Water Spheres", Harva rd University, (ruft Laboratory, Technical Report No. 106, (ATJ-9201h). August 1950. UNCLASSIFIED. C5 "Echoing Area Characteristics of Various Objects: Ninth Quarterly Progress Re(port," Ohio State Uniiversity Research Fourndation, Report.-302-?9, May 1949. CONFIDENTIAL. C6 Hamtren. S. D., "Scattering from Spheres," University of California, Antenna,Laboratory, Report No. 171, (ATI-83900), June 1 950. UNC LASSIFI ED. I1 C7 C8 Cc Brillouin, L., "On Light Scattiring by Spheres II," Columrbia Unive rsity, Appiie. d. -athea:rti cs Pane l, Report Columbia AMP-87-2,(OSRD- t4 ),;Ap)ril 1 944 UNC,ASS FI El D. Schultz, F. V., "StudiRes in Radar Cross-Sections i, Scattering by a Prolaitet Spheroidl. W1illow Runir Research Center, University of Michigan. Re)port TN4M -4, Marc' 1950. UNCLASSIFIIED. Si1ege(,, K. Nh., Gere, B. H., Marx, 1., Sleator, F. B., "Studies in Radlar Cross-Sections X1, The Numerical Determination of the Radar Cross-Section of a Prolate Spheroid," Willow Run Research Center, Univ-rsity of Mic higan, Report UMM- 126, Decemrber 1953. NC; LASSIF I ED. 96

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN UMM- 127 C10 Hansen, W. W., Schiff, L. I., "Theoretical Study of Electromagnetic Waves Scattered From Shaped Metal Surfaces," Quarterly Report No. 4, Stanford University, Microwave Laboratory, ATI-46568, September 1948. UNCLASSIFIED. Cll Siegel, K. M., Alperin, H. A., "Studies in Radar Cross-Sections III, Scattering by a Cone," Willow Run Research Center, University of Michigan, Report No. UMM-87, January 1952. UNCLASSIFIED. C12 Siegel, K. M., Alperin, H. A., Crispin, J. W., Hunter, H. E., Kleinman, R. E., Orthwein, W. C., Schensted, C. E., "Studies in Radar Cross-Section-IV, Comparison Between Theory and Experiment of the Cross-Section of a Cone," Willow Run Research Center, University of Michigan, Report No. UMM-92, February 1953. UNCLASSIFIED. C13 Sletten, C. J., "Electromagnetic Scattering From Wedges and Cones," Cambridge Research Center, Report CRC-E5090, July 1952. UNCLASSIFIED. C14 Hansen, W. W., "A New Type of Expansion in Radiation Problems," The Physical Review, vol. 47, January 15, 1935. C15 Siegel, K. M., Alperin, H. A., Bonkowski, R. R., Crispin, J. W., Maffett, A. L., Schensted, C. E., Schensted, I. V., "Studies in Radar Cross-Sections VIII, Theoretical Cross-Section as a Function of Separation Angle Between Transmitter and Receiver at Small Wavelengths," Willow Run Research Center, University of Michigan, Report No. UMM-115, October 1953. UNCLASSIFIED. I 97 - -

WILLOW RUN RESEARCH CENTER -UNIVERSITY OF MICHIGAN UMM-127 DISTRIBUTION To be distributed in accordance with the Terms of the Contract. - ---- - 98 - -- - - --