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SUMMARY TECHNICAL REPORT
OF THE
NATIONAL DEFENSE RESEARCH COMMITTEE
This document contains information affecting the national defense of the United States within the meaning of the Espionage Act, 50 U. S. C., 31 and 32, as amended. Its transmission or the revelation of its con- tents in any manner to an unauthorized person is prohibited by law.
This volume is classified^^^|^^B in accordance with security regu- lations of the War and N av^^^partments because certain chapters contain material which was (SEGSH at the date of printing. Other chapters may have had a low^WBIBfication or none. The reader is advised to consult the War and Navy agencies listed on the reverse of this page for the current classification of any material.
Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under con- tract OEMsr-1131 with the Office of Scientific Research and Development. This volume was printed and bound by the Columbia University Press.
Distribution of the Summary Technical Report of NDRC has been made by the War and Navy Departments. Inquiries concerning the availability and distribution of the Summary Technical Report volumes and microfilmed and other refer- ence material should be addressed to the War Department Library, Room 1A-522, The Pentagon, Washington 25, D. C., or to the Office of Naval Research, Navy Department, Atten- tion : Reports and Documents Section, Washington 25, D. C.
Copy No.
119
This volume, like the seventy others of the Summary Tech- nical Report of NDRC, has been written, edited, and printed under great pressure. Inevitably there are errors which have slipped past Division readers and proofreaders. There may be errors of fact not known at time of printing. The author has not been able to follow through his writing to the final page proof.
Please report errors to :
JOINT RESEARCH AND DEVELOPMENT BOARD PROGRAMS DIVISION (STR ERRATA)
WASHINGTON 25, D. C.
A master errata sheet will be compiled from these reports and sent to recipients of the volume. Your help will make this book more useful to other readers and will be of great value in preparing any revisions.
SUMMARY TECHNICAL REPORT OF DIVISION 4, NDRC
VOLUME 1
RADIO PROXIMITY FUZES FOR FIN-STABILIZED MISSILES
OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT VANNEVAR BUSH, DIRECTOR
NATIONAL DEFENSE RESEARCH COMMITTEE JAMES B. CONANT, CHAIRMAN
DIVISION 4
ALEXANDER ELLETT, CHIEF
WASHINGTON, D. C., 1946
RET
NATIONAL DEFENSE RESEARCH COMMITTEE
James B. Conant, Chairman Richard C. Tolman, Vice Chairman Roger Adams Army Representative1
Frank B. Jewett Navy Representative2
Karl T. Compton Commissioner of Patents3
Irvin Stewart, Executive Secretary
1 Army representatives in order of service :
Maj. Gen. G. V. Strong Maj. Gen. R. C. Moore Maj. Gen. C. C. Williams Brig. Gen. W. A. Wood, Jr.
Col. E. A.
Col. L. A. Denson Col. P. R. Faymonville Brig. Gen. E. A. Regnier Col. M. M. Irvine Routheau
2 Navy representatives in order of service :
Rear Adm. H. G. Bowen Rear Adm. J. A. Furer Capt. Lybrand P. Smith Rear Adm. A. H. Van Keuren Commodore H. A. Schade
3 Commissioners of Patents in order of service : Conway P. Coe Casper W. Ooms
NOTES ON THE ORGANIZATION OF NDRC
The duties of the National Defense Research Committee were (1) to recommend to the Director of OSRD suit- able projects and research programs on the instru- mentalities of warfare, together with contract facilities for carrying out these projects and programs, and (2) to administer the technical and scientific work of the contracts. More specifically, NDRC functioned by initi- ating research projects on requests from the Army or the Navy, or on requests from an allied government transmitted through the Liaison Office of OSRD, or on its own considered initiative as a result of the expe- rience of its members. Proposals prepared by the Divi- sion, Panel, or Committee for research contracts for performance of the work involved in such projects were first reviewed by NDRC, and if approved, recommended to the Director of OSRD. Upon approval of a proposal by the Director, a contract permitting maximum flexi- bility of scientific effort was arranged. The business aspects of the contract, including such matters as mate- rials, clearances, vouchers, patents, priorities, legal matters, and administration of patent matters were handled by the Executive Secretary of OSRD.
Originally NDRC administered its work through five divisions, each headed by one of the NDRC members.
These were:
Division A — Armor and Ordnance Division B — Bombs, Fuels, Gases, & Chemical Problems Division C — Communication and Transportation Division D — Detection, Controls, and Instruments Division E — Patents and Inventions
In a reorganization in the fall of 1942, twenty-three administrative divisions, panels, or committees were created, each with a chief selected on the basis of his outstanding work in the particular field. The NDRC members then became a* reviewing and advisory group to the Director of OSRD. The final organization was as follows :
Division 1 — Ballistic Research
Division 2 — Effects of Impact and Explosion
Division 3 — Rocket Ordnance
Division 4 — Ordnance Accessories
Division 5 — New Missiles
Division 6 — Sub-Surface Warfare
Division 7 — Fire Control
Division 8 — Explosives
Division 9 — Chemistry
Division 10 — Absorbents and Aerosols
Division 11 — Chemical Engineering
Division 12 — Transportation
Division 13 — Electrical Communication
Division 14 — Radar
Division 15 — Radio Coordination
Division 16 — Optics and Camouflage
Division 17 — Physics
Division 18 — War Metallurgy
Division 19 — Miscellaneous
Applied Mathematics Panel
Applied Psychology Panel
Committee on Propagation
Tropical Deterioration Administrative Committee
Library of Congress
201 5 490929
iv
NDRC FOREWORD
AS events of the years preceding 1940 re- vealed more and more clearly the serious- ness of the world situation, many scientists in this country came to realize the need of organ- izing scientific research for service in a national emergency. Recommendations which they made to the White House were given careful and sympathetic attention, and as a result the Na- tional Defense Research Committee [NDRC] was formed by Executive Order of the Presi- dent in the summer of 1940. The members of NDRC, appointed by the President, were in- structed to supplement the work of the Army and the Navy in the development of the instru- mentalities of war. A year later, upon the estab- lishment of the Office of Scientific Research and Development [OSRD], NDRC became one of its units.
The Summary Technical Report of NDRC is a conscientious effort on the part of NDRC to summarize and evaluate its work and to present it in a useful and permanent form. It com- prises some seventy volumes broken into groups corresponding to the NDRC Divisions, Panels, and Committees.
The Summary Technical Report of each Di- vision, Panel, or Committee is an integral sur- vey of the work of that group. The report of each group contains a summary of the report, stating the problems presented and the philos- ophy of attacking them, and summarizing the results of the research, development, and train- ing activities undertaken. Some volumes may be “state of the art” treatises covering subjects to which various research groups have contrib- uted information. Others may contain descrip- tions of devices developed in the laboratories. A master index of all these divisional, panel, and committee reports which together constitute the Summary Technical Report of NDRC is con- tained in a separate volume, which also includes the index of a microfilm record of pertinent technical laboratory reports and reference ma- terial.
Some of the NDRC-sponsored researches which had been declassified by the end of 1945 were of sufficient popular interest that it was found desirable to report them in the form of monographs, such as the series on radar by Division 14 and the monograph on sampling in- spection by the Applied Mathematics Panel. Since the material treated in them is not dupli- cated in the Summary Technical Report of NDRC, the monographs are an important part
of the story of these aspects of NDRC research.
In contrast to the information on radar, which is of widespread interest and much of which is released to the public, the research on subsurface warfare is largely classified and is of general interest to a more restricted group. As a consequence, the report of Division 6 is found almost entirely in its Summary Technical Report, which runs to over twenty volumes. The extent of the work of a Division cannot there- fore be judged solely by the number of volumes devoted to it in the Summary Technical Report of NDRC ; account must be taken of the mono- graphs and available reports published else- where.
The program of Division 4 in the field of elec- tronic ordnance provides an excellent example of the manner in which research and develop- ment work by a civilian technical group can complement and supplement work done by the Armed Services. The greatest responsibility of Division 4, under the leadership of Alexander Ellett, was to undertake the development of proximity fuzes for nonrotating or fin-stabilized missiles, such as bombs, rockets, and mortar shells.
Early work on fuzes of various types indi- cated that those operating through the use of electromagnetic waves offered the most promise ; the eventual device depended on the doppler effect, combining the transmitted and received signals to create a low frequency beat which triggered an electronic switch. During the last phases of the war against Japan, approximately one-third of all the bomb fuzes used by carrier- based aircraft were proximity fuzes. For im- proving the accuracy of bombing operations, the Division developed the toss bombing tech- nique, by which the effect of gravity on the flight path of the missile is estimated and allowed for. The success of this technique is demonstrated by its combat use, when a circle of probable error as low as 150 feet was obtained.
The Summary Technical Report of Division 4 was prepared under the direction of the Di- vision Chief and has been authorized by him for publication. We wish to pay tribute to the enter- prise and energy of the members of the Di- vision, who worked so devotedly for its success.
Vannevar Bush, Director Office of Scientific Research and Development J. B. Conant, Chairman National Defense Research Committee
FOREWORD
The primary program of Division 4, NDRC, was development of proximity fuzes for bombs, rockets, and trench mortar projectiles. The National Bureau of Standards [NBS] pro- vided facilities and personnel for the Division’s Central Laboratory and the Division (or its predecessor, Section E of Division A) served as the principal liaison between NDRC and NBS. In large measure the developments pre- sented in this Division 4 STR must be credited to the National Bureau of Standards. Credit also is due the Ordnance Department of the Army for excellent cooperation. The main- tenance of effective liaison was due largely to Colonel H. S. Morton, whose enthusiasm for the program coupled with intelligent criticism and suggestions based on sound technical knowledge contributed much of value.
The present volume summarizes the Divi- sion’s development of radio proximity fuzes. The technical direction of this development was throughout in the able hands of Harry Dia- mond, leader of the little radio fuze group organized at the Bureau of Standards in De- cember 1940, and finally Chief of the Bureau’s Ordnance Development Division. Throughout the program, he received invaluable technical assistance from W. S. Hinman, Jr., Chief Engineer of the aforementioned NBS division. The excellent presentation found here is due to the editor of these three volumes, A. V. Astin, Assistant Chief of the Ordnance De- velopment Division, NBS.
Other Division 4 contractors made valuable contributions to particular projects on which they were engaged. Deserving of special men- tion are the University of Florida for work on trench mortar fuzes, the Globe-Union Com- pany of Milwaukee for work on safety and arming devices and ceramic circuits, and the University of Iowa for improved recovery de- vices and a smooth working proof organization. The development of generator power supplies was largely carried out by the Westinghouse Company in Baltimore and by the Zenith Radio Corporation.
Reliability of radio fuzes depends at least as much on good production methods and tech- niques as upon good design. In the solution of production problems outstanding contributions were made by the Zell Corporation, Baltimore, and Bowen and Company, Bethesda, Maryland, who operated pilot lines; and by the Arnold Engineering Company, the Emerson Radio and Phonograph Corporation, the General Electric Company, the Globe-Union Company, the Philco Corporation, the Raytheon Manufactur- ing Company, the Sylvania Electric Products, Inc., the Westinghouse Electric and Manufac- turing Company, the Rudolph Wurlitzer Com- pany, and the Zenith Radio Corporation, who produced fuzes or fuze components.
Alexander Ellett Chief, Division 4
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vii
PREFACE
The Summary Technical Report of Division 4 has been prepared in three volumes : Volume 1, describing the work on radio prox- imity fuzes, the major work of the division; Volume 2, discussing bomb, rocket, and torpedo tossing, a new fire control method for airborne missiles; and Volume 3, a report on various miscellaneous projects. An overall summary of the Division 4 program appears as Chapter 1 in Volume 3.
The present volume treats the technical prob- lems relating to the design, production, and use of radio proximity fuzes for fin-stabilized (non- rotating) missiles, including bombs, rockets, and trench mortar shells. For a treatment of work on fuzes for spin-stabilized projectiles, the reader is referred to the reports of Section T of OSRD. For work on other types of proximity fuzes for fin-stabilized missiles, the reader is referred to Volume 3 of the Division 4 STR. The latter reference includes a general survey of various types of proximity fuzes and a de- tailed summary of the work done by Division 4 on photoelectric fuzes.
A primary consideration in the preparation of this volume has been to arrange the material so that it will be useful for reference purposes. To fulfill this objective, the various chapters are reasonably self-contained, and each chapter may be read separately without too much loss in meaning. This mode of presentation has, of course, resulted in some duplication of ma- terial, but it is believed that the advantages justify the extra space required. Numerous cross references between the chapters are in- cluded to facilitate expansion or clarification of various items.
For the reader who is interested primarily in the essential operating characteristics of the radio proximity fuzes placed in production, Chapter 5, “Catalogue of Fuze Types,” is the only part of this volume which need be read. The catalogue chapter also includes a descrip- tion of the important features of design for each of the various fuzes.
The introduction to the volume (Chapter 1) explains the objectives of the development pro- gram, how radio fuzes operate, and includes a
brief summary of the accomplishments in the development and production program.
Chapter 2 discusses in detail the basic theory of operation and shows how the required operating characteristics of a fuze may be con- verted into an engineering design problem. The material of Chapter 2 is fundamental to any fuze design involving interaction of radio waves with the target. Because of the great potential use of this theory in future development work, the treatment of Chapter 2 is much more thorough than would appear necessary merely as a summary of completed work.
The methods by which the electrical design problems were solved are discussed in Chapter 3. Section 3.4 of Chapter 3 deals with the de- sign of generator power supplies, one of the outstanding features of the later fuzes de- veloped by Division 4. Although this section is included in the electrical design chapter, it contains considerable material relating to the mechanical design of generators. A clear-cut separation of the mechanical and electrical de- sign requirements for the generator was not practicable. Chapters 2 and 3 are quite technical in nature and will probably be of interest only to scientists and engineers. These chapters may be omitted by the nontechnical reader.
Chapter 4 analyzes the problems of mechan- ical design and layout and includes a treatment of the arming and safety features of the fuzes.
Chapter 6 describes the production methods and summarizes accomplishment in the produc- tion program. Since the problems of reducing a laboratory design of a proximity fuze to a model which could be built in mass production were fundamental to the entire program, the story of this chapter is of basic importance. It should be of interest to both the technical and the non- technical reader.
Chapters 7 and 8 describe the methods of testing proximity fuzes in order that their quality might be evaluated and their perform- ance under operational conditions predicted. The former chapter is concerned with labora- tory test methods and quality control. A de- scription of testing apparatus is included. The
IX
X
PREFACE
latter chapter deals with field test methods and proving ground procedures in which opera- tional conditions were simulated.
Chapter 9 gives a somewhat more detailed analysis of the operating characteristics of the fuzes than is given in Chapter 5 in that the results of all important tests which were car- ried out on the fuzes are summarized. The chapter includes evaluations of performance for each of the fuze types under a variety of operating conditions. The operational experi- ence is also presented in this chapter.
An analysis of problems pertaining to countermeasures and counter-countermeasures has not been included in this volume.
The successful development of radio prox- imity fuzes, or VT fuzes as they are commonly called, involved the cooperative efforts of many organizations and individuals. A listing of all of the individuals who contributed to the suc- cess of the program would be an extremely difficult, perhaps even impossible, task. How- ever, the organizations which participated in the development program are listed at the end of the volume.
This volume was prepared by the staff of the Ordnance Development Division of the Na- tional Bureau of Standards, which served as the central laboratories for Division 4. Reports of the various contractors to Division 4 have
been used freely, and these are listed as refer- ences in the bibliography.
The editor wishes to take this opportunity to record thanks and appreciation for the efforts of the many individuals who cooperated in the preparation of the volume. In particular, some of these are: Dr. Robert D. Huntoon, who as- sisted in the overall planning of the volume and who was also the senior author of Chapter 2; Dr. Alexander Ellett and Mr. Harry Diamond, Chief, Division 4 and Chief, Ordnance Develop- ment Division, respectively, who offered valu- able suggestions and advice on numerous items ; other authors who are listed in the table of contents as well as in footnotes to the various sections which they prepared ; Mr. Theodore C. Hellmers, who prepared the photographs used in this volume (unless credit is otherwise in- dicated) ; Mr. E. W. Hunt and his staff for their diligent and painstaking efforts in the prepara- tion of other art work; Miss Lee Smolen and Mrs. Henrietta Leiner for preparation of bibliographical material; and Miss Helen Olm- stead, Mrs. Betty Hallman, and Miss Jane Grant for their untiring efforts in the prepara- tion, assembly, and correction of manuscripts.
A. V. Astin Editor
CONTENTS
CHAPTER PAGE
1 Introduction 1
2 The Radiation Interaction System 17
3 Electronic Control Systems 81
4 Mechanical Design 167
5 Catalogue of Fuze Types 209
6 Production 245
7 Laboratory Testing of Fuzes 278
8 Field Testing of Proximity Fuzes 312
9 Analysis of Performance 360
Glossary 433
Bibliography 437
OSRD Appointees 463
Contract Numbers 464
Service Project Numbers 467
Index 469
xi
Strike photograph of the first operational use of proximity fuzed bombs. The target is the beach area of I wo Jima during the pre-invasion bombing of the island. The characteristic crescent-shaped fragmentation patterns of air-burst bombs are clearly recognizable. (Army Air Force photograph.)
t,C RE'--' OR RT’" DOCTT MARK J
rT BEFORE SERVICING T NG AM PART OF THIS V , C Ac T TCATION .iU3T BE _CA T3E ,LEDT
Chapter 1
INTRODUCTION
LC REGULATION: BEFORE SERVICING OR REPRODUCING ANY PART OF THIS DOCUMENT, ALLjCLASSIFICATION MARKINGS MUST BE CANCELLED:
1 * OBJECTIVES AND MILITARY REQUIREMENTS
Radio proximity fuzes are intended to deto- nate missiles automatically upon approach to a target and at such a position along the flight path of the missile as to inflict maximum damage to the target.
The optimum position for detonation of the missile depends upon the nature of the target and the properties of the missile. Conditions of use divide possible targets into two major groups: (1) airborne targets, and (2) surface targets either on the ground or on water. These two applications are referred to variously as (1) antiaircraft, air-to-air, ground-to-air, and (2) ground-approach, air burst, air-to-ground, ground-to-ground.
As a class, proximity fuzes belong with time fuzes, in contrast with contact fuzes, since they are useful wherever contact of the missile with the target or penetration into the target is not necessary to inflict damage. Because of the au- tomatically accurate nature of their operation, proximity fuzes not only extensively replace time fuzes, but they make possible many new and important applications for which time fuzes would be ineffective. They also replace contact fuzes in many applications where contact with an object, not necessarily the target, is used merely as a triggering operation for the fuzes and not because contact is essential to inflict damage.
Military requirements for proximity fuzes became specific and well defined only after the development had passed the exploratory stage. Initially the requirements were quite general; (1) the fuze should detonate the missile “in the vicinity” of the target, (2) the fuze should be as small and rugged as possible, (3) it should be safe for handling and operational use, (4) it should perform reliably under a wide range of service conditions, (5) it should require a mini- mum of special equipment and training for its operational use, (6) it should be relatively im- mune to possible enemy countermeasures, and
(7) in antiaircraft weapons, it should have a self-destruction [SD] feature to operate, in case of a miss, after passing the target. Most of the foregoing requirements could not be more ac- curately specified until a certain amount of design experience was available or until actual fuzes were available for proving ground tests.
For example, the careful definition of the proper point on the trajectory for the fuze to function had to be based on experimental trials using fuzes against actual or simulated targets. Before the fuzes could be built for such tests, estimates were required concerning the ex- pected optimum conditions. In the antiaircraft case, it was fairly obvious that the position of function should be matched to the dynamic frag- mentation pattern of the missile so that the greatest number of fragments would be di- rected at the target. To achieve the proper directional sensitivity, a number of factors, as shown in Chapters 2 and 3, had to be balanced against each other, and the final specification of performance was based on numerous design compromises and field tests. In the ground tar- get case, no experimentally verified optimum burst heights were available until the end of 1944 and then only for limited types of missiles and targets/ For many important ground tar- get applications, optimum burst heights are still undetermined.
Some of the mechanical features were capa- ble of more exact specification. Although small size and ruggedness were objectives toward which improvement was continuous, certain minimum requirements were definite very early in the program. Bomb fuzes were to be bal- listically interchangeable with regular fuzes so that their use would require no modifications in bombing tables. Available stowage space in bomb bays made it necessary to impose limita- tions on overall length, and a maximum exten- sion of 5 in. beyond the nose of the bomb was prescribed, although shorter fuzes were pre-
a These statements refer specifical^~^G tfie ^uzes fur" fin -stabilized or nonrotating nB§Bila*lth<Mlit$s SftGM&fc^ry of rockets, and trench-mortar shells.
SEP 1 196p
Defense memo 2 August 1960
LIBRARY OF CONGRESS
2
INTRODUCTION
ferred. Standard fuze-well cavities in bombs fixed other dimensions. A minimum require- ment on ruggedness was that the fuze with- stand any vibrations or accelerations of the missile. There were also standard military rough-handling specifications but these were more of a requirement for packaging than for fuze design.
The arming and safety requirements, with one important exception, had to be worked out experimentally as the development progressed. The exception was the specification for an inter- rupted powder train between the detonator and booster, a standard Army Ordnance technique which was required of all proximity fuzes. Since proximity fuzes are, by their very nature, susceptible to their surroundings and unable to distinguish between friendly and enemy tar- gets, the arming problem is appreciably differ- ent than with ordinary fuzes. In general, longer “safe” times after firing or release of the mis- sile are desired for proximity fuzes, but an ideal safe period compromises the usefulness of the weapon. The details of the development of the arming and safety features and require- ments are discussed in Chapter 4.
The very necessary exploratory work on radio proximity fuzes, was done under rather general requests from the Services, including a conference on August 12, 1940, between rep- resentatives of the Navy Bureau of Ordnance and NDRC j1 Projects OD-27, dated January 14, 1941, and OD-3B, dated June 11, 1941, of the Army Ordnance Department; and Project CWS-19, dated August 30, 1941, from the Chemical Warfare Service. The pertinent mili- tary characteristics for fuzes covered by these authorizations were essentially as outlined.
After laboratory development and field tests had established general possibilities and limits for radio proximity fuzes, specific Service re- quirements were put forth based on anticipated operational needs. The first major project which was carried through to large-scale production was for the T-5 fuze to be used with the Army’s 4^4-in. (M-8) rocket. The desired characteris- tics for this fuze2’ 3 were, in addition to the general requirements stated above, (1) the complete fuze should fit into a cylindrical con- tainer approximately 2% in. in diameter and
5 in. long, with an allowable conical extension on the front end of the cylinder about 2 in.;
(2) at least 50 per cent of the fuzes were re- quired to function in the vicinity of an airplane target when fired on the rocket and within the lethal range of the fragments of the rocket;
(3) the fuze was to be armed and operative approximately V2 sec after firing; and (4) the fuze should have an SD element operating ap- proximately 9 sec after firing.
The T-5 fuze project was limited in that the intended use was confined to a single missile and for a single application, antiaircraft. It was complicated by the fact that the design of the missile itself was not complete and its dy- namic fragmentation pattern was unknown. A dynamic fragmentation pattern was assumed from information supplied by the Services, but, as shown in Section 1.5, the assumptions were not strictly accurate. One very important com- promise was made in the requirements for the T-5 fuze from the ultimate Service needs. This was in respect to the temperature range throughout which the fuze could be used. Un- impaired operation between —40 and +160 F was desired, but because of the limitations of the dry batteries which were to be used to power the fuzes the low-temperature requirement was waived. Actually, the relaxing of this require- ment in the fuze did not impair the usefulness of the complete weapon since the rocket itself had low-temperature limitations not too dis- similar from those of the fuze. In order to reduce limitations due to possible deterioration of the battery power supply during shipment and storage, the design was made to allow final assembly of the fuze in the field using freshly tested batteries.
Experience gained in the development and production of the T-5 fuze, combined with si- multaneous investigations for improved power supplies (Project SC-40), made possible much expanded, more rigorous, and more specific re- quirements for other radio proximity fuzes. These included fuzes for the following: (1) 10,000-lb light-case [LC] bomb, (2) 4,000-lb LC bomb, (3) 2,000-lb general purpose [GP] bombs against both land- and water-borne tar- gets, (4) 2,000-lb glider and controllable bombs, (5) 1,000-lb GP bombs against water-borne
SECRET
OBJECTIVES AND MILITARY REQUIREMENTS
3
targets, (6) antiaircraft bombs for plane-to- plane bombing, (7) fragmentation and anti- materiel bombs of various sizes, and (8) large chemical bombs of 500-, 1,000-, and 2,000-lb sizes.
The military requirements for these bombs were as follows:4*5
1. Adaptation to use in existing bombs, and to fit and drop in existing bomb racks.
2. Strength enough to withstand handling and shipping and, unarmed, drop safely on nor- mal ground from 8,000 ft.
3. No deterioration from storage at temper- atures from — 40 to +140 F.
4. A minimum of adjustment and assembly in the field.
5. A design which minimizes the possibility of triggering the fuze by enemy interference.
6. Suitability for day or night use.
7. Efficient operation at temperatures from —40 to +140 F.
8. Efficient operation when released at any indicated airspeed above 150 mph.
9. Efficient operation when released from al- titudes up to 35,000 ft.
10. A minimum of 1,500 ft to arm.
11. Consideration in design toward evolving a minimum number of fuze designs of suitable performance necessary to meet the require- ments of various sizes and types of bombs and targets.
Burst heights were specified for only two of the foregoing applications, the T-40 and T-43 fuzes for the 10,000- and 4,000-lb LC bombs.3 These heights were to be between 40 and 100 ft, with the mean preferably near 50 ft. This was believed to be the best height of operation for enhanced blast effect from these large high- charge bombs. The T-40 and T-43 were to be tail fuzes. The sensitivities or operating heights of the T-50 and T-51 fuzes intended for the other applications were not defined. It was, however, informally stated that, for antiper- sonnel and antimateriel use, burst heights of the order of 50 ft were desired. For the chem- ical bombs, burst heights of the order of 500 ft were believed best. Estimates in the former case were based on theoretical computations of fragmentation effect against shielded targets.11 The T-50 and T-51 fuzes were to be nose fuzes,
interchangeable with the M-103 contact fuze.
Following the development, production, and service testing of the T-50 bomb fuzes, minor changes, based on a fuller understanding of their operational properties, were made in the requirements for arming characteristics and for burst heights. These changes led to models T-89, T-90, T-91, and T-92, which are described fully in Chapters 4 and 5.
Modifications were also requested in the T-50 type fuze to allow its use on Navy rockets,7 the modified fuzes carrying the designations T-30 and T-2004 and differing from the T-50 mainly in arming characteristics.
Experience gained in the development of the T-50 and T-51 fuzes made it evident that the physical size of radio proximity fuzes could be reduced sufficiently to allow their use on trench- mortar shells. Theoretical computations14 indi- cated that a very appreciable gain in lethal effect could be obtained by air-bursting such shells. Accordingly, the Ordnance Department requested the development of the T-132, T-171, and T-172 fuzes10 for use on the 81-mm mortar shells. According to military requirements, these fuzes must :
1. Have a basic design also applicable to 105- mm and 155-mm mortar ammunition.
2. Fit directly into the fuze cavity of stand- ard 81-mm mortar ammunition.
3. Have sound ballistic design, minimizing any deleterious effect on projectile drag and stability as compared with fuzing with point detonating fuzes.
4. When packaged, withstand rough han- dling, shipping, storage over extended periods, moisture, weather, and temperature cycles from -40 to + 140 F.
5. When unpackaged, withstand loading op- erations, moisture, weather, and temperature cycles from —40 to +140 F for short periods, and withstand rough handling expected under service conditions incident to firing.
6. Be provided with a cap or cover to pre- vent entry of mud or water into the air passage after removal of the fuzed round or fuze from its packaging, such can or cover to be removed upon withdrawal of safety pin or pins.
7. Require a minimum of adjustment or assembly in the field.
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4
INTRODUCTION
8. Function at or near optimum mean effec- tive height on approach to ground over the range of angles of fall encountered with these projectiles.
9. Limit combined early bursts and duds to 15 per cent.
10. Not be readily affected by enemy jam- ming or other interference.
11. Have a secondary element capable of functioning on impact with minimum effect and independently of the primary element.
12. Operate without detrimental interac- tion, due to mutual interference, when fired at random from weapons spaced closely together.
13. Have an interrupted detonator-explosive train, safe against rough handling, dropping, or crushing, until properly armed by removal of safety pin or pins, acceleration of firing, and a fixed air travel.
14. Have an arming delay mechanism which will insure detonator safety up to 400 yd (ten- tative estimated distance) from the mortar and which will also delay fuze activation until flight characteristics of the projectiles are sufficiently stable to minimize early burst due to poor sta- bility or action of the projectile and to permit efficient fuze operation at the target.
15. Provide means for externally checking the safe position of the arming mechanism.
16. Exhibit the above safety and operating characteristics under the following conditions: (1) temperature —40 to +160 F, (2) all weather conditions, and (3) night or day.
The “mean effective height” referred to in requirement (8), although not specified, was understood to be of the order of 10 ft from theoretical computations,14 but final specifica- tions would have to await effect field trials.
It is to be noted that the requirements for T-132, etc., are much more detailed and rigor- ous than those for the T-5 fuze which had been laid down three years previously. In particu- lar, requirement (9) called for 85 per cent proper functioning of fuzes, whereas 50 per cent was allowed for the T-5.
One apparently innocuous requirement intro- duced for security reasons applied to all bomb and rocket fuzes developed by Division 4. This was that all vacuum tubes used in the fuzes were to fail at accelerations between 10,000
and 20,000<;.33 The purpose of the requirement was to restrict the use of tubes suitable for shell fuzes to that application, thereby reducing the possibility that, through recovery of dud fuzes by the enemy, shell fuzes would be copied and used against our own air forces. As shown in Chapter 3, this requirement introduced some difficulties, because design considerations for microphonic stability and for ruggedness are I quite similar. Thus, in the course of developing suitable antimicrophonic tubes for use in the bomb and rocket fuzes, designs were developed which were rejected because the tubes would not fail at high accelerations. The requirement was withdrawn in the fall of 1944 (when shell fuzes were committed to battle under condi- tions where they might be recovered by the enemy) and thus did not apply to the mortar shell fuzes developed by Division 4.
12 SELECTION OF THE DOPPLER-TYPE RADIO PROXIMITY FUZE
The requirement that a fuze operate in the vicinity of target may be fulfilled by making the fuze sensitive to one of a variety of energy forms: radio, optic, acoustic, magnetic, etc. A comparison of the possibilities and limitations of various energy-sensitive devices is given in Volume 3, Chapter 2, of the Division 4 STR. Here we are concerned only with radio meth- ods.
Among the radio types there are two general classes: active and passive. The active types generate and radiate energy and are sensitive to small amounts of energy after it is reflected from a target. Passive-type fuzes are merely sensitive to incident radio waves. In each of these general classes there are further divisions and subdivisions.
Active-type fuzes may operate by depend- ence on interference between the original and the reflected waves, or operation may depend on the transit time for a pulse or train of waves to travel from the fuze to the target and back to the fuze again. Interference may occur in several ways. If there is relative motion be- tween the transmitter and the reflecting target, the reflected waves when received at the fuze
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will differ in frequency from the transmitted waves (doppler effect). Interference results in a beat note equal to the difference in frequency. On the other hand, if the transmitter is fre- quency or phase modulated, interference with the reflected waves produces a signal which is a function primarily of the distance to the tar- get. This principle is equivalent to that of the well-known FM radio altimeter. Pulsed or in- termittent circuits to determine time or dis- tance to target operate on essentially the same principles as the common forms of radar rang- ing devices.
The simplest kind of passive proximity fuze requires the target to be a source of energy. Although this requirement can be satisfied for antiaircraft fuzes of the acoustic or infrared type, it would generally not hold for radio- sensitive devices. Consequently, a passive-type radio fuze would require auxiliary transmit- ting equipment as part of the fire control.
In selecting an operating method for a radio proximity fuze, probably the most important consideration was simplicity. It was believed that if the fuze was too complicated, it would be impracticable on two grounds: (1) its vol- ume would be too large to satisfy ballistic re- quirements, and (2) it could not be manufac- tured in sufficient quantities in time to be of any value. Since fuzes are expendable devices, to be used only once, an appreciably different attitude toward production was required for radio proximity fuzes than for other types of radio equipment. Furthermore, a radio fuze is a device on which no adjustment is possible during its operation, hence reliability was a requirement which could not be compromised by the manufacturing problem. Thus, it ap- peared imperative to keep the design of a radio proximity fuze as simple as possible but still fulfill the military requirements.
The simplest type of radio fuze is probably the passive type, but, since auxiliary fire con- trol equipment would be needed for its use, it does not meet the general requirement for “a minimum of special equipment and training” for its operational use. Passive-type radio fuzes were, however, seriously considered and investigated until it was definitely established that the transmitters required in active-type
fuzes could be built in large quantities and made to operate reliably during the flight of the missile.
Probably the simplest active-type radio fuze is the doppler type, since the transmitter in such a fuze requires no internal modulation or control circuits other than an audio-frequency amplifier. Furthermore, as is shown in detail in Chapters 2 and 3, there are sufficient design parameters available in doppler fuzes to adjust the position of operation along the trajectory of the missile approximately as desired.
All radio proximity fuzes developed by Divi- sion 4 to the stage of adaptability to large-scale production are based on the doppler principle. Chosen initially because of its simplicity, the basic method has proved adequate to meet the major military requirements. More complicated systems have been surveyed and tested briefly, but none of these appeared simple enough to reduce to a mass-production design in time to be of value.
13 OPERATION AND PRINCIPAL
COMPONENTS OF DOPPLER-TYPE FUZES
The actuating signal in a doppler-type fuze is produced by the interference with the trans- mitter in the fuze of the reflected energy from a target moving with respect to the fuze. The frequency of the reflected energy differs from the original by an amount (2v cos a)/X, where v is the velocity of the fuze in a coordinate system where the reflector is at rest, \ is the wave- length of waves radiated by the fuze, and a is the angle the velocity vector makes with the line between the missile and target. The inter- ference or combination of the two frequencies produces a low-frequency signal equal to (2v cos a) /l, which can be used to trigger an electronic switch. Selective amplification of the low-frequency signal is generally necessary.
It is shown in detail in Chapter 2 that the concept of interference of the original and re- flected waves is analytically equivalent to a load variation on the transmitting oscillator. Hence, an r-f circuit which responds to variations in its loading will generate a target signal of fre- quency ( 2v cos a) /l. This signal may be de-
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tected in a separate mixing circuit, oscillator diode [OD], or by a change in some parameter of the oscillator circuit, such as grid voltage, reaction grid detector [RGD] , or plate current, power oscillating detector [POD]. Tl;e designa- tions OD, RGD, and POD are further clarified in Section 3.1.
The principal elements of a radio proximity fuze are shown in block diagram form in Fig- ure 1. The dashed lines between the oscillator and detector indicate that the two functions may be combined.
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Figure 1. Block diagram showing principal components of radio proximity fuze, doppler type.
Operation of the fuze occurs when the output signal from the amplifier reaches the required amplitude to fire the thyratron. For a given orientation of the fuze and target, the ampli- tude of the target signal produced in the oscil- lator-detector circuit is a function of the dis- tance between the target and the fuze. Hence, by proper settings for the gain of the amplifier and the holding bias on the thyratron, the dis- tance of operation may be controlled. Distance, however, is not the only factor which requires consideration. Orientation or aspect is very im- portant, particularly against aircraft targets, since operation should occur at that point on the trajectory when the greatest number of fragments will be directed toward the target.
For most missiles, the greatest number of fragments are directed upon detonation ap-
proximately at right angles to the axis of the missile. The dynamic fragmentation pattern for an M-8 rocket is shown in Figure 2,b and its essential features pertaining to fuze design are typical of most missiles except that for higher- velocity projectiles, the side lobes are inclined forward toward the line of flight. The graph shows the density of the fragments per unit area of a sphere drawn about the missile as a function of the angle between the direction of the fragments and the axis of the missile. The angle 0m represents the latitude angle along which the greatest number of fragments are directed. The three-dimensional pattern would be that obtained by rotating the curve in Fig- ure 2A about the flight axis. The static frag- mentation pattern of a 500-lb GP bomb is shown in Figure 2B. The dynamic pattern, obtained by the vectorial addition of velocities due to the bomb’s motion and due to the explo- sion, would be tipped forward a few degrees.
For trajectories which would normally pass by the target without intersecting it, there will be optimum chance of damage if detonation of the missile occurs when the target makes an angle 0m with the missile. However, for trajec- tories which would intersect the target, the missile should come as close to the target as possible before detonation. Hence, the basic re- quirements for directional sensitivity of a proximity fuze for antiaircraft use are (1) the sensitivity should be a maximum in the direc- tion corresponding to maximum lateral frag- mentation density of the missile, and (2) the sensitivity should be a minimum along the axis of the missile. Directional sensitivity of this type can be obtained by using the missile as an
b It was erroneously assumed during the development of the T-5 fuze and in the absence of experimental data that the latitude (dynamic case) of maximum fragment density for the M-8 rocket would lie between 60 and 70 degrees. Actually the density of lethal fragments in this direction is greater than shown in Figure 2A be- cause the contribution of the relatively low-velocity fragments from the rocket body are not shown in the figure. For high-velocity missiles, such as antiaircraft shells, the component of velocity due to the shell’s for- ward motion gives a very appreciable forward tilt to the dynamic fragmentation pattern. Also, in the case of higher-velocity aircraft rockets [HVAR] such as the 5-in. HVAR, the latitude of maximum fragmentation density is about 66 degrees. Fuzes for this rocket (T-30) were developed later in World War II.
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antenna with the axis of the missile corre- sponding to the axis of the antenna. With the fuze in the forward end of the missile, such an- tennas are end-fed by means of a small elec- trode or cap on the nose of the fuze. Additional control over the sensitivity pattern of the fuze is possible by means of the amplifier gain char- acteristic. As pointed out previously, the fre-
For use against surface targets, proximity fuzes are designed for an optimum height of burst, depending on the nature of the target and the properties of the missile. When frag- mentation bombs are air burst, the possible damage to shielded targets is substantially in- creased. Figure 3 shows a cross-sectional view of a typical shielded target: a man in a fox-
Figure 2. Fragmentation patterns of missiles.
The amplitude represents the relative density of the fragment as a function of the latitude angle around the axis of the missile. Figure 2A is for the M-8, 4.5-in. rocket and shows the dynamic pattern; i.e., directional allowance has been made for the effect of the velocity of the rocket. The graph, which is based on data in reference 19, does not include the contributions of fragments from the rocket motor. The latter are large, slow-moving, relatively few in number, and add to the pattern shown in the region between 45° and 90°. Figure 2B is a static pattern for the M-43, 500-lb GP bomb and is based on data in reference 11. The effect of bomb velocity on fragment direction is very slight (due to the relatively low velocity of the bomb) and would shift the maximum of the pattern forward of the order of 5°.
quency of the target signal is {2v cos a) /l. The angle a varies rapidly as the missile passes the target, and if maximum gain occurs when a = 6m there will be greater likelihood that the missile will be detonated at the proper point on its trajectory. More detailed discussion of these features is given in Sections 2.8 and 2.11 and in Sections 3.2 and 3.5.
hole. The man is shielded from fragments from any bomb detonating either side of the hole and below the dashed lines. The angles <f>R and <f>L, which the lines make with the horizontal, are called the shielding angles for the respective directions. It is thus seen that, as the <j> s increase, higher burst heights will be neces- sary to expose the targets. An upper limit on
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burst height is set by the lethal range of the bomb fragments since these fragments lose velocity rapidly as they travel from the point of explosion. Hence, the height of an air burst should be great enough to expose an appreci- able number of targets but not so high that the fragments will be impotent when they strike the targets.
Most computations and evaluation tests for the optimum height of air burst for bombs have been on the basis of a 10° shielding or safety angle.c The optimum height varies only
Figure 3. Sectional view of a soldier in fox- hole, typical shielded target. Soldier is protected from fragments from explosions below dashed lines. Angle these lines make with horizontal are called shielding, or safety, angles.
slightly for the various striking angles and velocities with which bombs may approach the ground. Hence, it is desirable to design a fuze for ground-approach use which will give essen- tially constant burst heights for the various approach conditions.
An approach to this requirement is to have maximum radio sensitivity along the axis of the bomb, with essentially constant sensitivity
c See references 11, 12, and 13 for theoretical values and reference 16 for effect field tests. It should be pointed out that the size of the elementary target is a primary consideration in the computation of optimum burst heights. From this point of view, overhitting on targets of finite size is decreased as the burst height increases. Thus, an optimum burst height is determined by the lethal range of fragments on the one hand and a height where overhitting becomes excessive on the other.
to about 45 degrees on either side of the axis. (For most release conditions used operation- ally, bombs strike the ground with an angle to the vertical of less than 45 degrees.) A short dipole antenna mounted transversely to the bomb’s axis and on the nose of the bomb essen- tially meets this requirement. In addition, it is necessary to design the amplifier of the fuze to give constant amplification for the range of doppler frequencies which might be encoun- tered because of various approach velocities.
On the other hand, it was found that fairly good ground-approach performance could be obtained with fuzes with axial antennas by de- signing the amplifiers to compensate for the appreciable decrease in radiation sensitivity in the forward direction. For example, steep angles of approach in general mean high ap- proach velocities with higher doppler frequen- cies. Thus, a loss in radiation sensitivity with steep approach can be compensated by an in- crease in amplifier gain for the higher doppler frequency. Details of such design are given in Section 2.2.
A miniature triode is used for the oscillator in the fuze and a pentode for the amplifier. When a separate detector is used, a tiny diode provides the required rectification. A miniature thyratron serves as the triggering agent and a specially developed electric detonator initiates the explosive action. Details concerning the de- sign of these elements are presented in the vari- ous sections of Chapter 3.
Energy for powering the electronic circuits is obtained in the later fuze models from a small electric generator. This is driven by a windmill in the airstream of the missile. A rec- tifier network and voltage regulator are essen- tial parts of the power supply. Design details of the generator power supply, as well as earlier battery power supplies, are given in Section 3.4.
The arming and safety features of the radio proximity fuzes are closely tied in with the power supply. This is a natural procedure since an electronic device is inoperative until electric energy is supplied. Arming a radio proximity fuze (generator type) consists of the following operations: (1) either (a) removal of an arm- ing wire which frees the windmill, allowing it
PRODUCTION OF PROXIMITY FUZES
9
to turn in the airstream (bomb fuzes) or (b) actuation of a setback device freeing the drive shaft of the generator and allowing it to turn (rocket and mortar-shell fuzes), (2) operation of the generator to supply energy to the fuze circuits, (3) connection of the electric detona- tor into the circuit after a predetermined num- ber of turns of the vane corresponding to a certain air travel, and (4) removing a mechani- cal barrier between the detonator and booster prior to which explosion of the detonator would not explode the booster. Generally, operations (3) and (4) occur simultaneously by motion of the same device.
Additional safety is provided by the fact that unless the generator of the fuze is turning rap- idly the fuze is completely inoperative. A mini- mum airspeed of approximately 100 mph is required to start the generator turning. Details of the arming system are given in Chapter 4.
14 PRODUCTION OF PROXIMITY FUZES
The course of the development of radio prox- imity fuzes for fin-stabilized missiles and the actual nature of the devices placed in produc- tion for Service use were influenced by many factors other than fundamental technical con- siderations. Time and expediency had a major influence on all designs. In order to have fuzes available for use as soon as possible, tooling for large production was frequently started before development was complete. This meant that when further development indicated certain de- sign changes to be imperative or desirable the extent of the changes which were made was controlled by the degree of the changes required in tooling or by the amount of time which would be lost by making the changes. Further- more, no components could be included in the design which would take too long to acquire in the necessary quantity nor could production techniques be considered which were over- elaborate and time consuming.
Specific Service requirements varied as the course of World War II changed, and, because of the pressing demand for speed, fuze designs for the new requirements made much more use
of the tools and techniques employed in preced- ing models than if production had started out fresh. For example, the greatest urgency early in World War II was for antiaircraft weapons, and stress was placed on fuzes for both bombs and rockets for this purpose. When the Allies acquired undisputed air superiority, the major proximity fuze requirements were shifted to the ground-approach operation. Thus, the T-50 type bomb fuze, which employs the axial radio antenna, ideal for antiaircraft use and initially designed for that purpose, was adapted to ground-approach use. The T-51 fuze, which em- ploys the transverse antenna specifically devel- oped for ground-approach use, was used much less extensively for this application because its initial lower priority made it available later in World War II.
More detailed information relating to the sequential development of radio proximity fuzes is given in the history of Division 4. The subject is mentioned here only to emphasize that the technical phases of the development were not always controlled by straightforward engineering design considerations.
After the operation of a fuze design was found satisfactory by laboratory and field tests, it was necessary to determine its practicability for mass production. Pilot construction lines were used for this purpose, and it was the policy of Division 4 to require the construction of about 10,000 pilot-line fuzes with suitable performance characteristics before releasing a design to the Armed Services. Usually the tools developed for the pilot-line work were used also for final production. Large-scale procurement was handled by the Services, but Division 4 participated in many phases of it, largely in an advisory capacity. The various technical aspects involved in the production of radio proximity fuzes are presented in Chapter 6.
The radio proximity fuzes developed by Divi- sion 4 to the stage of large-scale production are as follows. More detailed information concern- ing the characteristics of these fuzes is given in Chapter 5.
M-8 Rocket Fuzes
1. T-5, an antiaircraft battery-powered fuze for the 4.5-in. M-8 rocket. This fuze is shown in
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Figure 4. Approximately 370,000 were pro- cured by the Army.
2. T-6, a ground-approach fuze, for use as an artillery weapon on the 4.5-in. M-8 rocket. This fuze is a variation of the T-5, having a longer
Figure 4. Radio proximity fuzes for rockets. These are from left to right: (1) T-5 fuze for 4.5 in. M-8 rocket for air-to-air use (T-6 ground- to-ground fuze is identical in appearance to T-5) ; (2) T-2004 fuze for 5-in. AR rocket for air-to-ground use; and T-2005 multiple-purpose fuze.
arming time, about 6 sec compared to 1.0 sec, and no SD element. It is identical in exterior appearance to the T-5. Approximately 300,000 of the T-5 fuzes were converted after comple- tion to T-6 fuzes.
3. T-12, a generator-powered fuze for use on the M-8 rocket. This fuze was not placed in large production primarily because of curtail- ment in requirements for the M-8 rocket.
Bomb Fuzes
1. T-50-E1, a generator-powered ground- approach fuze for use primarily on the 260-lb M-81 fragmentation bomb, the 100-lb M-30 GP bomb, and the 2,000-lb M-66 GP bomb. This fuze, which uses the bomb as a radio antenna, was planned for air-to-air use when develop- ment started but was changed to ground- approach application before development was completed. Its radio transmitter operates in the Brown frequency band. This fuze was set to
arm after 3,600 ft of air travel. It is shown in Figure 5.
2. T-50-E4 is similar to the T-50-E1 fuze ex- cept that its transmitter operates in a different frequency band (White band), giving optimum performance on the 500-lb M-64 and the 1,000- lb M-65 GP bombs. Approximately 130,000 T-50-E4 and T-90 fuzes were procured by the Army.
3. T-89, an improved T-50-E1 type fuze, giv- ing more uniform burst heights. It also differs from T-50-E1 in that arming setting can be checked more readily in the field. Approxi- mately 140,000 T-50-E1 and T-89 fuzes were procured by the Services. This fuze is similar in appearance to the T-91 fuze, shown in Fig- ure 5.
4. T-91 (later designation, M-168), a varia- tion of the T-89, developed specifically to meet a naval requirement of higher burst heights than the T-89 for low-altitude bombing. This fuze is set to arm after 2,000 ft of air travel. Ap- proximately 120,000 T-91 fuzes were produced.
5. T-92, a variation of the T-90 developed to meet the same performance requirement as the
Figure 5. Radio proximity fuzes for bombs. These are, from left to right: (1) T-50-E1 fuze for air-to-ground use on M-30 and M-81 bombs;
(2) T-91 fuze, a later and improved version of T-50-E1, for use on M-30, M-81 and M-64 bombs;
(3) T-51 fuze, air-to-ground use, for use on all bombs of 100-lb size or larger; and (4) T-82 fuze for use paralleling T-51.
T-91 of higher burst heights in low-altitude bombing. It is similar in appearance to the T-91 fuze. Approximately 70,000 were produced.
6. T-51 (later designation, M-166), a gen- erator-powered bomb fuze with a transverse antenna for ground-approach use on all GP, fragmentation, and blast bombs of 100-lb size
GENERAL EFFECTIVENESS OF PROXIMITY FUZES
11
or larger. Burst heights with the T-51 are gen- erally higher than with T-50 type fuzes. This fuze was set to arm after 3,600 ft of air travel. Approximately 350,000 were procured by the Services.
7. T-82, a generator-powered bomb fuze with transverse antenna of somewhat different physical dimensions than the T-51. It was de- veloped for the same general purpose as the T-51, but, when success of the latter was as- sured, further development of the T-82 was turned over to the Army.8 It had not reached the production stage at the time of the transfer.
Later Rocket Fuzes
1. T-30 (Navy designation, Mk-171), a gen- erator-powered rocket fuze for air-to-air use, particularly on the Navy’s HVAR and the 5-in. aircraft rocket [AR]. This fuze is physically very similar to the T-91 bomb fuze and only slightly different electrically. Its arming sys- tem is different in that the acceleration of the rocket is essential to its operation. This fuze had just reached a production rate of 10,000 per month at the end of World War II.
2. T-2004 (Navy designation, Mk-172), a generator-powered rocket fuze for ground- approach use. It is similar to the T-30, but is somewhat less sensitive and has a longer arm- ing time. Approximately 110,000 were pro- cured by the Services. A photograph is shown in Figure 4.
3. T-2005, a miniature generator-powered rocket fuze for either antiaircraft or ground- approach use (by a change-over switch). It is similar electrically to the T-30 and T-2004. De- velopment of this fuze was initiated by Divi- sion 4 but turned over to the Army for further work before the point of large-scale production was reached. A photograph of the fuze is shown in Figure 4.
Trench-Mortar Fuzes
1. T-132, a generator-powered ground-ap- proach fuze for use on the 81-mm trench-mor- tar shell. This fuze, shown in Figure 6 along with the T-171 and T-172, uses the body of the shell as an antenna. It also incorporates a novel production technique, i.e., printed or stenciled electric circuits. Tools were being set up for a
production rate of approximately 100,000 per month when World War II ended.
2. T-171, a generator-powered ground-ap- proach mortar-shell fuze, similar to the T-132
Figure 6. Radio proximity fuzes for trench mortar shells. These are, from left to right:
(1) T-132 fuze using electric circuits “printed” on ceramic plates; (2) T-171 fuze, electrically similar to T-132 but with standard electrical re- sistor and condensers; and (3) T-172 fuze with loop antenna.
except that it employs the more standard cir- cuit-assembly techniques. Tools were being set up for production rate of about 125,000 per month when World War II ended.
3. T-172, a generator-powered ground-ap- proach mortar-shell fuze with a loop antenna. This antenna has essentially the same direc- tional properties as the transverse antenna of the T-51 bomb fuze. Tools were being set up for a production rate of about 250,000 per month.
Development of the T-40 and T-43 bomb tail fuses (referred to in Section 1.2) for the 4,000- and 10,000-lb blast bombs was not completed because the T-51 nose fuze appeared to be ade- quate to meet all the requirements. As shown in Chapter 9, tests of the T-51 fuzes (with minor modifications) on M-56 (4,000-lb) bombs gave excellent performance. No 10,000-lb bombs were made available for field tests.
15 GENERAL EFFECTIVENESS OF PROXIMITY FUZES
Although the final answer on the effective- ness of a new military weapon is supplied by
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its performance in battle, the best quantitative measure of relative effectiveness under con- trolled conditions can be obtained from care- fully planned field trials. A number of evalua- tion tests have been carried out on radio proximity fuzes. These can be grouped into the following categories.
1. Evaluation of conformance to require- ments.
2. Evaluation as a weapon:
a. Antiaircraft use (fragmentation ef- fect) .
b. Air burst (ground approach on frag- mentation bombs and rockets).
c. Air burst on blast bombs.
d. Air burst on chemical bombs.
e. Air burst on fire bombs.
Most of the tests conducted by Division 4 other than strictly developmental tests were in the first category above. The Services also car- ried out extensive tests in the first category but generally after the fuzes were in production.
Tests and evaluation studies in category 2 above were usually carried out by the Services or by other NDRC divisions and therefore are not properly within the scope of this volume. The results, however, are of interest in giving a more complete picture of the evaluation of radio proximity fuzes and accordingly will be referred to briefly. Such evaluations, of course, depend primarily on the properties of the mis- sile which carry the fuzes and in no cases were the missiles designed for proximity operation. Now that proximity fuzes have been established as practicable devices, certain missiles, such as fragmentation bombs for air-burst use should be redesigned to increase greatly their effec- tiveness as weapons.
Typical missiles equipped with proximity fuzes are shown in Figure 7.
Evaluation of Conformance to Requirements
Detailed evaluations of the conformance of the fuzes to the military requirements are pre- sented in Chapters 5 and 9. In this section, a brief abstract is given of the most important results for production fuzes. Generally, the re-
liability of the radio proximity fuzes for bombs and rockets was about 85 per cent, that is, 85 per cent of the fuzes would be expected to func- tion on the target as required. Of the remainder about 10 per cent could be expected to function before reaching the target (random bursts) and 5 per cent not to function at all. The 10 per cent or so random functions were distributed along the trajectory between the end of the arming period and the target. In many thou- sands of tests, no fuze functions were observed before the end of the arming period.
Figure 7. Radio proximity fuzes on typical missiles. These are, from bottom to top: (1) T-132 fuze on 81-mm M-56 mortar shell; (2) T-91 fuze on M-81-A 260-lf fragbentation bomb;
(3) T-51 fuze on the M-64, 500-lb general pur- pose bomb; and (4) T-2004 fuze on 5-in. HVAR rocket.
General reliability and proximity sensitivity (function heights) for the various production models follow.
1. T-5 Fuze. Acceptance tests on over 4,000 T-5 fuzes against a mock airplane target showed the following results:
a. 81 per cent proper functions in the vicinity of the target.
b. 2 per cent functions just beyond the target.
c. 13 per cent early functions between arming and the target.
d. 4 per cent duds.
The time of flight in normal acceptance tests (see Chapter 8) was inadequate to allow test-
GENERAL EFFECTIVENESS OF PROXIMITY FUZES
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in g of the SD feature. Separate tests on the SD showed it to be 96 per cent reliable at an aver- age time of 8.5 sec after firing. Ninety per cent of the SD functions were between 6.5 and 11 sec. These figures refer to the mechanical SD (see Chapter 4) used in later models. An elec- tric SD used in earlier models (see Section 3.3) was less reliable.
The vicinity of the target was defined as within a 60-ft impact parameter of an 0.8-scale target of a medium bomber. For more detailed discussion of a proper definition of “vicinity of the target” see Section I.5.2.1921
2. T-6 Fuze. The percentage of proper func- tions for the T-6 ground-approach fuze depends on the time of flight of the rocket, the number of random functions increasing with the longer trajectories. For maximum range, tests on over 1,500 rounds indicated the following perform- ance.
a. 80 per cent proper functions.
b. 16 per cent random functions.
c. 4 per cent duds.
Proper functions were defined as operation between 6 and 100 ft above ground.
3. T-50-E1 and T-89 Fuzes. Acceptance tests on 100 lots (lots averaged about 1,000 fuzes and field tests were made on about 18 fuzes from each lot) of T-50-E1 and T-89 bomb fuzes showed
a. 83 per cent proper functions.
b. 13 per cent random functions.
c. 4 per cent duds.
Proper functions for ring-type bomb fuzes (axial antennas) were defined as between 6 and 100 ft over a water target. The average burst height was 33 ft.
4. T-91 Fuzes. The first lots of T-91 bomb fuzes were about the same quality as the T-50- E1 fuzes. However, later lots (T-91-E1 using the RGD circuit, see Section 3.1) showed the following average for 27 lots.
a. 92 per cent proper functions.
b. 7 per cent random functions.
c. 1 per cent duds.
The average height of function was 60 ft over a water target.
5. T-50-E4 and T-90 Fuzes. Tests on 130 lots of T-50-E4 and T-90 bombs showed
a. 78 per cent proper functions.
b. 19 per cent random functions.
c. 3 per cent duds.
The average height of function was 40 ft.
6. T-92 Fuzes. Tests on 50 lots of T-92 bomb fuzes showed
a. 58 per cent proper functions.
b. 34 per cent random functions.
c. 8 per cent duds.
The average height of function was 34 ft.
The inferior performance of T-92 fuzes was due to unusual dependence of the fuze on the electric properties of the test missile, the M-64 bomb. It was found that, on bombs which had been carefully prepared to reduce variable con- tact between the fin and the bomb body, scores equal to those with other fuzes were obtained. When it was definitely established that the poor performance of the T-92 was due to this cause and consequently could not be improved by more rigorous production control, further pro- curement was terminated. It had meanwhile been shown that the T-51 and T-91 fuzes, which had become available, would fulfill the applica- tions for which the T-92 was intended.
7. T-51 Fuzes (M-166). Field tests on 230 lots of T-51 bomb fuzes showed
a. 91 per cent proper functions.
b. 9 per cent random functions.
c. 1 per cent duds.
The average height of function over the water target was 110 ft. The proper function range included heights up to 200 ft for bar-type fuzes.
8. T-2004 Fuzes. Field tests on 75 lots of T-2004 rocket fuzes showed
a. 94 per cent proper functions.
b. 3 per cent random functions.
c. 3 per cent duds.
The average height of the proper functions was 30 ft.
1,5,2 Evaluation as a Weapon
Antiaircraft Use
A careful analysis of the T-5 fuze on the M-8 rocket as an antiaircraft weapon was made by the Applied Mathematics Panel [AMP].19'21 The study was based on the experimental per- formance of the fuze against a mock aircraft target, fragmentation data of the rocket, dis-
14
INTRODUCTION
persion data on the rocket when fired from an airplane, and vulnerability of a twin-engine enemy aircraft, in particular the JU-88, to fragmentation damage.
Conclusions of these studies were as follows :
1. When fired from 1,000 yd directly astern with a standard deviation in firing error of about 50 ft (17 mils), a single round has one chance in * 10 of preventing a twin-engined bomber from returning to base provided it cannot return to base on one engine.
2. If return to base on one engine is pos- sible, there is one chance in 16 that a single round will prevent its return.
3. If a delay of about 50 ft were incorporated in the fuze, to bring the vulnerable part of the target in a region of greater fragmentation density, the above probabilities would be in- creased to 1 in 4 and 1 in 6.
The greater effectiveness of the weapon with the delay was due to the fact (as shown in Fig- ure 2) that the latitude of greatest fragmenta- tion density of the rocket was approximately at right angles to the axis of the rocket, whereas the fuze, as shown in Chapters 2 and 3, had been designed from an assumed latitude of maximum density of about 70 degrees. A delay of the amount recommended in the AMP report would have brought the target in the region of maximum fragment density. Such a delay could have been incorporated readily in the fuze had the tactical demand for this weapon in 1944 been as high as it was in 1942. However, there appeared to be little likelihood that M-8 rockets would be used as air-to-air weapons, so the fuzes were not modified.
The probability of obtaining a crippling di- rect hit by an M-8 fired under the same condi- tions is about 1 in 100.
Limited tests and evaluations were made of the 5-in. AR and HVAR equipped with T-30 fuzes as antiaircraft weapons. At the Naval Ordnance Test Station at Inyokern, California, some 70 rounds were fired from a fighter air- plane at a radio-controlled plane in flight.18 At about 400-yd range, over 55 per cent of the rounds functioned on the target. Eight high- explosive [HE] loaded rounds were fired, four of which functioned on the target, and three of the four destroyed the targets. Presumably,
most of the rounds which did not function on the target were beyond the range of action of the fuzes.
The Applied Mathematics Panel made an in- formal study of the effectiveness of AR and HVAR equipped with proximity fuzes.22 For these rockets it was found, presumably because of their higher velocities, that the optimum burst surfaces were inclined forward from the equatorial plane of the rocket and not at right angles to it, as was the case for the M-8 rocket. No experimentally determined burst surface patterns were obtained for T-30 fuzes but, assuming the same burst pattern as for T-5 fuzes, the effectiveness was nearly optimum. For example, the probability of destroying an aircraft with an HVAR with a firing error of 25 mils at 1,000-yd range was 0.4, and with 15 ft optimum delay was 0.63. Further details are in the AMP report.
Air Burst for Ground Targets
The Army Air Forces [AAF] carried out ex- tensive evaluations of the effectiveness of air- burst bombs against shielded targets using T-50 and T-51 fuzes on M-81 (260-lb fragmen- tation) and M-64 (500-lb GP) bombs. Bombs were dropped on a large effect field covered with target boards 2x6 in. in trenches 1 ft deep. For equivalent airplane loads of properly func- tioning bombs dropped on 12-in. deep trench targets, conclusions from the AAF report are :16
1. Air-burst 260-lb M-81 fragmentation
bombs and 500-lb M-64 GP bombs produce about 10 times as many casualties as contact- burst 20-lb M-41 fragmentation bombs when trenches are 15 ft apart. (A casualty is defined as one or more hits per square foot, capable of perforating % in. of plywood.)
2. Optimum height of burst for maximurfi casualty effectiveness is between 20 and 50 ft, with only slight variation through this range.
The British carried out similar appraisals, using T-50 fuzes on M-64 bombs.26 There are several differences in details of the tests, par- ticularly in the matter of evaluating the effec- tiveness of surface-burst bombs. The British Ordnance Board made an appreciable allow- ance for the blast effect of both the contact-
GENERAL EFFECTIVENESS OF PROXIMITY FUZES
15
fuzed bombs and variable-time [VT] fuzed bombs and arrived at a superiority factor of 4 to 1 for the latter against shielded or en- trenched targets.
The AAF also evaluated the M-8 as an air- to-ground weapon with both VT (T-5) and contact fuzing.17 The summary report con- cluded that the weapon was relatively ineffec- tive against shielded surface targets, although the casualties per round with VT fuzing were about five times as high as with contact fuzing.
Air Burst for Blast Bombs
Studies by Division 2, NDRC,23 and by the British25 demonstrated that when large blast bombs are air burst at about 50 to 100 ft above ground, the area of demolition could be in- creased from 50 to 100 per cent. No full-scale tests were carried out to verify these conclu- sions, but it was established that the T-51 fuze could be used on both the 4,000-lb (M-56) American bomb (Chapter 9) and the 4,000-lb British bomb27 to give air bursts at the proper altitudes.
In cooperative tests by the Army, Division 4 and Division 2, NDRC,24’34 it was shown that air-burst bombs could be used in mine-field clearance. The advantages were primarily in increased reliability of clearance and absence of cratering. However, the use of air-burst bombs for this purpose does not markedly re- duce the number of bombs required to clear an area.
Air Burst for Chemical Bombs
A number of evaluations were made to deter- mine the effectiveness of air bursts on chemical bombs. In a carefully planned effect field test using T-51 and T-82 fuzes on 500-lb LC bombs, the British showed the areas of contamination with a mustard-type gas were 4 to 5 times greater than when the bombs were used with contact fuzes.30 The increase was due to a more uniform distribution of the vesicant and avoid- ance of loss of material in craters.
The Chemical Warfare Service and the Brit- ish cooperated in an extensive series of tests at Panama in simulated jungle warfare. A T-51 fuze with reduced sensitivity effectively pro- duced air bursts of chemical bombs below tree-
top canopies with efficient distribution of chem- ical materials.28’ 29
Air Burst for Fire Bombs
The Army Air Forces evaluated the effective- ness of T-51 fuzes on fire bombs and found that for high-altitude bombing the distribution of incendiary material was appreciably improved. In this application, the gain due to an air burst was due to the elimination of loss of material in craters.31
1 5,3 Operational Use of Proximity Fuzes
Proximity fuzes for bombs and rockets saw very limited operational use, primarily because they were introduced into action very late in World War II. Some of the factors which im- peded their initial operational use are dis- cussed in the history of Division 4. Other fac- tors, as well as a full summary of their use in World War II, are given in a memorandum by a member of the VT Fuze Detachment of the Ordnance Department.32 Some excerpts from the latter reference are given in Chapter 9.
Altogether, approximately 20,000 fuzes, pri- marily bomb fuzes, were used in action by the Army and the Navy in the Pacific, and in the European and Mediterranean Theatres of Op- eration [ETO] and [MTO]. In the last few weeks of the war in the Pacific, approximately one-third of all bomb fuzes used by carrier- based aircraft were proximity fuzes. The main targets were antiaircraft gun emplacements and airfields.
No thoroughgoing analysis of the effective- ness of the fuzes operationally was possible, although the general reaction was very favor- able. Since the fuzes were used in all theaters so late in World War II, the major uses were of a trial or introductory nature. In all cases, these trial uses were followed by urgent re- quests for more fuzes, which usually, and par- ticularly in ETO and MTO, did not arrive until after World War II was over. All initial uses were in 1945, in February in the Pacific and in March in ETO and MTO. Reports concerning the effectiveness of the fuzes against gun em- placement targets generally stated that anti- aircraft fire was either stopped or greatly re-
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16
INTRODUCTION
duced after the air-burst bombs exploded.
Although relatively little or no quantitative data as to the effectiveness of the fuzes was secured, their use was extensive enough to es- tablish their practicability as service items of ordnance equipment. Relatively little difficulty was experienced in the handling and use of the fuzes and none of these was serious or insur- mountable. Hence, with the effectiveness of proximity fuzes well established by effect field
studies and operational practicability estab- lished by combat use, proximity fuzes appear assured of a permanent and increasingly im- portant position in modern ordnance. The tech- nical information presented in the succeeding chapters of this volume not only serves to pro- vide a full understanding of the properties of the fuzes which were developed and produced, but it also provides a firm and logical basis for future development.
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Chapter 2
THE RADIATION INTERACTION SYSTEM
21 INTRODUCTION
rj 1 he PRECEDING chapter has explained what 1_ a proximity fuze is and has shown what the fuze must do by stating the military character- istics required for such a device. The basis upon which the radio reflection principle was selected as most suitable for a proximity fuze has been discussed, and some of the reasons for using the doppler principle have been pre- sented. We are now in a position to explain the working principles of the device and its engi- neering design.
In discussing the working principles we are concerned with two essentially independent sets of phenomena: (1) those external to the fuze mechanism, i.e., the emission and recep- tion of radiation and its interaction with the target; and (2) those within the fuze itself, i.e., internal circuit behavior.
The present chapter deals with the first group, external phenomena, which we call the radiation interaction system. To facilitate dis- cussion, an arbitrary dividing line is drawn at the point where the internal fuze circuit is electrically connected to the fuze antenna. As will be seen, it is possible to describe the ex- ternal phenomena so that their effect can be expressed as an appropriate variation of im- pedance at these antenna terminals. When the relation between the radiation interaction with the target and the variation of antenna im- pedance has been determined, the problem be- comes one of constructing a practical circuit which will respond properly to the changes seen at its terminals.
It should not be inferred from this division of phenomena, for the purposes of discussion, that antenna design and circuit design are en- tirely independent. Each must be designed with due regard to the other, and both designs are dictated by such practical considerations as physical limitations of components and tactical utility. In fact it will become evident as the dis- cussion proceeds that the working principles of
a By R. D. Huntoon and P. R. Karr.
the fuze are quite simple and that the real dif- ficulty in making a practical proximity fuze lies in reaching an adequate compromise between a host of closely interrelated factors. The co- ordination of these various factors is treated in Section 3.5.
Many of the phenomena treated in this chap- ter are shown to be negligible or unimportant for the type of doppler fuzes of immediate in- terest. The phenomena may, however, have appreciable importance for fuzes of other types or for more extensive applications of the pres- ent fuzes. For these reasons, the basic theory has been treated in appreciable detail by de- veloping considerable material found in ad- vanced textbooks on radiation and circuit theory. This approach should enable new in- vestigators in the field of proximity fuzes to familiarize themselves with the fundamental principles involved with a minimum of re- course to the technical literature.
22 SPECIFICATION OF PROBLEM IN TERMS OF ANTENNA IMPEDANCE
The fuze detects the presence of an obstacle in its radiation field by means of returning radiation reflected by the obstacle. The physical situation is thus characterized by an outgoing wave with a frequency determined by the fuze transmitter and a returning wave of much smaller amplitude, whose frequency may be different as a result of relative motion of fuze and reflector. In all the discussion which fol- lows, it will be assumed that the reflecting ob- stacles are linear reflectors, by which we mean that the strength of the reflected field is propor- tional to the strength of the incident field. It is shown in this section that the returning wave differs in frequency from the outgoing wave by an amount which can be calculated by the appli- cation of the doppler principle, and that under certain conditions, which hold for present fuze designs, this combination of outgoing and re- flected wave is exactly equivalent to a change
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17
18
THE RADIATION INTERACTION SYSTEM
in antenna impedance. The usefulness and limi- tations of this concept are discussed. f
2-21 Reflected Wave or Doppler Frequency Concept
Consider a radiating system R which radiates a carrier of frequency /. Its field in any direc- tion x will be of the form
E = (i)
Let the radiation be received in a system R'
moving with a velocity v in the direction —x, i.e., toward the system R. In this moving system of reference the field will be of the form
E' = A'ei2rf' [t' ~ (x'/c)l. (2)
The phase of the wave is relativistically invari- ant, so that
7) »)
Now V and x' are related to t and x by the
Lorentz transformation. Applying this gives
when it is remembered that v is —dx/dt.
At the present time relative velocity of fuze and target never exceeds 5,000 fps so that v/c is of the order of 5 X 10-6. Equation (4) can be rewritten
(5)
r =f(1+k + lcft) = f + i(1 + which is close enough to
r = / + J (6)
which is recognized to be the normal doppler frequency shift. Thus the frequency received at the target is given by equation (6) above. The target reradiates, reflects, on this frequency, and a second application of the above argument leads to
f" = / + p (7)
where /" is the frequency of the reflected wave as seen at the fuze. For current fuze designs, the doppler or difference frequency 2v/l is of
the order of a few hundred cycles per second out of a carrier frequency of the order of 100 me and the error introduced by neglecting rela- tivistic effects is of the order of 10-4 c.
2 2 2 Reflection Equivalent to Change of Antenna Impedance
The two-wave picture outlined above can be converted to the equivalent impedance picture quite simply. First, assume the system R' to be at rest, so that f — f' =/". Then the field of the system R, equation (1), can be written as
E = KIej2v[ft - - (8)
where the dependence of E upon I, the antenna current, is shown explicitly. This field is re- flected from the target at distance x with a loss in amplitude and a phase shift 5 and returns as reflected field Er, given by
Er = BKIeW* ~ (2*/x) + 5]. (9)
The constant B represents the loss at reflection and represents also the initial assumption that reflected field is proportional to incident field. The fuze antenna receives this reflected field E, and converts it to a voltage V r so that
Vr = B'KIej2v [ft ~ + «, (10)
showing that Vr is proportional to /, the trans- mitting antenna current. The term B' replaces B and now involves an additional factor trans- lating field to voltage.
At this point it is necessary to call attention to the fact that the radio fuzes herein described and to which the theory we are discussing is applicable use a common antenna for transmis- sion and reception and use the same terminals for transmission and reception. Thus the cur- rent I in equation (10) represents the trans- mitter current into the antenna terminals, and Vr represents the voltage across those same terminals arising as a result of the presence of the reflector in space. Since ( Vr/I ) is dimen- sionally an impedance, we may write
Vr = IZrej2*ft, (11)
where
Zr = B'Kej2* [( -2*/A) +6)' ' (12)
The constants B'K represent the magnitude of the reflected impedance Zr, and the term ej2^~2x/^
SPECIFICATION OF PROBLEM IN TERMS OF ANTENNA IMPEDANCE
19
shows the variation of the phase angle as the distance x to the target changes. In the above discussion, I has been assumed to be constant in the presence of the reflector. This assump- tion is made only for purposes of computing Zr ; the results obtained hold when I varies, as it normally does.
Suppose now that the target moves toward the fuze with a velocity V — dx/dt. Then the rate of change of total phase 4> of the imped- ance is
The frequency F with which the impedance Zr completes its phase cycle is given by
F
1 d<I> _ 2v 2 nit ~ +\’
(14)
a value identical with the doppler frequency derived above, equation (7). We thus see that the reflector can be replaced in the fuze antenna circuit by a reflected impedance Zr, whose am- plitude represents the strength of the reflected voltage and whose rate of change of phase cor- responds to the doppler frequency shift. In this derivation of the frequency F, we have neg- lected relativistic effects; these are, of course, negligible, just as in the preceding derivation.
For fuzes having a common antenna for transmission and reception, using common ter- minals for both, we can represent the behavior
Figure 1. Vector representation of antenna impedance in presence of reflector.
associated with a moving reflector in the radi- ation field by the vector diagram shown in Figure 1.
In this figure Zn represents the impedance
at the antenna terminals in the absence of all reflectors (free space). Its resistive and reac- tive components are Ru and X1± respectively. The term Zr represents the reflected impedance and Zi the total antenna impedance with the reflector present. When a target moves toward the fuze with a velocity v, the end of Zr traces out a spirallike figure with an angular velocity
= 2tF =
47i -v.
The radius increases as Zr increases.
2'2'3 Approximations Involved in Impedance Representation
Suppose we consider two systems, each en- closed in a box with only two terminals avail- able to the experimenter and no indications outside to show the contents of the box. Let box 1 contain a fuze antenna, space for radia- tion, and a moving reflecting target. Let box 2, identical in every external detail with box 1, contain within it a fixed impedance ZX1 and a variable impedance Zr with magnitudes selected according to the definitions above.
In a steady-state condition, i.e., with go = 0 and with the fuze in operation long enough for all transients to die out, no set of measure- ments can distinguish a difference between the contents of the two boxes, and they are for all purposes identical.
If we test the two arrangements by suddenly applying the r-f voltage to the terminals, there will be a difference in the way in which the steady state is reached. This difference is analogous to the difference in the transient be- havior of two circuits A and B, where B is identical with A except for a length of perfect transmission line attached to its input termi- nals. If a signal were suddenly applied to the input terminals of A, a certain transient re- sponse would be obtained at the output of A. If the same signal were suddenly applied to the input of the transmission line attached to B, the transient response at the output of B would differ from that at the output of A because of the delays due to the transmission line. The steady-state behavior of the two circuits, how-
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20
THE RADIATION INTERACTION SYSTEM
ever, would be identical. Thus in the case of the fuze circuit we can apply the impedance concept, which is a steady-state concept, to those cases in which the delays associated with the radiation link are negligible. We now pro- ceed to show that these delays are unimportant in cases of interest.
One effect of the finite transmission time of the waves is that at any time t the fuze receives a reflected signal which is characteristic of the target not at time t but at time (t —r/c), where r is the distance from target to fuze at the mo- ment when the signal which arrives at the fuze at time t started out from the target. This means that the fuze does not “know” its dis- tance from the target at any instant, but only what the distance was at a time (r/c) in the past. In the region of interest r/c is of the order of 10-6 sec, during which time the fuze moves a distance of the order of 10-3 ft. Thus this effect is seen to be of no importance in de- termining the position of function of the fuze. It may be pointed out, however, that for prox- imity fuzes which work on other principles, for example, the reflection of radiated sound, this effect may be of considerable importance.
Another effect of the delay associated with the radiation link is that it introduces an effec- tive “time constant” in the fuze circuit because of the effect which the reflected voltage has on the antenna voltage, which in turn influences the reflected voltage, etc. A rough estimate of the order of magnitude of this time may be ob- tained by assuming the fuze and antenna sta- tionary and computing the time required for the fuze voltage to reach a steady-state value after being switched on. The time required to reach equilibrium is assumed for the purposes of this discussion to be associated entirely with the propagation of the waves in space and not at all with delay characteristics of the fuze cir- cuit itself.
The presence of the reflector induces a volt- age in the fuze proportional to the voltage in- duced in the reflector by the fuze antenna. The above statement can be made more precise by including the time element; that is, suppose at time t = 0, the fuze begins to radiate. Some of the radiation “bounces” back from the reflector, reaches the fuze again at time A t, usually ap-
preciably less than 10-6 sec, and induces a volt- age in the fuze antenna. This causes a change in the radiation; this changed radiation is re- flected by the target again, and its effect is felt back at the fuze at time 2 At. This process goes on until equilibrium is reached.
For the sake of simplicity, assume that the distance of separation is such that the im- pressed and reflected voltage in the fuze an- tenna are always in phase. In this case the effect of the reflected radiation is to increase the voltage in the fuze antenna. Let k be the constant relating the voltage induced in the fuze antenna by reflected radiation to the volt- age in the fuze antenna, which was associated with the original radiation. For many cases of interest k is of the order of 0.01. Then the vari- ation in the fuze voltage starting from t — 0 may be represented as in Figure 2, in which no attempt has been made to represent the true scale. In the figure F0 represents the voltage at t — 0. The expression for this variation is
F (t) = F0 + kV(t- At), (15)
which applies for t ^ At. For t < At, V ( t ) = F0. The equilibrium voltage Vm is the limit of the series
Foo = F0 (1 + k -f~ k2 -f- /c3 -}- • • •), (16)
- ,~E- <17>
For k << 1, we have
Fro « (1 + k) F0. (17a)
Furthermore
F (A0 = (1 + k) F0. (18)
Thus we see that for small k the first reflection is responsible for most of the voltage change. This would be true for any other assumed phase relation between the impressed and re- flected voltages in the fuze.
If desired, we may replace the stepwise vari- ation by a smooth curve, as shown roughly in Figure 2 ; this smooth curve may be represented analytically. To do this we replace V (t — At) in equation (15) by the quantity [V (t) — At ( dV/dt )], the first two terms of the Taylor expansion.
SPECIFICATION OF PROBLEM IN TERMS OF ANTENNA IMPEDANCE
21
This gives us the differential equation
m = F„ + *[r(0 - At ^2], (19)
whose solution is
V(t) = - ^ |\ - A-2 *e(1 “ *> - l)HkM) ]. (20)
This equation is, of course, to be applied only for t — A t.
From equation (20) we find that
and
V(At) = (1 + k) Vo,
agreeing with the previously obtained results. The order of magnitude of the effect described above is seen to be quite negligible for the fuzes
K3v0
t
Figure. 2. Variation of voltage in fuze antenna; fuze and target stationary.
described here. This effect may, however, take on fundamental importance for fuzes operating on other principles, such as those working on acoustic or pulse-time principles.
2'2'4 Implications of Impedance Concept
The advantage of regarding the basic effect of a reflector as an impedance change can be seen when an attempt is made to describe the phenomenon in terms of another concept which
m
appears at first plausible, namely, the concept of the effect of the reflection as a generator e in series with the radiation impedance Zllf as in Figure 3. The reflector does indeed create a voltage e in the antenna. This voltage e how- ever, changes the current I in the antenna, ivhich in turn changes e, and so on. This effect of the change in I upon e must be taken into account, and the impedance concept does this, whereas the generator concept as ordinarily applied does not do so; we do not ordinarily think of a generated voltage e as being affected by the current changes which it produces in the external circuit. Of course, in those cases in which the reflected voltage e is small enough so that its effect on / is negligible it may be treated as a generator.
Another important aspect of the impedance concept is its essentially geometric character. It will be shown by more detailed analysis in the following sections that the reflected imped- ance in an antenna due to the presence of a reflector is a function only of the geometric configuration, of the directive properties of the antenna, and of the character of the reflector. The power level at which the antenna radiates has no effect on the reflected impedance ; this, of course, is not true of the reflected voltage. This lack of dependence of the re- flected impedance upon power level implies that
Figure 3. Generator e in series with fuze antenna impedance, Z\\.
fuzes with widely differing power outputs can be made which have the same sensitivity to reflection. This is indeed true ; fuzes have been made with radiated power outputs ranging from % mw to 1 w, with equal sensitivity to reflection. From the point of view of freedom
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22
THE RADIATION INTERACTION SYSTEM
from interference, however, it is fairly obvious that the higher power level is desirable. That is, the reflected voltage increases with the power level and therefore any extraneous radiation would have to be so much the stronger to in- duce, in the fuze, signals comparable in magni- tude to those coming from the reflector.
2 3 MUTUAL INTERACTION OF SYSTEMS OF TWO-TERMINAL NETWORKS INVOLVING RADIATION
In the preceding section it has been shown that, with certain approximations, the effect of a reflecting target is equivalent to a change in the input impedance of the fuze antenna. To the extent that this is so, the interaction phenom- ena between fuze antenna and target are de- scribable in terms of the steady-state analysis of coupled networks. The familiar concepts of mutual impedance and reflected or coupled im- pedance will be used. In fact the antenna imped- ance change to be evaluated is identical with the reflected or coupled impedance of circuit theory.
2,3,1 Fuze Problem as Interaction of Two-Terminal Networks
For fuzes of the single-antenna type, devel- oped by Division 4, the problem of the inter- action with the target reduces to that of com- puting the reflected impedance. The actual tar- gets encountered by the fuze radiation may be relatively simple, as in the case of ground ap- proach where the fuze can be considered as in- teracting with its image, or complicated, as in the case of an aircraft target with its compli- cated mode of excitation and complicated re- flection pattern. In the latter case it is custom- ary toftdetermine performance of a fuze on the basis of its interaction with a simple target, such as a half-wave reflecting dipole, and by experiment to relate the reflection from the complicated target to that from a simple target.
Thus in the argument which follows in this section the problem will be set up on the basis of mutual interaction between a system of n
simple two-terminal networks connected by ra- diation. In some cases one of these networks will represent the target antenna. When the theory has been worked out formally on this basis, the problem of a complicated target will be discussed in more detail.
2 3 2 Fundamental Equations
We now formulate the problem in a more precise way. Let the fuze and reflecting objects be considered as a system of antennas. If the ground is involved, we consider it as perfectly conducting and replace it by the image of each of the real antennas. For the fuze problem the fuze antenna and its image are driven ; all other antennas are parasitic. If some of the other an- tennas are driven by appropriate generators, we are then concerned with fuze operation in the presence of interference or intentional coun- termeasures. This case is subject to separate treatment, which is not within the scope of this volume.
In general, if we have the fuze antenna inter- acting with 7i — 1 additional antennas, we may set up n equations :
V\ — IiZn -f I2Z12 + I3Z13 + ' ' ' + InZin,
V2 = I1Z2I + I2Z22 + I3Z23 + * ' * + InZ2n, (21)
Vn ~ IlZnl + hZn2 + 1 3Z n3 + ‘ ‘ * + InZnn,
where 7y is the current in the jth antenna and Vs is the voltage impressed on the jth antenna. The set of equations (21) is a well-known way of representing the interaction between n cou- pled circuits or n antennas. On account of the reciprocal relations between antennas, Zti = Zj{.
The meaning of the Z’ s can be elucidated quite simply. If, for example, we open-circuit all antennas except No. 1 so that all Us except /1 are zero, we have Vi = I,Z1U so that Z1X is the free-space impedance of antenna No. 1 and Vi and 1 1 are the free-space voltage and cur- rent, respectively. IiZ2i is the open-circuit voltage of antenna No. 2 due to current 7i in antenna No. 1. The term Z2 1 is the mutual impedance between No. 1 and No. 2. The input impedance of No. 1 in the presence of an arbitrary number of other antennas is
MUTUAL INTERACTION OF NETWORKS INVOLVING RADIATION
23
(Vi/Ii) = Zx. When the n antennas are too far apart to influence each other, the ZJ s vanish (i ¥= j) leaving only the Zu’ s.
As has already been mentioned, the ground is considered as a perfectly conducting plane, infinite in extent. Modifications required for an imperfectly conducting ground are considered later. It is well known that we may “remove” the ground plane and replace it by images of each of the antennas above ground. The rela- tion of the currents in an image and a real antenna are shown in Figure 4 for two con- figurations. The arrows point in the direction of instantaneous current.
If the components of current normal and parallel to the surface are always as shown, the boundary conditions at the reflecting surface will be satisfied and the field of the image above the plane is identical with the reflected field.
Since each of the images contributes to the total effect on the fuze antenna, they may ap- preciably affect the operation of the fuze. When the target and fuze are far removed from ground, the effect of their images becomes neg- ligible. This is essentially true of the applica- tion of the fuze against enemy aircraft in flight for fuzes as now constructed. The influence of the ground in this case will be discussed in more detail later.
To take account of the effect of the ground we include the images in the set of n equations, letting the odd numbers represent real anten- nas and even numbers the image antennas. Thus antenna No. 1 represents the fuze, No. 2 its image, No. 3 a real antenna, and No. 4 its image, and so on, each even number represent- ing the image of the odd number preceding.
In the notation of equation (21) the bound- ary conditions will be satisfied if we put
Ir = -/(r- i) (r even).
Since
ZT = Z(r - i), Vr = —V(r- !).
It will now be found that the odd-numbered equations from equation (21) form a complete set of n/2 equations to specify the solution for the n/2 currents in the real antennas. The re- maining equations can be shown to form an identical set and so contribute nothing further.
Specific Fuze Equations
In the typical fuze situation only the fuze antenna is driven. In equations (21) this is rep- resented by putting V1 = V and V2 = — V with all other Vi = 0. Let us consider this case and solve for V/I lf the apparent input impedance Zx of the fuze antenna. As previously stated, we use only the odd-numbered equations.
A sufficiently general case which includes all
REAL T REAL
ANTENNA ANTENNA
'7/77777 ^7777777
< ■ IMAGE IMAGE
Figure 4. Relation of currents in real and image antennas, for horizontal and vertical cases.
fuze problems of immediate interest arises from the consideration of two real antennas and their two images. For this case antenna No. 1 is the fuze, antenna No. 2 its image, antenna No. 3 is the target, and antenna No. 4 is its image.
For this special case the appropriate equa- tions are
V = IiZn — I1Z12 + I3Z13 — IsZu 0 = 1\Z\3 — I1Z2Z + I3Z33 — I 3Z 34
where we have utilized the fact that Zif — ZjV By symmetry, it is clear that Z23 — Z14. Incor- porating this in equations (22) we get for the input impedance Zx of the fuze
v V _ „ v (Z13 - Zu)2
"1 ^11 _ 12 77 7, •
Il 33 — Zj 34
(23)
Equation (23) shows that the impedance of the fuze antenna is its free-space value ZX1 plus additional terms representing the presence of target and ground. Three cases of interest arise.
Case I. Ground Approach. In this case the fuze uses the ground as a target and antenna No. 3 with its image No. 4 are absent. This means that there are no nearby reflectors ex- cept the ground. For this case Z13 = Zu = 0 and Z 1 reduces to
Z\ — Zu — Z12.
(24)
SECR
24
THE RADIATION INTERACTION SYSTEM
The coupled impedance is the mutual impedance Z12 between the fuze and its image. This leads to an important concept in understanding fuze operation against the ground ; i.e., in the ground-approach case the fuze can be thought of as being fired by its image. Since object and image are connected by a line normal to the plane, the vertical distance from fuze to plane is a determining factor.
Case II. Isolated Airborne Target. It is now assumed that antennas No. 1 and No. 3 are far removed from ground in comparison with their separation. This makes
Z12 = Z\\ = Z34 = 0.
The result is
Z, = Zn ~ f-, (25)
Z/33
and the coupled impedance has the value (Zi32/Zw). An interesting point should be men- tioned here in connection with jamming fuzes. If antenna No. 3 represents a jammer antenna instead of a target and if Z33 includes some negative resistance incorporated by feedback of some sort, Z33 can be made much smaller than the Z33 obtained if the feedback is re- moved. Thus a negative resistance jammer will build up a signal of magnified form and may cause the fuze to function before it should normally.
Such a scheme has difficulties of realization in practice which may make it impossible.
Case III. Airborne Target ivith Ground In- terference. In this case the full equation (23) is applicable and must be considered in some detail. If the target is not moving with respect to its image, as in the case of a test target, Z34 will be a constant and reasonably small com- pared with Z33. To a good approximation we may use Z33 alone. Thus equation (23) includes:
1. Z12 representing the interaction of the fuze antenna with the ground.
2. Z]32/Z33 representing the interaction of the fuze antenna with the target plus two other terms of the same order as this which may lead to interference.
This is as far as the argument can proceed without detailed knowledge of the mutual and self-impedances involved. We now turn atten- tion to the values of impedance to be expected.
2 4 ANALYTIC EXPRESSIONS FOR MUTUAL IMPEDANCE, RADIATION FIELDS ONLY
2 41 Basis of the Argument
We have developed above general expressions for the apparent input impedance of the fuze antenna when in the neighborhood of other antennas, among which may be included the image of the fuze antenna. These equations will now be made more specific, so that they can be applied to actual cases.1’ 4* 9
In the argument to follow we will confine our- selves to the case of radiation fields alone, leav- ing the problem of correction due to induction and quasi-static components to Section 2.10. The corrections are not necessary to predict fuze operation in a large majority of cases.
By neglecting the corrections it is possible to set up a general argument which makes no as- sumptions about the nature of the current dis- tribution on the fuze antenna or the mode of interaction with the reflected radiation. All we need to know about the fuze antenna is that: (1) it has two terminals for connection to the oscillator circuit; (2) when current flows through these terminals, radiation appears in the surroundings with a distribution which can be measured experimentally; and (3) the loss of energy by radiation appears as a resistance in the antenna circuit to which the oscillator is connected.
To derive the necessary expressions we will first express the field strength E of an antenna at point P in space in terms of (1) the distance r from the antenna, (2) the experimentally meas- ured radiation pattern /(0,</>), (3) the gain G of the antenna as calculated from (4)
the series radiation resistance Rs, and (5) the driving point current I into the antenna ter- minals.
The meaning of Rs may be clarified by repre- senting the system as in Figure 5, where the box is the fuze system which emits radiation. If we integrate the energy flow at infinity when a current I flows into the terminals, we find that a certain amount of power is carried away by radiation. If this power is W, then by definition 2TU 2TT
tls |JJ2 0r JJ*'
FORMULAS FOR MUTUAL IMPEDANCE, RADIATION FIELDS ONLY
25
Now there may be other components in the box which dissipate energy. They are not included in Rs.
If we measure the input impedance at the terminals TT when the box is in free space in
Figure 5. Representation of fuze system emit- ting radiation.
the absence of reflectors, the result is Zu. When reflectors are present, the result is Z u as defined previously. The above definition of Rs implies that all the antenna current I flows through Rs , meaning that Rs is in series with I. Likewise the coupled impedance representing the reflec- tor will also be in series with I. The argument upon which equations (21) are based then means that we consider the antenna as equiv- alent to the circuit in Figure 6. Thus ZX1 — Rs + Ra + jX8 and A Z represents the reflected im- pedance. The term Ra represents the ohmic losses in the antenna, which are quite small and will be neglected unless otherwise specified.
When the field relations have been derived, it will then be necessary to determine the response of the antenna to radiation falling upon it. This will be derived with the aid of the reciprocity theorem. The two concepts will serve to solve the fuze problem in so far as pure radiation fields are concerned.
Field Equations for Arbitrary Antenna
We assume a spherical coordinate system, with the origin at the center of the antenna and the antenna lying along the polar axis. The electric field strength E is a vector function of position. If we describe a large imaginary sphere around the antenna, then a plot of the field strength E, on the surface of the sphere, as a function of the polar angle and the azimuth angle <f> is known as the space radiation pat- tern of the antenna. If we normalize the values
of \E\ found around the sphere so that the maximum value is unity, the dependence on 6 and <£ is known as The actual value
of the field strength at any point ( 0,<f> ) on the sphere is given by
\E\ = £0/(W), (26)
where E 0 is the maximum value of \E\ on the surface of the sphere. We assume that /(0,<£) has been determined experimentally (see Sec- tion 2.8) .
Figure 6. Series equivalent circuit of fuze antenna.
The power W radiated through the sphere is obtained by integrating the Poynting vector over the surface of the sphere and is given in mks units by
2jt n
w = r¥o f f p (®**> sin md4, (27)
where
W
Ed2 f2 2Z0
(28)
2tt 7 r
f f r si
sin dddd(t),
and
Z o = V (mAK),
the “intrinsic impedance” of free space, \i and K being the permeability and dielectric constant respectively of free space, or air. The term Z0 = 120t r ohms.
Taking into account equations (26) and (28), we write
E = \ {/(0,4>yM ■ <2”/X)1}, (29)
where l is the wavelength. This expression ig-
SECRET
26
THE RADIATION INTERACTION SYSTEM
nores a possible additive phase shift which may be a function of It will be introduced
when needed.
We may now introduce the concept of gain of an antenna. If we compare two antennas, each of which radiates so as to produce equal values of E0 at a given distance r, then the an- tenna which radiates less power has the greater gain G. An antenna for which the space radi- ation is spherical, i.e., one which radiates equally in all directions, has the lowest possible gain. From equation (28) we see that for two antennas, No. 1 and No. 2, with equal values of E0 at the same value of r
G* _ Wi _ 7i
Gi W 2 72
(30)
For an isotropic radiator y = 4tt. If we arbi- trarily assign this antenna a gain of unity, we have for any antenna
G
4 7T 7 '
(31)
Typical values of G for representative antennas will be found in Figures 21 through 24. Equation (29) may now be transformed:
E = \ - (2"A)1}- (32)
As already indicated, we put
Ra = JJJ2 , (33)
and rewrite equation (32) as
E = 7 ypff- {m^VC -2'rA)}( (34)
where G = |/| e,ut. The factor j correctly re- lates the phase of E to that of h in the case of an elementary dipole. For other antennas, there may still be an additional phase shift, as men- tioned above. This is the final equation relating the field to the antenna and shows the radiation field as a function of position around the fuze antenna. To solve the fuze problem we need to know how this arbitrary antenna responds to fields as a receiver. A discussion of the problem follows.
2 43 Mutual Impedance Between Two Arbitrary Antennas
In the following discussion we assume that the radiation is in the form of plane waves. This in effect means that the absolute value of the field does not vary over the length of the antenna for distances at which we are inter- ested.
We know that a current in one element sets up a voltage in another. These may be coupled by radiation, in which case the radiation field from one antenna carrying current h generates a voltage in the other and we mgy say that the impressed field on an antenna generates a volt- age at its terminals. Since the antenna is a linear circuit element, we can say that the volt- age at its terminals is proportional to the field intensity acting upon it. If this field varies along the antenna, it will be necessary to pick some reference point in space and say that
V = IE, (35)
where E is the value of the field at this refer- ence point and l is a constant of proportion- ality having dimensions of length, usually called the effective length. The term V is the open- circuit voltage at the antenna terminals. It is customary to select the feed point of the an- tenna as the reference point. If this is done, E will then represent the field intensity at this point in space if the antenna is assumed to be absent while the field intensity is determined.
Now consider two arbitrary antennas, No. 1 and No. 3, like those treated in Section 2.4.2, separated by distance r with currents h and /3 at the feed points. Assume that h gives rise to a voltage V3 at the terminals of No. 3 when /3 is zero, and assume that /3 gives rise to a volt- age V1 at the terminals of No. 1 when h = 0. By means of equations (35) and (34) we can write
J' 3 = h -1 yj~] ^ Vi^, <£13) (cos r)jeA 2’rr/X),
(36)
Vi = h £ (cos r)je“
Here we introduce the angle x to take account of any skew relation between the two antennas.
ANALYTICAL FORM OF REFLECTED IMPEDANCE
27
Here fi(613y<f>i3) denotes the value of f(Oy<f>) for antenna No. 1 in the direction joining the fuze and target antennas No. 1 and No. 3 re- spectively, and f3(031y<j>31) has an analogous meaning.
At this point we shall call upon the Rayleigh- Carson reciprocity theorem. The statement of this theorem as given by Carson is as follows :95
“Let an emf E /, inserted in any branch, des- ignated as No. 1, of a transducer, produce a current /2' in any other branch, No. 2; corre- spondingly, let an emf E2" inserted in branch No. 2 produce a current //' in branch No. 1; then I/'E/ — I2'E2".”
A transducer is defined as “a complete trans- mission system which may or may not include a radio link, which has accessible branches, either of which may act as the transmitting branch while the other acts as the receiving branch.”
The theorem of reciprocity applied here means that
F3 Vi „
T = T = Zl3
O 1 3
= lj (COS r )je* ~ 2"A).
(37)
Equations (36) and (37) give
h /i (^13,013) = h °4^3 3 f 3(031, <f>n)j
(38)
or
h _ h
IZqRssGs , f \ Iz0rsiGl { , \
V — 4^ — j 3(031,931) yl — ^ JlWl3,<Pl3;
Thus for any antenna we may write
l
ZqR8G
M+)
= c
(39)
(40)
where C is a constant not involving any of the variables in equation (39). Finally
l = C
(41)
showing that as a receiver the antenna behaves
the same as a transmitter in its dependence on Z0 Rs, G, and
The mutual impedance between two arbitrary antennas can now be expressed. Antenna No. 1 impresses a field on antenna No. 3 as given by equation (34) ; antenna No. 3 receives it with an effective length l3 given by equation (41).
7 V3 GEl CZ0 /~d e> p ri
^13 ~ ~T ~ ~f — — ~A V .ttsi/£S3CriCr3 •
1 1 1 1 4 TTf
/i(013,<M /3(031,03l) (cos r)jej( - 2vr/x\ (42)
If we can evaluate the constant C for any two antennas, we have it for all antennas. In Sec- tion 2.14 it is shown that C has the value (2k/ Z0) . Inserting this into equation (42) gives
Z13 — 2^ a/ RslRssGiG3 fi(du,4>u)
f 3(631, <t>3i) (cos r)jej( “2irr/x). (43)
Equation (43) represents the mutual imped- ance between two arbitrary antennas separated far enough so that the radiation field (1/r term) is the only one of importance.
We have seen in Section 2.3 that the antenna impedance of the fuze in the presence of reflect- ing targets can be represented as the sum of its self-impedance in free space plus terms in- volving mutual impedances Z{j and the self- impedance of the reflectors. Equation (43) gives the analytic form of the mutual imped- ances Zijy if 1 and 3 be replaced by i and j, respectively.
We are now in position to apply this general formula to special cases representing a fuze approaching ground (interacting with its image) or a fuze approaching an airborne tar- get well away from the ground.
2 3 ANALYTICAL FORM OF REFLECTED IMPEDANCE9
The analytic expression equation (43), de- rived in the preceding section, will be applied to three special cases and appropriate working formulas discussed. The general properties of the reflected impedance common to all three cases will then be discussed.
b Bibliographical references pertinent to this section are 1, 13, 16, 17, 22, 27, 51, 53, 93.
secretI
28
THE RADIATION INTERACTION SYSTEM
The general equations for the total antenna impedance of the fuze discussed in Section 2.8.1 were applied to three special cases with the following results :
Case I. Ground Approach.
Z ! = Zn - Z12. (24)
Case II. Airborne Target Far From Ground.
Zx = Zn - (25)
Case 111. Ground Interference Case.
Zx = Zxl - Zx2 - (f13 ~ yu)'. (23)
6 33 — ^34
Each of these equations is of the form
Z\ = Zn — Zr, (44)
where Zv represents the reflected impedance. The vector interpretation of this equation has already been given in Figure 1.
Ground-Approach Equation
A fuze approaching ground, in the absence of other reflectors, is interacting with its image and Zr — Zi2. Furthermore, since antenna No. 2 is the image of antenna No. 1, we see that
Rsl = Rs2)
Gi = G2,
fl (012,012) = f2 (021, 02l),
T = 0,
r = 2h (h = height above ground).
Introducing these relations in equation (43), we have
Zr = Zxx = ^ GR.fi 2 (0,2 ,0,s)je(-*'*A). (45)
Equation (45) gives the detailed form of Zr for approach to a perfectly reflecting ground of large extent. As in equation (29) and sub- sequent equations a possible additive phase shift is ignored. From the results obtained in the case of the perfect reflector, we may ex- trapolate to actual grounds (plane reflectors) by the use of a reflection coefficient n. For pur- poses of these applications, the effective reflec- tion coefficient n for a given surface is defined in such a way that the signal magnitude re-
ceived by a fuze circuit, because of the presence of the surface, is n times the signal that would be received from a perfect reflector in the same position as the actual reflector.
This definition was set up to avoid possible errors in using the reflection coefficients de- rived for plane waves on the classical theory. (The equiphase surfaces of radiation from the fuze antennas have appreciable curvature at the usual distance of interest in fuze applications.) As a matter of fact, however, it has been found that the values of n found according to the above definition agree well with the published values of n based on the plane wave theory and, to the accuracy needed for fuze calculations, are independent of the height above the ground. Additional comments regarding n are to be found in Sections 2.9 and 2.14.
The reflection coefficient n has been measured by moving a fuze over a perfect reflector then over ground and comparing results (see Sec- tion 2.9) .
When the reflection coefficient is included, we have
Zr = l ^ GRs fl2 (0i2,0i2)^(->4^/x). (45a)
Airborne Target Equation For target and fuze a long way from ground
With the aid of equation (43) we get * ■ -&)'■
^Slfis3b?lG?3/l2(013,013)/32(031,03l)CQS2T ^ -j^r/ \ (4Q)
Z33
Equation (46) is limited in its application to cases where the target can be considered as a single antenna with a single feed point. Thus it represents the case for a dipole reflector or a strip of “window.” If the target can be repre- sented as an array of simple antennas, then Z, would involve mutual interaction with the whole family, including terms arising from the mutual interactions between members of the array.
If the target is not made up of linear anten-
SECRET
ANALYTICAL FORM OF REFLECTED IMPEDANCE
29
nas but is a geometric shape capable of excita- tion in a complex manner, equation (46) cannot be used as it stands, since it is obvious that we cannot cut a complicated target arbitrarily and reproduce its complicated current distribution by feeding it at one point.
If we knew the current distribution on the target arising in response to the radiation from the fuze, we might proceed as follows: (1) find the number and location of the feed points nec- essary to reproduce this distribution, (2) deter- mine for the target when excited by
each feed alone, (3) treat each feed with its f as a single antenna, (4) measure the mutual impedance between feed points, and (5) proceed with the general equations (21). For any ordinary target such a process is im- possibly complicated, and we resort to more tractable methods.
Again we assume the fuze and the target to be far enough apart so that we can consider the fuze radiation to consist of plane waves at the target. We then determine the reflecting power A of the target as follows: (1) We irradiate the target with plane waves with a field inten- sity Eif and (2) we measure the field Er reflected back along the direction of the incident radi- ation. If this field Er is measured at distance r from the target, A is defined by
Er = ^4 (47)
The (1/r) dependence of Er is consistent with our initial assumptions concerning the plane waves from the fuze. Note that A has the di- mensions of a length.
For a single linear antenna, it follows from the definition of A that A for such an antenna is given by
A = 2^ G3t/*32 (03i,$3i) cos t. (48)
As an example, consider A for a resonant half- wave reflecting dipole oriented for maximum reflection. In this case Rs 3 = Z33; G3 = 1.64, /32 = 1 cos x = 1, and A3 = 0.26. Typical values of A for other simple reflectors are given in a paper by Mott.93 In particular,
A (sphere) = Ja, where a is the radius of the sphere;
Z/2
A (flat sheet) = — where L 2 is the area of the sheet.
A
We now express Zr in terms of A as defined above with the aid of equation (48) and get,
Zr = A ~ fl.A/i2 (0„,<fos) (cos (50)
For each antenna, x is the angle between the plane of polarization of the incident radiation and the plane formed by r and the axis of the antenna.
If the antenna is a complicated structure, the meaning of A in equation (50) will require modification to include effects of the twisting of polarization of the incident radiation.
In the case of an actual aircraft target it would be necessary to know A at all angles, since the fuze sees a continually varying aspect as it approaches the target. Thus the calcula- tion of Zr by the use of equation (50) would require analytic expression of A as a function of direction toward the fuze.
The necessary information can be achieved in a more expeditious manner. An actual fuze is set up and the target moved past it slowly while the signal in the fuze is recorded. The recorded wave can be reproduced and used directly for testing fuze circuits. Such experi- ments are described in detail in Section 2.11.
To relate these measurements with our cal- culations the strength of the reflection was com- pared with the reflection from a resonant half- wave dipole, which can be computed directly from equation (46), giving
Zr = 0.042^y RalGJ{2 (0,3,<*«i3)e-jW\ (51)
for the dipole orientation which gives maxi- mum reflection.
In general we find that the maximum reflec- tion from the aircraft as it passes the fuze is N times the reflection from a dipole given by equation (51). It has the same dependence upon distance as a dipole for approaches that are not too close. The term N will not be a con- stant for a given target but will depend on A.
From Mott’s paper93 we find that A for a flat sheet of area L2 is L2/A, and A for a dipole is 0.26A. Thus, a sheet of area L2 is the equivalent of N dipoles, where
„ 3.88L2
A2 '
(49)
30
THE RADIATION INTERACTION SYSTEM
With the aid of equation (51) this shows that Zr is independent of \ for the case of a flat sheet.
253 Ground Interference
The general equation covering this case for a fuze and one target is given by equation (23) :
Zi = Zn - Zn - (y13 ~ y“)2. (23)
The detailed treatment of this case for a complicated target is beyond the scope of this report. However, certain general properties can be observed.
The symbol Zr consists of two terms, the first representing the reflection from the ground and the second the reflection from the target, in- cluding the effect of the images. Now, in gen- eral, Z34 is small compared with Z33 ; it will be 10 per cent or less for a dipole if the separation is 4 l or more. Thus we may write Zr as
7 7 , (Zu ~ ZU)2
Zjr ~ Zri2 ~\ ,
^33
with reasonable accuracy in so far as absolute magnitudes are concerned.
When the distance between antennas No. 1 and No. 3 is large compared to the distance between No. 1 and No. 2, |Zi3| is nearly equal to \Z14\ and the effect of the target is compli- cated by phase relations between Z13 and Zi4, giving rise to interference in the reflection which may be quite pronounced. However, when the fuze gets close to the target, or when the distance from fuze to target is much less than the distance between target and ground, Zu and Z12 are small, and the signal is approximately equal to the free-space signal.
The situation is further complicated by the directional properties of target and fuze. In each impedance Zijt f(6,<j>) must be evaluated in the direction (0^,0^) from each antenna.
Any further discussion must be limited to special cases. One particular example is of in- terest. Neglecting directional factors, we com- pare the strength of the reflection from ground with the reflection from a resonant half-wave dipole oriented for maximum reflection to the fuze. We wish to determine at what distance r
from a dipole the reflection is the same as from the ground at distance h.
From equations (51) and (45) \Z12\ = \Z13\ when
0.042^/^ (ft,,*.) = |^/i2 (012, <M.
Now if the radiation pattern of the fuze be such that
fl2 (013,</>13) = /l2 (012,012),
then the signals are equal when r = V 0.52 \h. If X is about 10 ft and h is 10,000 ft, then r = 230 ft.
In the early days of fuze design this limita- tion caused some needless concern. In the first place the reflection from an airplane is of the order of 10 times that from a dipole. In the sec- ond place the radius of action of practical fuzes described in this volume is about 75 ft. In the third place the orientation with respect to the ground and the relative motions involved make the ground signal less important.
Only in special cases where the fuze is used against airborne targets near the ground does the ground reflection become a limitation on fuze operation.
254 Special Considerations of Transverse Antenna Fuze
In the preceding discussion it has been as- sumed that the fuze can be represented by a single antenna. This applies for fuzes using the missile as the antenna. In the cases of fuzes with transverse dipoles as antennas (T-51 and T-82), the expected variations of antenna im- pedance are complicated by the presence of the body of the missile near the fuze antenna. If the transmitter and receiver circuits are not elec- trically and mechanically balanced with respect to the missile, longitudinal currents are excited in it and these radiate energy. As a result there is in effect an additional antenna in the system, and its contribution to the performance of the fuze must be considered. Furthermore, even if perfect balance is obtained, the missile serves as a director or reflector behind the fuze to alter
ANALYTICAL FORM OF REFLECTED IMPEDANCE
31
its sensitivity pattern (see patterns in Section 2.8). We are not here concerned with this latter effect. We are concerned with the results of in- cidental unbalance that arises in the manufac- ture of fuzes.
To study them we idealize the system as two thin antennas arranged at right angles and con- cern ourselves with the reflected impedance Zr when this system approaches the ground. To the extent that we can represent the system by two thin antennas the general arguments of Section 2.8 can be applied.
The arrangement to be considered is shown in Figure 7. «
GROUND PLANE
Figure 7. Representation of transverse dipole and projectile, with their images.
Antenna No. 1 is the fuze antenna. This case was treated in Section 2.3 for another purpose and led to equation (23), which is
Zl = Zn - Zn ~ (y3 ~ |h)2. (52)
Z/33 — Z/34
To interpret this equation we expand and get
Zi = Z 11
Z3 + 2
3 — Z34
ZnZu Z 33 — Z 3.
Z33 — Z 3,
(53)
The first two terms of equation (53) represent the interaction of the T-51 or T-82 fuze with its image in the absence of any vehicle. Zri rep- resents the free-space impedance and Z12 the reflected signal. This has been generally inter- preted as the actual working signal in the T-51 fuze when used. If the balance is perfect, Z13 — 0 and equation (53) reduces to
which shows that even though the projectile is not excited directly by the fuze antenna it nevertheless contributes to Zr. In general ZM is small compared to Z33 and serves to modulate the second-order reflection terms. We will neg- lect it in comparison with Z33 in the remainder of the discussion. Also we may use Z33 and Z4 4 interchangeably, since they are images of each other. The term (Zi42/Z44) represents the re- flection from the image of the projectile as a target for the fuze antenna.
To discuss the problem further we need a co- ordinate system. We choose the z direction as the axis of the missile with x and y axes per- pendicular to it, the x axis being the axis of the transverse dipole. We also choose a as a polar angle. It is the angle between z and the normal to the ground, that is, the striking angle of the projectile referred to the vertical. The term 5 is an azimuth angle measuring the angle be- tween the x axis and the plane including the axis of the projectile and the normal to the ground (plane of incidence). To estimate the order of magnitude of this effect we shall make the further assumption that antenna No. 3, representing the projectile, is a resonant half-wave antenna. We shall also consider the radiation pattern of such an antenna to be f(0) — sin 6, when 0 has the meaning pre- viously assigned ; this is a good enough approx- imation to the true pattern for this argument.
The field components from the x-axis dipole will be
Er = 0,
Ea = ki cos a cos 8, (55)
E 8 = ki sin 8,
where
*1 = 7 A. (56)
The component Ea will be in the vertical plane containing antenna No. 4 and will give rise to a voltage in it. The term E& will always be per- pendicular to the plane and will produce no voltage in antenna No. 4. Thus Z44 will be
„ _ Eg U
•£14 — j ,
Z\ — Zn — Z12 — ~ 14 7 , (54)
Z/33 — Zj 34
h
h
U COS a COS
5,
(57)
SECRET
32
THE RADIATION INTERACTION SYSTEM
or
. 2A IRsiGi RsaGi .
Z 14 1 = — ^ — -j— cos a COS o sin a. (08)
We then find
4A2 RsiGiGa •> s • 9 /-n\
/ r cos- a cos- 5 sin- a. (o9) r2 (4tt)2
when we assume the projectile is resonant, so that Rs 4 = Z44. This will give rise to a change (Z,.)4 1 in antenna impedance in antenna No. 1 given by
= RsiGiGa cos2 a cos2 5 sin2 «. 47 rr
(60)
We compare this with the so-called normal im- pedance change
i Zu\ = RsiGi (1 — sin2 a cos2 5). (61)
27rr
The worst case we will be interested in will be 8 = 0, a = 45 degrees, and
|Zl2I = 2 VrR,lGl>’ (62)
l(Zr)i\ = R,iGiGi. (63)
The signals arising from Z12 and (Zr)4 will have an unknown phase relation depending
upon striking angle and the size of the pro-
jectile. We consider the worst cases where they may be in or out of phase. The interference will change the response by the ratio
(A/47rr) G, ± (\2/167rV2) G1G4 1 . 0.13A
(X/4irr) G1 1 ± “• (64)
For heights of operation of r = 10A (that is, h = 5A) the maximum change in reflected sig- nal will be approximately ±1.3 per cent. For other angles a < 45 degrees, 8 0 degrees, the
correction will be less, being 0 for 8 = 90 de- grees and all values of a.
We thus conclude that the variations in height of burst from the source are small for a per- fectly balanced transverse antenna.
A greater source of error is the unpredictable value of 8. For a = 45 degrees the reflected sig- nal changes from 1 to % as 8 varies from 90 to 0 degrees.
We now turn our attention to the correction
arising when the antenna is not perfectly bal- anced. In this case Z13 ^ 0. There will be two terms of interest.
|
4 - Zl*2 Z 33 ' |
(65) |
|
D 2ZuZu B = 7 • " 33 |
(66) |
The term A is a fixed term independent of r or h and shows merely the amount of reflected impedance in antenna No. 1 by virtue of its ex- citation of antenna No. 3 by some unbalance. This term, being constant, will give rise to no signals. It is merely a measure of the coupling between antenna No. 1 and antenna No. 3.
The term B gives rise to an additional signal. As before we will consider only absolute values and disregard relative phases, since the abso- lute values will indicate the maximum value of the corrections that may arise.
To estimate the coupling we note that IiZ14 represents the free-space voltage at antenna No. 1. If Z13 is small we can say also that hZls represents the voltage coupled into antenna No. 3. We define k by the relation
|
7 \Z\ 3 |
Z 13 |
|
|
IiZu |
zli |
Experiments have shown that k is of the order 0.01 for well-balanced fuzes and may be as large as 0.1 for very poor balance, so poor in fact that the arrangement would never be used. These values are based upon the center point of the parasitic antenna as the reference point.
Now 'Zn | is about 300 ohms and |Z33j >73 ohms. Hence |Z13| is approximately 3 ohms and
|
1 B |
JX3 |
Z14 |
— ft nor pont rvf |
Zi4 |
|
I Z\2 |
- 73 |
Z12 |
O Lcll t DI |
Z 12 |
For all angles of approach that are of interest |Zi4j < Z12 1 so that the correction is less than 10 per cent. If the unbalance becomes large this correction becomes sizable and can lead to a considerable change in function height. In most cases the projectile is nonresonant and |Z33| is considerably greater than 73 ohms. Thus inci- dental unbalance is not so important when the projectile is nonresonant. When resonance is approached the response becomes critical to unbalance as has been experimentally observed.
SECR
ANALYTICAL FORM OF REFLECTED IMPEDANCE
33
2,5 5 General Properties of the Reflected Impedance
We are primarily interested in the two basic equations, the ground-approach equation and the airborne-target equation. We repeat them here for convenience.
47 rh
GJts.Pidn, *12)
(ground approach) , (45)
and
RsiG&i* (013, *18) (cos T)e-**'A
Z7rrz
(airborne target), (50)
or in alternative form for a linear antenna re- flector
(cos2
Zaa
(46)
It should be remembered that the phase factor should carry an undetermined constant phase shift, related to the antenna properties of tar- get and fuze.
f2 (0,*) . Thus the radiation patterns become characteristic of a given vehicle, and Rs can be adjusted to match the transmitter properly with the assurance that Rs will have little effect on Zr/Rs.
A particular example is most enlightening. For antennas whose length lies in the range 0 X/2, G varies from 1.5 to 1.64, about a 10
per cent change. The term /2(0,c/>) in the worst direction only differs by 15 per cent in the two extreme cases. Thus the quantity Zr/Rs is practically independent of antenna length in this range. On the other hand, Rs varies from 73 ohms for a half-wave antenna to zero [as (LA)2] for short antennas, where L is the length of the short antenna. We can thus state generally that all fuzes, whose re- sponse to a fixed value of (Zr/Rs) is the same, will have practically the same response to a given target no matter what the length of the fuze antenna is, provided it is considerably less than a half-wave long. The statement is also true for all loop antennas whose dimensions are small compared with l.
For longer antennas /2(0,*) is sensitive to l, and each must be considered as a special case.
Doppler Frequency
As seen in Section 2.2 the phase has a fre- quency F = (2v/l), if | ( dh/dt ) | or j ( dr/dt ) j be replaced by v. This is identically the doppler frequency.
Dependence upon Rs
Let us write Rs for Rs i. We note that Zr is proportional to Rs, as would be expected, since it is the power dissipated in Rs that accounts for the radiation fields which make the inter- action possible.
It will be observed in a later section that the dimensionless quantity (Zr/Rs) is most con- venient for assessing fuze circuit response. It exhibits the effect of a reflector as a fractional change in antenna impedance which depends only upon the nature of the target and the directive properties of the fuze antenna (which are relatively independent of Rs).
It has been found experimentally that small changes in the antenna feed point can change Rg over a wide range with almost no effect on
Dependance on Distance
The magnitude of (Zr/RJ depends upon the distance through the dimensionless ratio r/l or h/l. This means that 1 is a scale factor in determining fuze performance. Response to the presence of a target is determined by the number of wavelengths in the distance to the target; thus, for example, the signal received from ground reflection at a given height is greater for greater a.
Dependence on Direction to Target : Definition of Directivity
The size of Zr/Rs is proportional to Gi/i2 (0i3, *13). Now Gi is a constant for a given fuze so that /i2(0,*) tells how well a fuze “sees” targets in various directions. The term /i2(0,*) is the power radiation pattern of the fuze antenna ; it is called the directivity pattern in this report. A plot of /2(0,</>) will show (other things being equal) the distance at which a fuze will function upon approach to a target.
SECRET
34
THE RADIATION INTERACTION SYSTEM
Now it will be observed that
GJiKtaju) = Wu _ F(ei3,<t>n), (67)
47T W
where JE13 is the power radiated per unit solid angle in the direction (^13,^13) and W is the total power radiated. Thus F(0i3,<£i3) repre- sents the fraction of the total power radiated per unit solid angle in the direction (#13, <£13) • Thus f2 (Ois,<fnz) is an indication of how effi- ciently the total radiated power is used.
Typical directivity patterns are described in Section 2.8.
Independence of Power Level
It is clear, as was anticipated in Section 2.2, that Zr/Rs does not depend upon the power level at which the fuze radiates.
26 CIRCUIT RESPONSE TO ANTENNA IMPEDANCE MODULATION
Series and Parallel Expressions for (Zt/Rs)
Differential Signals
The foregoing analysis has been based upon the concept of series antenna resistance and re- actance. In actual cases, however, it is often more convenient to deal with the equivalent parallel quantities. We therefore proceed to de- rive expressions for the changes in parallel antenna resistance and reactance due to a re- flector.
We deal with the two circuits in Figure 8. The terms and \X8, or \XV and A Rp, are the changes in antenna resistance and reactance resulting from the presence of a reflector; Rp and Xp, or R8 and XH, are the free-space values.
It is easily shown that in the absence of the incremental quantities we have
RP
X
V
Rs 2 + X82 Rs 9
Rs 2 + X*2 X8 '
(68)
(69)
consider the differentials of Rp and Xp as equiv- alent to their increments.
Then
dR„ = || (RS - X,2) + Jr (2 S,R,), (70)
and
dXp = dR, + ~s (X,2 - R?). (71)
By defining Q = X8/Rs and by appropriate manipulation we find
dRp _ dRs (1 - Q2\ dXs (2 Q \
' Rp ~ Rs\ 1 + Q2) ^ Rs \l + Q2)’ V ; and
dXp 1 r dRs • 2Q dXs(Q* - 1)1 ,
Q [^(1 + Q2) RS(Q2 + 1) J*
Now as we have seen, dRs and dXs are the components of a vector Zr which may be writ- ten as
Zr = \Zr\e*, a = (74)
where x represents the distance r or h from fuze to target. The term 8 depends on the par-
SERIES CIRCUIT PARALLEL CIRCUIT
Figure 8. Series and parallel equivalent fuze circuits.
ticular case being discussed, but is unimportant for our present purposes. It will be found con- venient to use the dimensionless ratio ( Zr/Rs ) which we define as a new vector M and write
M= M 0eja,
where
For small increments of impedance we may
(75)
CIRCUIT RESPONSE TO ANTENNA IMPEDANCE MODULATION
35
If we define an auxiliary angle (3 by the relations 1 - Q2
sm 0 =
cosjS =
1 + Qv
2 Q
l + Qr
We can rewrite equations (72) and (73) as
TT2 = M 0 sin (a - /»),
xL p
dX p M o / Q\ T7 “ -Q cos (a -
(76)
(77)
For purposes of convenience, it may be de- sirable at times to work in terms of the admit- tance Y, which is defined through the relation
Y =
Y =
Rs + jX.’ Rs
Rs2 + Xs2
Y = G — jB,
Xs
Rs2 + Xs2’
(78)
where the conductance G and susceptance B are seen to be
G =
B =
Rt
Rs2 + X*2’ X,
(79)
Rs2 + XX
From equations (68) and (69) it is seen that
conductor, the impedance Zr becomes a sizable fraction of Rs. We need expressions for the cor- rections that may be needed in interpreting such tests. By replacing Rs by ( Rs + A#s) and Xs by ( Ms -f- AXS) in equations (68) and (69), we get
it = r+i„cosa[MoSin(a +/3) + rriXf“2}
(82)
it = . ~ Mo . [gM«c°B(«+0 + rtwM
1 + -Q-sina L
(83)
It will be observed that these equations re- duce to the differential forms when M0 is small enough. For larger signals the equations indi- cate the presence of a “d-c shift” which is small when Q is large. They also show that equation (76) is in error by a fraction equal to M0 even for very large Q. Thus in tests where M0 is 10 per cent the field measurements are accurate to 10 per cent and can be corrected if desired. Some caution must be used in applying equa- tions (82) and (83) to an actual case since in- duction fields will also contribute to Zr at about the same separation that leads to large M0.
However, in most fuze applications M0 is about 0.5 per cent, and the differential forms have ample accuracy.
|
and |
G = k |
(80) |
|
|
II Q3 |
|||
|
Therefore |
dG |
dRp |
|
|
and |
G |
RP |
(81) |
|
dB |
dXp |
||
|
B |
Xpm |
||
|
Finite Signals |
It will be observed later in the chapter that the actual working signals when the fuze is operating normally are so small that the differ- ential representation given above is completely adequate. However, when tests are made on the fuze by measuring its response close to a large
Specification of Fuze Circuit Parameters
It has been shown that both the resistive and reactive components of the antenna are altered by the presence of a reflector. To make a work- ing fuze it will be necessary to devise a circuit which will respond in some manner to the change in antenna impedance. Such circuits are described in detail in Chapter 3.
For purposes of further analysis we assume that the voltage or current in some part of the fuze circuit changes in response to the antenna variations and that this change is used to actu- ate the fuze. We will call this particular fuze parameter V, representing a voltage, although it might as well represent a current. In order to continue the discussion of the antenna prob-
36
THE RADIATION INTERACTION SYSTEM
lem, we assume that the behavior of the circuit is known and that
V = f (In Rs, In X8) = g (In Rp, In Xp), (84)
where for purposes of convenience we express the functional relationship in terms of the natu- ral logarithm of the impedance components. Thus
(85)
We define
o _ ^ c SV
p d In Rp ’ s ~ d In Rs'
T = dV • T - dV
p d In Xp’ s ~ d In AY
(86)
The quantities Sp, Tp or their corresponding transforms Ss, Ts describe the behavior of the fuze circuit when the antenna impedance varies. Ss and Sp are called the series and parallel re- sistance sensitivities respectively and Ts, Tp are called reactance sensitivities in a similar man- ner. All four quantities are functions of X8, Rs or Xp , Rp which make up the free-space input impedance Z0 of the antenna. In Chapter 3 the values of these quantities for typical circuits will be derived.
With the aid of the definitions of equation (86) we may write
dV
dV
dV
dV
r» dR s . rp dX s
^ Ts X?
or dR p „ dX p
u ' 1 p y ’
n p p
T
M o (Ss cos ^ sin a) ,
(87)
o[sp sin (a
Tp _
688)
Mo | Sp sin (a + 0) + ^ cos (a + /S) J.
If we make use of the complex notation and always consider dV to be the real part of a cor- responding complex quantity, we may write
dV = MS = MoS0eX° ~ *>,
where
*-(*•- if)
(89)
S = ^.Spsin/3 - “cos0^ - j^S pcos0 - ^sin/3^:
(90)
(91)
tan 7)
T 2QSP - ^ (1 - Q2) QSs = Sp (1 - Q2) + 2 Tp '
(92)
The appearance of the terms TJQ and Tp/Q in equations (91) suggests redefinitions of Ts and Tp to include Q. This can be done (see Chapter 3), but Ts and Tp so defined will then not have the logarithmic form commonly used for Ss and Sp. We keep the Q to maintain sym- metry with the commonly accepted notation.
Since we are dealing with different mathe- matical representations of the same antenna the voltage change dV will be the same no mat- ter which representation is used. This was im- plicit in equation (89).
The basic equation (89) represents in simple form the response of the fuze circuit to a mov- ing target. While q is a fixed quantity for any given fuze, a (=r —4? tx/\ -f- 8) varies with fuze- target separation and therefore with time. The voltage change is seen to be proportional to M0 and to S0, the r-f sensitivity. If the fuze has re- actance sensitivity as well as resistance sensi- tivity, both contribute to S0 and give rise to a phase shift r\ in the voltage wave dV. By a proper selection of antenna coupling, it is often possible to operate near a resonance of the driving circuit, whereupon Tp approaches zero and there is little or no phase shift q.
Inasmuch as dV is proportional to M0, a space plot of the variation of antenna imped- ance will likewise be a space plot of the varia- tion of output voltage. This is a most impor- tant point to remember. For it means that the voltage out of the r-f system can be plotted point by point for a slow relative motion of fuze and target to give detailed information on the performance in rapid motion. All that need be changed is the time scale ; the fuze an- tenna goes through its sequence of variations in whatever time is required for the fuze to move through the region of influence, and the wave form will be identical in every case. This as-
ANTENNA IMPEDANCE
37
sumes, of course, that the circuit is capable of following the time variations, which experi- ence has shown is no restriction.
The space variation of M which gives the voltage variation has been called the M wave and is so referred to in the discussion which follows. Extensive use is made of point-by-point plots of the M wave in testing fuzes.
We note that S may be measured as dictated by convenience in terms of either series or parallel components, and that the complex form of S is completely specified by either set of measurements, as shown by equations (89), (90), and (91). In many cases Ts/QSs and Tp/QSp are small compared with unity, so that
Ss = — Sp = zSzSq = ±|*S|.
In any case the basic equation (89) which represents the situation is
dV = MS = M0S0eK«-'K
We apply this to the two special cases in which we are interested.
For the ground-approach case we have, uti- lizing equation (45a),
M = Si, G^e^e’a- (03)
For the airborne target we have from equa- tion (50) #
M = (cos r)e/a. (94)
Subscripts previously used in connection with A, G, /, 0, and $ will no longer be carried ex- cept in cases where there may exist a possibility of misunderstanding.
2 7 ANTENNA IMPEDANCE0
The previous section has shown that a knowl- edge of the components of Zxu the free-space antenna impedance, is essential if circuit re- sponse to the reflected impedance arising from reflection is to be predicted. This section is con- cerned with the values of antenna resistance and reactance observed in actual cases.
c The following bibliographical references are perti- nent to this section: 6, 8, 11, 28, 30-34, 37, 38, 49, 50, 52, 54-60, 62-67, 69.
Specifically the resistance and reactance sen- sitivities of the fuze circuit are functions of ( XS,RJ or (XV,RV) and must be evaluated at the particular operating point characteristic of the particular antenna used. Since the various missile-antenna combinations present widely different impedances, it becomes necessary to measure, or in some cases to calculate, the sen- sitivity parameters for a given circuit over a large range of load impedance, so that the an- tenna can be designed to have an operating point as near as possible to the optimum point for circuit response. It should be pointed out here that there are limitations to the antenna impedance that can be achieved within the limits set by the tactical situation and by speci- fied military characteristics. Likewise the val- ues of S can be changed by circuit design only, within certain limits set by present-day vacuum tubes. Thus antenna design must be coordi- nated with circuit design to give optimum per- formance within the limits of both. In addition it is necessary to set up dummy antennas for testing fuzes. A knowledge of actual antenna impedance is essential here also. In this section we are concerned with the antenna impedances that can be effectively achieved. Chapter 3 will give details about the circuit performance under the load and load variations presented by the antenna.
2-71 Specification of Antenna Terminals
In all the previous discussion the fuze an- tenna has been treated as a two-terminal box which sends out radiation. No detailed knowl- edge of the internal circuit was assumed. We imagine this antenna to be connected to a circuit whose sensitivity is specified. Now when the whole is connected together, a given reflec- tor in space sets up a certain A V in the r-f circuit. Once the whole arrangement is con- nected, the antenna terminals lose their iden- tity and their location becomes arbitrary. Thus if we open the arrangement at any two points (see Figure 9) and call everything on one side of the cut the fuze circuit and everything on the other side the antenna, the values of Xv, Rp and Sp and T}) must be so related that the value
SECRET
38
THE RADIATION INTERACTION SYSTEM
of AF calculated by their use is independent of the particular pair of points selected as an- tenna terminals.
Thus in specifying fuze performance or an- tenna performance we are at liberty to select any two terminals within the network as an- tenna terminals. It has been customary in vari- able-time [VT] fuze work to consider all the circuit elements inside the fuze electronic as the fuze circuit, even if the assembly contained some antenna impedance matching network, and consider the points where the leads from this circuit are connected to the external radi-
"I
III
□
TARGET
Figure 9. Arbitrary division into fuze circuit and antenna.
ating system as the antenna terminals. The dis- cussion of the antenna problem has assumed that the only ohmic losses in the antenna are radiation losses. Experiments have shown this to be a valid assumption with the antenna ter- minals just specified. If some other pair of points is selected so that some energy-absorb- ing coupling elements are included in the net- work, due account must be taken of these losses.
2 7 2 Experimental Measurement of RP
The parallel radiation resistance Rp is meas- ured by a substitution method. A typical fuze circuit is used as an indicator. In the fuze circuit several quantities, such as diode voltage V d or oscillator grid voltage Eg, oscillator plate current Ip, and carrier frequency /, are all func- tions of (Xp,Rp). The fuze is first placed on the projectile on a high stand and the free-space values Vd or Eg, Ip, and / noted. The fuze is then removed from the projectile and placed in a shield box. Reactance and resistance are added to the antenna terminals until the free- space values are duplicated. It is assumed that the shield box does not load the fuze at all, so that the amount of resistance across the ter-
minals when the load is duplicated repre- sents Rp.
In making this measurement the exciting cap or bars are often not removed. The resistors are merely substituted across the points that have been previously agreed upon as the an- tenna terminals. The shield adds reactance to the antenna so that direct measurements of Xp are not obtained this way.
To show that the shield does not introduce serious losses, the whole antenna is removed from the fuze and resistors substituted directly across the fuze terminals. The size of the ar- rangement is so small compared to X that radia- tion is negligible and the substituted resistance represents Rp . By such tests it has been shown that shield losses are negligible, so that the more convenient shield box can be used where desired. In making this comparison test it is necessary to remove dielectric insulators so that losses in them do not confuse the measure- ments.
In the case of fuzes which use the projectile as the antenna, the radiation load is removed by putting a shield can over the nose fuze, as shown in Figure 10. Such an arrangement re- places radiating currents in the antenna by nonradiating currents inside the shield can and thus substitutes can losses for antenna losses in measuring Rp. If both are small compared with the true radiation losses, this substitution causes negligible error. The final proof that the errors are negligible is obtained by making a pole test (see Section 2.12) and comparing actual signal with calculated signal based upon
SHIELD BOX
Figure 10. Method of removing radiation load without removing projectile.
the measured values of Rp and Sp. Within an ex- perimental error of less than 10 per cent there is agreement.
It is interesting to note here that the absolute ohmic value of the substitution resistors used for the measurement of Rp need not be known.
SECRET
ANTENNA IMPEDANCE
39
Since M is proportional to dRp/Rp, only ratios of resistances are needed, and any set of resis- tors whose r-f resistance is a constant fraction of the d-c resistance may be used. It has been found that International Resistance Company [IRC] type F-l or F-% resistors fulfill this requirement; in fact their r-f values are quite close to their d-c values. However, if it is of importance to know the power radiated, as is the case in jamming calculations, the true value of the r-f resistance must be known. It has been customary for all collaborating lab- oratories to use equivalent sets of r-f resistors supplied by a central laboratory.
2 7-3 Specification of Xp
The quantity Tp/QSp appearing in equation (91) is in many cases so small that it can be neglected, as has already been mentioned. To see this, the value of TP/QSP at the operating point must be evaluated, a procedure which re- quires knowledge of Xp. The question immedi- ately arises: Is the total apparent reactance across the antenna terminals the correct value of Xp, or should we use only the part that appears by virtue of radiation? The argument above about specification of antenna terminals implies that either arrangement should give the same answer. The r-f section of the fuze can be represented in block diagram as in Fig- ure 9. The target in space gives rise to a cer- tain XV out of the terminals to the audio-con- trol circuit. We are at liberty to divide the whole arrangement at any convenient place by a line xx and call the left part the fuze and the right part the antenna. If the calculations are performed properly, the result must be the same no matter where xx is chosen. We choose to put the fixed part of the antenna reactance to the right of xx and call it a part of the an- tenna. Similarly, if there are dielectric losses in the antenna mounting, we can assume them to be represented as a resistance across the antenna terminals and put it to the left of xx as a part of the fuze circuit. This is the adopted convention. As a matter of fact we can, if we desire, divide the Xp any way we choose be- tween fuze circuit and antenna.
To illustrate the point we show that the quan- tity Tp/Q is independent of how Xp is defined
Suppose
dV
dXp’
(95)
This does not Then
X,
2 xfC9
affect the generality of the result.
dV = dV dCp dX p dC p dX p
and
Tp = XI dV_ = -1
Q Rp dXp fRp dC p
(96)
(97)
which shows that Tp/Q is independent of how Cp is defined.
2 7,4 Measurement of Xp
In the following discussion Xp is considered as the total reactance across the antenna ter- minals. The term Xp is measured by a direct substitution method. The fuze is mounted on a missile, and values of Vd or Eg, Ip, and / are recorded. The fuze is then removed from the vehicle and the circuit disconnected from the antenna at the previously selected terminals. Resistors and condensers are placed across the terminals until Vd, Ip, Eg , and / are duplicated, thus duplicating Rp and Xp. For all fuze designs now used Xp is capacitative. To a good approxi- mation Xp is the capacity across the antenna terminals as measured by low-frequency meth- ods. This is shown by the fact that Xp varies only slightly with projectile size.31
2.7.5 Effect of Feed Geometry
upon Rp and Xp
Figure 11 shows the effect upon Rp of chang- ing the size of the exciting ring on the T-50 type of fuze, with the spacing from ring to ground held constant at 1 in. Results are shown for several bombs, two carrier frequencies (White and Brown) for ring lengths ranging
40
THE RADIATION INTERACTION SYSTEM
from 14 to 3 in. As expected, an increase in ring length decreases Rp.
The effect of ring length upon Cp is shown in Figures 12 and 13 for Brown and White fre-
Figure 11. Rp as function of ring size; BRLG- type fuze; gap width, 1 in.; solid lines, Brown frequency; broken lines, White frequency; curves 1, M-30 100-lb bomb; curves 3, M-64 500-lb bomb; curves 4, M-65 1,000-lb bomb; curves 5, M-66 2,000-lb bomb; curves 6, M-81 260-lb bomb.
quencies respectively, with a constant gap size of 1 in. In Figures 12 and 13 the capacity is shown as 6.9 ppf for all the bombs, for a ring length of 1 in. This is not precisely correct, as capacities associated with the various projec- tiles vary somewhat; the curves are meant to indicate the variation of the capacity with ring size. The value 6.9 ppf is not far from correct, however; for all the bombs, the true range of values at the 1-in. point is about 6.9 ± 0.5 qpf. An increase in ring length increases Cp.
The effect of gap size upon Rp and Cv is shown in Figure 14. The size of the gap in the range shown (spacings from 1/2 to 1 in.) has
virtually no effect upon Rp. The term Cp, of course, decreases as the spacing is increased. It thus becomes possible, within the limitations of space requirements, to vary the gap size to bring Cp to a favorable value without affect- ing Rp.
In the case of transverse center-fed dipoles (T-51, T-82) Cp is increased by increasing the size of the dipoles or by reducing their separa- tion. The term Rp decreases when the size of the dipole is increased While it is an
advantage to get lower Rp by using longer dipoles, air resistance and operational difficul-
1/4 1/21 2 3
RING SIZE (INCHES)
Figure 12. CP as function of ring size; BRLG- type fuze; gap width, 1-in.; Brown frequency; curve 1, M-30 100-lb bomb; curve 3, M-64 500-lb bomb; curve 4, M-65 1,000-lb bomb; curve 5, M-66 2,000-lb bomb; curve 6, M-81 260-lb bomb.
ties increase with increasing length, and these considerations serve to limit the length of an- tenna which may be used. Electric efficiency must be subordinated in this design.
SECRET
ANTENNA IMPEDANCE
41
Typical Values of Rp and Xp
Figure 15 shows the value of Rp as a function of carrier frequency for several common bombs using a standard T-50 ring; the feed must be specified since Rp depends on it. The large range of values for all bombs at any one fre-
RING SIZE (INCHES)
Figure 13. CP as function of ring size; BRLG- type fuze; gap width, 1 in.; White frequency; curve 1, M-30 100-lb bomb; curve 3, M-64 500- lb bomb; curve 4, M-65 1,000-lb bomb; curve 5, M-66 2,000-lb bomb; curve 6, M-81 260-lb bomb.
quency illustrates clearly the difficulty of de- signing a single fuze which will work on all bombs. It was for this reason among others that the T-51 type transverse antenna fuze was designed. The T-51 with its independent an- tenna has radiation resistance relatively inde- pendent of projectile size.
The logarithmic spread in Rp among the vehicles tends to decrease as the frequency is lowered, The mean value of Rp increases. Until recently, as shown in the next chapter, it was
1/2 5/8 3/4 7/8 I
S PACING - RING TO BASE OF CAP (INCHES)
Figure 14. Effect of gap size upon RP and CP ; BRLG-type fuze; M-65 1,000-lb bomb; White frequency.
not feasible to operate fuze circuits into a mean value of Rp as high as 40,000 ohms. The im- proved reaction grid detector [RGD] circuit
B-35 BH5 B+5 W-IO W+IO W+30
FREQUENCY
Figure 15. RP as function of carrier frequency; T-50 ring; curve 1, M-30 100-lb bomb; curve 2, M-57 250-lb bomb; curve 3, M-64 500-lb bomb; curve 4, M-65 1,000-lb bomb; curve 5, M-66 2,000- lb bomb; curve 6, M-81 260-lb bomb.
(SWHOI
42
THE RADIATION INTERACTION SYSTEM
5" HVAR
Figure 16. Scale outline drawings of a number of missiles for which VT fuzes were designed. Fuzes with longitudinal excitation were designed for all missiles shown. Transverse antenna fuzes were also designed for bombs. To show the relative size of fuze and missile, the outline of the fuze is shaded.
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DIRECTIVITY PATTERNS
43
described in Section 3.1 makes it possible to use one frequency for a large number of projec- tiles by allowing operation at a high value of Rp.
Complete tables of Rp and Xp are not avail- able for all projectiles. Table 1 gives the values at important frequencies for fuze projectile combinations of current interest. The range of missile sizes for which fuzes were designed is illustrated in Figure 16. Photographs of typical fuze and missile combinations are shown in Figure 7 of Chapter 1.
Table 1. Typical values of Rp and Xp for various fuze-projectile combinations.
|
Fuze type |
Projectile |
Carrier frequency |
RP (ohms, ap- prox.) |
(ohms, ap- prox.) |
|
T-91 |
M-30 bomb (100-lb GP) |
Brown |
20,000 |
300 |
|
T-91 |
M-66 bomb (2,000-lb GP) |
Brown |
40,000 |
300 |
|
T-92 |
M-64 bomb (500-lb GP) |
White |
11,000 |
200 |
|
T-92 |
M-65 bomb (1,000-lb GP) |
White |
10,000 |
200 |
|
T-132 |
M-43 mortar with M-56 tail |
White + 20 |
20,000 |
150 |
|
T-132 |
M-56 mortar |
White + 20 |
6,000 |
150 |
|
T-171 |
M-43 mortar with M-56 tail |
Brown |
90,000 |
300 |
|
T-171 |
M-56 mortar |
Brown |
60,000 |
150 |
|
M-166 |
White + 35 |
150,000 |
600 |
|
|
T-2005 |
HVAR rocket |
Brown |
3,800 |
150 |
|
AR 5-in. rocket |
Brown |
3,600 |
150 |
|
|
T-5, T-6 |
M-8,4|-in. rocket |
White + 30 |
8,000 |
300 |
28 DIRECTIVITY PATTERNSd
We come now to a more detailed study of the properties of /2(0,<£), the power radiation pattern or directivity pattern. The importance of /2(0,0 ) was indicated in Section 2.5 above, where it was shown that the reflected impedance Zr, due to an object situated in a direction (0i3><£i3) relative to the fuze, is proportional to fi (013,013). Furthermore, the gain G is a func- tion of
d Bibliographical references pertinent to this section are 6, 8, 36, 40, 47, 50, 52, 54-60, 62, 63, 64, 68.
281 Measurement of Directivity Patterns Experimental Setup
The simple convenient method which has been devised for the measurement of directivity patterns may be understood with the help of the photographs in Figures 17, 18, and 19. In Figure 17 the antenna, which consists in this case of the projectile plus the fuze in its nose, is mounted horizontally on a platform about 15 ft above the ground. The platform is free to rotate about a vertical axis (Figures 18 and 19). The receiver (Figure 17), consisting of a dipole antenna feeding a detector, is situated about 150 ft from the transmitter. Power is fed to the transmitting antenna by means of a care- fully choked line coming from the power supply on the ground. The line is attached to the an- tenna at a voltage node. The whole setup is situated in an open field. The radiating antenna can be rotated through any angle and the re- ceiver signal plotted as a function of this angle. The plate supply of the transmitting oscillator is based upon an a-c source of 60 c. Full-wave rectification with no filtering is used; there is thus a plate modulation frequency of 120 c which can be detected at the receiver.
In the type of fuze antenna shown in the photograph, the directivity pattern has cylin- drical symmetry because of the symmetry of the projectile. In such a case the directivity has no dependence upon 0, and the pattern may be represented analytically as /2(0). The angle of rotation about a vertical axis is then equal to 6 ; when the nose points directly at the receiver ^ = 0°. The detector used is of the square law variety, so that the audio signal is directly pro- portional to the square of the field strength or to f2(0).
Where cylindrical symmetry is not present, the pattern must be taken in several planes to get a reasonably complete set of values for f2 (0,0) . Such asymmetry may occur when the antenna is separate from the bomb, as in the T-51 and T-82 type designs, the bomb acting as a parasitic reflector or director.
Detector Circuit
Some notes may be added concerning the de-
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:ET|
44
THE RADIATION INTERACTION SYSTEM
tector circuit, shown in Figure 20. The circuit and physical layout are symmetrical, with a view to obtaining balance with respect to ground. This has the effect of minimizing the effect of any vertically polarized components of the field caused by reflection from the ground, which otherwise could alter the apparent shape
Figure 17. Field setup for obtaining directivity patterns.
of the directivity pattern, especially affecting the symmetry of the patterns.
The r-f chokes are for the purpose of reduc- ing interference from transmitters operating in or around the broadcast region. These chokes have a high impedance at the carrier frequen- cies used in fuze antennas but a low impedance at lower frequencies. The coupling condensers
vacuum-tube voltmeter, preceded if necessary by an amplifier.
The output of the detector follows quite accu- rately a square law for outputs up to 100 mv.
Figure 19. Platform of Figure 18 shown lowered to ground.
The output may be kept below this level by adjusting the power supply feeding the trans- mitting antenna.
Figure 18. Rotatable platform holding fuzed bomb for directivity pattern measurements.
Reflections from Ground
The reflections from the ground contribute to the output of the detector and therefore may
in the grid circuits prevent the grids from being shorted by the chokes at direct current. The condenser from the plates to ground serves as an r-f by-pass; it has a high impedance to audio frequencies.
The audio output is fed to a Ballantine-type
Figure 20. Detector circuit; components are enclosed in metal box mounted between arms of receiving dipole.
change the apparent directivity pattern. This matter has been studied and is presented in some detail as supplementary material in Sec-
DIRECTIVITY PATTERNS
45
tion 2.15, where it is shown that the ground reflection introduces negligible error for the simple radiation patterns now used.
By means of the equipment described above a large number of directivity patterns have been obtained. The patterns fall into two classes: (1) patterns for fuzes which use the projectile as the antenna (longitudinal excita- tion), and (2) patterns for fuzes which use a separate antenna such as a short transverse
Figure 21. Directivity pattern for M-64 bomb at B — 16; longitudinal excitation; G = 1.55.
dipole or loop (transverse excitation). The pat- terns will be discussed according to this classi- fication.
Longitudinal Excitation Typical Patterns
In longitudinal excitation the fuze proper is connected to the projectile at one end. The an- tenna, consisting of fuze and projectile, is split by an insulator near the end for the purpose of feeding energy to it. The exact position and size of the gap over the range used, while im- portant in determining the antenna impedance, have little effect upon the pattern. Therefore it will not be necessary to specify the feed exactly
in describing the patterns for longitudinal ex- citation.
A preliminary idea of the character of the patterns may be obtained from Figures 21, 22, and 23. These show the directivity patterns f2(6) plotted versus 0 on polar coordinate paper; for these antennas, the directivity pat- tern is not a function of <£, cylindrical symme- try being present. Figures 21, 22, and 23, for a 500-lb GP bomb (M-64) at three carrier fre-
Figure 22. Directivity pattern for M-64 bomb at B -f- 15; longitudinal excitation; G = 1.9.
quencies, demonstrate the effect of changing the frequency. As the carrier frequency is raised, which means the antenna becomes elec- trically longer, the pattern departs more and more from the simple sin 6 pattern of an ele- mentary dipole (shown in Figure 24). The minor lobes in the pattern for a carrier fre- quency of W + 10 (see Figure 23), will be noted. In these patterns, as in all the patterns obtained with longitudinal excitation, the radi- ation is more intense off the end of the antenna away from the feed point. This will be dis- cussed below in greater detail. The values of G for each pattern are given in the captions to the figures. These values were obtained by graphi- cal integration of the patterns. The effect of using one frequency for exciting various pro-
46
THE RADIATION INTERACTION SYSTEM
jectiles is shown in Figure 25. Figure 25 repre- sents a series of patterns at W + 10 for the M-30, M-81, M-64, M-65, and M-66 bombs. In this figure the patterns are plotted in rectangu- lar coordinates.
Since tactical utility has required that the fuze be located in the nose of the projectile, we are interested in the values of f2(0,<f>) in front of the equatorial plane, i.e., for 6 < 90 degrees in the patterns of Figure 25. It is immediately
Figure 23. Directivity pattern for M-64 bomb at W + 10; longitudinal excitation; G = 2.6.
may be expected from qualitative arguments. The antenna may be thought of, crudely, as a piece of transmission line with a generator at one end and an impedance at the other end. A wave starts out from the generator ; some of it is absorbed in the impedance at the other end (radiation) ; the rest is reflected back. Since the amplitude of the wave traveling from the generator is greater than that of the return wave, the part of the radiation due to the for-
Figure 24. Directivity pattern for infinitesimal dipole; /2(0) = sin2(0) ; G — 1.5.
evident that there is a wide range in Zr for targets in the range 10 to 90 degrees off the nose. This is a complicating factor which re- quires that more than one frequency be used in designing longitudinal antenna fuzes.
This is an unfortunate complication that could largely be avoided if the feedpoint could be located in the rear of the projectile.
General Features of Longitudinal Patterns
The directivity patterns obtained with longi- tudinal excitation have several general fea- tures worthy of note. Some of these have already been mentioned and will be treated here in somewhat more detail.
“Lean” of Patterns. The patterns “lean” away from the feedpoint. This characteristic
ward wave, primarily forward radiation, is more dominant than the part due to the return wave.
For end-fed antennas, at a given frequency, the asymmetry is greater the greater the thick- ness of the antenna relative to its length. Cen- ter-fed antennas, even if of considerable thick- ness, have symmetrical patterns.
Patterns like those experimentally obtained may be computed by assuming an antenna cur- rent distribution with features as above de- scribed. That is, suppose we assume that the antenna current I is given by an expression of the form :
/ = ejUt - z) _ RIie-j(2n/\)(L - z)
(98)
In equation (98), h represents the amplitude
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DIRECTIVITY PATTERNS
47
of a wave traveling in the positive z direction, z is the running coordinate of the antenna with the feedpoint at the end z = 0, L is the length of the antenna, and RIX represents the ampli- tude of a return wave. Thus R is a reflection coefficient whose magnitude is less than unity, and 5 represents a phase shift occurring at re- flection. Thus 1 represents a return wave super- posed upon a forward wave.
Now the angular dependence E (6) of the
|
//} |
1 |
|||
|
- |
'il |
1 |
||
|
f¥ |
' H \ III |
« |
||
|
- 1 // |
i # \ |
\ HI v// |
m ¥ |
|
|
. 0 |
/ • A 1 /\ 1 ^ |
\T ./ .j— a n 1 AA 1 |
1 or\ IAA u |
in ion |
e (DEGREES)
Figure 25. Directivity patterns at W + 10; longitudinal excitation; curve 1, M-30 100-lb bomb; curve 3, M-64 500-lb bomb; curve 4, M-64 1,000-lb bomb; curve 5, M-66 2,000-lb bomb; curve 6, M-81 260-lb bomb.
remote radiation field produced by a linear an- tenna of length L is given by
L
E(e) a sin 9 J I(z)e l * cos e\ yZ} (99)
0
where I (z) is the current distribution along z.
It has been found that if I (z) be taken as in equation (98), then normalized values of E2(6) obtained from equation (99) agree well with experimentally obtained patterns when R and 5 are adjusted empirically. The picture of a for- ward wave and a return wave appears to be adequately correct to allow extrapolation and interpolation for changes in antenna size.
Small-Angle Radiation. Experimental meas- urement of patterns and the theoretical compu- tations of patterns outlined above (see Section 2.10) both lead to the conclusion that, for small angles, we may express the directivity pattern as
P(6) = a sin2 d, (100)
where a is a different constant for each projec- tile. This is a valuable generalization that facil- itates computation of Zr for cases arising in practice.
Effect of Projectile Geometry. Because of the considerable thickness of the projectile anten- nas, their physical lengths are considerably less than their “electrical” lengths. For a given physical length, an increase in thickness serves to increase the electrical length.
Effect of Tuning or Loading. The pattern de- pends only upon the frequency and the antenna geometry. There is, of course, no effect due to tuning or loading the antenna circuit.
Comparison of Patterns for Fuze Work
One of the desiderata of a proximity fuze is that it be usable without modification on vari- ous projectiles. It thus becomes necessary to examine, among other things, the variations in the directivity patterns for the various projec- tiles. This variation, for longitudinal excitation, has already been illustrated in Figure 25, where it is shown that at a particular frequency the patterns vary considerably. In the search for an optimum operating frequency for a prox- imity fuze for bombs, a large number of direc- tivity patterns was taken at various frequencies for the several bombs and a comparison of f2(0) was made. In this comparison, relatively small values of 0 are of importance in the ground-approach application since it is these that are encountered under terminal conditions for ordinary bomb releases. Because of the ap- proximate law f2{6) — a sin2 6, relative values for the various projectiles at one angle, i.e., 0 =: 30 degrees, will hold, roughly, for smaller angles. Figure 26 presents the values of
for various bombs for a range of frequencies. From Figure 26 it is seen that the expected
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THE RADIATION INTERACTION SYSTEM
variation in signal covers a very wide range, except at frequencies of 50 me and below. This agrees with the discussion in Section 2.5.6, which indicated that the signals for various bombs tend to approach the same level as the electrical length of the antenna is shortened below 1/2. Until close to the end of World War II it was not feasible to use frequencies as low as 50 me, because the values of parallel radiation resistance encountered at these low frequencies (see Figure 15) would not permit efficient matching to the driving circuit, thus
Figure 26. Relative signal strength Mo/h = (X/47 r) Gp(e) at 6 = 30°, over a range of fre- quencies; longitudinal excitation; curve 1, M-30 100-lb bomb; curve 2, M-57 250-lb bomb; curve 3, M-64 500-lb bomb; curve 4, M-65 1,000-lb bomb; curve 5, M-66 2,000-lb bomb.
leading to low S values for high Rp. If the re- flected signal is to be nearly the same at all heights for different projectiles using the same fuze, the product S0M0 must be constant. The term M0 depends upon the directivity pattern and So depends upon the operating point Rp. To hold the spread of S0M0 to reasonable values, it was found necessary to use two different radio frequencies in order to accommodate the fuze to various bomb sizes. It will be seen in Section 2.8.4. that transverse excitation largely avoids this difficulty. Toward the end of World War II a circuit was developed which could be matched to the high values of parallel radiation
resistance encountered at low carrier frequen- cies. This made possible the design of a more nearly universal longitudinal excitation fuze for bombs.40
Transverse Excitation Transverse Dipole
Fuzes working on this principle use a short transverse dipole as an antenna. The body of the projectile is not intentionally used as a part of the fuze, although it introduces complica- tions as shown in Section 2.5.4. Space limita- tions are such that the transverse dipole is short compared to a half wave, and the direc- tivity pattern tends to be like that for a short thin wire antenna, f2{6) — sin2 6 (see Figure 24). The close presence of the body of the pro- jectile modifies the pattern so that it is no longer a figure of revolution about the antenna axis. In some cases the projectile acts like a director, making the radiation toward the back of the projectile greater than toward the front. A certain amount of asymmetry with respect to the bomb axis is sometimes present because of a slight unbalance in the feed.
An unbalanced feed for the transverse dipole, aside from the effects discussed in Section 2.5.4, gives rise to a directivity pattern which does not have axial symmetry. In Section 2.5.4 it was seen that the longitudinal currents give rise to a correction which is small if the longi- tudinal currents are kept small.
To verify the fact that these currents are small the radiation pattern of the fuze-projec- tile combination is measured with equipment arranged similarly to that shown in Figure 17. The projectile axis is horizontal and the axis of the transverse dipole is vertical. The re- ceiver, which is sensitive only to horizontally polarized radiation, does not receive the energy radiated by the transverse currents flowing in the fuze dipole and the projectile behind it. It receives only the radiation from the longitudi- nal currents and gives a pattern like those for axial feed (see Figures 21, 22, 23, and 25).
The strength of the axial radiation is com- pared with the strength of the dipole radiation by putting the fuze dipole in the horizontal posi- tion and pointing the projectile directly toward
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DIRECTIVITY PATTERNS
49
or away from the receiver. In this orientation the longitudinal currents do not radiate toward the receiver, and the received signal is that from the transverse dipole alone, modified by the reflecting properties of the projectile. As a result of the two measurements, two field in- tensities are obtained which show the relative amounts of energy radiated by the longitudinal and transverse currents. In order to suppress the longitudinal currents it has been found necessary to use a relatively long wavelength so that the projectile is nonresonant.
When the directivity pattern is measured with fuze dipole horizontal and projectile horizontal, an asymmetric pattern like that in Figures 27
Figure 27. Directivity pattern for M-57 bomb at W -(- 35; transverse excitation; pattern taken in plane determined by longitudinal axes of dipole and bomb.
and 28 is obtained. The right-left asymmetry arises from the addition of the patterns from longitudinal and transverse currents. The fore- aft asymmetry arises from the reflecting prop- erties of the projectile. For short projectiles (see Figure 27) the fore-aft asymmetry is less marked than for larger ones.
As we have seen, if the longitudinal current is small its effects can be neglected. Thus, to a good working approximation, we can take the directivity in the directly forward direction to be unity and the directivity in other directions
forward of the equatorial plane as cos2 a or sin2 6.
When the transverse dipole is used, the size of the projectile has but little effect on the radia- tion resistance, provided the diameter is not too
Figure 28. Directivity pattern for M-64 bomb at W + 35; transverse excitation; pattern taken in plane determined by longitudinal axes of dipole and bomb.
large and the projectile does not form an effec- tive shield by imaging the dipole. This type of antenna is effective on all types of American bombs which the fuze will fit. It is not satisfac- tory with the British-type square-nosed bombs like the 4,000-lb LC, since this kind of bomb forms an effective shield unless the fuze is mounted on an extension. The British have found by extensive tests that a short extension makes the fuze quite satisfactory on this bomb.
Furthermore, the vehicle has only a relatively minor effect on the pattern, as we have seen, so that the fuze operation becomes relatively inde- pendent of the size of the projectile. In addi- tion, the transverse type of excitation will op- erate with nonconducting projectiles, such as the plywood belly tanks arranged with bomb fins used as fire bombs.
Loop Excitation
It is possible to obtain transverse excitation by means of a transverse magnetic dipole. This
50
THE RADIATION INTERACTION SYSTEM
is achieved by means of a small loop antenna, about 3 in. in diameter, whose plane includes the axis of the projectile, as in the T-172 fuze. The polarization of the radiation is different from that of an electric dipole, as shown by Table 2.
Table 2. Polarization of radiation in loop and dipole fuzes.
|
Dipole |
Loop |
|
|
Er |
0 |
0 |
|
Ea |
A — cos a cos 5 |
A . 9 — sin 5 |
|
r |
r |
|
|
A . |
A |
|
|
Ed |
— sin 5 |
— cos a cos 5 |
|
r |
r |
The coordinate system for Table 2 is as de- fined in Section 2.5.4. Aside from the polariza- tion change the argument is similar to that outlined for the transverse dipole, including unbalance effects. Similar radiation measure- ments are required, with due consideration for the polarization.
29 WORKING SIGNALS;
GROUND-APPROACH CASEe
This chapter is primarily concerned with the variations of antenna impedance as the fuze approaches a reflecting target. This variation has been described by M, and the variation of M from point to point in space has been called the M wave. It has also been shown that the voltage change dV out of the r-f system can be specified in terms of circuit parameters.
dV = MS. (89)
In other words, the voltage out of the r-f system is proportional to M, and in so far as relative wave form and amplitude are concerned M can be considered as a working signal set up by the reflecting target. Chapter 3 deals with the prop- erties of circuits and the values of S that can be achieved.
The method of utilization of this signal has been indicated in Chapter 1 and will be briefly recapitulated here. The voltage dV is applied to an amplifier; the output of the amplifier is applied to the grid of a thyratron; when the
output of the amplifier is of the proper magni- tude and phase the thyratron discharges through a detonator which initiates the firing train resulting in the burst. In most cases the transmission time of the signal through the fuze and detonator are negligible. A treatment of the delay to be expected is given in Chapter 3, which deals with the audio amplifier and firing circuit. Since delays are generally small, the basic problem of the design is to make the output voltage of the amplifier reach the firing level at the moment when the projectile is in a position such that its burst would do the maxi- mum amount of damage. While the necessary adjustments could be made empirically upon the basis of field trials, it is extremely helpful to be able to predict the expected point of func- tion from the fuze parameters and the ballistic problem. Such a knowledge allows treatment of many cases based upon performance in a typical case; it also aids recognition of abnor- mal performance.
We proceed to show how the prediction is made for the case of a bomb approaching the ground. For the sake of clarity we first treat a special case in Section 2.9.1 and then turn to a discussion of each of the factors involved in Section 2.9.2.
2 91 Prediction of Height of Function
The case selected is that of the ring-type fuze (longitudinal excitation and White frequency band) on the M-64 (500-lb) bomb, released from level flight by an airplane flying at 200 mph from an altitude of 10,000 ft over earth which has a reflection coefficient of 0.5.
The equation governing this case, equation (93), has been derived in Section 2.6.2. Utiliz- ing it, we have
dV = MS = G/2(0,0)ey[(-4'vx) + J
(101)
Equation (102) represents an audio-frequency voltage with peak amplitude
MoS0 = (102)
and frequency
|
dh |
2 |
dh |
|
dt |
." * |
dt |
e Bibliographical references pertinent to this section are 12, 16-22, 27, 35, 39, 40, 70, 71, 74.
SECRET
WORKING SIGNALS; GROUND-APPROACH CASE
51
For a falling bomb dh/dt is essentially con- stant over the last few hundred feet of flight, and we can take dh/ dt as the vertical component of the striking velocity. Thus equation (101) represents a voltage of constant frequency and rising amplitude in the range in which there is appreciable reflected signal.
Let us assume that the steady-state voltage amplification of the amplifier is known in the form of a curve g(F), henceforth denoted sim- ply by g and that the net holding bias of the firing thyratron is B. Then we can say that the height of burst h is approximately
h = XnSo £ r-(e,<t>) (104)
Equation (104) is based upon the tacit as- sumption that there is no delay in the amplifier and detonator, and further it ignores the fact that the thyratron can only fire when the volt- age is positive, thereby introducing an uncer- tainty in the height of operation of approxi- mately (X/ 2). The nature of these corrections will be discussed in more detail in Section 2.9.2.
The quantity B/g represents the peak voltage into the audio-control circuit that is necessary to fire the detonator.
We now insert appropriate values in equation (104) for our special case as follows: G/4jc =
0.208, the vertical component of striking veloc- ity = 740 fps, and the striking angle = 18.5 de- grees, the wavelength = 8.2 ft, and /2(18.5 de- grees) = 0.085. The audio frequency F is (2 X 740) /8.2 = 180 c. Typical values of G, B , and So, are 80, 4.4, and 15, respectively. Using these values, equation (104) gives h — 20 ft.
This is the height of burst to be expected if only radiation fields are involved. Actually the induction field introduces a correction, as shown in Section 2.10, when the magnitude of h ap- proaches X.
2,9,2 Factors Affecting Magnitude and Frequency of Impedance Signal M
Having taken a brief overall view of the vari- ous factors determining the point of function of a