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Pn eateseen tients Peer Preyer rh nT.) spate ere Vote bebet A Ariat tb debedatetet gee 6b h¢OFEOO ToEO o HINA) IOHM/18i Oemcu SUMMARY TECHNICAL REPORT OF THE NATIONAL DEFENSE RESEARCH COMMITTEE Manuscript and illustrations for this volume were prepared for publication by the Summary Reports Group of the Columbia University Division of War Research under contract OEMsr-1131 with the Office of Scientific Research and Development. This vol- ume 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 concern- ing the availability and distribution of the Summary Technical Report volumes and microfilmed and other reference 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, Attention: Reports and Documents Section, Washington 25, D.C. Copy No. GAS This volume, like the seventy others of the Summary Technical 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 THE COMMITTEE ON PROPAGATION, NDRC VOLUME 1 HISTORICAL AND TECHNICAL SURVEY = pe wi, & GRAPHIC INSTITUSION WOCDS HOLE OCE OFFICEH OF SCIENTIFIC RESEARCH AND DEVELOPMENT VANNEVAR BUSH, DIRECTOR NATIONAL DEFENSE RESEARCH COMMITTEE JAMES B. CONANT, CHAIRMAN COMMITTEE ON PROPAGATION CHAS. R. BURROWS, CHAIRMAN WASHINGTON, D. C., 1946 NATIONAL DEFENSE RESEARCH COMMITTEE James B. Conant, Chairman Richard C. Tolman, Vice Chairman Roger Adams Frank B. Jewett Karl T. Compton Army Representative! Navy Representative? Commissioner of Patents* Irvin Stewart, Hxecutive Secretary 1Army Representatives in order of service: Maj. Gen. G. V. Strong Col. L. A. Denson Maj. Gen. R. C. Moore Col. P.R. Faymonville Maj. Gen. C. C. Williams Brig. Gen. E. A. Regnier Brig. Gen. W. A. Wood, Jr. Col. M. M. Irvine Col. E. A. Routheau 2Navy 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 3Commissioners 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 suitable projects and research programs on the instrumentalities of warfare, together with contract facilities for carrying out these projects and programs, and (2) to administer the tech- nical and scientific work of the contracts. More specifically, NDRC functioned by initiating 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 experi- ence of its members. Proposals prepared by the Division, Panel, or Committee for research contracts for performance of the work involved in such projects were first reviewed by NDRG, and if approved, recommended to the Director of OSRD. Upon approval of a proposal by the Director, a.con- tract permitting maximum flexibility of scientific effort was arranged. The business aspects of the contract, including such matters as materials, 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 Ordance 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 ad- ministrative 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 be- came a reviewing and advisory group to the Director of OSRD. The final organization was as follows: Division 1—Ballistic Research Division 2—FEffects of Impact and Explosion Division 3—Rocket Ordinance Division 4—Ordnance Accessories 5—New Missiles 6—Sub-Surface Warfare Division Division Division 7—Fire Control Division 8—Explosives Division 9—Chemistry Division 10—Absorbents and Aerosols Division 11—Chemical Engineering Division 12—Transportation Division 18— 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 NDRC FOREWORD A EVENTS of the years preceding 1940 revealed more and more clearly the seriousness of the world situation, many scientists in this country came to realize the need of organizing scientific research for service in a national emergency. Recommenda- tions which they made to the White House were given careful and sympathetic attention, and as a result the National Defense Research Committee (NDRC) was formed by Executive Order of the President in the summer of 1940. The members of NDRC, appointed by the President, were instructed to supplement the work of the Army and the Navy in the development of the instrumentalities of war. A year later, upon the establishment 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 sum- marize and evaluate its work and to present it in a useful and permanent form. It comprises some seventy volumes broken into groups corresponding to the NDRC Divisions, Panels, and Committees. The Summary Technical Report of each Division, Panel, or Committee is an integral survey of the work of that group. The first volume of each group’s report contains a summary of the report, stating the prob- lems presented and the philosophy of attacking them, and summarizing the results of the research, develop- ment, and training activities undertaken. Some vol- umes may be “state of the art” treatises covering subjects to which various research groups have con- tributed information. Others may contain descrip- tions of devices developed in the laboratories. A master index of all these divisional, panel, and com- mittee reports which together constitute the Sum- mary Technical Report of NDRC is contained in a separate volume, which also includes the index of a microfilm record of pertinent technical laboratory reports and reference material. 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 inspection by the Applied Mathematics Panel. Since the material treated in them is not duplicated 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 vol- umes. The extent of the work of a division cannot therefore be judged solely by the number of volumes devoted to it in the Summary Technical Report of NDRC; account must be taken of the monographs and available reports published elsewhere. Though the Committee on Propagation had a com- paratively short existence, being organized rather late in the war program, its accomplishments were definitely effective. That so many individuals and organizations worked together so harmoniously and contributed so willingly to the Committee’s efforts is a tribute to the leadership of the Chairman, Chas. R. Burrows. The latest information in this field was gathered from the four corners of the earth, organ- ized, and dispatched to the points where it would aid most in the prosecution of the war. Much credit must be given, not only to the mem- bers of the Committee and its contractors, but also to the many other individuals who gave so generously of their time and effort. This group included a num- ber of our Canadian and British allies. In addition to the assistance given the war effort, a considerable contribution has been made to the knowledge of short-wave transmission and especially to the inter- relation of this phenomenon with meteorological con- ditions. Such information will be most valuable in weather forecasting and in furthering the usefulness of the whole radio field. VANNEVAR Busu, Director Office of Scientific Research and Development J. B. Conant, Chairman National Defense Research Committee Vv FOREWORD 5 Dm success of the propagation program was the result of the wholehearted cooperation of many individuals in the various organizations concerned, not only in this country but in England, Canada, New Zealand, and Australia. The magnitude of the research work accomplished was possible only because of the willingness of the workers in many organiza- tions to undertake their parts of the overall program. In fact, the entire program of the Committee on Propagation was carried out without the necessity of the Committee exercising directive authority over any project. Dr. Hubert Hopkins of the National Physical Laboratory in England and Mr. Donald E. Kerr of the Radiation Laboratory at the Massachusetts Institute of Technology, who were working on this phase of the war effort when the Propagation Com- mittee was formed, were instrumental in giving a good start to its activities. The largest single group working for the Committee was under Mr. Kerr. The existence of a common program for the united nations in radio wave propagation resulted from the splendid cooperation given the Propagation Mission to England by Sir Edward Appleton and his Ultra Short Wave Panel. Later, through the cooperation of Canadian engineers and scientists, Dr. W. R. McKinley of the National Research Council of Canada and Dr. Andrew Thomson of the Air Services Meteorological Division, Department of Transport, Toronto, Canada, undertook to carry on a part of the program originally assigned to the United States. The program was further rounded out by the willing- ness of the New Zealand government to undertake an experiment for which their situation was particu- larly favorable. Dr. F. E. 8. Alexander of New Zealand and Dr. Paul A. Anderson of the State College of Washington initiated this work. Needless to say, the labor of the Committee on Propagation could hardly have been effective without the coopera- tion of the Army and Navy. Maj. Gen. H. M. McClelland personally established Army coopera- tion, and Lt. Comdr. Ralph A. Krause and Capt. Lloyd Berkner were similarly helpful in organizing Navy liaison and help. Officers and scientific workers of the U. S. Navy Radio and Sound Laboratory at San Diego, Califor- nia, altered their program on propagation to fit in with the overall program of the Committee. Capt. David R. Hull, Bureau of Ships, understanding the importance of the technical problems, paved the way for effective cooperation by this laboratory. Dr. Ralph Bown, Radio and Television Research Director, Bell Telephone Laboratories, integrated the research program undertaken by Bell Telephone Laboratories for the Committee on Propagation. This joint research program included meteorological measurements on Bell Telephone Laboratories prop- erty by meterologists of the Army Air Forces work- ing with Col. D. N. Yates, Director, and Lt. Col. Harry Wexler of the Weather Wing, Army Air Forces. The accomplishments of the Committee on Propaga- tion are a good example of the effectiveness of co- operation—all parts were essential and none more than the rest. I want to thank Dr. Karl T. Compton, President of the Massachusetts Institute of Technology, who was always willing to discuss problems of the Com- mittee and who helped me to solve many of the more difficult ones, and also, Prof. 8. S. Attwood, Univer- sity of Michigan, whose continual counsel through- out my term of office was in no small way responsible for the success of our activity. Credit is also due Bell Telephone Laboratories, which made my services available to the government and paid my salary from August 1943 to September 1945, and to Cornell University, which has allowed me time off with pay to complete the work of the Committee on Propagation since September 1945. Cuas. R. Burrows Chairman, Committee on Propagation Vil * ¥ + . tr ‘ . 7 ‘ i i a * ' “ i ’ fp +e) it t ns i ; : it i ' . Ky ¥) ies PREFACE N THIS SERIES of three volumes, which is part of the Summary Technical Report of NDRC, the Com- mittee on Propagation is presenting a record of its activities and technical developments. The material presented, concerning as it does the propagation of radio waves through the troposphere, is of permanent value both in war and in peace. The present volume is divided into four parts. Part I outlines the organization and activities of the NDRC Committee on Propagation, gives the mecha- nism used for coordinating the various Service and civilian organizations interested in propagation, and makes recommendations for continued activity in studying propagation phenomena. Part II gives a critical overall view of the technical developments in the study of tropospheric propaga- tion. Outlined is the general theory of both standard and nonstandard propagation together with descrip- tions and results of transmission experiments carried out in widely separated parts of the earth and de- signed to test the theory. Included also is a resumé of the meteorological factors affecting propagation of waves and their attenuation in the atmosphere. The second, third, and fourth Conferences on Propagation, under the auspices of the NDRC Com- mittee on Propagation, were held in February 1944, November 1944, and May 1945, respectively. The bulk of the technical material presented at the con- ferences is published in Volume 2 of this series and in Part III and Part IV of the present volume. These comprise the material dealing with the theory of both standard and nonstandard propagation. Certain re- ports have been omitted, primarily because the material was superseded by later studies or is covered adequately elsewhere. The General Bibliography lists reports on tropo- spheric propagation issued by numerous Service and civilian organizations of both the United States and the British Empire. With a few exceptions, original reports listed in the Bibliography for this volume have been microfilmed. A few, such as summary reports issued by the Columbia University Wave Propagation Group and the compiled Propagation Conference Reports, are included in the present series. Acknowledgment is due to the many authors who have contributed to this series, not only for the material and its oral presentation at the conferences, but also for their willingness to prepare the material in form for permanent record. STEPHEN 8S. ATTWOOD Editor 1x CONTENTS CHAPTER PAGE RSRUTIMT ETE Ss cao ae ebetone cats Stn coset Eee he ta OnORetio ncn airs Here Sener ae Taee il PARE HISTORY 1 OnicimpandeOreaniz aloe ah ce cigar rarer ea dane: 5) 2 Objectives and Research Agencies...................... 9 3 Chronolomicalelye conde oye. n ite races 3 Na kee ee Pee: 13 4 NESUincEAMasecOMMendatlOnsr le hens aera ene 25 Ae Tal SUMMARY 5 SusNCBiCl IPROORGANIOI « . soa peereseaceechonsaesahneacac 31 6 Elementary Theory of Nonstandard Propagation......... 42 7d Meteorological Measurements......................... 50 8 TPDNSONISSOM JDPGOSAIMEMUS. 5 4 aseoeeoseekeseeuscnasunse 58 9 General Meteorology and Forecasting.................. 75 10 Scattering and Absorption of Microwaves............... 82 PART III CONFERENCE REPORTS ON STANDARD PROPAGATION 11 A Graphical Method for the Determination of Standard Coverdver@ lantsperre twee hn ek a fe Sl aes ee 93 12 Nomographie Solutions for the Standard Case........... 95 13 Theoretical Analysis of Errors in Radar Due to ANTONCSTONCIG INCIECHOMNe Sheek escseeebaogeeueaeonsaees 106 14 Diffraction of Radio Waves over Hills..................110 15 Siting and Coverage of Ground Radars.................113 16 Variations imekacion Coverages ise sn eee ee 178 xi xii CONTENTS CHAPTER PAGE IPA JOY CONFERENCE REPORTS ON NONSTANDARD PROPAGATION 17 Tropospheric Propagation and Radio Meteorology........ 189 18 Theoretical Treatment of Nonstandard Propagation in the Diftraction: Zone. 0 as ae ee ere ee eae 226 19 Characteristic Values for the First Mode for the Bilinear M Curves fGen ee SO ae 228 20 Incipient Leakage in a Surface Duct.................... 233 21 The Solution of the Propagation Equation in Terms of Hankel Bunctionsaesd.c) laren ane ce. een rare er 237 22 Attenuation Diagrams for Surface Ducts................ 240 23 Approximate Analysis of Guided Propagation in a INonhomorencousPAtmosplh ene aint eee 244 24 Some Theoretical Results on Nonstandard Propagation. . .247 25 Perturbation Theory for an Exponential M Curve in Nonstandand@lzro accion einen een rarer 249 26 First Order Estimation of Radar Ranges over the Open OCCT ie hee SLES alata oo eater 256 20 Convergence Hifects in Reflections fromTropospheric Toayersi cami Acer ocak ot eee re eek ten ere 258 Bilohioemayolny—Wolwwne t,o co caccccocuacvavccvenesve0s 261 GeneraleBiblioeraphya nee eee reer 277 OSRD°Appointeds).) 20.2 ene ee oe 310 Contractsi: ©. Bese keloe. cab gallo ates ete eee, See eae 311 Service Projects ainuc. .¢ he) sone en Ce eee 312 INTRODUCTION | eal REPORT IS a summary of the activities of the Committee on Propagation, NDRC. It is divided into three parts, each of which deals with a particular type of activity or record. Part I is an account of the administrative activities of the Committee, its origin, organization, and work, with a description of the needs of the armed forces which called it into being. It is divided into four chapters for convenient reference. In general, the technical aspects of the problems set before the Committee, and of the work undertaken to solve those problems, are touched on in Part I only suffi- ciently to make clear the needs of the Services and the steps taken to satisfy those needs. Actual chronology is adhered to as far as possible with any departures indicated where they occur. This part of the report is designed to serve not only as a record of the Committee’s work but to assist any future eroup in the organization of a similar program, should the occasion arise. Chapters 1 and 2 describe the organizational setup, liaison channels, objectives, the changes which occurred, and the reasons for making them. Chapter 3 relates the chronological activities of the organization. Chapter 4 summarizes the results accomplished and also contains a critique of the organization and its work, as evaluated by the chairman, with recommendations for future investi- gation in this field. Part II is a technical description of the develop- ment of propagation work during World Wir II and the results obtained by the various organizations engaged in this work. Chapter 5 begins with a defi- nition of certain basic concepts and proceeds with a review of so-called standard propagation as known at the beginning of the war. For a rapid survey of the vast body of information that has since been acquired, Chapter 6 reviews nonstandard propaga- tion from an elementary theoretical viewpoint. The principal discovery made during the war is that the effective range of radar and short-wave radio equip- ment depends essentially and critically on the distribution of the refractive index in the lower strata of the atmosphere. In Chapter 7 the newly developed methods for the measurement of the refractive index variation are described, and a collec- tion of typical refractive index curves resulting from actual measurements in various parts of the world is presented. Chapter 8, the central chapter of Part II, gives a brief chronological record and the principal results of the major propagation experiments performed in Great Britain, Canada, and the United States. Because short and microwave propagation charac- teristics are determined by the physicial condition of the lower atmosphere, they are intimately connected with the evolution of the weather on a large scale as studied by the forecasting meteorolo- gist. The relationships between the dynamics of the air and the distribution of refractive index are presented in Chapter 9. A review of the climatic and seasonal conditions involved in various parts of the world and of the bearing of all these factors upon the forecasting of radio propagation conditions is included. Finally, in Chapter 10, the results of investigations on the atmospheric absorption of microwaves and of the scattering of short and microwaves by radar targets and by raindrops are summarized. The data given in this report refer only to the transmission of the higher frequency bands, above about 30 me. Parts III and IV are devoted to the presentation of 18 reports, out of 61 published in the Summary Technical Report, which were presented before the second, third and fourth conferences on propagation held in February, 1944, November 1944, and May 1945, or were published by the Columbia University Wave Propagation Group. Those appearing in Chap- ters 11 through 15 are concerned with standard propagation; Chapters 16 through 27 with nonstand- ard propagation. The remaining 43 reports are pub- lished in Volume 2. One of the main functions of the Committee was to bring about a rapid exchange of information between the laboratories and Service units working on the subject, thus making the results available to all workers technically concerned with the military application of radar and other short wave radio equipment. To fulfill this function the Columbia University Wive Propagation Group operating under contract with the Committee periodically published a comprehensive bibliography on propagation, begin- ning in the spring of 1944. Its fifth and last edition, issued in August 1945, is included in this volume. This bibliography is a rather exhaustive documenta- tion of the efforts made during the war in this field by Great Britain, Canada, New Zealand, Australia, and the United States. Reference to papers and reports is made in the main body of this summary by siperior numbers. PARTI Chapter | ORIGIN AND ORGANIZATION 1 ORIGIN |ip aucusr 1943, Dr. K. T. Compton, a member of the National Defense Research Committee [NDRC], in the course of discharging his duties resulting from his “radar mission” to England, asked Dr. Chas. R. Burrows of the Bell Telephone Labora- tories if he would undertake the coordination of research work on radio wave propagation in the United States under the auspices of NDRC. This was the initial step in the formation of the Committee on Propagation. During the Compton radar mission the urgent need for radar information in the armed forces was discussed by Dr. Compton and Sir Ed- ward Appleton. The Committee on Propagation of the National Defense Research Committee was organized in August 1943, under the chairmanship of Dr. Burrows. This body was created for the purpose of coordinating American scientific investigation of the propagation of electromagnetic waves through the lower atmos- phere (troposphere), correlating the United States research with that being carried out in Great Britain and other countries of the United Nations and trans- mitting the information obtamed to the Armed Forces in usable form, as speedily as possible. It was decided that the propagation phenomena referred to could be divided into two classes: one, the effects of the troposphere itself on electromag- netic radiation of the wavelengths under discussion and, two, the effects of the earth’s land and water surfaces in reflecting radiation incident at various angles. A British memorandum dated April 28, 1943 was drawn up, inviting specific United States cooper- ation in investigation of the following problems: 1. The entire question of effects of tropospheric conditions near and over a continental land mass similar in size, climate, and topography to Europe, on radiation of radar frequencies, in meteorological environments ranging from polar to tropical, with particular emphasis on obtaining quantitative data. British facilities and environments for this investi- gation were limited. 2. An exhaustive study of propagation under desert and moist tropical conditions, particularly with transmitter and receiver at heights of less than 100 ft. 3. Propagation under temperate climatic condi- tions with either the receiver or transmitter at heights from 5,000 to 10,000 ft. 4. Experiments to determine the dependence of the reflection coefficient on the ang’e of incidence with the surface of a rough sea. 5. Experiments along nearly optical paths over various kinds of topography likely to be encountered in field operations. Exhaustive knowledge of this aspect of the general propagation problem appeared to be an urgent necessity, and comparison of United States and United Kingdom experience was con- sidered highly desirable. It was felt that such investigations, correlated with parallel work on those aspects of the research which could be carried out in Great Britain, would produce early results of great importance to the successful prosecution of the war. It was extremely important for the armed forces to know with reasonable accuracy the coverage to be expected with given radar or radio communica- tion equipment under various conditions of terrain and meteorology. In order that this coverage could be determined it was necessary to know the laws governing electromagnetic wave propagation, and these laws could be derived only by an extensive theoretical and experimental research program. The urgency and importance of the entire matter of cover- age become obvious when the following pertinent aspects of modern warfare are considered: 1. The development of highly mobile and powerful instruments (such as the improved tank and other surface combat vehicles, and of long range, high speed bombardment aircraft employed for strategic attacks on the means of production and civilian morale, as well as for tactical purposes) which per- mitted the principal belligerents to readopt a war of movement, instead of one of static fortification and attrition, and made the development of devices for detecting the presence and movements of enemy mobile units vitally necessary. 2. The necessity of protecting extremely extended sea and land supply lines from successful attack by enemies who early realized that their major hope of ultimate victory lay in cutting those lines. 3. The enormous extent and diversity of the various theaters of operations, necessitating inte- b) 6 ORIGIN AND ORGANIZATION grated global communications over vast areas of unfavorable terrain and with thousands of mobile units. Very early in the conflict it was realized that only the British development and organized employment of radar had permitted that country, with a numeric- ally inferior air force, to defeat the Luftwaffe deci- sively in the Battle of Britain, in which the German High Command had hoped to destroy the Royal Air Force and open the way for a successful invasion of Great Britain. Karly warning radar permitted the British commanders to conserve their small resources of men and materiel by sharply reducing air patrol- ling, and by conducting interceptions with an exac- titude which conserved men and aircraft flying hours to the utmost. With the importance of radar thus established, its use was rapidly expanded and extended into new applications. To protect the extremely long sea supply lines from crippling submarine attacks, radar detection devices were developed expressly to detect surfaced submarines as the only practicable means of searching wide areas of ocean under varying conditions. With the entry of the Japanese into the struggle, the field of operations became truly global, and the demands made on detection and communication equipment became more severe in all respects. Rapid improvement was made in the performance and reliability of radio and radar equipment to meet these increased demands. With these advances in design and manufacture and the speedy accumulation of a large amount of factual data on equipment performance in the field, it soon became apparent that meteorological condi- tions in the troposphere had very serious influence on the operational efficiency of such apparatus. In particular, it was noted that the reliable coverage area of a given installation varied considerably with — weather conditions, with the result that confidence in early warning radar and very high-frequency communication links was reduced, and this loss of confidence affected field operations seriously. It thus became vitally necessary to investigate as rapidly and completely as practicable the causes of such variations, with a view to discovering ways of mini- mizing reductions of coverage and reliability and to improving the general overall performance. The need for this investigation was communicated from units in the field through regular liaison channels to the National Defense Research Committee [NDRC] in the United States, and to the Depart- ment of Scientific and Industrial Research in Great Britain. Certain researches into the problem were begun independently in the two countries. During the course of the discussion perviously referred to between Dr. Compton and Sir Edward Appleton, the need for a body to coordinate these researches was revealed. The magnitude and complexity of the problem, occasioned by the extreme variations in equipment, siting, terrain, and meteorology in the various theaters of operations, made it essential to divide the investigation so as to avoid gaps or duplication of effort. This could be achieved only by integrating research programs through a coordinating body. Accordingly the radar mission under the chairman- ship of Dr. Compton, upon its return to the United States strongly recommended the formation of such a body. 1.2 ORGANIZATION A preliminary conference on propagation was held July 1 and 2, 1943 at the Massachusetts Institute of Technology, at which most of the interested United States agencies were represented. This conference was held under the chairmanship of Donald E. Kerr, leader of the propagation group of the Radiation Laboratory and was called specifically for the following purposes: 1. To make those attending acquainted with each other and with the work then in progress. 2. To review and summarize the general status of microwave propagation knowledge in the United States. 3. To compare general measurement techniques. 4. To standardize terminology and methods of presenting data. 5. To formulate a program for future research and recommend any necessary redistribution of emphasis. The general conclusion reached by this conference was that the following subjects were of greatest importance: 1. Perfection of the technique of radar range forecasting to a degree which would make it immedi- ately useful to the services, even if this had to be done in a preliminary form. 2. Continuation of both theoretical and experi- mental investigation of the mechanism by which the properties of the atmosphere and earth affect micro- ORGANIZATION wave propagation, under widely varying conditions of climate and terrain. 3. Measurement of the reflection coefficients of land and sea surfaces over a wide range of angles of incidence, for the entire radar frequency spectrum, with a view to immediate application to radar coverage problems in the services. 4. Establishment in the immediate future of an agency which could perform the following functions: a. Serve as a clearing house for all microwave propagat on information in the United States and organize future conferences of represen- tatives of agencies working in the propaga- tion field. b. Review the available knowledge from time to time and recommend any necessary redis- tributions of effort by investigating bodies. ec. Act as responsible agency for the entire United States propagation investigation in dealing with groups working in similar fields in the United Kingdom and other Allied countries. Following this conference, Dr. I. I. Rabi, Head of the Research Division of the Massachusetts Institute of Technology Radiation Laboratory, suggested that Division 14 of NDRC take the initiative in setting up a microwave propagation committee to organize the more adequate program outlined in paragraph 4 of the preliminary conference’s conclusions. During a subsequent consultation between Dr. Compton and Dr. Ralph Bown, Radio Research Director of the Bell Telephone Laboratories, Dr. Burrows was sug- gested as chairman of the proposed NDRC Commit- tee on Propagation. Dr. Burrows was chairman of the Radio Wave Propagation Committee of the Institute of Radio Engineers and had made numerous contributions to the knowledge of propagation. Under the NDRC Committee on Propagation a nation-wide program was proposed, to coordinate the work of such investigative bodies as the Radia- tion Laboratory, Bureau of Standards, Weather Bureau, various Army and Navy agencies, certain institutions cooperating with Division 13 of NDRC on direction finder problems, the Wave Propagation Committee of the Joint Communications Board [JCB], and such other bodies as the Committee on Propagation, after its official organization, might find helpful in furthering its program. On August 24, 1943, Dr. Burrows agreed to accept the chairmanship of the proposed Committee and at once began the work of organization and of surveying in | the activities of groups in the United States already engaged in propagation studies. The initial membership of the Committee as proposed by Dr. Burrows, after consultation with the men concerned and heads of the NDRC Divisions directly interested, was as follows: Dr. J. A. Stratton, Office of the Secretary of War. Dr. J. H. Dellinger, National Bureau of Stand- ards. (Chief of Section 13.2 and representing Divi- sion 13, NDRC.) Dr. H. H. Beverage, Radio Corporation of Amer- ica (representing Division 15, NDRC). D. EH. Kerr, Radiation Laboratory, MIT (repre- senting Division 14, NDRC). A recommendation for these appointments was submitted to Dr. James B. Conant on October 5, 1943. The Committee on Propagation was originally planned to be a part of Division 14, but shortly after its formation it was raised to the level of an NDRC committee, because the broadened scope of its direc- tive, as issued in November, clearly took in aspects of the propagation problem outside the field of Division 14 alone. Prior to this crystallization of the Committee personnel and while the group was in the formative stage and still under the jurisdiction of Division 14, Professor S. 8. Attwood of the University of Michigan also served as a member. Later Prof. Attwood was detached from the Commit- tee to direct the Columbia University Division of War Research Wave Propagation Group [CUDWR- W PG], which was responsible under a contract to the Committee for the preparation of reports. This and other contracts are discussed in Chapter 2. During the closing months of 1944, Dr. Stratton resigned from membership. Shortly thereafter the membership was enlarged to include Dr. T. J. Carroll of the War Department and (somewhat later) M. Katzin of the Naval Research Laboratory. During the first year the Committee operated without the services of a technical aide. Late in the summer of 1944, Dr. A. F. Murray and 8. W. Thomas served temporarily in this capacity until a full-time aide could be obtained. This post was filled by R. J. Hearon from December 1944 until January 1946. The Committee retained the services of Dr. C. E. Buell, Chief Meteorologist of American Air Lines, who served as a consultant from March 15, 1944. Following completion of his work as director of the CUDWR-WPG, in October 1945, Prof. Attwood was made a consultant to the Committee. 8 ORIGIN AND ORGANIZATION 1.3 LIAISON CHANNELS In general, liaison between the Committee and those organizations directly represented on it was through the individual concerned. Thus Dr. Dellinger provided liaison with Division 13, Mr. Kerr per- formed the same service for Division 14, and Dr. Beverage acted in this capacity for Division 15. Dr. Stratton served as liaison with the Office of the Secretary of War. In order to provide a similar close link with the Wave Propagation Committee of the Combined Communications Board [CCB], Dr. Burrows was appointed to membership on this Committee. In addition to these direct channels, a number of specialists from various Service organizations were appointed as liaison officers, in order to keep the work of the Committee closely coordinated with Service requirements and to speed the dissemination of information. Captain D. R. Hull acted in this capacity for the Navy, with R. S. Baldwin as alternate. Later Lt. Comdr. W. B. Chadwick was appointed as an addi- tional liaison officer for the Navy Department. Lieutenant Colonel J. J. Slattery served in this capacity for the Army, to supplement the liaison already provided through Dr. Stratton. Also, at the request of the chairman of the Committee on Propagation, Comdr. F. W. Reichel- derfer, Chief of the Weather Bureau and Chairman of the Combined Meteorological Committee, assigned Lt. Col. H. Wexler to the Committee in the dual capacity of technical advisor on meteorology and as liaison officer for the CCB. Somewhat later Dr. Carroll and Comdr. D. H. Menzel were appointed to transmit propagation problems of the Army and Navy, respectively, to the Committee on Propagation under a directive of the JCB. In addition, use was made of established channels for contact with many agencies, including those in Allied countries. These channels included the Office of Scientific Research and Development Liaison Office, the Naval Coordinator of Research and Development, the War Department Liaison Officer, and the Office of Field Service. Chapter 2 OBJECTIVES AND RESEARCH AGENCIES 2.1 DIRECTIVE AND OBJECTIVES HE ORIGINAL DIRECTIVE for the Committee on Propagation was issued by Dr. James B. Conant, NDRC Chairman, in November 1943 and read as follows: It shall be the duty of the Propagation Committee of the NDRC to organize and coordinate a program designed to secure the answers to problems on propagation of importance to the war effort. Its reeommendations of contracts should be transmitted to the NDRC through Divisions 13, 14, and 15, and the supervision of the contracts remains with the Divisions which transmit the recommendations to the NDRC. It shall give consideration to the needs of Divisions 13, 14, and 15 within the field in which it is limited. Information secured by this Committee and by corresponding sections of Divisions 13, 14, and 15 shall be made mutually available as desired by the groups and may be used by the groups for the purpose of carrying out their missions. It is further understood that one of the duties of the Committee on Propagation is to assemble and analyze, and make available to appropriate agencies, all information in regard to propagation of importance to the wa” effort. The directive was purposely made broad enough to permit investigation in any direction promising useful results. In view of this breadth, it was neces- sary to establish a priority list of specific problems for immediate attack. Proper choice of the problems on this list was of great importance to the successful accomplishment of the Committee’s objectives and accordingly was taken up at the first regular meeting, held on October 13, 1943. During the course of this meeting the specific functions of the Committee were also defined, as follows: 1. To coordinate the research then going forward in the United States and to initiate any new work necessary to round out the program. 2. To review completely the existing data on propagation, correlate it, put it into a form usable in the Services, and disseminate it through author- ized liaison channels being set up for the purpose. 3. To cooperate with similar agencies in the United Kingdom and other Allied nations for exchange of information and coordination of research, with a view to avoiding duplication of effort or of gaps in the investigation. With the establishment of these specific functions, two operational problems were selected as being of the highest priority. These were the tracking of storms and estimation of their properties with radar equipment and the prediction of range for all types of radio equipment employing that part of the electromagnetic spectrum above 30 mc. The additional problems of determining necessary radar facilities, radar navigation along a shore line, and siting of direction finder equipment, were dis- cussed, but it was decided that these subjects were either outside the province of the Committee or were being adequately considered by other agencies. The following research problems were also agreed upon: 1. Propagation in nonhomogeneous media. a. Meteorology. (1) A thorough review of avail- able instruments and methods for making atmospheric soundings and initiation of a program of manufacture of suitable types. (2) Development of techniques for employ- ing these instruments by means of sounding balloons, aircraft, etc. (8) Determination of the dielectric constant of the troposphere as a function of height, at locations within the United States or possessions where condi- tions in strategically important war theaters are reasonably well simulated. (4) Repetition of operations of (3) in selected strategically important regions or their meteorological equivalent, to obtain sample refractive index distributions. (5) Conduction of meteoro- logical weather analysis concurrently with functions under (3) and (4). (6) Sponsorship of further research into world-wide meteoro- logical conditions, their diurnal and seasonal variations, and their effect on propagation. b. Theoretical analysis of propagation. (1) Ex- tension of analytical methods to permit bet- ter physical understanding of the effects of varying refractive index distribution. (2) Preparation of working formulas for deter- mining field strength and fading charac- teristics. c. Establishment of experimental propagation measuring circuits in locations where results of (4) above make such experiments advis- able, these experiments to be correlated with simultaneous meteorological observation and 9 10 OBJECTIVES AND RESEARCH AGENCIES weather analysis. Three frequencies were considered the minimum number capable of yielding a useful result. Those selected were 24,000, 3,000, and 200 me, with 10,000 me considered as an alternate for 24,000, if equipment for the higher frequency was un- available. The characteristics of both one- way and two-way continuous wave and pulse transmissions were to be considered. d. Development of a technique for forecasting propagation conditions in the field, suitable for tactical and strategic use. e. Application of points mentioned above to specific operational problems in selected regions. 2. Measurements of absorption of K-band radia- tion by atmospheric moisture in various forms and by dust or other scatterers. 3. Study of the effects of the earth’s land and water surface on propagation. a. Determination of reflection coefficients of various surfaces for specular reflection and its effect on coverage of various radar and radio equipments. b. Study of back-scattering echoes from land and sea surfaces (ground clutter and sea return), with particular emphasis on effects at the highest frequencies to be employed. 4. Investigation of storm echoes. 5. Study of the shielding, diffraction, absorption, and depolarization effects of trees, hills, man-made structures, and other topographical features. 6. Compilation, analysis, integration, and publi- cation of propagation information obtained, in forms suitable for use by the armed forces. This extensive program of investigation neces- sarily required agreement on an appropriate division of effort among United States, British, and other agencies available for the work. This division is discussed in the chronological record of the Com- mittee’s, activities in Chapter 3. 2.2 INVESTIGATING BODIES Very early in its existence the Committee con- sidered at length how best to implement the required research program. The conclusion was reached that making use of existing research agencies qualified to work in the propagation field, rather than setting up an independent research agency, would be most productive. This decision was influenced consider- ably by the serious shortages of personnel and equip- ment, and it was estimated that setting up a separate agency would have retarded progress of the investi- gation six months to one year. During the course of its investigations the Com- mittee maintained connections with a total of about 66 separate agencies in the United States, Britain, Canada, New Zealand, and Australia, including the principal organizations within the armed forces of the Allied countries interested in propagation phenomena. Reports, recommendations, and requests from all these various agencies were received, analyzed, acted upon, and filed. This accumulated body of in- formation on propagational phenomena is listed in the Bibhography. These papers are referred to again in Chapter 4 under a summarization of the results of the Committee’s work. Of the agencies conducting actual theoretical or experimental research on radiowave propagation, the principal ones in the United States were as follows: 1. Bell Telephone Laboratories [BTL]. 2. Camp Evans Signal Laboratory. 3. Columbia University Division of War Research [CUDWR]. a. Radiation Laboratory. b. Wive Propagation Group. 4. National Bureau of Standards, Interservice Radio Propagation Laboratory, [IRPL]. 5. Radiation Laboratory, Massachusetts Institute of Technology [MIT-RL]. 6. U.S. Naval Research Laboratory. 7. U.S. Navy Radio and Sound Laboratory. 8. U.S. Army Signal Corps Operational Research Branch. 9. Radio Corporation of America. 10. Radio Research Laboratory, Harvard Uni- "versity. 11. U.S. Army Air Forces, Weather Division. There were also 2 agencies in Australia, about 21 in Britain, 2 in Canada, and 2 in New Zealand. The number of agencies investigating propagation pheno- mena in the Allied countries totaled about 39. This relatively large number was necessitated by the importance, urgency, diversity, and complexity of the problem, and the physical difficulties of conduct- ing direct experimental investigation with usable accuracy under war, and at times under combat conditions. During the course of the Committee’s work, CONTRACTS AND PROJECTS 11 members visited the various investigating agencies to correlate the work when necessary, obtain first- hand information of the special aspects under investi- gation, or suggest a line of attack. Such visits are deseribed in Chapter 3. 2.3 CONTRACTS AND PROJECTS The entire organization and work of the Committee was carried on under the auspices of Army and Navy Project AN-16, pursuant to a recommendation of the Combined Meteorological Committee [CMC] of the Combined Chiefs of Staff, dated December 7, 1943. This recommendation was made to the National Defense Research Committee in response to a request by the Combined Chiefs of Staff dated December 4, 1943 and channeled jointly through the War Depart- ment Liaison Officer and the Coordinator of Research and Development. The Combined Chiefs of Staff asked specifically that: 1. The Committee on Propagation of NDRC be requested to act as a coordinating agency for all meteorological information associated with short wave propagation. 2. The Committee on Propagation be requested to forward periodically to the CMC a list of all reports and papers dealing with the meteorological aspects of short wave propagation which have been received or transmitted by that Committee. Originally contracts arranged with various agen- cies for research into propagation phenomena were handled through the contract machinery of the appropriate division of NDRC, specific recommen- dations for the terms of the contract being drawn up by the Committee. The NDRC later changed the manner of arranging contracts of the Committee on Propagation so that the Committee would recommend, and assume direct responsibility for, the contracts. At the same time the contracts that had already been let by Divisions 13, 14, and 15 involving radio wave propagation were transferred to the Committee on Propagation. Such further extensions to these contracts as were required were arranged and recommended by the Committee on Propagation. Contract OEMsr-1207, let for the Committee, with Columbia University through the contract machinery of Division 14, was active from Novem- ber 1, 1943 to October 31, 1945. This contract was for collecting, analyzing, and integrating data on radio and radar wave propagation. Under its terms the CUDWR set up a Wave Propagation Group, directed by Professor $. 8S. Attwood, who had served on the Committee while that body was a part of Division 14. This group consisted of a scientific staff and stenographic and clerical personnel, and it handled the work described above, as well as periodic publication of reports for distribution according to a list approved by the NDRC chairman’s office. Contract OEMsr-728, with the State College of Washington, which was originally let through Division 14 and taken over by the Committee on Propagation after its formation, terminated on October 31, 1945. Work under this contract was under the direction of Dr. Paul A. Anderson of this college. The contract was a general one for the purpose of ‘‘carrying on experimental and analytical investigations in connection with the study of micro- wave propagation.” The first research conducted under its terms was a study of propagation along an overland path in the Pacific Northwest, where climatic and topographical conditions differed from those at San Diego and on the Hast Coast. Another project under this contract was the development of a portable low-level sounding instru- ment for measuring temperature and humidity gradi- ents in the lower atmosphere. Subsequently this apparatus was adopted by the U.S. Navy and several other United Nations military and scientific agencies. Production of an improved model of this equip- ment was also carried out, with subsequent deliveries to the Army Air Forces [AAF], the Naval Research Laboratory [NRL], the Department of Scientific and Industrial Research in New Zealand, and to Dr. Paul C. T. Kwei and Dr. Eugene T. Hsu for use in China. Performance of the sounding apparatus under tropical conditions and tests to determine the feasi- bility of predicting nonstandard radar coverage by means of atmospheric soundings were the objects of another project, which was carried out in Panama in collaboration with the NRL. Another very important project under this contract was Office of Field Service Project SWP-3 which was for the purpose of exploring meteorological condi- tions in the Southwest Pacific theater to determine their effects on radar coverage, and to assist the AAF in establishing a forecasting service for the tactical exploitation of nonstandard propagation in that region. A member of the State College of Washington group working under this contract was loaned to 12 OBJECTIVES AND RESEARCH AGENCIES the NRL staff to assist in an experiment at Antigua early in 1945. This experiment investigated and established the existence of surface air layers having significant effects on radar coverage over large areas of the ocean. Contract OEMsr-1502 between the Committee and the Jam Handy Organization of Detroit was in force from May 7, 1945 to December 31, 1945. The contractor undertook the production of a motion picture and various other training aids, designed primarily for use by the armed forces in educating ~ personnel concerned with propagation phenomena, and secondarily to acquaint all agencies concerned with progress made. Contract OEMsr-1496 between the Committee and the University of Texas was in force from June 1, 1945 to October 31, 1945. This contract required the contractor to develop equipment for, and make measurements of, deviations in angle-of-arrival of microwaves propagated through the lower atmos- phere. It was designed also to supplement and expand knowledge of the deviations in angle-of-arrival already obtained through experiments conducted by the BTL. These deviations were considered large enough to affect the accuracy of gunlaying radars and similar equipments. Contract OEMsr-1497 with the Humble Oil Company of Texas was in force from June 2, 1945 to October 31, 1945. Under its terms the contractor undertook construction of certain field strength measuring equipments for use in experiments being carried on as part of Project AN-16 in the Naval Research Laboratory, Navy Radio and Sound Laboratory, and the Army’s Camp Coles, Camp Evans, and Watson Laboratories, and by the New Zealand Joint Communications Board. These five contracts make up the total of direct contractual relationships entered into by or on behalf of the Committee on Propagation but represent only a small portion of the work on propagation problems carried on in the United States. The bulk of actual research was conducted under contracts let by Divisions 13, 14, and 15 and by the Service in conjunction with laboratories and industrial com- panies. The Committee served as the integrating, analyzing, and disseminating body for the results of all such work bearing on the propagation problem. In addition to carrying on the general integration of reports and papers from all sources (see list of sources in the Bibliography), the Committee spon- sored three conferences which were attended by representatives of most of the agencies investigating propagation phenomena. A similar conference was held before the Committee was in being, and a report of the proceedings was published by the Wave Propagation Group of the MIT Radiation Labora- tory. The fourth and last conference on propagation, the third held under sponsorship of the Committee, was attended by 236 persons, representing approxi- mately 59 separate agencies in and out of the armed forees of the Allied nations. This meeting took place May 7, 8, and 9, 1945 in Washington, D. C. Full reports of this and previous conferences are listed in the Bibliography. Chapter 3 CHRONOLOGICAL RECORD 3.1 COMMITTEE ACTIVITIES ‘| [es COMMITTEE ON PROPAGATION was organized in Division.14 of the National Defense Research Committee, in response to an urgent request by Sir Edward Appleton, Director of the Department of Scientific and Industrial Research of Great Britain. This request was specifically for United States cooperation in a more adequate investigation of radio Wave propagation. Observed variations of radar coverage and performance over a considerable range of climatic and meteorological conditions had already revealed the need for a thorough understanding of the influences of such conditions on radio wave propagation, particularly at frequencies above 30 me. Also, the effects of back scattering of radiation from the sea surface (sea return) under various wind and wave conditions and of land surface topographies of various types on radio wave propagation, particu- larly at angles approaching the horizontal, were already known to be serious. These and similar factors had been established by reports from opera- tional installations as having profound significance in the operational employment of radio devices, and the fundamental mechanisms producing these effects were not well understood. A preliminary conference on propagation was held at the Massachusetts Institute of Technology [MIT] Radiation Laboratory [RL], July 1 and 2, 1943. A report of this conference was published by the Laboratory. It contained a statement of the general program of investigation held desirable and recom- mendations for setting up a body to coordinate the activities of research agencies with needs of the armed forces and with work on the problem already in progress in Allied countries. This body, which became known as the Committee on Propagation, was organized as explained in Chapter 2, with Dr. Chas. R. Burrows as chairman. Dr. Burrows accepted the chairmanship on August 24, 1943, proceeded immediately with organization of the full Committee, and began the task of estab- lishing and correlating a program of research. Dr. Burrows and Donald E. Kerr, head of the Wave Propagation Group at the Radiation Labora- tory and a member of the Committee on Propaga- tion, conferred in Washington on September 2 with Dr. A. F. Murray of NDRC and with Doctors H. Hopkins and W. Ross of the British Central Scientific Office. A complete set of reports of British work on propagation was available in this office, and this was placed at the disposal of Dr. Burrows and the Committee. The desirability of extending the investi- gation down to 27 me was discussed in connection with improving the efficiency of certain equipments using those frequencies. On September 3, Dr. Burrows and D. E. Kerr con- ferred with Dr. J. A. Stratton in the Office of the Secretary of War regarding Dr. Stratton’s serving on the Committee and the possibility of minimizing or eliminating ground return in radar operation at low angles. Comdr. F. W. Reichelderfer, head of the Weather Bureau, was also contacted, and the use of radar in locating storm areas was taken up. During the remainder of September the organiza- tion of the Committee was pushed forward, with the result that the names of Stratton, Dellinger, Beverage, and Kerr were formally proposed for membership to the Office of the Chairman, NDRC. The first official meeting of the Committee on Propagation was held on October 13, 1943, with the following members and representatives of interested agencies: Dr. Chas. R. Burrows, Chairman; Dr. J. H. Dellinger, Division 13, NDRC; D. E. Kerr, Division 14, NDRC; Dr. H. H. Beverage, Division 15, NDRC; Dr. J. A. Stratton, War Department; J. H. Teeter, representing the Chairman, NDRC; Dr. H. G. Hopkins, representing the British Central Scientific Office; and Lt. (jg) J. M. Bridger, repre- senting Captain D. R. Hull of the Navy Depart- ment. The field of propagation was reviewed, the specific functions of the Committee were defined, and a list of definite problems for both immediate and longer term consideration was drawn up. It was agreed that the Committee would confine itself to the study of tropospheric propagation, at least at first, with special emphasis on problems of nonstandard propagation. On October 15 Professor 8. S. Attwood of the Uni- versity of Michigan agreed to assist Dr. Burrows in directing the activities of the Committee. Later 13 14 CHRONOLOGICAL RECORD Prof. Attwood was appointed Director of the Colum- bia University Wave Propagation Group [CUDWR WPG] which operated under contract OEMsr-1207, to integrate, analyze, and disseminate reports of research. This contract went into force on Novem- ber 1, 1943. Dr. Burrows, Prof. Attwood, and D. E. Kerr flew to England November 22, 1943, to confer with British investigators and secure integration of the United States and British programs. As a result of this visit, a unified program of research was agreed upon, with certain divisions of effort to prevent duplication of particular phases of the work, and to insure covering all practical aspects of the problem. The British agreed to continue experiments on wavelengths of 9, 6, and 3 cm, with parallel measurements of meteorological factors, and also to undertake measurements at 1.25 em when equipment became available. The effects of hills and trees on the shorter wavelengths was also to be studied. They were also to continue theoretical investigations already under way with special emphasis on use of the Manchester University differential analyzer. It was agreed that American agencies would make detailed measurements to determine the character- istics of water vapor diffusion in a warm air mass blowing over cold water, with accompanying radio transmission tests at wavelengths of roughly 10 and 50 cm. A team of research workers was to be organ- ized and equipped to make simultaneous propagation and meteorological measurements at locations pro- viding conditions similar to those encountered by radar-using personnel of the armed forces. Tests on 1.25-cem waves were to be made along the eastern coast of the United States as apparatus permitted, to provide data on propagation conditions typical of the eastern coast of a large continent. It was agreed also that Dr. John E. Freehafer of MIT-RL would be sent to Britain in order to obtain © closer cooperation in theoretical attacks being made on these problems. It was further agreed to make a study of atmos- pheric absorption, particularly at 3-cm and shorter wavelengths, and of absorption by rain, fog, dust, and other such phenomena. The reflection coefficient of the sea for radiation of 10-em and possibly 3-cm and shorter wavelengths was to be studied for graz- ing angles less than 5 degrees, and the back-scatter- ing effect was also to be investigated. Storm echoes and their possible tactical uses were also to be treated. In addition, the United States was to set up and maintain a group to compile, analyze, integrate, and disseminate propagation information. It was jointly agreed to interchange samples of meteorological instruments most useful for measure- ments in connection with propagation studies. Upon return to the United States of this mission, in January 1944, offices were occupied in the Empire State Building, New York City, jointly with the Wave Propagation Group of Columbia University Division of Wir Research. On February 12, 1944, a meeting was held at which liaison representatives from the armed forces presented certain urgent Service requirements and outlined experimental programs that the respective branches were prepared to undertake in cooperation with the Committee. One of the most urgent needs in the Services was for a handbook and other instructional aids, prepared in the simplest practicable form for the use of opera- tional personnel with limited technical background. It was proposed that the Columbia University Wave Propagation Group, which had been set up in accord with the program agreed on with the British, should undertake the preparation of such aids to instruction. At a meeting held February 15, 1944, a statement outlining the propagation problem was drawn up, with proposals for Service cooperation in experiments devised to provide solutions to the most urgent aspects of the question. This statement set forth the NDRC Committee’s view that the problem of “non- ionospheric propagation in a nonstandard atmos- phere” should be given highest priority, and it gave details of experiments proposed or already under way. Five specific experiments were outlined, in each of which the assistance of the Services was required. These were as follows: 1. Organization and equipment of a complete transportable field unit for conducting propagation experiments, which could be sent to any region considered likely to yield results useful in the opera- tional theaters. This experiment would require con- siderable apparatus and a team of trained research, operational, and maintenance personnel. Dr. Paul Anderson of the State College of Washington provided a considerable amount of material on this project. 2. An over-water experiment along a path between Cape Ann and Cape Cod was to be carried out by MIT-RL, to obtain information on propagation characteristics along the eastern coast of a continent. These data would be applicable to similar regions in COMMITTEE war theaters, particularly near the Chinese north- east coast. 3. A detailed experiment was considered desirable in a region where stable temperature inversions were produced in the atmosphere by subsidence of upper layers of air. Such experiments were already being conducted by the U. $8. Navy Radio and Sound Laboratory |NRSL] along several over-water paths near San Diego, California. 4. An experiment near the Panama Canal Zone was planned by the Navy in cooperation with the State College of Washington group under Anderson, to establish a correlation between meteorological conditions of that region and radar performance. It was expected that this would provide a good test of equipment and methods under tropical conditions and that the information obtained would apply in other similar regions. 5. An experiment was proposed to be conducted in Florida, with the aid of Signal Corps and Air Force personnel utilizing equipment already in the area. It was expected that this project would yield considerable information on means of predicting propagation characteristics for localities climatically similar. Meantime the Columbia University Division of War Research Wave Propagation Group [CUDWR WPG], directed by Prof. Attwood and operating under contract OKMsr-1207, was preparing a report on tropospheric propagation for radar operators, offic- _ers, and other operating personnel, at the request of the Combined Communications Board [CCB] and Combined Meteorological Committee[CMC]. This re- port, compiled from all established data on variations in radar coverage available, was prepared in as non- technical and popular a style as possible. It received the approval of the Wave Propagation Committee of the CCB, and about 30,000 copies were distributed to the armed forces of the United Nations during June 1944 under the title Variations in Radar Cover- age (JANP-101). This report helped to clarify the problem of nonstandard propagation for Service personnel and to throw light on certain peculiarities in radar performance and coverage variations caused by newly discovered meteorological conditions (see Chapter 16). During early 1944, a bibliography of publications on propagation was prepared and published by the CUDWR WPG. Ata meeting on February 28, 1944, a direct request from General MacArthur to NDRC was laid before the Committee, which asked that a group of scien- ACTIVITIES 15 e tists be sent to Australia to study radar and commu- nication problems in that area of the Pacific theater. It was finally arranged that the communication part of this request would be handled by the Signal Corps and that the radar portion would be fitted into the general research program already in process of organization. Out of the series of meetings and conferences held during February, a program of four principal points was developed which was presented on March 4, 1944, to the Wave Propagation Committee of the Joint Communications Board. This program was accepted and put into effect soon afterward, as follows. 1. A working group under the direction of Dr. Anderson proceeded to the Canal Zone to conduct meteorological measurements in cooperation with the Navy. Following completion of this work, the group proceeded to Australia and’ performed similar investigations as requested by General MacArthur. This work was carried on under contract OEMsr-728, with the State College of Wishington. Arrangements were also made for training a group of about 20 Army and Navy officers in use of the meteorological measurement technique and apparatus developed by Dr. Anderson. These officers were later to be sent into the field to organize teams for making meteorological soundings. 2. The Wave Propagation Group of the MIT-RL under D. E. Kerr conducted a study along an over- water path on the east coast of the United States, as outlined previously. 3. The NRSL investigation of propagation under subsidence conditions was continued. 4. Propagation conditions over land were planned for study by Canadian Army research groups. Pre- liminary discussions were held with these groups early in 1944. On March 13, Dr. Burrows and Prof. Attwood con- ferred with the staff of the NRSL in San Diego in connection with the investigation of propagation under subsidence conditions. The research was in- tegrated into the general program and reported to the Joint Communications Board [JCB] on March 29. As a result of this visit the NRSL agreed to modify and expand its propagation research extensively to include tests over a number of different paths, using both one-way and radar transmissions, with simul- taneous meteorological measurements. These experi- ments were to be measurements of propagation on three representative frequencies along a 108-mile 16 CHRONOLOGICAL RECORD over-water path between Los Angeles and San Diego, and comparable frequencies between San Diego and San Pedro, a distance of 80 miles over water, using suitable antenna heights. Atmospheric soundings were to be taken from a ship at a point midway along such paths and also on shore as near the midpoint as possible. Measurements with a blimp to determine the extent of uniformity of the inversion layer were also projected. Measurements were to continue on fixed radar targets located at various altitudes and along various azimuthal bearings. Field strength measurements were also to be made from an aircraft flown at sig- nificant altitudes over the transmission paths, the results to be correlated with meteorological data. The chairman assisted inauguration of this expanded program by using the Committee’s powers and in- fluence in obtaining additional apparatus required. In addition, information was exchanged with mem- bers of a British scientific delegation who were present, and considerable effort was directed to ob- taining a meteorologist for full-time work with the NRSL group conducting the experiment. - On April 3, Dr. Burrows, Comdr. J. L. Reinartz, and Lt. Comdr. D. H. Menzel visited Panama to observe the experiments being conducted jointly by Dr. Anderson’s group and the Navy. As a result of this visit, substantially better and more extensive cooperation between the scientific group and Service forees in the area was obtained, and an analysis of the data obtained to date was secured, which revealed occurrence of a predictable surface duct condition. A conference was held in Washington on May 2, 1944, at which representatives of the various research agencies of the United States interested in propaga- tion were present. A large amount of propagation information was exchanged by presentation of many papers describing various experimental and theo- retical researches going on in various countries. The complete record of papers and proceedings was published by the CUDWR WPG and is contained in the Bibliography at the end of this volume. Special consideration was given to the question of symbols and nomenclature by a committee headed by Prof. Attweod. A list of such symbols was pre- pared by this committee and was accepted without dissent by the Wave Propagation Committee of the CCB on May 17, 1944. On May 23 the chairman of the Committee on Propagation presented to the NDRC a report on what had been accomplished up to that time by the Committee and its plans for the ensuing year, to- gether with budget requirements. The budget was approved with minor deletions in the items covering contingencies. On June 29, 1944, a meeting was held at which the progress of the various experimental projects was reviewed in some detail. Two Armed Service requests were also taken up. The first, submitted by Comdr. Menzel and Dr. T. J. Carroll, dated June 12, 1944, outlined the general needs of the Services. Copies of this letter were forwarded to the Committee members for their consideration before the meeting convened. The second was received from General Colton, in the Office of the Chief Signal Officer, and specifically requested a theoretical investigation of the effects of low-level tropospheric layers on propagation at wave- lengths near 10 and 3 cm. After discussing specific requirements of the services as laid down in the Menzel-Carroll letter, certain of the questions were referred to appropriate agencies for solution. In particular, MIT-RL undertook to study the effects of refraction on gunfire control radars operating in the 10- and 3-em bands. Most of the other questions raised were already under inves- tigation but were not yet sufficiently advanced to permit of conclusive answers. General Colton’s re- quest was considered to be covered by the action taken in connection with the Menzel-Carroll letter. In addition to progress reports from United States research agencies, a report on British work was sub- mitted, particularly on the status of 9-6-3-cm experi- ments over the Irish Sea. Little useful correlation between propagation and meteorological factors had yet been obtained in this experiment. Projected British experiments included investigation of absorp- tion and attenuation of 10- and 3-em band radiation in oxygen, in water in all forms occurring in the atmosphere, and in salt spray. Late in June 1944, the need for closer liaison between the Committee and CMC was met by the appointment of Major H. Wexler of the Army Air Forces, Weather Division, as a technical advisor. This also strengthened the meteorological represen- tation associated with the Committee, which had not formerly been completely adequate. The Committee met at the Radiation Laboratory on August 4, 1944. During this meeting plans were laid for an extensive conference on propagation to be held in Washington, D. C., on November 16 and 17, at which representatives of research agencies in COMMITTEE ACTIVITIES 17 all the countries engaging in propagation research could present findings to date. Plans were laid for Dr. Anderson’s trip to the Southwest Pacific theater in response to General MacArthur’s request for investigation of propagation phenomena. This project was of considerable im- portance and is more fully described elsewhere in this report. A report by Dr. Svein Rosseland, assistant to Prof. Attwood in the CUDWR WPG, was heard, on work going on in England and on data brought back to that country by Dr. Booker. These data described radar echoes from points more than 1,500 miles from the 200-me Bombay, India, station, which had been observed during the season following the northeast monsoon. Other reports were heard on Bell Telephone Laboratories [BTL] experiments on K band along a path to Atlantic Highlands and similar experiments by MIT-RL near Boston. No nonstandard propaga- tion had been observed at Atlantic Highlands, but some had occurred in the Boston area. Experiments of MIT-RL along a ten mile path had indicated the impossibility of measuring the effect of oxygen and water vapor outside the labora- tory itself. Dr. W. H. Furry described the work of preparing coverage diagrams for radar and VHF (very high frequency) communication equipment under ground- based duct conditions. Owing to the volume of calculations required in this work it was decided to obtain use of the Harvard University automatic sequence-controlled calculating machine, which would effect a probable reduction in the time required from an estimated nine or ten months to about three weeks. This proposal was subsequently carried out. Dr. Beverage presented certain problems of Divi- sion 13, particularly the need for supplying the best information on’ probable coverage to signal officers in the field at the earliest possible date. Estimates based on the % earth radius formula tended to be pessimistic. Dr. H. Goldstein presented information on the problem of fluctuating signals. Instability in the equipment was a source of great difficulty, but, when this had been overcome, such results as were obtained indicated that most fluctuation was due to inter- ference. Plans were made for a field trip to observe the extensive MIT-RL experiments proceeding on four different wave bands along a path between Race Point and Gloucester. On this trip the entire ap- paratus and organization of the experiment were inspected and discussed. A detailed memorandum of the Committee’s current work was submitted on August 10 to the Chiefs of NDRC Divisions 13, 14, and 15, in order to keep these groups informed of developments. The breakdown of activities described five well-controlled experiments which were under way in different meteorological environments and the theoretical attack proceeding in Britain and the United States. These experimental attacks on the problem have been described earlier in outlining the Committee’s program for the year. The memorandum referred to here specifically invited Division comment on the program in progress and requests for other investi- gations if additional ones seemed desirable. A Committee meeting on September 21, 1944 considered new humidity measuring instruments and reviewed progress of the work under way at RL. This was reported by D. E. Kerr as nearing the conclu- sion of the experimental work. The matter of educa- tional films to disseminate propagation information to the Services was brought up, and the need for a technical aide to the Committee who should be familiar with NDRC procedure was discussed. Dr. Burrows stated that efforts were being made to obtain a contractor who would make meteorological measurements along the BTL to Mt. Neshanic prop- agation path, for correlation with the transmission data available at BTL. These measurements were later undertaken by the Airborne Instruments Lab- oratory [AIL] of Mineola, Long Island. The matter of eventual demobilization of OSRD was discussed, particularly as to effects of such demobilization on investigations of propagation then in progress, The Committee met again on November 15, 1944 to consider replies received from Divisions 13, 14, and 15 to the memorandum outlining its program in progress submitted on August 10 and to transact other business. The matters of calculation of radar coverage diagrams for nonstandard conditions, of the range and reliability of very high frequency [VHF] and ultra high frequency [UHF] communica- tions links, and the choice of frequencies for such links were taken up in detail. After thorough con- sideration, a reply was drafted for the Divisions concerned, particularly Division 13, stating that available information on propagation did not permit preparation of accurate coverage diagrams for such communications circuits on any other basis than 18 CHRONOLOGICAL RECORD that of 44 earth radius, as was already being done. It was expected that work then in progress would modify the limitation as it progressed. In the matter of choice of VHF, UHF, and super high frequencies [SHF], information was not yet available, but surveys under way were expected to provide some back- ground, although the intricacy of the problem did not encourage hope of an early complete solu- tion. The difficulties involved in the preparation of field strength contours appeared so formidable that requests from the Services for preparation of such contours was withdrawn, and a new request was substituted. This asked that workers on theoretical or observational and experimental programs forward as informal memoranda such examples of correlations between meteorological conditions and propagation characteristics as could be applied directly in the field, with suggestions for possible tactical applica- tions. This substitute request was received by the Committee in November. In addition, an important report by Dr. Anderson from the Southwest Pacific theater was considered which described the progress of project PDRC-647 which members of the State College of Washington staff had undertaken under Contract OEMsr-728. Its objectives were to explore meteorological condi- tions in the Southwest Pacific theater to determine their effects on propagation, and to assist the Army in establishing a forecasting service for the tactical exploitation of nonstandard propagation in that region. After several conferences between Dr. Anderson’s group, various Australian agencies, and representa- tives of the Air Signal Office, Far East Air Force [FEAF], headquarters for the mission was established at the Radio Physics Laboratory at Sydney. Meet- ings were held here with Professor F. W. G. White and representatives of the Royal Australian Air Force and Royal Australian Navy. The following facts were brought out. The Australian and NDRC programs supplemented each other without duplica- tion of effort, making revision of plans unnecessary. An acute need existed for definite information con- cerning low-level meteorological conditions in the oceanic areas of the Southwest and Central Pacific. This information could best be obtained by NDRC and United States Army groups. Rough forecasting of nonstandard propagation along the southeast, south and southwest coasts of Australia was possible, correlating superrefraction data collected from radar stations with synoptic meteorological data. Observations from North Australia showed no similar clearcut correlations. Reports from New Guinea and the Solomon Islands were too meager to be useful. A Radio Physics Laboratory [RPL] experimental program was projected at a location near Darwin, Australia, which would be correlated with land, ship- based, and aircraft soundings and synoptic weather. A low-level sounding equipment was delivered to RPL for use in these experiments. A conference was held at the Radio Development Laboratory in New Zealand at which a low-level sounding equipment was delivered and trial sound- ings taken by Dr. Anderson. As a result of this meet- ing, a long-range program was agreed on in addition to the work already being conducted by New Zea- land agencies. This program would take advantage of the unusual conditions offered by the persistent Fohn winds which override the cold water at the eastern coast. Dr. Stephenson of Dr. Anderson’s group began the collection of meteorological and oceanographic data available in Australia preliminary to the selection of optimum sites for radar-weather observations. New information was available on continental and general equatorial meteorology but very little for the ocean area to the west and north of New Guinea. Recommendations for establishment of a limited number of radar-weather stations in the Biak-Owi- Noemfoor region were submitted to the FEAF late in August. These recommendations were approved after some discussion, but the plans were changed when FEAF headquarters suggested the usefulness of an Army radar-weather team with sounding equipment in the projected operations at Leyte. Preparations were made to take advantage of this suggestion. Consideration was given to determination of the low-level conditions characteristic of the Southwest and Central Pacific oceanic areas, with tentative conclusions from data secured during the summer of 1944 that strong ducts to 40 or 50 ft and weaker stratifications to 800 or 1,000 ft were common in the region, especially in late afternoon. In the dol- drum region standard conditions were the rule. The need for more complete measurements was pointed out, and the use of PT boats and seaplanes to obtain them was secured. Approval for measurements in the region near COMMITTEE Saipan was also obtained, and arrangements were begun for the transfer of personnel to that theater. Further informal conferences were held with Australian and British groups, from which these conclusions were drawn. General meteorological data did not provide sufficient information quickly to be of practical use in forecasting propagation in a given area. Instead, intensive ground-based and aireraft soundings offer the most practical means for setting up a short-range forecasting service for radar and radio communication coverage. At a formal conference with the same groups a policy to be adopted by the Australian Services was decided upon. An operational program similar to the NDRC Office of Field Service program was outlined by the members and approved for immediate inau- guration. A radar-weather school was to be set up in the Meteorological Section of the RAAF for training radar-weather officers. Arrangements for manufacturing sounding equipment were also made, with almost all components planned for production in Australia. Plans for expanding the operational program at Leyte were laid, and arrangements for observations at Saipan were also concluded. Measurements at Woendi Island were planned to continue until definite results were obtained, and arrangements were also made for transferring direction of the project to an officer of the Fifteenth Weather Region Headquar- ters, after which all civilian personnel with the exception of Mr. Grover would return to the United States. Mr. Grover would remain for the purpose of maintaining contact between the U. 8. Army, Australian, and NDRC programs. Finally, recommendations for future procedure in this theater were made, which included maintaining at least one civilian research meteorologist in the area, and perhaps a group with the Army in China. Another conference on propagation was held during November 1944, attended by representatives of the investigating laboratories and armed forces of the Allied Nations. A large number of papers were delivered on propagation and related subjects. A full report of this conference was prepared by the CUDWR WPG and distributed to approved agencies. At the next meeting of the Committee, held on December 9,1944, anumberof new matters were taken up, as well as the status of work already in progress. A group of British research workers, who had been conferring with United States propagation workers during a tour of laboratories in this country, reported ACTIVITIES 19 on their findings. Dr. Booker also gave a detailed account of the work going on in Australia, as seen by him during a visit to that country which he had just concluded. The joint United States-British program was discussed, as well as methods of interpreting results of propagation experiments, calculations of coverage diagrams, and the proper dissemination of a report, Tropospheric Propagation and Radio Meteor- ology, which had been prepared by CUDWR WPG. This report, distributed in December, was a compact but thorough summary of the established informa- tion on propagation obtained to the date of its prep- aration. It was on a practical but much more quan- titative level than Variations in Radar Coverage issued earlier under auspices of JCB. It proved to be of considerable value to radar officers, particularly in improving the confidence and efficiency of radar operating and siting personnel, who had previously had at best only qualitative conceptions of such ef- fects as superrefraction and trapping of radiation in ducts. A subcommittee of the Committee on Propagation met on December 30, 1944, and heard a personal re- port by Dr. Anderson on his mission to the Southwest Pacific during the middle of the year just ending. From the results of this mission it was apparent that low-level ducts existed over substantial areas of the ocean in the trade wind regions which had profound effects on propagation characteristics of radar and VHF radio frequencies. These propagation charac- teristics were also found to vary markedly with heights of transmitting and receiving antennas. After consideration of these findings, the subcommittee decided that a carefully controlled experiment under sunilar conditions was an urgent necessity, in order to reduce these qualitative indications to reasonably accurate quantitative data, which could be applied by operational personnel in theaters where similar conditions existed. It was decided that an experi- ment conducted directly by the Navy at a suitable location in the Caribbean area would be most prac- ticable, and plans were drawn up for a detailed investigation by one-way and radar transmission on several frequencies. In response to a request from Brigadier General Borden the Committee arranged on December 14 for establishment of a meteorological sounding station in the Southwest Pacific [SWP] area. On December 19 a letter was drafted and despatched to Dr. E. M. Marsden, Director of Scientific Developments in the Department of Scientific and Industrial Research in 20 CHRONOLOGICAL RECORD New Zealand. This letter commented on the work already accomplished, as reported to the Committee by Dr. Anderson and Dr. Booker, and invited expan- sion of the investigation, particularly to determine the effects on propagation of a hot, dry, air mass mov- ing from the land out over the sea. This condition existed in many other operationally important regions of the Western Pacific and was known to affect seriously the performance of coastal radar installations. On January 1, 1945, Dr. Stratton asked to be re- lieved of his responsibilities as a Committee member and accepted in lieu thereof an appointment as a consultant, which capacity permitted him more time for discharging his duties in the Office of the Sec- retary of War. At a meeting held on January 5 many questions were taken up, and progress made in the preceding year was reviewed. The following projects were reported as proceeding concurrently. 1. The Navy experiment along an over-water path in the Caribbean area, where thin surface ducts were prevalent. 2. Experiments where relatively dry air moved from the land over a water surface. These included the MIT-RL experiment near Cape Cod and analysis of the data obtained, and experiments going on in New Zealand. 3. Propagation over a land surface where radiation cooling produced temperature inversions in the lower air layers. An experiment was being conducted in Arizona by NRSL, and another was being prepared in Canada by the Army Operational Research Group. 4. Experiments along an over-water path where subsidence of an upper air mass produces duct condi- tions. The NRSL was conducting such experiments near San Diego, which offered conditions typical of certain other areas in the Pacific. 5. Developments of meteorological theory for low- level ducts in purely oceanic air. This work was going on at MIT-RL. 6. Development of atmospheric sounding equip- ment for the armed forces. This work was going on at the State College of Washington. 7. An educational program designed to provide the Services with up-to-date information on the propagation question. This was being carried out by Columbia University. 8. Mathematical calculations of wave propagation characteristics. These calculations were being con- ducted by CUDWR WPG and by MIT-RL. In addition, certain new questions were taken up with a view to arranging experiments to provide the answers. These were the matters of accuracy of gun-laying radars as affected by variations of .the refractive index, the reflection coefficient of open sea surfaces, and radar cross sections of ship and airplane targets. The latter two questions were being undertaken by NRL, and the former was believed possible of solution by BTL. The business matters of improved liaison with Pacific theaters and of the budget for the ensuing period were also taken up. At other meetings held during January 1945, organizational, personnel, and equipment matters were taken up and settled as facilities permitted. Dr. Carroll, of the War Department Radio Propaga- tion Section, was appointed a Committee member on January 12. Possible cooperation with China was discussed, following a discussion by Dr. P. C. T. Kwei of Wuhan University, of research carried on in China before and during the retreat from the Japanese invasion. During the month of February the Committee on Propagation established liaison with the Watson Laboratories of the Army Air Force which had recently begun operations. In February also the Committee heard an address by Dr. 8. K. Mitra of the Council of Scientific and Industrial Research in India and established liaison with that body. The question of utilizing the services of Dr. Kwei and his assistant, Dr. Eugene Hsu, in obtaining ionospheric information after their return to China was also discussed. On March 6, 1945, a detailed report by Dr. Carroll on uses of tropospheric propagation in the Army was submitted to the Committee. This report had been prepared during January and provided a great deal of information needed by the Committee in continuing the propagation investigation. At later meetings in March, the matter of utilizing the services of Dr. Kwei and Dr. Hsu was settled affirma- tively, and a meeting was held with representatives of the Coast Guard to establish a better liaison link with that service. Martin Katzin of NRL was appointed a Committee member early in April. Later that month the Chairman prepared a report for Col. D. N. Yates, Chief of the Weather Division, AAF’, on the problems COMMITTEE involved in correcting existing errors in fire control radars, due to refractive effects. The fourth conference on propagation was held in Washington in May 1945. This conference was the largest and most comprehensive yet held and was attended by 236 representatives of about 59 separate agencies of the Allied Nations. A réport of this conference was published as usual by the CUDWR WPG and distributed through authorized channels. A great deal of important data was pre- sented at this conference, including showing of a motion picture produced in Britain which presented in effective form much information on nonstandard propagation, particularly propagation in ducts of stratified air layers. Another short motion picture prepared in Canada was presented in which radar echoes from snowstorms were shown on an acceler- ated time scale. Progress of such storms was readily followed by radar observation, and the importance of microwave propagation for this and similar applications was made apparent. At the close of the conference the chairman announced that a contract had been negotiated with the Jam Handy Organization for production of a motion picture to present pictorially the uses of propagation data by the armed forces. With the collapse of the enemy in Europe, little shifting of the Committee’s program was required. The Committee was formed too late in the war to be of major help in the European theater so from the start the efforts were aimed at the solution of propa- gation problems of the war in the Pacific the- ater. A meeting late in June 1945 considered advances in theoretical methods of attacking the propagation problem and agreed on certain standard symbols for representing the quantities involved, to avoid confusion between investigating agencies. Two additional contracts were arranged during June, the first with the University of Texas for the measurement of variations in angle of arrival of microwave radiation under varying meteorological conditions. This question has a very direct bearing on the troublesome question of improving accuracy of radar controlled gunfire, which played such an important part in defense against Japanese suicide plane attacks. The second contract was negotiated with the Humble Oil Company on July 2, 1945, for the manufacture of a number of field strength measur- ing equipments which were required by various ACTIVITIES 2) Service agencies of the United States and Allied nations. A particularly important meeting of the Committee took place on July 13 in Washington. This meeting was attended by several representatives of the Allied Nations, including Professor D. R. Hartree, J. M.C. Scott, and Lt. Comdr. F. L. Westwater from England, and Drs. Kwei and Hsu from China. The progress of the theoretical attack on wave propaga- tion through a nonhomogeneous atmosphere was thoroughly discussed by Prof. Hartree and Dr. C. L. Pekeris of the Analysis Section of CUDWR WPG. Dr. A. T. Waterman of the Office of Field Service reported on work being done in the Southwest Pacific by D. EH. Kerr. In the investigation of the diffi- culties of operation of the MEW radar on Saipan he confirmed the existence of a low-level evaporation duct discovered by Dr. Anderson and Dr. Stephenson in that area. Elevated ducts, the presence of which had been suspected by Dr. Anderson from analyses of radiosonde data, were definitely determined to exist at heights ranging from 1,000 to 2,700 ft, as a result of Kerr’s investigations. Dr. Waterman also described a survey of Service interest in scientific developments conducted in the entire area commanded by General MacArthur, in which a number of ways were found for OSRD to assist the Army Air and Ground Forces. The Pacific Branch of OSRD was organized so as to furnish a consulting staff under a director, a pool of scientists available for emergency field work, and a laboratory for solution of emergency field problems. This work was to be under directorship of Dr. K. T. Compton, and it seemed very desirable to have a representative in close touch with this OSRD unit in the field. Dr. Anderson stressed the importance of conduct- ing additional research in the Southwest Pacific area, and the need for informing the Services in that theater more fully of the operational advantages to be gained directly from such research. He went on to report progress in development and production of the equipment developed under the State College of Washington contract for making atmospheric soundings. Lt. Comdr. Westwater reported on the overland propagation experiment going on at Suffield, Alberta, which was not yet completed, and described the meteorological conditions obtaining along the trans- mission path. These were of the type producing variations in the vertical angle of arrival of micro- wave radiation transmitted at angles near the hori- i) bo zontal, and Dr. Burrows suggested that this experi- ment might be integrated with the Committee’s angle-of-arrival project for determining refractive errors in gun-laying radar systems. Methods for taking atmospheric soundings were reviewed, and a new combination kite and balloon was described in a report by M. Katzin of NRL. Dr. Carroll reported on extensive tests on prac- tically all types of VHF military voice communica- tion sets, which were being planned in California. He reported that radio propagation tests were going to be correlated with meteorological measurements made with wired sondes. The appointment of Dr. Kwei as the Committee’s representative in China was discussed, and Dr. Kwei described the communication facilities to be made available for handling ionospheric propagation data obtained in China for transmission to the Committee. He urged that more scientifically trained personnel be transported to China when possible, to offset the very great lack of such persons to assist in the work. Dr. Carroll described experiments going on in Florida supplementary to those being conducted in California, designed to answer questions about the maximum reliable range for VHF communications sets under varying conditions. Meteorological measurements made offshore in the Boston area by the Radiation Laboratory Wave Propagation Group were described by Dr. R. B. Montgomery. These established the existence of ducts and at times substandard layers varying in height from 100 to as much as 700 ft, with complex distributions of refractive index. These measurements were especially important as they were known to parallel conditions to be expected in similar regions off the North China and Japanese coasts. Work in progress on all other projects was also discussed, including angle-of-arrival experiments and the overland tests going on in New Zealand, Canada, and Arizona. Mr. R. J. Hearon reported on the new contracts, with particular reference to the direct Service interest in each. The whole future of propa- gation investigation was then considered, particu- larly with reference to the future employment of the propagation group at MIT-RL. It was the opinion of some Service representatives that the operation of this research establishment should be conducted under joint Army-Navy control. It was found impos- sible to reach definite conclusions as to a program to continue after eventual demobilization of OSRD, but general opinion was that a contract under the CHRONOLOGICAL RECORD Chiefs of Staff or other coordinating group might be made with MIT or a similar organization. It was decided to continue discussion at the next meeting. On July 2, 1945, a summary of projects for consideration by the proposed Research Board for National Security [RBNS] was prepared for presen- tation when that body should become active, This included a considerable list of propagation, meteor- ology, and equipment problems requiring further research. At the date of writing, the exact status of this proposal with the RBNS is not known. With the decisive change in the course of the war which took place during July and August 1945, emphasis was shifted from operational propagation problems to organizational and administrative mat- ters, particularly reports, demobilization, and recom- mendations for a continuing program. On July 30, a letter was circulated among the members and representatives of the Services request- ing consideration of certain definite questions relating to future propagation research and reviewing such opinion as had already been expressed on the matter. Service interest in a continuing program had already been manifested, and it was felt particularly impor- tant that action be taken before the teams of ideally suited research workers at MIT and other labora- tories were demobilized. Upon the Japanese surrender in August 1945, the principal efforts of the Committee were directed to accomplishing contract terminations, preparation and submission of a final report, and demobilization of the organization. At a meeting on August 28, the matter of contract terminations was settled, and additional discussion of future propagation research was held. A meeting of the Committee on Propagation was held in Washington on October 30, 1945, to discuss termination of the various projects and related mat- ters, including preparation of a Summary Technical Report and a history, and the probable future of propagation research. This was expected to be the last full meeting of the Committee, and a large amount of business was transacted which can be mentioned only briefly here. The entire membership was present, with liaison officers of various Services concerned and several representatives of contractors and of British and Australian research agencies. Dr. Saxton reported that future work in the United Kingdom was under discussion but that a de- cision had not yet been reached. He described certain experiments proposed for trial in New Zealand, for COMMITTEE which meteorological equipment was needed, and another which might be handled in South Africa. He also explained that the Canadian experiments along a land path near Suffield, Alberta, were con- tinuing and that Sir Edward Appleton was of the opinion that the Ultra Shortwave Panel in Great Britain would continue to function into the peace. Dr. Anderson reported that meteorological appa- ratus consisting of six sets of the lower atmosphere sounding apparatus developed at the State College of Washington was ready for transfer to New Zealand and that about forty sets of castings for the equip- ment were also available for distribution. Mr. Munro announced that propagation research was to continue in Australia at the Radio Physics Laboratory and that the Radio Propagation Com- mittee, a subcommittee of the Radio Research Board, would continue to function. He described the postwar policy for this investigation as favoring an expansion of the investigation with transfer of workers from projects. Fields of investigation in which work was proceeding or planned included tropospheric and ionospheric propagation, scattering from clouds and layers in the middle atmosphere, and a study of radio noise levels. Analysis of Service data was being conducted, a report on extra-long range echoes observed near Darwin had been issued, and a statis- tical survey of superrefraction along the Australian coast was under preparation. Lieutenant W. E. Gordon, AAF, described angle- of-arrival measurements being conducted in New Jersey by BTL, simultaneously with meteorological measurements by the Weather Division of the AAF. Angles varying from 0.7 degree above to 0.1 degree below the line of sight were observed over the 1214- mile path, the nonstandard angles always coinciding with measured nonstandard atmospheric refractive conditions. On two occasions multiple paths had been observed. Dr. E. W. Hamlin reported progress of the University of Texas group which was to study angle of arrival by measuring phase difference. He an- nounced that the Office of Research and Inven- tions of the Navy had agreed to take over the project on an interservice plan of participation, with cooperation of Army and Navy laboratories, and active exchange of information with BTL and other interested agencies. It was also expected that AAF and other field stations would collaborate. Dr. W. M. Rush described progress in construction of the receivers for field strength measurement under ACTIVITIES 23 the Humble Oil Company contract. Of the 24 units scheduled, 18 were to be completed by October 31, 1945. In addition, he announced that the company was interested in geophysical surveys over the Gulf to distances of 30 miles offshore by means of radar measurements and would be glad to cooperate with the University of Texas and Service groups. The chairman announced that steps were under way to declassify all propagation information and to make it feasible for all organizations interested to obtain copies of pertinent material published by NDRC. Captain D. R. Hull announced that the name of the NRSL was shortly to be changed to Navy Electronics Laboratory [NEL] and that facilities in Arizona were soon to be available for cooperation with the University of Texas. D.E. Kerrannounced the transfer of signal strength measuring receivers from RL to NRSL [NEL] and went on to describe a field expedition conducted by himself for the Operational Research Section of the Office of Field Service. He stated that the cause of the poor operation of the MEW was poor adjustment of the equipment. He confirmed the existence of strong superrefraction. He also mentioned contacting a part of Dr. Anderson’s group in Manila and de- scribed the necessity for disseminating knowledge of propagation effects among operating personnel in the field, particularly in the Army. He also described use being made of radar for storm detection by the Southwest Pacific Weather Force and a series of educational talks being conducted with radar officers in the Philippines when the war ended. Dr. Carroll briefly described results of propagation tests made by the Signal Corps along several over- water and over-land optical paths in California, on 100, 250, 1,450, and 4,500 me. Hlevated ducts had been observed, but surface reflection was found to be of greater importance. General conclusions from these tests indicated the importance of reflection from sea and land surfaces and the desirability of employing diversity reception with antennas spaced vertically. Dr. Dellinger described his trip to a conference on radio held in Brazil, at which two government departments of that country had expressed willing- ness to undertake ionospheric observations in cooperation with a world-wide network. These departments had requested equipment and instruc- tions for this work, which were to be supplied. M. Katzin of NRL referred to the Antigua experi- ment completed early in the year and described a 24 CHRONOLOGICAL RECORD similar experiment planned for the Pacific, employ- ing a mobile laboratory and aircraft, with combina- tion one-way and radar transmission. He also men- tioned that NRL and NRSL (NEL) were planning a rather extensive propagation investigation which, however, would not interfere with the work planned for the Navy at the University of Texas. Dr. Beverage announced that the activities of Division 15 of NDRC were to end almost completely on October 31, 1945, and added that some projects were being transferred to the Services but that no propagation studies were active. Prof. Attwood announced termination of the Col- umbia contract (OEMsr-1207) as of October 31 and stated that 34 reports had been written under its terms, with some still awaiting distribution. He also mentioned that the Navy was taking over the Anal- ysis Section of the Wave Propagation Group under a new contract with Columbia University. John Campbell of the Jam Handy Organization described progress in the production of a film cover- ing many aspects of propagation phenomena, which was due for completion about December 10, 1945. Lt. Comdr. W. B. Chadwick described a Navy plan for predicting radar propagation conditions up to 24 hours in advance and transmitting such infor- mation with measured M curves to a central station for correlation and dissemination. He was of the opinion that the end of the war would probably halt this project, making it necessary to return the matter to research groups. Lt. Col. J. J. Slattery and K. A. Norton announced that the Signal Corps planned to extend and continue propagation experimentation in general, in coopera- tion with other Services and industrial and scientific establishments. The chairman requested comment on projected future propagation studies. Dr. Dellinger stated that many questions yet to be answered seemed appropriate for investigation by a national research organization and by the new elec- tronics department of MIT. He added that there was an organization, the Union Radio Scientifique Internationale, with Sir Edward Appleton as inter- national chairman and himself as chairman of the American section, which would exercise a definite interest in the propagation field. D. E. Kerr expressed the opinion that MIT would not be in a position to undertake as large a program as had been suggested and added that after current projects were closed there would still be on hand a large amount of unanalyzed data, which could not be used unless an agency were found to make the analysis. Major Wexler announced that the Army Weather Service would continue to cooperate with groups making propagation measurements and added that the Air Force was negotiating through the Signal Corps for basic research in storm detection by radar to be done at MIT. The chairman announced that in view of the end of hostilities, no new conference on propagation would be called by the Committee. Following a vote of thanks to the Chairman proposed by Dr. Dellinger the meeting was adjourned. This was the last full meeting held by the Committee, but members re- mained active for a considerable time longer, carry- ing on the necessary work of demobilizing the organization. With general demobilization of the Committee imminent and terminations of contracts already taking effect, the principal work of the Committee was concluded. After termination of the Columbia contract, it was felt advisable to appoint Prof. Att- wood a consultant to the Committee to assist with final solution of administrative questions, and this was made effective November 1, 1945. An office for conducting correspondence and preparing this report was maintained in the Empire State Building in New York City, under the auspices of the NDRC Summary Reports Group. With submission of this report for publication, the work of the Committee may be considered closed. Chapter 4 RESULTS AND RECOMMENDATIONS 4.1 RESULTS ee TABULATION of the results of the Committee’s work must be based to a degree on certain intangibles difficult to evaluate. This is because a substantial proportion of the overall result was a change in the attitude of agencies and personnel concerned with the performance of radar and radio equipment using the frequencies above about 30 me. The complete analysis and understanding of propa- gation of these frequencies through the troposphere still lies in the future and will undoubtedly require much additional experimental and theoretical work, conducted without the restrictions of wartime secrecy and urgency. However, a considerable overall tangible result was also achieved, both in establishing the basie theory of tropospheric propagation and in development of methods and instruments for measuring meteorological factors influencing such propagation. In the earlier stages of the war, nonstandard (at first called “‘anomalous’’) propagation caused several confusing and disconcerting incidents, due to misun- derstanding of the phenomena. The instance later called “‘The Battle of the Pips,” which took place near the Aleutians, was paralleled in other theaters many times. In this case echoes returned from islands ordinarily beyond radar range caused such confusion that fire was opened and an attempt made to engage nonexistent enemy units. Such puzzling and exasperating variations in radar and radio performance caused serious loss of confidence in equipment and was of considerable operational sig- nificance. This has been considered more fully in Chapter 1, as it was directly related to the origin of the Committee. The general effect of such publications as Varia- tions in Radar Coverage, of which upwards of 30,000 copies were distributed, Tropospheric Propagation and Radio Meteorology, and numerous other reports prepared and distributed for the Committee by the Columbia University Division of War Research [CUDWR] Wave Propagation Group [WPG] under contract OEMsr-1207, was to restore confidence in the equipment and its use and to focus attention on other causes of unreliability, which previously were often masked by or confused with the effects of propagation variations. These other sources of vari- able performance, principally misadjustment of or defects in equipment caused by the rigors of field service, became easier to track down and eliminate, because they could be distinguished from propaga- tion effects with reasonable success when the latter were understood. Another general result of the Committee’s work was a considerable modification of siting principles for radar and radio equipment. The results of the Caribbean over-water experiment, and of similar tests conducted at San Diego, Cape Cod, and across the Irish Sea, conclusively demonstrated the frequent existence of relatively stable horizontal layers of the lower atmosphere, in which the vertical distribution of refractive index was such as to cause substantial departures of actual radar coverage and radio com- munication range from the values obtained in a standard atmosphere. In particular, it was deter- mined that, over much of the tropical and semi- tropical areas of the oceans, such layers were prevalent during many months, varying in thickness and intensity with wind speed and other measurable meteorological variables. These surface layers often produced large increases in radar ranges on surface craft and low-flying aircraft for radars of appropriate frequency sited in or close above the duct. These investigations also revealed that under certain conditions a reverse effect could occur, in which the radiation was refracted downward much less than in a standard well-mixed atmosphere, with the result that coverage was less than normal. In extreme cases the radiation might even be bent upward away from the surface, resulting in ranges less than optical. In the course of arriving at these general results, methods and instruments for measur- ing the meteorological factors producing these effects were developed, particularly the Massachusetts Institute of Technology [MIT] psychrograph and the State College of Washington [WSC] wired sonde, with techniques for interpreting the data in approxi- mate terms of radar performance. These instruments and techniques were made available to the armed forces of the Allied Nations. A total of about 550 reports on various aspects of 25 26 RESULTS the propagation problem were received from the nu- merous investigating laboratories. These reports were analyzed and the essential information contained was put into forms suitable for the use of operational personnel and distributed to the Services of the United States and the other Allied Nations. Such dissemination usually was in the form of publications by the CUDWR WPG, which issued a total of 34 such reports to a large distribution list. These reports and the very much larger number of scientific papers from which they were prepared are listed in the Bibliography. 42 CRITIQUE The greatest handicap to the work of the Committee on Propagation was the delay in recognizing the need for such an organization. In the rush to get elec- tronic equipment that would allow the realization of the many new war inventions, the fact that the tactical use of these equipments depends upon their quantitative performance, which in turn depends upon the transmission medium, was neglected. As a result when this need was finally recognized the few experts in this field were deep in important war work and the committee decided to work with existing laboratories, letting new contracts for specific proj- ects rather than setting up a central laboratory late in the war. The work of the committee should have begun with the conception of the ideas of the new radio systems, radar, loran, VHF (very high fre- quency) communication systems, guided missiles, ete. Then there would have been time to have established a central laboratory for carrying out propagation research and evaluating the performance charac- teristics of equipment. 43° FUTURE PROPAGATION RESEARCH During the latter part of 1943, Committee members and liaison officers gave considerable attention to the matter of propagation research which would be desir- able to have continued into the postwar period. Studies were made of the knowledge already obtained with a view to outlining the principal gaps in that knowledge and developing a general program for filling them, which could be carried on by such organizations as the Service laboratories or the Research Board for National Security. The results AND RECOMMENDATIONS of these studies are given here, divided roughly into suitable categories. PROPAGATION PROBLEMS 1. Subnormal propagation through fog and sus- pended water and ice particles. 2. Modifications of the coverage diagram when the radiation source is located in or below the hori- zontal layer exhibiting nonstandard variations of refractive index with height. 3. Errors produced in operation of direction finders, navigational equipment, and gunlaying radar by varying factors of tropospheric propagation. 4. Effects on atmospheric reflection of variations of frequency, pulse rate, pulse length, radiated power, and other variable parameters. 5. Correlation of variations of horizontal and vertical angle of arrival of radio waves with simul- taneous meteorological measurements and evaluation of resulting variations in propagation characteristics. 6. Determination of frequencies permitting great- est security under various meteorological conditions. 7. Measurements of absolute signal strength and characteristics of the transmitted signal. 8. Determination of atmospheric noise levels in all important regions and the variation with season, frequency, and meteorology. 9. Phenomena responsible for long distance propa- gation in the 100- to 200-me region. 10. Characteristics of propagation in the region between 50 and 500 ke. 11. Tropospheric propagation measurements over various types of terrain and water surfaces to deter- mine, more accurately, coverage, angle of arrival, reflection, scattering, and absorption over the range in which the refractive index of the troposphere shows significant change. 12. Further theoretical analysis of propagation ’ phenomena and comparison with observed experi- mental results. METEOROLOGICAL PROBLEMS 1. Particle sizes and distribution for all forms of atmospheric water. 2. Survey of the Pacific area similar to the German Meteor study of the Atlantic. EQUIPMENT PROBLEMS 1. Development of improved equipment for measur- ing variations of atmospheric refractive index. 2. Development of improved equipment for gener- FUTURE ating, detecting, and measuring radiation in the part of the frequency spectrum under consideration. 3. Required field strengths necessary for satisfac- tory operation of systems employing this range of frequencies. 4. Types of equipment suitable for determining location, intensity, and movement of storms, and distinguishing them from permanent echoes. 5. Handbooks of standard and nonstandard propa- gation and of standard performance of radar equip- ment. Some of the points listed are not strictly propa- gation questions, but their investigation will require PROPAGATION RESEARCH i) to | the active assistance of propagation experts for solution. It is expected that systematic investigation will do much to eliminate the factors of uncertainty in siting and operation as well as in design of radio equipment operating in the frequency bands con- sidered, particularly when better methods and apparatus have been developed for determining the performance of the equipment itself. Such methods and apparatus were by no means satisfactory during the war, with the result that uncertainty as to the actual condition and performance of equipment in the field further complicated the already formidable problem of determining propagation characteristics. . » ie, i \ ey PART IT SUMMARY Chapter 5 c STANDARD PROPAGATION 5 INTRODUCTION B’ STANDARD PROPAGATION is meant radio wave propagation through an atmosphere free from irregular stratifications, particularly of vertical dis- tributions of water vapor and temperature. With irregular stratification the propagation is said to be nonstandard and will be treated extensively in the later chapters. In this chapter the fundamental general relations between transmitted and received power is first re- viewed; then the main factors influencing the trans- mission of electromagnetic waves such as refraction, diffraction, and dielectric properties of the ground are surveyed; and finally the computation of the field at the receiver for various heights of transmitter and receiver above a homogeneous smooth earth of given electromagnetic properties is very briefly dis- cussed. The last subject divides naturally into the determination of the field above the line of sight and the determination of the field below the line of sight in the earth’s shadow. - The text of the present chapter largely follows the book, issued by the Columbia University Wave Propagation Group [CUDWR WPG] under the title Propagation of Radio Waves through the Standard Atmosphere which is Volume 3 of the Summary Technical Report of the Committee on Propagation. 5.2 POWER TRANSMISSION Certain relations occur so frequently in wave propagation problems that it is convenient to summarize them here before entering into a descrip- tion of the characteristic features of short wave propagation. Some of these are mere definitions; some are consequences of electromagnetic theory. It is convenient to use, as a standard antenna, one which has a length which is small compared to the wavelength, designated as “doublet.’”’ Such doublets may be used for both the transmitting and receiving antennas. In the latter case it is assumed that the load resistance is matched to the output resistance of the antenna. In free space, optimum transmission is achieved when the two doublets are parallel to each other and perpendicular to the line connecting their centers. If their distance apart, d, is large com- pared to the wavelength, the ratio of power trans- mitted to maximum useful power received is found from electromagnetic theory to be Py _ ff BXN\? P= (Sy. (1) where \ and d are measured in the same units. Here P, is the power delivered to a matched load at the output terminal of the receiver and P, the power fed to the transmitting antenna. The gain G of any directive antenna is the ratio of the power transmitted by a doublet to the power transmitted by the antenna in question, to produce the same response in a distant receiver, when both transmitting antennas are adjusted for maximum transfer of power. The gain of a receiving antenna is similarly the ratio of the power delivered to the transmitting antenna when a doublet receiving an- tenna is used to the power delivered to the transmit- ting antenna to produce the same response when the antenna in question is used at the receiver. Two methods of expressing antenna gain are in common use: the one just indicated where the gain is measured as the ratio of the power in the optimum direction relative to that of a doublet, and the other where the gain is that relative to a hypothetical iso- tropic radiator which is one assumed to radiate the same power density in all directions. Simple geomet- rical considerations show that the gain of a doublet over that of an isotropic radiator is 3/2 so that the gains expressed in the former system are converted into the latter system by multiplying them by 3/2. In the equations below, the gain is expressed relative to the doublet. If transmission takes place, not in free space, but over a conducting ground, in a refracting atmosphere, etc., the power ratio will be expressed as = = c.c.(5) A,’ , (2) where GG2 are the antenna gains of the transmitting and receiving systems, respectively, and A, is the 31 Osi- STANDARD PROPAGATION d (KILOMETERS) o pb Ww rx) = ow b ° ° ° 2° oO °o 8 6 rs) ° ! o L + o i N C) wn S Ww iy¥) ° te) ° ° te) ° fo) o 2 Oo ° oo 0 fo) 9 fo) ne) w b — w w \(METERS) Oll- ool- 06- 08s- OL- Frcure 1. Nomogram for free space transmission between parallel doublets. “Hath factor.”’ The nomogram, Figure 1, gives this relation for Gj=G2.=A,=1. Often the electric field at the position of the receiver is desired. It is given by 3V/5 5 V/ PGA, K = (3) where # is in volts per meter, P; in watts. If H is known, the power delivered by the receiving antenna to a matched load is 1207 or (4) The combination of equations (3) and (4) gives again the general transmission formula (2). The lower limit of possible receiver sensitivity is set by the thermal noise in the receiving system. At ordinary temperatures the thermal noise power in watts is very approximately Proise = 4- 107PAS, (5) where Af is the radio-frequency bandwidth of the recelver in megacycles. The minimum power P,,;, required for intelligible reception being usually in excess of the thermal noise power, it is customary to use the ratio Prin/ Poise expressed in decibels as a measure of the receiver sensitivity. Ten times the logarithm of this ratio (to the base 10) is the sensitivity of the receiver in decibels above thermal noise. As may be seen from this brief outline, the problem of transmission in free space is a very simple one from the engineering viewpoint. There are certain ques- tions regarding noise limit, receiver sensitivity, and matching of the load which constitute refinements of the above procedure. They are of interest primarily for those concerned with receiver design; apart from these the problem of power transmission may be con- sidered solved by these formulas. The most impor- tant and difficult part of ultra short wave propagation then becomes the quantitative determination of the path factor A, as a function of the geometry of the transmission path, electromagnetic properties of the ground, refractive properties of the atmosphere, ete 5.3 OPTICAL PROPERTIES OF THE EARTH’S SURFACE AND ATMOSPHERE REFLECTION COEFFICIENTS In dealing with standard propagation it is usually assumed that the ground has electromagnetic prop- erties which are constant over the length of the transmission path. Deviations from this idealized behavior are treated below as diffraction phenomena. The electromagnetic properties of the ground are completely described by its complex dielectric constant, € = & — Je; = & — JO0or, (6) where «, is the relative dielectric constant, « the con- 09- ol OPTICAL PROPERTIES OF THE EARTH’S SURFACE AND ATMOSPHERE 33 140 120 100 80 60 DIELECTRIC CONSTANT 40 20 L €|=60 OX FOR O=3.61 MHOS PER METER ao Ee ductivity in mhos per meter, and \ the wavelength in meters. In general, and especially in the micro- wave region, e«, and e, are themselves functions of the frequency. Figure 2 shows the variation of the real and imaginary parts of the complex dielectric constant of sea water at 17 C for ultra-high fre- quencies according to the best available experi- mental data. The reflection coefficient is given by Fresnel’s formulas. Let y indicate the angle between the incident ray and the horizontal reflecting surface. Then, for horizontal polarization sin y — Ve, — cos? R= pee = , 7 sin y + Ve, — cos? p 7) and for vertical polarization P= fee e, sin Wy — Ve, — cos? p (8) e.sin yy + Ve, — cos? py’ where p designates the magnitude of the reflection coefficient, and ¢ the phase lag of the reflected ray at reflection. Figure 3 illustrates the amplitude of the reflection coefficient for sea water as a function of Mpa i lL eh 20 22 24 26 1100) HORIZONTAL POLARIZATION _200Mc; VERTICAL POLARIZATION > 415° Ss Ssy y 5 1° (EP P BEP Pp EP Ficure 3. Amplitude, p, of the reflection coefficient versus reflection angle, y, from y = 0 to W = 5.5° for sea water. the angle y for several frequencies. Figure 4 shows the corresponding phase lag at reflection. 34 STANDARD PROPAGATION ° VERTICAL POLARIZATION 180 | 4 l0oMc 160 146 ; | (BOOME! | 120 q 100 — 500Mc’ 80 ee ® 66 [3000Mc 5| a : aoe o 20 ° 5° eo ae £2 a> YS oF & 4B SommEssy Ficure 4. Phase lag, ¢, of the reflection coefficient versus reflection angle, y, from Y = 0 to W = 5.5° for sea water. From the practical viewpoint the following sum- mary may give an overall picture of the more out- standing features of ground and sea reflection. For horizontal polarization over the sea the reflec- tion coefficient may be taken as unity and the phase shift as 180 degrees for frequencies up to and includ- ing the centimeter range, for practically all angles of reflection. Over land there is a slight decrease of the amplitude of the reflection coefficient with increasing angle; for instance, for a frequency of 200 me, at an angle of 15 degrees the reflection coefficient has decreased to 0.9 or slightly more for moist soil and to 0.8 or slightly more for dry soil. These statements apply when the ground or sea surface is reasonably smooth. In order to decide whether a surface is smooth or rough, Rayleigh’s criterion, explained below, is usually applied. When the surface is rough or wavy, irregular scattering predominates and re- duces the intensity to a small part of the value attained with a smooth surface. For vertical polarization the curve of the magnitude of the reflection coefficient versus the angle goes through a minimum (see Figure 2). When the imagi- nary term of the complex dielectric constant is negligible so that the ground behaves like a pure dielectric material, the reflection coefficient goes to zero at a certain angle (Brewster angle). Ordinary soil nearly fulfills this condition. For mstance, at a frequency of 200 me the Brewster angle occurs at about 12 degrees with moist soil and at about 21 degrees with dry soil. For the ocean surface, and vertical polarization, the imaginary part of the dielectric constant cannot be neglected, and the reflection coefficient as a func- tion of the angle does not vanish at any angle but goes through a minimum, the pseudo-Brewster angle. The actual variation of amplitude and phase lag is represented in Figures 2 and 3 for the small angles of reflection which are most important in practice. When the ground is rough the reflection coeffi- cient for both types of polarization is reduced to a very small value. For 10-cem waves and still more for shorter ones, most types of land are rough. A reflec- tion coefficient of 0.2 may be taken as representative for an average ground covered with vegetation. A slightly ruffled sea is a fairly good reflector for 10-em waves but appears somewhat rough at shorter wave- lengths. STANDARD REFRACTION Numerous experiments have resulted in the fol- lowing formula for the refractive index of moist air: 79 4,800 @=) Mss (» e+ Tr) (9) where n = the index of refraction, p = the barometric pressure in millibars (1 mm mercury = 1.3332 mb), eé = partial pressure of water vapor in milli- bars, T = absolute temperature. The mixing ratio, s, which is practically equal to specific humidity, is connected with e by the relation l| e = 0.0016I1ps . (10) A recent analysis?’78 has shown, moreover, that this expression for refractive index must, on theoretical grounds, be substantially independent of frequency down to the shortest waves employed in microwave engineering. In an average atmosphere temperature, pressure, and water vapor density decrease with height, and, in the lowest few kilometers where most of the short and microwave propagation takes place, it may be assumed to a good approximation that the decrease of refractive index with height is linear though the rate of decrease is somewhat dependent on the cli- mate. In middle latitudes it is given by OPTICAL PROPERTIES OF THE EARTH’S SURFACE dn ah (11) = —().039 - 10-* per meter . Refraction at the boundary of two media is fa- miliar from optics and is expressed by Snell’s law: Ny COS ay = Neo COS ae , (12) where 7 and ne are the refractive indices of the two media and a; and ay the angle between the boundary and the direction of the ray in the first and second media respectively. In the atmosphere the refrac- tive index is a continuous function of height, and the sudden change of direction at a boundary is then replaced by a curvature of the rays. Equation (12) can be written (13) n COS @ = No COS a , where n and a are now continuous functions of the height and the subscript 0 designates a reference level. The above formulas refer to a plane earth. If the earth’s curvature is taken into account so that the planes relative to which the angle a is measured are replaced by spheres about the earth’s center, for- mula (13) must be modified; and the mathematical analysis shows**? that it is replaced by Nr COS & = NoFo COS ay (14) where r is the distance from the center of the earth to the level considered. If now we set r = ro (1 + h/ro) where h = r — 1 and h/ro is a small quantity and, furthermore, if we note that with a linear gradient of n n= MN + oh (15) we obtain on substituting into (14) and neglecting small quantities of the second order 1+ Bie h|cosa = cosa. (16) To dh Tt results from this equation that a linear gradient of refractive index has the same effect on refraction as the curvature of the earth, 1/ro. By introducing an effective earth’s radius it is possible to eliminate the refraction term entirely and to treat the atmos- phere as if it were homogeneous. This device was first introduced by Schelleng, Burrows, and Ferrell,?* and has since been generally accepted. Some German writers have introduced a quadratic function to represent the variation of refractive index with height in the atmosphere, *** the coefficients of the quadratic terms being characteristic of the air mass or type of AND ATMOSPHERE 35 atmosphere involved. This has the advantage of per- mitting a close fit with observed refractive index curves up to heights of 6 to 8 km. It seems, however, that the advantage of the greater analytical simplic- ity of the linear refractive index curves far outweighs the increased accuracy of the quadratic form, and the latter has therefore not found acceptance in this country and Great Britain. It is customary to designate the effective, or modi- fied earth radius by ka where k is a numerical con- stant and a replaces 7) used above and represents the mean radius of the earth. Hence 1 dn 1 a dh ka’ (Ud) and by comparison with equation (11) it follows that (18) since dn/dh = — 0.039 - 10-6 = — 1/4a. The earth’s radius a = 6.37 - 10° meters. In view of this result coverage diagrams of radar and radio communication sets are commonly drawn with a % earth’s radius. In such a diagram the rays, which are curved in a “true” geometric representa- tion, appear as straight lines. The value k = % does not, of course, represent a universal law. It is merely an expression of the fact that the rate of decrease of the refractive index with height has, in the middle geographical latitudes, a certain average value. In arctic climates & as a rule is somewhat smaller, lying between #% and %, while in tropical climates k is somewhat larger, between 4, and %. In temperate and tropical climates, the main factor determining the magnitude of k is the humidity gradient in the lower atmosphere. In Figure 5 is shown a nomogram from which the ap- propriate value of 1/k can be read directly as function of the gradient of relative humidity and air tempera- ature. The table has been computed under the as- sumption that the temperature gradient has the “standard” value of —0.65 C per 100 m, but the value of k is relatively insensitive to variations in the temperature gradient. Usually the value of k = % is referred to as the standard case, but this term is also used to designate more generally an atmosphere with a linear refrac- tive index distribution where & might differ somewhat from “%. Experience shows that the atmospheric conditions under which the refractive index is a linear function of height are quite common, but this 36 STANDARD PROPAGATION 12 (RH) —25C -5C 208 455 1.4 TR 20% hee ae 354 . He 304 OR a5 50% ee oe ~202 PENSE - = Be 041 .051 8 ae oun =30 Tea Ly ED I >> ll ed Fa 3 es oO 6 = 1S 2 F ? 4 | : 54-4 + 4 ; > L WwW =) 4h 9 L 3 ee a 5 ° 3h 0 L 3 °o Ls [ calle Ld [ e ir ea | a Ab pe REL HUMIDITY GRADIENT ° ° 5 = eee % PER 100 METERS ————»>_\’ S 30 25 20 ° 1 1 1 ' 1 ae hana: <2 2 a 230 = &G <2) “5 -6 or -8 -9 -10 ot “12-13 Ficure 5. Graph: 1/k versus RH gradient and temperature for 100 per cent RH at ground. Add correction tabulated to obtain 1/k for RH at ground ~ 100%. is only one case out of several that may, and do, arise in the atmosphere. A full appreciation of the limitations of the concept of standard refraction requires some knowledge of the phenomena of non- standard propagation which will be dealt with ex- tensively in later chapters. ROUGHNESS OF THE GROUND In order to estimate how closely the ground ap- proximates the condition of an ideal reflecting sur- face, a rule is required that gives results sufficiently accurate to be used in radio and radar practice. The subject has not been very thoroughly explored, but Rayleigh’s criterion for roughness, originally devel- oped for optical purposes, has been applied with good success. Since it seems to be the only criterion of its kind and since it is often necessary to decide whether the terrain in front of a given radio or radar site is reflecting, it deserves some detailed consideration. The principle of Rayleigh’s criterion is illustrated in Figure 6. The roughness is assumed to be pro- duced by a large number of elevations in the reflect- ing plane of average height H. One such “hump” is shown in the figure together with two rays one of which is assumed to be reflected from the ground sur- face and one from the top of the “hump.” The dif- ference in phase between the two rays is 2Hy(27/)). Fieure 6. Geometry for Rayleigh’s criterion for rough ground. The criterion now requires that the surface be con- sidered as rough when this phase difference exceeds a/4 radians. This gives for the critical value of H, when y is in degrees, \ in meters, nN If n is the “lobe variable,” that is, a quantity equal to 1, 3 ---(n — 1), ---at the first, second, OPTICAL PROPERTIES OF nth interference maximum of the direct and ground- reflected rays, namely, (20) where fy is the height of the transmitter above the ground, the criterion can be written in the form hy Lela oreeaee (21) Although admittedly rough, the criterion indicates the order of magnitude of the angle above which specular reflection will be greatly reduced in favor of diffuse scattering of the type which, in ordinary optics, is produced by a dull, white surface. It is reasonably safe to assume that for angles exceeding the critical angle the amount of specular reflection will be reduced to a small fraction, perhaps to the order of one-fifth, of the value of the reflection under ideal conditions. DIFFRACTION BY TERRAIN A number of the influences of the earth’s surface upon wave propagation have the common charac- teristic that they represent deviations of the actual earth from the idealized model of a smooth sphere endowed with homogeneous electrical constants. Diffraction by the earth’s average curvature is not included among the effects considered here since it is dealt with extensively in Volume 3. There are two main classes of phenomena that fall under the general heading of diffraction. One is the diffraction by obstacles, such as hills, trees or houses, and the other is the diffraction by the structure of an otherwise fairly level ground, in particular, rough- ness and horizontal variations of dielectric constant. The diffraction by hills and similar obstacles of the terrain is commonly treated theoretically by means of the Fresnel-Kirchhoff diffraction theory as found in textbooks on optics. The only problem which is sufficiently simple to admit of a direct application to short wave transmission is that of diffraction by a straight edge. It is not necessary that the edge be perpendicular to the line connecting the transmitter and receiver but for the validity of the theory it is necessary to suppose that the distances from the diffracting obstacle to the transmitter and receiver are large compared to the height of the obstacle, which means that the angles of diffraction are small. THE EARTH’S SURFACE ry AND ATMOSPHERE 37 FIELD IN SHADOW BE! HIND DIFFRACTING RIDGE DB BELOW FREE SPACE \ AN Hl \ CHER 45 015 0.2 03 0.4 0.6 ee 1 6 om Fieurs 7. Field in shadow behind a diffracting ridge. X= Figure 7 shows a nomogram from which the field strength in the shadow of a diffracting edge can be read in decibels below that of free space. The geo- metrical significance of the quantities used is illus- trated on the figure. Such experiments as have been made show a gen- eral agreement with theory, but it is difficult in prac- tice to realize conditions of transmission that ap- proach ideal ones, to which the Fresnel-Kirchhoff theory refers. When appropriate values are taken for the reflection coefficient of the ground and the four components of the resulting field are added vectorially, good agreement has been found between experiment and theory for selected terrain. (See Chapter 15 of this volume.) Sometimes the terrain conditions are often so complicated that they do not readily lend themselves to idealization by simple geometrical models. For these reasons the Fresnel- Kirchhoff diffraction theory has been of only limited value in short wave radio propagation. A case which quite often can be described ade- 38 STANDARD PROPAGATION quately by an idealized model is that of a sudden change of the dielectric properties of the ground, as at a coast line.*4°-#46 Tf the land is rough while the sea surface produces full specular reflection, the coast line can be considered as a diffracting straight edge with respect to the image antenna, rays of which represent the field reflected by the sea surface. The straight edge serves to cut off that part of the radia- tion from the image that would represent reflection from the land area. The geometrical conditions are shown schematically in Figure 8. For the details of VERTICAL SECTION PLAN VIEW Ficure 8. Diffraction by a coast line. the analytical treatment the reader is referred to the comprehensive report on standard propagation con- tained in Volume 3 of the Summary Technical Re- port of the Committee on Propagation. The distor- tion of the coverage diagram of a radar set caused by this type of diffraction is often quite large and be- comes important operationally at frequencies of 100 to 200 me. This is illustrated here by a computed coverage diagram shown in Figure 9. If diffraction is SS WITH DIFFRACTION NN — — — WITHOUT DIFFRACTION e 9 v w z TITTVITSTITTTTSISIT AA IAS AS SAT AGA TTT Z. 7. 7 OISTANCE FiGurE 9. Coverage diagram for coast line diffraction (relative field strength). (Heights exaggerated 3.5 to 1.) not taken into account the coverage pattern shows a constant amplitude through higher angular elevations reached only by the direct rays since the ground re- flection is negligible. At lower angular elevations rays reflected from the sea add to the direct rays. and the “lobe” type of pattern appears. It is clear that if the diffraction effect were neglected very serious errors of the estimated coverage would result. Similar methods can be used to treat diffraction caused by cliffs, edges of wooded areas, lakes, etc., but these cases are not so often of importance in radar practice. 54 THE ELECTROMAGNETIC FIELD FIeLp STRENGTH DISTRIBUTION If a transmitter is erected over a plane, ideally re- flecting earth, the well-known lobe pattern results FREE SPACE FIELD = Figure 10. Typical coverage diagram (lobes) over plane earth. (Figure 10), the curves being ones of constant field strength. The field is given by EH = Ey - 2 sin (7au) hd (22) where h, and he are the transmitter and receiver heights, and d the distance from transmitter to receiver. The maxima and minima occur at the positions in space where hike = = dd, (23) 4 with n=1, 3, 5- - -for the maxima, n=0, 2, 4: - -for the minima. If ho > hy, the angle of elevation is ¥ = h2/d and the formula for the maxima and minima can be written LN YS Ti (24) If the earth curvature is taken into account the pattern remains essentially the same above the line of sight, but a number of corrections enter which change somewhat the position and strength of the THE lobes. The problem is primarily one of geometry, taking into account the modification of the direc- tion, phase, and intensity of the reflected ray caused by the earth’s curvature. It can be solved by suit- able numerical and graphical methods such as are given in Volume 3 where the details are extensively treated. It may suffice here to enumerate the main modifying factors. If a tangent to the earth is drawn at the point of reflection (Figure 11), the distances h’; and h’s of transmitter and receiver from this line are the equiv- RECEIVER FicureE 11. Geometry over spherica earth. alent heights in terms of which the problem is a plane-earth problem for that particular ray. They are smaller than the heights above the ground h; and he, but clearly they are functions of the angle of elevation. Thus a set of implicit equations has to be solved for each angle of elevation giving h’; and h’» as functions of hi, he, and d, whereupon the inter- ference between the direct and reflected rays is computed as in the case of a plane earth. In addition to the modification of direction and phase at reflection, there is also a change in intensity of the reflected ray caused by the fact that the reflecting surface is curved. This modification is taken into account by the divergence factor, a purely geometrical quantity which is part of the reflection coefficient, reducing the intensity of the reflected ray. The behavior of the field below the line of sight requires a more powerful line of attack. The line of sight itself is given by a tangent to the earth’s surface passing through the transmitter. The distance from the transmitter to the horizon, when a modified earth’s radius ka is used is dp = V/ 2kah, . (25) ELECTROMAGNETIC FIELD 39 When k = %, hy is in meters and d, in kilometers, this becomes dp = 4.12 Wh, . The diffraction region actually extends at least from the lower surface of the first lobe downward to the earth’s surface. In the diffraction region well below the line of sight, the field strength decreases very rapidly and very nearly exponentially with the distance. Figure 12 shows a typical example for the ground NX 7 x wana yrs (26) [K. aie 0.001 0.0005 0.0001 —— te) 10 20 30 40 50 60 70 80 90 IC » d IN KILOMETERS Ficure 12. Field strength versus distance for fixed height, vertical polarization. constants indicated. The ordinate is the ratio of field strength to the free space field; the transmitter and receiver heights are fixed and d is plotted as abscissa. Above the line of sight the typical lobe pattern is exhibited. The decrease of the field in the diffraction region is the more rapid the shorter the wavelength. In the centimeter band this decrease is so rapid that for most practical purposes the field is nonexistent near the ground at distances exceeding the horizon distance by more than a few kilometers. Figure 13 shows a similar diagram for fixed distance and variable receiver height. Mops The description of the electromagnetic field above the line of sight is adequately given by means of rays and their phases as used in optics. This method ob- viously breaks down in the diffraction region into which the rays do not penetrate. For this region a solution of the wave equation is required. Many distinguished mathematicians have contributed vary- ing techniques for solving the wave equation. The 40 FREQUENCIES 3000 MG 100,200,500 MG HORIZONTAL POLARIZATION HEIGHT IN METERS 10 -200 0B STANDARD PROPAGATION PLAT TL INNINC ET NALA TIT N, i : : NS X Va ay ES . pens Sear ae soe) as Pe -120 -80 Ficure 13. Field strength versus height of receiver for fixed distance relative to radiation field at one meter from transmitter. theory in its present form as applied to short and microwave propagation has been worked out by van der Pol and Bremmer?® for vertical polarization and Marian C. Gray for horizontal polarization. The results of the theory may be summarized as follows. The electromagnetic field can be represented as an infinite series of the form I= 1 Vd >, 6.06.4 Till) Tein) (OR) where Hp is the free space field and c, and ¢, are complex constants depending upon {the wavelength and the electromagnetic ground constants. hi and ho are again the heights of the transmitter and receiver above the ground, d is the distance between the two; U,, are the height-gain functions, and e is the base of natural logarithms. The formula is symmetrical with respect to the interchange of transmitter and re- ceiver, in agreement with the principle of reciprocity. THE Each of the terms which compose the sum (27) is called a mode. The coefficients ¢,, are complex con- stants with their real parts positive. They represent therefore an exponential decrease of the field strength with distance. The real part of ¢, is the attenuation factor of the mth mode expressed in nepers per unit distance. The height-gain functions U,, are found to increase with height above the ground. The increase is first slow but eventually becomes exponential and remains that way for large heights. The real part of ¢,, the attenuation factor, in- creases with increasing mode number; hence, if the receiver is far enough from the transmitter, all modes except the first one become very small and the sum in equation (27) reduces to its first term which can be computed without much difficulty. This applies when the heights h; and hy are fairly small. The height-gain functions increase with height the more rapidly the higher their order, and as one approaches the line of sight the number of modes that contribute to the field strength becomes large. It is true that the series (27) converges everywhere, ELECTROMAGNETIC FIELD Al but above the line of sight the number of terms re- quired for a good approximation is so large that the expression is useless for numerical work. Here the methods of ray optics become applicable. It is usually found that, at a given distance d, the field in the lower part of the diffraction zone can be computed by using one or a few terms of the series (27). At large heights above the line of sight the field is determined by the methods of ray optics, and the two curves can be joined with a good degree of accuracy by graphical means on a decibel diagram. This has been done in Figures 12 and 13. The series (27), though simple in external appear- ance, still proves extremely difficult to evaluate. Burrows and Gray,”* however, have simplified the mechanics of evaluation to such a degree that nu- merical data can be obtained by means of a small number of graphs. The detailed procedures employed in computing field strength and contour diagrams by the method of modes are summarized and collected in Volume 3. Chapter 6 ELEMENTARY THEORY OF NONSTANDARD PROPAGATION 6.1 HISTORICAL Dees 1941 anp 1942, short and microwave radar sets became available in England and were installed along the Channel and North Sea coast. Very soon it was found that at certain times these sets were able to pick up targets such as ships and fixed echoes from the French coast which were well below the line of sight and which under the conditions of standard propagation would have given entirely negligible responses. A relationship with the weather soon became apparent. In 1942, enough had become known to establish most of the correla- tions between excessive ranges and meteorological conditions which have remained fundamental and which are based on the picture of refraction in the lower atmosphere that is now generally accepted. Later on similar effects with radar sets were dis- covered all over the world. An example in point is in the Mediterranean where nonstandard propa- gation, during certain seasons, is the rule rather than the exception. These conditions will be dis- cussed in more detail in the chapter on radiometeor- ology. The most extraordinary ranges, perhaps, were found in the Indian Ocean where radar sets operat- ing at frequencies of 200 me were found on occasion to record fixed echoes from as far away as 1,500 miles. The mechanism of this phenomenon is not yet fully understood. In the Pacific theater extended ranges have also been observed; but, on account of the vast territory covered, the technical difficulty of all operations, and the inadequacy of meteorological coverage, it is difficult to evaluate the results systematically. Up to the present, reports on the conditions responsible for nonstandard propagation have been received from many parts of the world which vary widely in their characteristic features and dependence upon season, weather, time of day, properties of the ground, etc. It is possible to lay down certain general rules, but on the whole the phenomena are exceed- ingly complex. During 1943 and 1944, a number of systematic experiments on nonstandard propagation were car- ried out by the British and American Services and affihated organizations. Most of these were one-way 42 transmission experiments that have a number of advantages over radar experiments, but some of the latter also were undertaken. Extensive transmission experiments were conducted by the British in the Irish Sea and the Americans in Massachusetts Bay, the state of Washington, southern California, and Arizona, and in the West Indian Ocean. These experiments will be described in the next chapter. Because of the nature of the subject, it will be profitable to discuss the theory before the experi- ments and to give, in this chapter, an outline of our present conceptions of the theory of nonstandard propagation. 6.2 REFRACTIVE INDEX Nonstandard propagation takes place whenever the rate of variation of the refractive index in the lower atmosphere deviates considerably from the “Standard” linear slope defined by equation (11), Chapter 5. The variation might consist either in a deviation from linearity, which is the most common case, or in a linear slope in the lowest layers that is widely different from the value assumed for the standard. The refractive index is a function of tem- perature, pressure, and the partial pressure of water vapor, given by equation (9), Chapter 5. The de- pendence of the refractive index on pressure leads to a regular decrease with height, but the change of barometric pressure with the weather produces only an insignificant effect on the gradient. The variations of refractive index in the lower atmosphere owe their existence to stratifications in which the temperature and moisture changes rapidly with height. In order to express refraction in quantitative terms Snell’s law for a curved earth is used as given by equation (14), Chapter 5: Mr COS @ = Noy COS ao « (1) Now let n=1+(n—1)withn-1<1 P= @ (1 + * with hg 1 (2) a a cosa = (: — x) witha < 1 TYPES OF VW CURVES 13 where a is the earth’s radius. Similar expressions are valid for the quantities having the subscript 0. Multiplying out and neglecting quantities that are small of the second order, one obtains ey) 1 ‘ 5 Be = eh) - (i “ n— No + ; (h — ho) = It has become customary to introduce the modified refractive index MW by nt+e=14+M-10-, (4) whereupon Snell’s law assumes the form (fi = My) - 10-* = 3 (a? — ap”) . (5) This equation indicates how the angle a between a ray and the horizontal changes as a function of M/ which, in turn, is a function of the height, both explicitly by equation (4) and implicitly because 7 is a function of the height in a stratified atmosphere. 6.3 TYPES OF M CURVES An M curve is a diagram in which M as abscissa is plotted against the height h as ordinate. Extensive experience has led to a classification of M curves which is shown in Figure 1. The six types exhibited STANDARD TRANSITIONAL SUBSTANDARD h h / i) 7 M M M SIMPLE SURFACE TRAPPING GROUND-BASED S SHAPE ELEVATED S SHAPE INVERSION eli h INVERSION LAYER | DUGT '\ INVERSION LAYER Figure 1. Types of MW curves. comprise all cases that are of practical interest. M curves of a more involved structure are rare. In all cases it is assumed in accord with experience that at sufficiently high elevations the M curves become linear and have, or nearly have, the standard slope. The height at which these variations in refractive index occur may vary from a few feet to several hundred or even a few thousand feet though they are likely to be found at very low elevations in cold climates and at higher elevations in warm climates. The meteorological conditions which yield these curves will be dealt with extensively in Chapter 9, and few indications may suffice here. Ordinarily, on going aloft the temperature decreases at a slow and fairly steady rate. When, instead, the tempera- ture increases with increasing height, a phenomenon known to meteorologists as a temperature inversion, equation (9), Chapter 5, shows that n decreases with increasing height. This does not necessarily imply that M decreases with height since, by equation (4), M contains the term h/a, which increases with height. If, however, the variation of temperature is sufficiently great, a decrease or inversion of MW results. Such an inversion produces a duct, a term which refers essentially to certain meteorological phenomena and whose exact significance is explained below. A variation of humidity over the layer has an effect essentially analogous to, but distinctly more pronounced than, the effect of temperature. In this case M increases with height with a decreas- ing moisture content and vice versa. Variations of humidity are common in the lower atmosphere, and they constitute the main cause of refractive index variations, with temperature variations frequently a contributing factor. The six cases shown in Figure 1 are as follows: the standard case which needs no further comment; the transitional case where the moisture or tempera- ture variation is not great enough to produce a true inversion of the M curve but merely results in a nearly constant value of M in the lowest strata; the substandard case in which M increases more rapidly with height than in the standard case; and three cases of ducts. The simple ground-based duct or sur- face trapping, consists in an M inversion immediately adjacent to the ground or sea. There are two types of elevated M inversions distinguished by the posi- tion of the minimum value of M aloft. If this mini- mum is larger than the value of M at the ground so that the vertical projection from the minimum inter- sects the M curve, it is considered a true elevated, S-shaped duct. If this minimum is less than the value of M at the ground it is an elevated M inver- sion but a ground-based duct. In dealing with these M curves it is universally assumed that the stratification is the same over the 44, ELEMENTARY THEORY OF NONSTANDARD PROPAGATION whole length of the transmission path. This is a severe restriction, but it has proved indispensable up to date in order to make the problem susceptible to mathematical treatment, and it is reasonably often fulfilled in practice. Oe RAY TRACING In order to understand the mechanism of trans- mission of radiant energy in a duct the course of rays issuing from the transmitter is traced according to equation (5). Note that for the small angles with the horizontal at which these phenomena occur, dh Oa dx?’ (6) where x designates the horizontal distance. Hence from equation (5) o= {P= fu [en2 Since M is a given function of height, equation (7) gives in integral form the relation between distance and height, where a is the angle with the horizontal of the ray emitted by transmitter and Mo is the value of M at the transmitter height. Practicable graphical methods of ray tracing have been developed and used extensively to compute actual coverage diagrams. ®®: 68: 69,71,76,82,98,99 Three schematic pictures of ray tracing, showing the main phenomena of interest, are presented in Figures 2, 42 (i = Mp) > 10-9. () OR SEA LEVEL My upward curvature of the rays. On the left-hand side of each diagram the M curve is plotted. By equation (5) we have a=, if M = My, — 4a? -: 108. (8) The vertical lines drawn on the M curve diagram are the values of My — 4 ao? - 10° for the rays selected. Wherever this line intersects the M curve the corresponding rays become horizontal and there- after reverse the sign of dh/dx. In the case of Figure 3 these reversals combine with reflections from the ground to make a family of rays oscillate between an upper limit, different for each ray, and the ground. The limiting angle of emergence beyond which re- versal no longer occurs is designated by (2 or 2’) in Figures 3 and 4. The duct is the vertical interval cut out by the intersection of the vertical line desig- nated by 2 with the M curve or with the ground. The terms trapping, superrefraction, or guided pro- pagation are often employed to describe these phe- nomena. A word might be said here about the substandard case which, although much less frequent than the duct, is of operational significance. It is readily seen ~ that in this case the rays undergo a strong upward curvature in the layer in which there is a substandard slope of the M curve. As a result of this the apparent horizon distance is reduced, and the ranges of radar and radio equipment for targets or receivers near the ground are greatly diminished. M curves of the TRANSMITTER DIFFRACTION REGION ————* DISTANCE x Figure 2. Rays in the standard atmosphere. 3, and 4. These figures are plane earth diagrams in which the ordinary downward curvature of the earth has been eliminated and replaced by an additional substandard type occur often when fog is present but are not uniquely correlated with fog. In order to compute coverage diagrams on this RAY TRACING 45 Ficur® 3. Rays with a ground-based duct. 2 GLOOea ay, M- My ——— ep =r ov 3 9] DISTANCE x Ficure 4. Rays with an elevated duct. basis it is necessary to know the phases associated with the rays so as to determine their mutual inter- ference. If this is done by an appropriate graphical or numerical method, contours of constant field strength can be drawn. Figure 5 shows, typical coy- erage diagrams computed in this way,!4* correspond- ing to a value of hi/X = 20. The lines separating the “detection zones’ from the “blind zones” indi- cate ranges at which a medium bomber would just become visible to the particular radar to which these diagrams apply. Diagram 1 shows the undistorted lobe diagram for standard refraction while dia- grams 2, 3, 4, 5 show the coverage diagram for various types of ground-based and elevated ducts. In Figure 6 is shown the variation of field strength with height for various distances for the M curve shown on the left-hand side of the figure.7? The transmitter is at a height of 60 m. In all diagrams shown in this section the vertical scale is vastly exaggerated as compared to the horizontal scale. It may readily be shown that when the representation is such that the earth is curved, the contours of constant height can be represented by parabolas in the approximation where the true vertical elevations are small compared to the hori- zontal distances involved. 46 ELEMENTARY THEORY OF NONSTANDARD PROPAGATION ALTITUDE IN FEET 7000 2 GROUND BASED DUCT TRANSMITTER HEIGHT-100 FEET FREQUENCY- 200 MC ELEVATED DUCTD_ NORMAL LIMITING COVERAGE RANGE IN NAUTICAL MILES 50 Figure 5. Calculated coverage diagram. ee GENERAL CHARACTERISTICS OF DUCTS It is evident that the number of types of M curves that one can construct a priori is almost unlimited. In practice both the types actually occurring and their variability within each type of classification are severely limited by meteorological conditions. M, as defined by equation (4), is the sum of two parts, the true refractive part (n — 1) and the earth curvature part h/a. At higher elevations the absolute moisture in the atmosphere decreases, and irregular variations of temperature become more and more exceptional so that eventually, at a relatively great height, any MW curve approaches the standard curve. An additional limitation comes from the fact that both the temperature and moisture variations in any one climate are subject to definite limitations. An extreme moisture change occurs when there is a boundary separating a nearly or fully saturated warm air mass from a very dry cool air mass. Tem- perature inversions involving differences of more than 10 to 15° C are quite exceptional. As a conse- quence of this both the actual height of the M inversion as well as the difference AM between the maximum of M at the bottom and the minimum at the top of the inversion are limited. The height of the M inversion layer may be only a few feet if it is close to the ground or sea surface. It frequently is of the order of 50 to 100 ft or even larger. Under particularly favorable conditions in warm climates, elevated M inversions may have heights of several thousand feet. The duct itself can be appreciably thicker than the M inversion layer, as may be seen from the structure of the last two M curves in Figure 1. Again, the decrease AM over the height of the in- version is limited for the same reasons. For low ducts values of the order of AM = 5 to 10 are com- mon. Somewhat larger values will sometimes occur. The maximum value observed is about AM = 40 in high-level inversions at San Diego which originate in the singular climatic conditions found there. An important consideration for the detailed mathe- matical treatment of duct propagation is the shape of the knees of the M curve. This, again, depends on the physical nature of the atmospheric stratification. Very often the inflections are so sharp that a succes- sion of two or three straight lines furnishes an excel- lent approximation. These are known as bilinear and trilinear ducts and are of very common occurrence, especially with elevated ducts and a large class of ground-based ducts. On the other hand, there are also ground-based ducts in which the corners are extremely well rounded. It follows from the restrictions on the numerical values of M that there are severe limitations on the angle a for which duct effects can occur. Thus AM = SURVEY OF WAVEGUIDE THEORY 17 250 STANDARD GRADIENT 200 GEOMETRICAL- HORIZON 150 un x Ww = Ww = 100 50 ° 1.0 (0) 1.0 to) 1.0 (0) FIELD IN ARBITR. UNITS. ARROWS SHOW FREE SPACE FIELD Ficure 6. Variation of field strength with height for various distances. 10 represents a change of one part in 10° in the re- fractive index. Now from equation (5), we have by differentiation AM - 108 = ada. (9) For a complete reversal of a ray we must have Aa — a, and then a is proportional to the square root of AM. In the above case, where AM = 10, we find that ais of the order of 3 - 10%, or about 10 minutes of are. Carrying considerations of this type into a little more detail it is found that the major effects of nonstandard refraction occur only for rays which emerge from the transmitter at an angle of less than Yo degree. For angles between 14 and 11% degrees the refractive effects produced by the typical non- standard M curves consist merely in minor modifica- tions of the standard coverage pattern, while for angles above 114 degrees the refractive effects are negligible. 66 SURVEY OF WAVEGUIDE THEORY The ray tracing method presented in Section 6.4 is only a rather rough approximation to the true solution of the wave equation. It neglects diffraction, which on closer investigation is found to be very important. In order to visualize this, the waveguide analogue was introduced at an early stage of the development. Consider a two-dimensional wave- guide consisting, for instance, of two parallel plane sheets of copper of infinite extent. The propagation of an electromagnetic wave in such a guide is some- what analogous to that in a duct. The reversal of the vertical component of the rays by refraction in the duct corresponds to the reflection by the walls in the case of a metallic waveguide. It is well known that wave propagation under these conditions can be described by the methods of geometrical optics only to a very rough approximation. Soon after the discovery of ducts the accurate theoretical treatment of duct propagation was initiated in England. 677707, 73/88/34 The general result of these investigations may be summarized as follows. For an atmosphere of arbitrary stratification the field can be formally ex- pressed by the series development, equation (27) of Chapter 5. The constants appearitf~ therein and the height-gain functions involved are, however, different from the standard case and depend on the particular MW curve involved. The solution, therefore, consists again of a superposition of ‘modes’? which decay exponentially with distance from the trans- mitter. The height-gain functions do not, in general, increase with altitude all the way up from the ground. In the case of a duct the height-gain functions of the lowest modes have a pronounced maximum in the duct, similar to the curves for the overall field strength shown in Figure 6. This maximum becomes flatter and eventually disappears entirely for the height-gain functions of the higher modes. It is useful to supplement the rather complex 48 ELEMENTARY THEORY OF NONSTANDARD PROPAGATION mathematical development into modes, represented by equation (27) of Chapter 5, by a simpler type of analysis which connects it with the ray picture. For the sake of simplicity let the phenomena be two- dimensional, confined to the horizontal x direction and the vertical z direction. If the wavelength is small enough compared to the dimensions of the duct, the electromagnetic field at some distance from the transmitter may, in any sufficiently small volume element, be represented by a plane wave whose wave front is perpendicular to the direction of the rays. Such a plane wave may be written as dea Ty i ae (10) Confining ourselves for the moment to the case of the plane earth, it is found from electromagnetic theory that 2nn : Ke + 2? = ea) (11) where n is the refractive index in the volume element considered, and } is the free space wavelength. Since k and l are proportional to the directional cosines between the direction of the ray and the 2 and z axes, we may put pes 2 oan ps ok ea ae a, a a (12) where a is the angle between the ray, or the normal to the wave, and the horizontal. The further mathematical analysis shows that, for a horizontally stratified medium where n is a function of z only, we have k = constant. In view of equation (12) this gives us n cos a = constant, which is just Snell’s law for a plane earth, as enunci- ated before. The ray picture, being a rough approximation, gives an electromagnetic field in some regions and none in others. In the rigorous solution of the wave equation there is some electromagnetic field strength everywhere. Consider in particular the region just above a duct. There are regions of “‘shadow”’ above the duct caused by the fact that some of the rays are bent downward in the duct. Clearly, at the point of reversal of a ray, a = 0 and hence / =0. If we proceed farther upward in a duct n decreases, and it follows from equation (11) that if nm decreases sufficiently / must eventually become imaginary. Instead of a wave component in the z direction we then have an electromagnetic field which decreases exponentially as we go upwards. In the top layer of a duct, the decay takes place very gradually because the change in refractive index is extremely slow. Eventually, however, n must begin to increase again as we go still farther upwards from the duct and there comes a height where / is again real and an ordinary wave is again possible. This behavior might be likened to that of a metal foil so thin as to be partly transparent for the waves considered. The duct thus may be likened to a waveguide bounded on one side by a solid reflector, the ground, and on the other by a semi-transparent reflector. The mathematical theory of ducts has therefore often been designated as leaky waveguide theory. A closer study of the height-gain functions which appear in the mode formula, equation (27) of Chap- ter 5, shows that in the presence of a duct the leak- age across the upper boundary of the latter is the more pronounced the higher the order of the mode, and that for sufficiently high modes there is almost no confinement of the electromagnetic field within the region of the duct. In consequence of this fact the exponential damping with horizontal distance, which is characteristic of each mode, is more pro- nounced for the higher modes, because for these modes the electromagnetic energy rapidly “leaks away” from the duct. At large distances from the transmitter the field in and near the duct is therefore described by the lowest mode alone. This depends, of course, partially on the relative strength of excita- tion as well as on the attenuation of the various modes. Another aspect of the wave theory of ducts which is of great practical importance is the cutoff effect. It is well known that any ordinary metallic wave- guide has a cutoff frequency below which the guide cannot transmit an electromagnetic wave. The mathe- matical treatment of the duct shows that there is a similar lower limit of frequency for transmission through a duct, but, because of the “leakage” phenomenon, it is found that there is no sharply defined cutoff frequency but a gradual decrease of the duct’s ability to confine radiation within itself with decreasing frequency. Figure 7 is a graph giving representative values for what may be taken as the cutoff frequency of a duct as a function of its height in feet and AM, the decrease of M in the in- version layer. These values are the result of a some- what crude approximation and should not be taken to indicate more than the order of magnitude of the frequency at which this effect occurs. REFLECTION FROM ATH ENT KEN 100 d IN FEET Fieure 7. Maximum wavelength trapped in a simple surface duct. Duct width din feet. A M is total decrease of M in duct. Amax = 2.5d V A M 10-8 67 REFLECTION FROM ELEVATED LAYERS Reflection from elevated layers has so far been observed systematically only under the rather spe- cial meteorological conditions at San Diego, but it probably occurs elsewhere, though with a lesser degree of regularity. It appears when there is a strong elevated MM inversion. Such an M curve is very nearly equivalent to a true discontinuity of refractive index, and the effect on a wave traversing such a region is similar to that of a boundary between two media, the more nearly so, the larger the M- Inversion gradient. If there is a true discontinuity, an incident wave is split up into a reflected and a transmitted wave. If the discontinuity is replaced by an M inversion layer, the reflected wave still persists but becomes weaker the less steep the in- version. The distinction between this phenomenon and the apparent reflection in the duct where the ELEVATED LAYERS 19 rays become horizontal before turning downward is usually fairly clear-cut. The true reflection described here occurs primarily in waves which are so long as to be below the cutoff. There exists a case of gradual transition between two media with different refractive indices for which the wave equation can be integrated.‘44' 4% This can be applied qualitatively to the case,’” in so far as earth’s curvature can be neglected. Figure 8 shows the calculated ratio im decibels of N= soxin | r ST SeELaE NS STRATUM DECIBELS REFLECTION RATIO 89° \89°14" 89°10 80 . 89°18 89°20' 89° 21" LAA A ANT 200 300 400 500 600 700 D _STRATUM THICKNESS A WAVELENGTH {0} 100 Ficure 8. Calculated reflection ratio in decibels. reflected to incident wave for various angles of in- cidence plotted against the ratio of thickness of the transition layer to wavelength as abscissa. The verification of this theoretical concept in the San Diego experiments will be discussed in the next chapter. Chapter 7 METEOROLOGICAL MEASUREMENTS Gol INTRODUCTION HE DIRECT MEASUREMENT Of the refractive index of air is carried out in the laboratory under closely controlled conditions. The variations of the refractive index in the atmosphere which are of paramount importance for propagation problems are determined indirectly by measurements of the tem- perature and humidity. From the values of these latter the refractive index is computed by equation (9) of Chapter 5. There has been no reason, so far, to doubt the reliability of this procedure, and specu- lative assumptions of the failure of this relation which have been brought forward at times during the war have not been accepted. This chapter describes measuring equipment that was especially developed during 1943 to 1945 to study refractive index variations. Following this description is a collection of actual M curves which have been measured in different parts of the world bo | to TEMPERATURE AND HUMIDITY ELEMENTS The value of the refractive index n, or of M as defined by equation (4), Chapter 6, is sensitive to relatively small changes in temperature and especially in humidity. Both accuracy and speed in determina- tion of M are required. Speed is especially necessary because a considerable number of points generally are needed to determine the shape of an M curve. Electrical methods have been used almost exclusively for these measurements, though an ordinary psychro- meter will do in the absence of more specialized equipment. There is no particular difficulty in measuring the temperature with suitable accuracy, such as +0.2 C. The electric resistance element used in the Bureau of Standards radiosonde is well suited to the purpose and is commercially available. More recently ther- mistors have been used. At stationary installations in England ordinary nickel or platinum resistance thermometers have been installed, primarily for recording purposes. 50 Humidity may be measured either directly, or indirectly by measuring the wet bulb temperature. Hair hygrometers are unsuitable because of their large time lag. For the direct measurement of humidity electrolytic resistance elements, such as are standard in the U.S. Weather Bureau radiosonde, are used. The active agent in this type of element is an aqueous solution of lithium chloride which is deposited as a film on a small cylinder. The resist- ance of the solution is highly sensitive to changes in relative humidity of the surrounding air. In England a variant of this principle has been employed where the lithium chloride solution is absorbed in a cotton cloth. In the indirect method of measuring humidity a thermistor of cylindrical form is surrounded by a moist wick which, with proper aeration, indicates the wet bulb temperature. To insure insulation the element is covered with several coats of insulating lacquer before the wick is attached. The main problem in all these devices is that of time lag. When mobile carriers such as captive balloons, kites, airplanes, or ships are employed, it is in general necessary to obtain an individual reading within less than a minute, and the response of the measuring elements to the temperature and humidity of the ambient medium must be reasonably close within the time available. The time lag constant is the time required to attain the fraction 1 — (1/e) = 0.63 of the total change, if the temperature (or humidity) is changed suddenly. For the temperature elements the time lag constant is several seconds in an air stream with a velocity of 2 to 5 m per sec. The lag depends somewhat on the position of the element relative to the air stream and is a maximum when the element is perpendicular to the stream. The lag constant of the same element, used as wet bulb indicator with wick applied, is only slightly larger than that of the dry element. The lag constant of the Bureau of Standards humidity element has been measured in several laboratories, and there seems to be some controversy as to its exact value, the results varying from a few seconds to about 45 sec,??8 the latter in an air stream of 2 to 5 m per sec. 38 THE WIRED SONDE 51 ~_ THE WIRED SONDE Temperature and humidity elements of the type described are combined in a lightweight assembly which can be moved rapidly through the lower atmosphere. Such equipment, when first built in England, used dry and wet thermopiles,2??7_ and soon thereafter the same method was adopted by the State College of Washington, 225782284 and, with slight modification, by the Navy Radio and Sound Laboratory [NRSL] at San Diego. ****88 This design uses a combination of a resistance temperature element and an electrolytic humidity element. The instrument developed by the Radiation Laboratory of the Massachusetts Institute of Technology uses dry and wet resistance elements. ?”° The physical assembly consists of bakelite tubing, in which the two elements are mounted perpendicular to the axis. The tube is surrounded by a radiation shield of aluminum foil. Wet and dry bulb instru- ments need artificial aeration in calm air which is provided by a small electric fan. Among the instru- ments containing electrolytic humidity strips only the late model of NRSL incorporates artificial aera- tion. Other instruments of this type, when used in calm weather with a captive balloon, are aerated by giving the cable a few jerks of several feet amplitude. In both captive balloon and kite equipment only the measuring elements are carried aloft with fine wires in the cable to connect with the rest of the circuit. The assembly that is carried aloft is therefore quite light, weighing only about a pound in the case of nonaerated instruments and 3 to 4 pounds for aerated ones. Figure 1 shows a wiring diagram for the Washington State College sonde. The diagram is largely self- explanatory. The switches 8; S2 S3 are contained in the pile-up of a single relay and are actuated by a miniature worm-geared motor as shown. They reverse the current through the elements in order to avoid polarization, while at the same time maintaining constant polarity at the meters. The period of reversal is 0.5 sec and the 1,000-pf condensers in parallel with the meters serve to smooth the inter- rupted current. Figure 2 shows a schematic wiring diagram for the dry and wet bulb resistance elements of the Radiation Laboratory instrument. The resistance of the thermal element X controls the bias of one triode of the double triode 6SN7 which acts as a vacuum tube R-H METER 0-50 MICROAMP + SONDE ELEMENTS __ RH CABLE T 1 See, T METER 0-50 ONS micRoamp ©Y 2G Ficure 1. Circuit diagram for State College of Wash- ington wired sonde. +8 (105 v) 20 x RECORDER 10,000 200,000 Xx ELEMENT 10,000 Figure 2. Circuit diagram for electronic amplifier for measuring temperature. (Radiation Laboratory, MIT.) voltmeter to compare the resistance of the thermal element with a standard resistance. A 1-ma recording meter is placed between the two plates. In operation the dry and wet elements are switched into the circuit alternately. Calibration of the amplifier is obtained by switching a series of precision resistors in steps of 1,000 ohms into the circuit in place of the thermal element. The stability of this voltmeter is such that with a change in line voltage between 95 and 120 v there is no observable change of the meter at any given deflection. 52 METEOROLOGICAL MEASUREMENTS 74 REFRACTIVE INDEX MEASUREMENTS The methods which have been used to make refractive index measurements in the lower atmos- phere are the following: 1. Stationary installations on towers, usually with automatic recording on the ground. Aerated wet and dry bulb instruments are installed at several heights giving a continuous survey of the MW curve between the ground and the top of the tower. 2. Installations similar to (1), on shipboard, with the meters or recording equipment in the ship’s cabin. In order to explore the humidity distribution in the lowest layers adjacent to the sea surface, the instruments have been mounted at the end of a beam that pivots about a horizontal axis fastened to the side of the ship. This device has been used extensively in the Irish Sea experiments. Artificial aeration of shipborne installations is not usually necessary because in calm weather the necessary velocity of the air is provided by the motion of the ship. 3. Airborne installations. The unit is mounted at a convenient place on the outside of the plane where it is not affected by motor exhaust or propeller slip stream, with the meters or recorders in the ship’s cabin. Comparatively slow-flying planes have been used for such measurements, not only in order to minimize the dynamic temperature correction, but also because in a fast-flying plane too long a column of air will be sampled during the period of relaxation of the instrument. In airplane measurements it is necessary to keep track of the altitude of the plane by means of a carefully calibrated altimeter. 4. Captive balloons and kites. In these devices only the measuring unit is carried aloft, the indicating or recording meters remaining at the ground. Three wires are required when the instrument 1s nonaerated and two additional ones when an aeration motor is provided. The wires are of thin insulated copper, stranded together into a cable, although more recently aluminum wires have been tried because of their greater mechanical strength.?*° The fine wires of the cable are wound in a high-pitch spiral around a strength member consisting of fishline and then glued to the latter. Considerable effort has been spent on the development of these cables which constitute the most critical part of the balloon sonde equip- ment. For details the reader is referred to the reports listed under Meteorological Equipment in the Bib- liography (Report WPG-14). Captive balloons are used in calm weather and in winds not exceeding about 4 m per sec. For higher wind velocities the balloons become difficult to mani- pulate, and a kite is then used to carry the measuring unit aloft from the ground or even from shipboard. Small barrage balloons have a greater lift than ordinary weather balloons and can be used in. the same winds as kites because of their streamline shape. They are, however, less mobile and require more hydrogen than the smaller balloons. The cable for the balloon or kite is wound on a drum, and connection with the stationary meters is made by means of slip rings. The height of the balloon or kite is determined by the length of cable paid out together with a rough measurement of the angle of the cable. Captive balloons reach heights of several hundred feet without difficulty and even heights of 1,000 to 2,000 ft are not infrequent. tes) OTHER METEOROLOGICAL INSTRUMENTS It is hardly necessary to say that measurements of atmospheric temperature and humidity are pos- sible and have been made, with instruments of a more conventional type. In the early stages of our knowledge of nonstandard propagation, surveys were 1200 1100 1130 1000 14 OCT 1943 WAYLAND, MASS. 900 800 HEIGHT, FEET tu) fo} to) Figure 3. Representative standard M curve. (386 M units per 1,000 ft.) made by means of an ordinary psychrometer held out of the window of a slowly cruising plane and aerated by the slip stream. The British installations HEIGHT, FEET HEIGHT, FEET HEIGHT, FEET OTHER 10 JUNE i943 OFF BOON ISLAND 141 9 JUNE 1943 OFF BOON ISLAND 1200 1000 METEOROLOGICAL INSTRUMENTS 1400 28 SEPT 1943 NEAR MARBLEHEAD 8 OCT 1943 NEAR MARBLEHEAD 800 600 1020 27 SEPT 1944 400 1941 10 OCT 1944 200 330 Ficure 6. M curves from New Zealand, east coast near Cook Strait. 320 6 330 350 M o4. METEOROLOGICAL MEASUREMENTS $000 1H8-10 Mi 4000 3000 Rr Wi Ww we 2000 M CURVES 30 SEPTEMBER 1944 260° TRUE 1000 a t = | I =F 350 360 370 380 390 400 410 420 430 440 450 460 470 480 Fiaure 7. M curves from a flight west of San Diego. REPRESENTATIVE OBSERVED M CURVES uw wn 600 400 300 200 100 1300 MARCH 9, 1944 HEIGHT, FEET 500 400 300 1600 MARCH 9, 1944 100 2100 MARCH 9,1944 MARCH 9, 1944 Ficure 8. M curves from Taboga Island near Balboa, Canal Zone. commonly use multijunction dry and wet thermo- piles which have the advantage of not requiring elaborate calibration. In connection with captive balloons this type of equipment is somewhat clumsy in that the cold junctions have to be carried aloft in a Dewar flask. It should be noted here that the ordinary noncaptive radiosonde as used in the routine meteoro- logical observations of the U.S. Weather Bureau and of the Armed Services is not suitable for radio- meteorological purposes. The reason is that these sondes are designed to give representative data only at definite and fairly large vertical intervals, 100 ft or more. These are too widely spaced to yield a representative M curve, as the characteristic features of the latter are usually concentrated in the lowest strata of the atmosphere. Wind measurements are of importance in connec- tion with propagation problems, for reasons which will be given in detail in the chapter on weather forecasting. They are particularly significant at coasts when off-shore winds or land and sea breezes are present. Sensitive and carefully calibrated anemometers with ordinary wind vanes prove adequate for measurements of this type. Special equipment such as supersensitive anemometers, developed for particular purposes such as chemical warfare problems, are not usually needed because the large area covered by radio transmission paths or radars renders too detailed measurements useless. 0 REPRESENTATIVE OBSERVED M CURVES A small catalogue of M curves that have been actually measured in various parts of the world by means of the equipment described previously con- cludes this chapter. Most of the curves presented were taken over the ocean merely because the METEOROLOGICAL 800 600 1515 13 OCT 1944 400 NEAR BIAK D NEW GUINEA 1100 30 NOV 1944 NEAR SAIPAN HEIGHT, FEET 200 38 390 390 400 410 Ficure 9. M curves from the New Guinea area. majority of experimental measurements have been made there. Experience indicates that there is not much difference in the types of M curves over land and over sea except that standard propagation con- ditions will in general be much more common over land for reasons that will appear in Chapter 9. In all these graphs the actually measured points are entered so that the reader may gain an idea of the degree of accuracy obtained with this equipment. Figure 3 shows a standard curve as measured at the coast of Massachusetts. The linearity of the refractive index in this case is not an accident but is the result of the definite physical condition of thorough turbulent mixing in the lower atmosphere, as will be explained in more detail in Chapter 9. Since this is a fairly frequent condition, standard curves are actually quite common, and in them the measured points cluster well around a straight line as shown in Figure 3. Figures 4 and 5 show a set of nonstandard curves selected from a large series of measurements taken on the Massachusetts coast in the summer and fall of 1943.7!° Here the M curves are quite irregular, perhaps more so than is common at other locations. These curves show various types of ducts, some of them rather weak, others with a decrease of M as much as 20 units or even more. Figure 6 is a set of M curves that were measured on the east coast of New Zealand, at a point some 100 miles south of Cook Strait.22 These curves provide good examples of the type of M curves that consist of several very nearly linear sections. Figure 7 illustrates the typical elevated duct found in the San Diego region. Both below and above the inversion region the M curve is standard. The various curves shown were measured at several distances on a flight from San Diego outward. MEASUREMENTS 140 120 100 80 Fb wi w w ne x © w x= 60 1100 21 NOV 1944 100 MI NORTH OF HUMBOLDT BAY 40 20 (0) 382 384 386 388 M Ficure& 10. Detailed MW curve taken over the ocean near New Guinea. The curves of Figure 8 were taken at Taboga Island, some 15 miles south of Balboa, at the eastern entrance to the Panama Canal. They show various familiar types of ducts; two of the curves represent transitional cases where the M curve is steeper than standard but does not bend backward. Figure 9 shows two soundings from the tropical Western Pacific. The curve at the left was taken at Biak Island, New Guinea, and is remarkable for the presence of two ducts, a ground-based and an elevated one. The curve at the right was taken at Saipan. Figure 10, taken near New Guinea, shows in more REPRESENTATIVE OBSERVED Wo CURVES 57 100 80 Ee un 60 w <= =x oO rr) 40 = 1900 1715 20 MARCH 1945 2 MARCH 1945 20 J WATER SURFACE WATER SURFACE 0) a O 340 350 360 370 380 390 400 340 350 360 370 380 390 400 Figure 11. M curves over the ocean at Antigua, British West Indies. detail the structure of the low maritime duct which experiments at Antigua in the West Indies which in this case is only about 30 ft high.2”” This type of are reported in Chapter 8. Two typical soundings duct has been studied carefully in the transmission taken near Antigua are reproduced in Figure 11.1% Chapter 8 TRANSMISSION EXPERIMENTS 8.1 BRITISH EXPERIMENTS I THE DEVELOPMENT of short and microwave communication and radar, the British were first to make systematic transmission experiments on a large scale. A number of such experiments were carried out at wavelengths below 50 cm, beginning about 1936 with some transmission paths over land, some over sea; and experiments in the 10-em band were undertaken in the early years of the war. These experiments will not be reported individually because the earlier results are reproduced and verified in the later and more elaborate trials. Instead, attention will be confined to two major experiments, one over the sea and one over land.*'!° Tue Irisu Sra EXPERIMENT This transmission experiment represents a cooperative enterprise undertaken jointly by the Radio Division of the National Physical Laboratory, the Telecommunications Research Establishment, Signal Research and Development Establishment, The Ministry of Supply, The Naval Meteorological Service, The Meteorological Office, and the General Electric Company, Ltd. One-way transmission with stationary apparatus was carried on in the winter of 1943 to 1944 and continued in operation until the end of the war. Practically all the transmission is over the sea at wavelengths of about 9, 6, and 3 em. At each fre- quency the transmitted signal consists of square pulses, with equal on-off periods and a repetition frequency of 1,000. The 1,000 cycle component of the- modulation is rectified in the receivers to operate the recording milliammeters, and provision is made for monitoring the transmitter power and the sensi- tivity of the receivers in terms of a suitable standard. Parabolic mirrors 48 in. in diameter are used for all transmitters and receivers and are permanently mounted inside the station buildings behind large canvas-covered “windows.” There are two transmission paths, 57 and 200 miles in length, which run roughly from south to north, but diverge from each other by about 17 degrees and have the transmitting station in common 58 at the southern tip in South Wales. There are trans- mitting stations A and B at 540 and 90 ft above sea level respectively. The receivers, C and D, for the short path are in North Wales at two heights, and E and F, for the long path, in Scotland at two heights. In units of the geometrical horizon distance the lengths of the various transmission paths are as follows. AD BD AE AF BE _ BF 1.40 2.40 3.82 492 5.63 8.45 AC BC 0.89 1.21 It has not been found possible to utilize all these paths at the same time, because the amount of records accumulated proved too great for evaluation, but selected runs at various frequencies and for several paths have been made. There is an elaborate setup for measuring meteoro- logical conditions simultaneously with the intensity of the transmitted signal. A weather station is located at each of the three terminals, but the main meteorological program is carried out from ships which ply along the transmission paths. The Admiralty has detailed three ships for the sole purpose of making these measurements so that the transmission path is continuously covered by at least one ship on duty. The ships are provided with elaborate meteorological equipment of the type described in Chapter 7. RESULTS The following is a qualitative summary of some of the results obtained thus far. 1. There is general agreement between signal variations over the two paths, though the short period variations often differ. 2. Signals are obtained over the long path only when the signal strength over the short path BD is high. But if the latter condition is fulfilled, the former does not always follow. 3. There is a marked diurnal variation when the general signal level is low or moderate with strong signals in the late afternoon or evening and a minimum between 6 a.m. and 9 a.m. 4. There is evidence of an appreciable seasonal variation with high level for a greater fraction of the time in summer than in winter or spring. BRITISH 5. Low level occurs commonly, but not always in conditions of fog or low visibility. 6. Low signal level is usually observed at the passage of warm fronts and high level at the passage of cold fronts. 7. Generally speaking, high signal level tends to occur in periods of anticyclonic weather. A typical record of signal strength for 9-cm waves, representing hourly mean values for a month, is shown in Figure 1. These records are from two EXPERIMENTS 59 Hatch and the General Electric Laboratories at Wembley. The wavelength is in the 10-cm band, and transmission, monitoring, frequency control, and recording are fully automatic. The path is optical except for some houses and trees near the receiver which introduce a diffraction loss estimated at 30 db. As is generally the case with paths that are optical or nearly so, the fluctuations of received intensity are far less than in the case of long non- optical paths. Figure 2 shows a record for one month 17 iT) 20 21 22 23 24 25 26 27 26 29 WwW 16 19 (ree Ait fot Hfigte ttt 6 Pee al 8 feet 10 i l2 13 14 «15 a MAG Nt A Haaemert cit 2 Nif AU Oar | Vsranoano [4 WV | 27 28 29 30 22 23 24 25 26 Figure 1. Signal strength in decibels above 1 pv receiver input. S band hourly means, June 1944. (Irish Sea experiment.) (C = cold front, W = warm front, O = occluded front.) links of the short path, both nonoptical. Important meteorological phenomena, especially passage of fronts, are shown at the top of the diagram. W indi- cates warm, C cold, O occluded. Note in particular the standard and the free space level indicated on the lower record and the free space level on the upper. The standard level for the latter would be about 33 db below the zero line. This record, which is by no means exceptional, gives a fair idea of how vastly the signal exceeds the magnitude calculated for standard conditions. At the same time it shows the highly irregular character of these phenomena and the difficulty of correlating them in a simple way with the weather or other conditions. OVERLAND PaTH An experimental overland path 38 miles has long been operated in the neighborhood of London between the Admiralty Signal Establishment at Whitwell 1 pvr 19 7 @ WM JB 1B » 15 WTP a Ss oP oo ey ml a a ts tS 30,16. 17, 8, 19 | 20,21 , 22, 23 24, 25, 26, 27,28 29 30 a 25 25 20 20 wa; 19 "20 ‘21 "22°23 "24°25 26°27 28°29 30 i768 Ficur& 2. Whitwell Hatch-Wembley path, March 1944. S band hourly mean intensities in decibels above 1 pv receiver input. in 1944. The large diurnal fluctuations in amplitude with maxima above normal in the early morning hours occur in the beginning of the month and at several occasions later, especially from the 21st to the 26th. These are related to weather conditions 60 TRANSMISSION with clear skies, as will be explained in Chapter 9. The work undertaken in England on experimental transmission paths of various types is quite extensive, and the preceding description hardly gives an idea of the variety of experiments made and results obtained. Most of the experiments are of a smaller size than the ones described here. 8.2 EXPERIMENTS AT THE EASTERN COAST OF THE U.S. In the early years of the war a transmission experiment was undertaken by RCA Communica- tions, Inc., between New York and two points on Long Island." The short path of 42 miles was optical, but the long path of 70 miles was nonoptical, the receiver being about 400 ft below the trans- mitter’s line of sight calculated on a 4 earth’s radius basis. Transmission was carried out on 45, 475, and 2,800 me. The results show what has been confirmed by later experiments, that the amplitude of fluetua- tions is larger the higher the frequency. On the optical path the range of fluctuations of the 45-me signal averages only +3 db, whereas over the same path the 475-me and 2,800-me signals exhibited fluctuations which were in excess of 40 db, so far as they could be measured. As was to be expected, the 2,800-me signal fluctuated more than the 475-me one. Over the nonoptical path all three signals show very wide fluctuations of intensity, the rate and amount again increasing with the frequency. In the course of these experiments a certain amount of meteorological study was carried out and fore- casting of propagation conditions was done on a tentative basis. The general results again fore-shad- owed the more complete data obtained by later studies, and a description of the details will be omitted here. Similar experiments were carried out simultane- ously by the Bell Telephone Laboratories [BTL] on optical paths near New York City. The wavelengths employed were 10, 6, and 3 cm.!°°174 Here we find clearly established the different signal or fading types that are described in detail below. A very extensive program of transmission measure- ments was carried out by the Radiation Laboratory of Massachusetts Institute of Technology [MIT]. The meteorological records were made in cooperation with the U.S. Army Air Forces. The first measure- ments were made in 1942, and experiments on a very large scale were carried out in 1944, 3:19 12) 153, 183 Pwo EXPERIMENTS optical transmission paths were operated in 1943, a 22-mile path over the sea and a 45-mile path over land. A 10-cm continuous signal was used, and the strength was monitored by means of thermistors. The antennas were dipoles with 30-in. parabolic reflec- tors. The received signal was automatically recorded on meters having a range of 60 db. The signals received were correlated with meteorological observa- tions, the results of which will be given below. In the spring of 1944 a new over-water transmission path was installed which was operated simultaneously with the 22-mile one. This path was nonoptical, 41 miles long, and crossed Massachusetts Bay from the southern tip of Cape Ann to the northern tip of Cape Cod near Provincetown. Transmission over this path was carried on with 256-cm waves, 10-cm § band, 3-em X band, and 1.25-em K band. The 256-cm equipment used Yagi antennas and operated with continuous waves. The microwave transmitters used pulses with a repetition frequency of 700 ¢ and used parabolic reflectors as antennas. The transmitter for the short path was about 120 ft above mean sea level, and the transmitters for the long path were at a similar height. The two receivers were about 136 and 30 ft above mean sea level. The transmitter power was monitored and continuously recorded during the experiments while the receivers had automatic frequency control with apparatus which searches for the signal if it is lost. The auto- matic gain control of the receivers was arranged to give a spread of the signal over 70 to 80 db. The receivers were directly calibrated by means of signal generators and a very close check was kept on their performance throughout. The rectified output of all receivers was fed directly into recording milliammeters. Coincident with the operation of these transmission paths there was a very extensive meteorological program determining sea and air temperatures and atmospheric humidities by means of fixed installa- tions, captive balloons, ships, and airplanes. The distribution of the refractive index along the trans- mission path was thus known in considerable detail during practically the whole course of the experi- ments. Concurrently with these measurements, a program of forecasting the transmission conditions was carried out. RESULTS The results obtained on the various transmission paths on the east coast of the United States are EXPERIMENTS AT THE EASTERN COAST OF THE U, S. 6l HIGH AND vaRiAgLE =—S=—% SSS SS SS SS = fe ts Sauee=== Hic ReceweR | Ao == \ =e = See ee : sa= = eda eee oe arf TOYA A : SSS = DB BELOW | WATT Ss po oes Sao — Saar SS : X BAND HIGH RECEIVER OB BELOW | WATT x : STANDARD AND STEADY . SEPTEMBER 18, 1944 X BAND HIGH RECEIVER DB BELOW | WATT DB BELOW | WATT X BA rea gecenven == = DB BELOW | WATT Ficure 3. Microwave signal types Sa and X band, Massachusetts Bay. OB BELOW t WATT OB BELOW | WATT DB BELOW | WATT OB BELOW | WATT DB BELOW | WATT TRANSMISSION EXPERIMENTS =_TIME, ae —— F598 F HIGH AND STEADY = AUGUST 6, 1944 NEAR STANDARD AND STEADY = - AUGUST 11, 1944 -. — NEAR STANDARD WITH FAST VARIATIONS = - AUGUST 8, 1944 nie = NEAR STANDARD WITH SLOW VARIATIONS : AUGUST 31, 1944 LOW AND VARIABLE AUGUST 16, 1944 Ficure 4. Signal types at 256 cm (117 me per sec), Massachusetts Bay. EXPERIMENTS AT THE rather closely similar to each other, and the graphs presented here may be taken as being characteristic of all of them. Figure 3 shows the signal types observed at the microwave frequencies, S band and X band. The first type is well above the standard level with high signal on the average. It has roller fades with periods of from 2 min to an hour or so which may go down to the minimum detectable level. These periods are generally shorter at any time on the X than on the S band. When this type of signal was present on the S band, it was almost invariably present on the X band and on both the short and long paths. It always occurred simultaneously on the high and low receivers at any frequency. The second type is high and steady at anywhere from 5 to 30 db above the standard, generally higher on the X than on the § band. Most of the time this type occurred simultaneously on both bands, but there were some occasions when the S-band signal was of the high and steady type while the X one was of the first type, high with roller fades. The third type of signal is about standard and fairly steady which may be a limiting case of the high and steady variety. It does not necessarily occur on both frequencies and on both high and low receivers at the same time. The fourth type is standard on the average, with scintillations of more than 10 db. The reason for the difference between this and the preceding type has not yet been established. The scintillations may occur on either the 8 or X band while at the same time the other signal is steady. The fifth type, known as “blackout,” is far below standard and shows strong scintillations. In general it occurs simultaneously on both frequencies, both paths, and on both high and low receivers. Figure 4 shows a similar set of signal types as observed with 256-cm waves. These are distinct from those observed at the microwave frequencies not only in appearance but also in times of occur- rence. In general no relation has been found to exist between the signal type at this frequency and that observed simultaneously on S or X band, although ‘on rare occasions such a relation is indicated; the type may remain constant on one frequency and change on the other. Steady signal is most frequent at 256 cm, but the other types shown also occur fairly often. Variations of 30 to 40 db overall take place, and the variations may be fast or slow. A statistical study of the frequency of occurrence EASTERN COAST OF THE U.S. 63 of various signals reveals some rather interesting features. Table 1 shows the frequency of occurrence of above standard, standard, and below standard types on the S and X bands during three typical weeks in the summer of 1944. In these statistics the range of the standard signal was taken as +5 db for the S band and +10 db for the X band. The behavior of the K-band signal is quite similar to that of the other two. Taste 1. §S and X bands, July and August. Per cent of | Per cent of Per cent of time above time below time Date standard standard standard July 10-16 63 36 1 Aug. 21-27 97 3 0 Aug. 28-Sept. 3 80 15 5 As the season progressed into the fall, standard signal became more common and substandard signal less frequent especially in the S band. This is shown in Table 2. TABLE 2. S and X bands, September and October. Per cent of Per cent of Per cent of time above time below time Date standard standard standard Sept. 25-Oct. 1 S 58 15 27 xX 80 10 10 Oct. 16-22 Ss 76 2) 22 X92 0 8 These statistical results are characteristic of the over-water path near a coast used in the experiments of the Radiation Laboratory; and, while the signal types shown in Figures 3 and 4 are about the same in overland paths, the relative frequency of incidence for the various types is quite different. This frequency depends not only on the location of the path but, also as shown above, on the season. A more detailed analysis shows that it also depends on the particular weather situation, which may prevail for periods of several days or longer. It has been mentioned before that the signal patterns on the S and X bands and those on the high and low receivers are closely parallel. Figures 5 and 6 show these correlations graphically; the first is between the § and X bands and the second is between the high and the low S-band receivers. In contradis- tinction there is practically no correlation between 64 TRANSMISSION EXPERIMENTS X BAND DB BELOW 1 WATT fon) fe} LOW RECEIVER DB BELOW 4 WATT 117 MC DB BELOW 1 WATT 20 HIGH EPT 18-24 1944 ee le 100 80 60 40 20 DB BELOW 4 WATT S BAND Figure 5. Correlation between S- and X-band signal strengths, Massachusetts Bay. 100 80 60 40 20 DB BELOW 1 WATT HIGH RECEIVER Ficure 6. Correlation between signal strengths at high and low receivers, Massachusetts Bay. HIGH SEPT 18-24 1944 RECEIVERS 100 80 60 40 20 OB BELOW 1 WATT S BAND Ficure 7. Correlation between 117-me and S-band sig- nal strengths, Massachusetts Bay. the S-band and 117-me signal levels, as Figure 7 indicates. It is hardly necessary to state that the high signal levels occur when the meteorological measurements show the presence of a duct and the substandard signals occur when the M curve is of the substandard type. It will not be possible, in this summary report, to enter into the detailed relationship between signal strength and M distribution. In a general way the experimental results confirm the electromagnetic theory in so far as it has been worked out at present. Another aspect of the short wave transmission that has been studied in these experiments is the relationship between radio and radar transmission. Since radar involves two-way transmission, its path factor, as defined in the beginning of Chapter 5, is the square of the path factor for one-way trans- mission. Therefore the change with distance in the received-field strength is more rapid with radar than with the one-way radio. In order to study this relationship, two small mobile radar sets on the S and X bands were set up near the transmitter of the long path, at Province- town. Echoes from natural targets along the coast of the mainland were studied in connection with the soundings and correlated with the one-way trans- mission measurements. In Figure 8 is shown a correlation between the signal strength of the X-band radar and the signal strength of the high X-band OCT 9-15 1944 SIGNAL STRENGTH OF TARGET AT EASTERN POINT DB BELOW 1 WATT DB BELOW 1 WATT SIGNAL STRENGTH Fiecure 8. Correlation between one-way and radar sig- nal strengths over the same path. X band, Massachu- setts Bay. EXPERIMENTS IN NORTHWEST 05 receiver of the long transmission path. The radar target is near the one-way receiver so that both paths are practically coincident. When the radar signal was below the limit of sensitivity, it is indicated on the graph by this limit so that the lower points of the diagram really have little physical significance. If a straight line is drawn, averaging the variation of the higher points, its slope is roughly 2:1 as should be expected. S BAND SEPT 4-10 1944 200 180) 160 80 RANGE IN STATUTE MILES 60 40 20 to) 100 80 60 DB BELOW 1 WATT SIGNAL STRENGTH Ficure 9. Correlation between maximum radar ranges and one-way signal strength. X band, Massachusetts Bay. Figure 9 shows a correlation between the one-way signal strength on the S band and the maximum range of fixed echoes detected by the S-band radar along the coast. It is interesting to note that super- standard radar ranges do not appear until the one- way signal has reached a certain, rather larger value. The one-way signal does not seem to be able to increase much beyond this value, whereas the range of detectable radar targets rises with extreme rapidity. ‘3° EXPERIMENTS IN NORTHWESTERN UNITED STATES AND CANADA Srare COLLEGE oF WASHINGTON PRosEectT During 1943, a series of transmission experiments were carried out by a group of workers from the State College of Washington under the auspices of Division 14, NDRC.134, 137,164, 228 The first series of tests were made in the neighborhood of Spokane over 14- and 52-mile optical paths and over a 112-mile nonoptical path. Later in the same year a transmis- sion path 20 miles long with receivers both below and above the optical horizon was installed on the east side of Flathead Lake, Montana. Among the tests carried out by this group was an experimental telephone communication on 10-cm waves which gave excellent results. The earlier experiments demonstrated the necessity of having detailed data on the refractive index variation in low levels and thus led to the development of the State College of Washington wired balloon sonde, described in the preceding chapter and of basic importance for further propagation work. The first model of the sonde was used systematically in con- nection with the Flathead Lake transmission path. The location of these experiments has a climate of a continental type, there being several mountain ranges between these spots and the Pacific coast. The air is comparatively dry, and the structure of the lowest strata is subject to the large variations of temperature and of stability typical of continental conditions. The general results of these tests are similar in many respects to those found at the east coast of the United States. The signal types are analogous, but the times and frequencies of occurrence are often quite different. In the Flathead Lake experiments, where strong ducts were often present, signal level variations of 50 db were observed for the optical path, 55 db for the nonoptical paths. The correlation between the observed M curves and the received signal strength was extremely close, high signal levels being observed when the measured M curves showed the presence of a duct; and standard signal levels, when the M curve was of the standard type. Similar observations were later made many times over in other experiments such as those at Massa- chusetts Bay, already described. Figure 10 shows typical signal records in form of hourly maxima and minima over a three-day period for the 20-mile path on Flathead Lake. Though the 66 TRANSMISSION EXPERIMENTS i mi ii mi 0B BELOW 70- FREE SPACE \ i ito- YF yf 120- "PINE (57-FT STATION) SEPT 16 2t 5 Ke} 15 20 6 Wl SEPT 17 SEPT 18 16 2l 2 7 12 17 22 TIME IN HOURS ——s il FREE SPACE \ "BEACH (I6-FT STATION) SIGNAL LEVEL AS A FUNCTION OF TIME SEPT 16 TOI8 Ficure 10. Variation of signal strength over 3 days. Two receivers on 8 band, Flathead Lake, Montana. path itself is entirely over water, the over-water trajectory of the air is limited by the dimensions of the lake. Both receiving stations are below the line of sight, the upper by 91 ft, the lower by 132 ft. There is, in this graph, a rather clearcut distinction between periods of standard propagation with a comparatively limited margin of variability of the signal, and periods of superrefraction accompanied EXPERIMENTS by very deep fades. This behavior is found in most propagation experiments but is perhaps rarely as well marked as in this graph. Another feature of interest is the fact that the maximum signal level is fairly close to the free space level. This has been found to hold approximately in a number of other propagation experiments where, in the presence of a duct, the maximum received level seems to occur not far from the theoretical free space signal level. No explanation for this behavior has been given, and it may be purely accidental. Figure 11 presents, for part of the same period as REPRESENTATIVE DETAILED SOUNDING SEPT 16 14715 (0) 270 280 290 300 (N-1) X 10S&—» IN NORTHWEST 67 the Canadian Wave Propagation Committee. They were started in the last year of the war and are still under way at the writing of the present report. These tests promise to throw light upon certain aspects of the propagation problem that are difficult to investigate elsewhere. The equipment is located on the prairies of western Canada. The transmission path is over terrain that is as near perfectly level as can be found. The ground is covered with short grass and is without trees or houses. The region forms part of a large flat area in which the atmosphere can be expected to be much more homogeneous than — SEPT 16 ---- SEPT 18 "k" AS A FUNCTION OF TIME SEPT 16 AND 18 15 TIME 12:00 - 18:00 O'CLOCK 16 17 IN HOURS ——> Fieure 11. Values of k as a measure of M or N gradient for part of period shown in Figure 10. shown in Figure 10, the value of & as a function of time at a point on the transmission path. Here k is a measure of the slope of the M curve in the lowest strata. Combining equation (17), Chapter 5, and equation (4), Chapter 6, we have 1/ka dM /dh - 10°. Thus when k is negative a duct is present. It will be seen that the incidence of negative values of k correlates well with high signal strength in Figure 10. CANADIAN EXPERIMENTS The Canadian transmission experiments are being undertaken by the Tropospheric Subcommittee of — in more densely populated regions. Extensive meteoro- logical measurement by means of stationary installa- tions, captive balloons, and airplanes are being carried out simultaneously with the transmission experiments. The path is 27 miles long with receivers mounted on a tower at several altitudes. The trans- mitters operate on the 5 and X bands and are pulsed. In addition, radar measurements are being undertaken by means of corner reflectors that are spaced at regular intervals along a path 45 miles long. It may be expected that valuable results will soon be received on the completion of these experi- ments. 68 TRANSMISSION EXPERIMENTS oa Ey D m ALTITUDE IN FEET X 10° = w 300 320 340 360 380 400 420 440 460 480 500 Ce ae 10° om / N \ ! ALTITUDE IN FEET X 107° uo a p 7 \ | \ —— NOVEMBER 1,.1943 ---- NOVEMBER 9, 1943 50 RANGE IN NAUTICAL MILES Figure 12. Signal strength at several elevations as function of distance. (Near San Diego.) 8.4 EXPERIMENTS IN THE SOUTHWESTERN UNITED STATES The Navy Radio and Sound Laboratory at San Diego has performed a considerable number of propagation experiments which have substantially aided our understanding of the phenomena of guided propagation. Moreover the meteorological conditions found in this part of the United States are rather unique; and, while they are not, perhaps, reproduced’ at many other places of the earth, they are so clear- cut and regular as to facilitate greatly experimental investigations and their interpretations. The meteorological conditions at San Diego during most of the year are characterized by the presence of a high-pressure area and high-level subsidence. In more concrete terms, there is a surface stratum of comparatively cool and moist air on top of which there is a layer of very dry, warm air. The transition between the two strata is as sharp as can be found anywhere, and the transitional layer is often no more than a few hundred feet thick. The height of the transition layer above the ground is usually between 1,000 and 3,000 ft and sometimes as much as 4,000 ft. — During the winter of 1942 to 1943, a series of measurements were made on the intensities of arti- ficial fixed echoes of a 700-me radar located near San Diego,!?*%5 and these were compared with measured temperature and humidity gradients in the lower atmosphere. A pronounced correlation between excessive echo ranges and nonstandard M gradients at once appeared. The quantitative aspects of these correlations will not be discussed here since they are very similar to others of this type already reported. Another set of observations where the receiver was located in a plane is shown in Figure 12.3 The receiving antenna was a Yagi, mounted in the nose of the plane, records being made when the plane was flying over the ocean toward the transmitter which was a 500-me radar. Figure 12 represents the results of flights at various altitudes on two different days, the maxima of the signal strength curves corres- ponding to the “lobes” of the transmitter pattern. On one of these days a duct was present as shown in the inset where M is plotted against height. The dot-and-dash straight line in this diagram represents the condition dh/dM = constant. The most con- EXPERIMENTS NEAR SAN DIEGO 69 80 MILE LINK SAN PEDRO TO SAN DIEGO TRANSMITTER AND RECEIVER AT 100 FT. ALTITUDE SEPTEMBER = Ww ut . wu e A BASE OF TEMPERATURE INVERSION @ SAN DIEGO RAYSONDE ore ° oe) = © WIRED SONDE & AIRPLANE ° 7 OOO Agia e & 0% 7 °F © a &°, 8, , — 0 hs ° ° e 2000 > ePo °° . eo o e ° Oo W b e eto es oo 00 Or 0 FOr} oo F OFS © Manthe + e no 05,9 0 . = OP % ° if . %o 5% 7 °° = 0 Sao = — ————— ancen | —— he 0 w ° -60 fe) a < a a OCTOBER Ficure 13. Signal strength over 80-mile path, San Diego to San Pedro, correlated with height of temperature inversion. spicious feature of Figure 12 is the difference between the signal distribution in the absence and presence of a duct at 500 ft, the lowest level measured, whereas the intensities agree fairly well at the higher levels. This behavior is in full agreement with the general predictions of propagation theory. Nevertheless, the detailed interpretation Jed to a slightly different TRAPPED wp OW fF GD nA N @ NUMBER OF MODES -30 -20 10 O DB ABOVE FREE SPACE 10 20 -30 -20 -I0 O Figure 14. Computed number of modes trapped versus observed field strength, San Diego Bay. result from that expected, as was brought out by subsequent experimental investigations. In 1944 a one-way transmission path was operated between San Pedro and San Diego, an over-water path?”%° 80 miles long with both terminals at an elevation of 100 ft, which were thus well below the optical horizon. Three fairly low frequencies, 52, 100, and 547 me, were used. Figure 13 shows a field strength diagram of bihourly means for a period of about six weeks in the early fall of 1944. At the top of these diagrams is shown the height of the base of the temperature inversion, which is a quantita- tive measure of the height of the elevated duct. In order to compare these data with the results of duct theory, Figure 14 shows the number of lowest modes, trapped in the elevated duct, plotted against the signal strength. For each point indicated, the number of trapped modes is calculated by simple waveguide theory from the measured M curves while the field strength is that simultaneously measured on the transmission path. For the lowest frequency, 52 mc, the duct is always beyond cutoff and no trapping should occur; nevertheless, the field strength record shows considerable fluctuation. As seen from Figure 14 there is no correlation be- TRANSMISSION EXPERIMENTS Mere Pee OO FO! (OMOs = Role 10S NNO TIO MEO EEO! BSS 5a eee ies Poh Ve me cairc eo mm ommnc Ome PC eanaeae Gita) wees Bee Pee py RO EXPERIMENTS AT tween the field strength and the number of modes that, theoretically, are transmitted by the duct. On the other hand, there is a very pronounced inverse correlation between the height of the inversion layer and the strength of the received signal. This is just what should be expected on the basis of reflection, as distinguished from ray bending, from the elevated layer of M inversion. The principle of this reflection phenomenon has previously been outlined at the end of Chapter 6, Section 6.7. Further study shows that the rate of change of the field intensity and its varia- tion with frequency are just of the magnitude re- quired by the theory. Figure 15 shows a ray-tracing diagram on which the paths of the reflected rays are indicated. Summarizing the results of this experi- ment, it may be said that the phenomenon of reflec- tion from an elevated layer has been well established qualitatively and, in some respects, quantitatively. The meteorological conditions at San Diego are rather singular, and so far such reflection occurring in a systematic fashion has not been described elsewhere though indications of similar effects have occasional- ly been reported. Another transmission experiment was made by the Navy Radio and Sound Laboratory in the Arizona desert in December 1944.188 The path was nonoptical, 47 miles long, and the frequency used was 3,200 mc. The desert air is extremely dry so that the contribution of water vapor to the refractive index is small and the change in M owing to changes in humidity with height is nearly negligible. During the clear nights a pronounced temperature inversion develops from radiative cooling of the ground, a ground-based duct thus being formed. The received field strength varied in close correlation with the formation and disappearance of the duct, with a pronounced diurnal period. The overall results of this experiment are again in excellent qualitative agreement with the predictions of the duct theory. At the same time the experiment also furnished an opportunity for studying the development over land of low temperature inversions which are valuable for radiometeorological forecasting. Bb EXPERIMENTS AT ANTIGUA Operational experience in the Pacific Ocean led to the conclusion that low ducts are very common over the ocean surface in subtropical and tropical climates. Tn order to study these ducts, an experiment was un- ANTIGUA 71 dertaken by the Naval Research Laboratory in the spring of 1945.!% The island of Antigua, one of the Leeward Islands of the Lesser Antilles in the British West Indies, was chosen as the site. The prevailing winds there are northeasterly and the air has an over- water trajectory of several thousand miles before arriving at the island and is therefore considered characteristic of large portions of the central Atlantic and Pacific oceans. There is almost no diurnal and only a limited seasonal variation in the air at the lowest levels. Equipment for the transmission experiments was comprised of S-band and X-band sets provided by the Radiation Laboratory, MIT. The transmitters with parabolic antennas were mounted on a ship at heights of 16 and 46 ft. There were two parabolas for each height and each frequency, one set pointing to the stern and one to the bow, so that measurements could be made on both the outward and inward runs of the vessel. Receivers were located at heights of 14, 24, 54, and 94 ft on a tower at the edge of the water. Monitoring and automatic recording were similar to those used in the transmission experiments pre- viously described. Records were obtained while the ship was traveling away from the receiving station and again on its return. Signals could usually be de- tected up to 190 miles for some combination of transmitter and receiver heights. Direction finding equipment was used for keeping the ship on its course, and fading of the signal caused by the ship’s being off course could be readily detected and rectified. An extensive program for measuring low-level M curves paralleled the transmission measurements. Since the weather conditions at Antigua are quite steady there is little variation in these curves, as shown by two typical ones illustrated in Figure 11 of Chapter 7. The low-level duct indicated by these graphs has been found present at all times in this location. Typical field strength records for the S band and the X band are shown in Figures 16 and 17, respec- tively, the most outstanding feature being the varia- tion of field strength with antenna heights. For the S-band transmission, the field strength increases - slightly with increasing antenna height but not nearly so fast as it would under standard conditions. For the X band, on the other hand, the field strength, as a rule, is increased by lowering the antennas. This behavior can be explained on the basis of the mode theory of duct propagation as outlined in Chapter 6. For the shorter wavelength X band, we have genuine ~] i) TRANSMISSION EXPERIMENTS trapping, so that the field strength is greatest when the transmitter or receiver or both are in the duct. In terms of the height-gain functions of equation (27), Chapter 5, it appears that these functions of the lowest mode or modes have a pronounced maximum in the duct and decrease rapidly above it. For S-band transmission there is a transition between the com- plete cutoff, indicated by a highly simplified wave- guide theory, and complete trapping. This inter- mediate effect is caused by some leakage of this wave train from the duct and the retention by the duct of a portion of its wave-guiding properties. The height- gain functions, while still much larger in the duct than in the case of standard propagation, no longer have distinct maxima but show a gradual increase S BAND IN MARCH 19-21 Transmitter Power=4,2x\0° Watts with height from the ground. This case is particu- larly interesting because it clearly exemplifies the possible variety of conditions intermediate between trapping, as described by the ray tracing of geo- metrical optics, and the diffraction around the earth’s surface characteristic of standard propagation. Figure 16 shows two regions with distinctly different slopes in the curves of power versus dis- tance. This probably indicates that two different modes predominate in these two regions. The pattern shown in Figure 16 can occur if for some distance near the ground the height-gain function of the second mode is greater than that of the first mode. The second mode, however, is attenuated more At moderate rapidly with distance than the first. = 40 FREE sexe SPACE LEVEL = a ee : 60 db BELOW | WATT 70 RECEIVED POWER, 80 LEGEND 100 20 Fieure 16. Signal strength as function 80 of range. S band, Antigua experiments. ANGLE-OF-ARRIVAL MEASUREMENTS 13) X BAND IN = MARCH 1{9-2l Transmitter Power= 3.1 x10* Watts EEC 40 50 at fo) (e} TomaT x fe} Toe os en a vt @ = RECEIVED POWER, db BELOW | WATT LEGEND 46-94 90 46529) —— —\— AS 6} == — A(B2Geeo conos00ce 100 + RANGE IN MILES i 20 40 60 80 100 120 140 160 Figure 17. Signal strength as function of range. X band, Antigua experiments. distances from the transmitter the second mode prevails, but at greater distances it will become RADAR ECHO STRENGTH VS RANGE . t+——APS-I5A RADAR smaller than that of the first which decreases less WWAPRIL 1945 rapidly with distance. Finally Figure 18 shows a set of curves for attenua- tion versus distance of the target for an X-band radar on Antigua. Again it is evident that, on the whole, the lowest elevation of the radar gives the largest signal strength. DECIBELS hs fon bo} DIAM_DISH AS) (I= 29 IN.—— 4 APR 86 ANGLE-OF-ARRIVAL MEASUREMENTS SPMm Lo nh Seem Oran eon SOM MSO Toy Ol qyae ol, 5 2 RANGE NAUTICAL MILES Because the effects of nonstandard propagation Figure 18. Radar echo strength as function of range. are most pronounced at great distances from the X band, Antigua experiments. Target is a PC boat. 74 TRANSMISSION transmitter, they are most important for early warn- ing radar and communication work. These effects were investigated earlier than the question of the deviation of the angle of arrival from that prevailing in a standard atmosphere. This deviation, though small, may nonetheless be significant for fire control radars operating in the microwave band. The angle of arrival may vary by several minutes of arc because of ducts, and this effect was first studied systema- tically by BTL in 1944.10 182 Figure 19 is a schematic view of the receiving 6 INCHES WIDE (15° HORIZONTAL BEAM) ANTENNA SWINGS +.75° Figure 19. Sharp-beamed antenna for angle-of-arrival measurements. antenna used for such measurements. This antenna is a section of a parabolic cylinder arranged so that its beam, at the center of swing, is directed toward the transmitter, this being the angle at which waves arrive on a day with standard propagation. The antenna measures the vertical angle of arrival, and a duplicate antenna rotates about a vertical axis and measures the horizontal angle. The antennas are periodically swung through an angle which is A ONLY (RECORD 1) SIGNAL AMPLITUDE TIME ——> ko secs A+B (RECORD 2) Fiaure 20. Typical record of angle-of-arrival measure- ments. Top, direct ray only. Bottom, direct and ground- reflected ray. set to include the largest variations of the angle of arrival. Figure 20 shows a typical record of received field strength versus time for a periodic swing, the upper record representing the presence of a direct EXPERIMENTS ray only, and the lower indicating both a direct and a ground-reflected ray. Observations near New York during the summer of 1944 were made on two optical paths 24 and 12.6 miles long with a common receiving antenna. These measurements are estimated to be accurate to 0.04 degree, and they indicate that the greatest variation of the horizontal angle of arrival is 0.10 degree. Fluctuations within this magnitude, however, are quite common. The maximum in the vertical angle for the long path was 0.46 degree above the standard for the direct ray and 0.17 degree below the standard for the reflected ray. No correlation between depar- tures from the standard of the direct ray and the ground-reflected ray has been observed. When the direct ray was 0.46 degree above the standard, it was apparently being trapped and ‘no reflected ray was observed. The greatest spread observed between the direct and reflected rays was 0.75 degree, as compared to a standard of 0.35 degree. The variation of vertical angle over the short path was less than over the long one, the greatest change in angle being an increase of 0.28 degree over the standard for the direct ray while that of the ground-reflected ray was too small to be observed. The Evans Signal Laboratory analyzed some low-level meteorological records which were made simultaneously and in the near vicinity of these transmission experiments. The angles of arrival were determined by ray-tracing methods and were in satisfactory agreement with the observations. The difference between angles in standard atmospheres of various climates was also analyzed theoretically, and the results show that the maximum angular deviations are less than the tolerance of present-day fire control equipment. For early warning radars where the target is perhaps 75 to 100 miles away, the difference in bending of the rays between standard atmospheres of moderate and warm climates becomes appreci- able. In this case differences in estimated height vary by as much as 2,000 ft, if the target height is determined by the first signal in the lowest standard lobe. Measurements of the angle of arrival by BTL were continued in 1945, and the results, though not yet published, give more details and corroborate the previous observations. During the second half of 1945, the Electrical Engineering Department of the University of Texas has embarked on a program to study the angle of arrival. Chapter 9 GENERAL METEOROLOGY AND FORECASTING nb: INTRODUCTION ib CHAPTER 5, equation (9) was given for the refractive index as Ti 4 8 ” G@— 1) - 10°= 7 (p = ae =) a) 1 ‘L On adding to this the term (h/a)10® the “modified refractive index M”’ of equation (4), Chapter 6 is obtained, namely M = (n—1+4 7) - 10. (2) When the temperature increases with height, other things being constant, n — 1 decreases with height and when this decrease is strong enough it will outweigh the increase of M caused by the term h/a. Similarly, a decrease of moisture with height will produce a decrease of n — 1 which, if strong enough, will again produce a negative slope of the M curve. In Chapter 7 we have dealt with these changes purely from the observational viewpoint. Now the origin of these variations owing to the physics and dynamics of the lower atmosphere will-be considered. A knowledge of general meteorological conditions may enable a trained weather forecaster to predict, from weather maps and other pertinent data relat- ing to the structure of the lower atmosphere, the presence of ducts and other meteorological factors affecting transmission. The first attempts at radio forecasting were made as early as 1943 by the British Meteorological Office in conjunction with the services operating the radar sets along the North Sea and Channel Coast. While the correlation between forecasts and observed results was imperfect, results were promising enough to encourage further studies. Since then, the forecasting technique in the British home waters has been developed to a considerable degree of effectiveness. Studies regarding the relationship between the dynamics of the lower atmosphere and radio wave propagation have been initiated by the interested Services in various parts of the British Empire, particularly in Australia where a number of interest- ing correlations have been discovered. In the United States the problem was first systematically attacked by the propagation group of the Massachusetts Institute of Technology Radiation Laboratory [MIT-RL], and at about the same time by the Army Air Forces Tactical School in Florida. The latter established a training course for radio meteoro- logical forecasters, a number of whom participated in offensive operations in the Pacific at Leyte and later. In connection with the transmission experiment across Massachusetts Bay, which was described in Chapter 8, a forecasting unit was established coopera- tively by MIT-RL, the AAF, and the U. S. Weather Bureau at Boston. Regular forecasts were made and checked by both meteorological and radio observa- tions. The pertinent information required for radio meteorological forecasting was assembled by a number of agencies in England?*4 and in this country. The most extensive American texts on the subject have been issued by Headquarters, Weather Divi- sion, AAF,?** and by the Columbia University Wave Propagation Group.’ The latter report, Tropos- pheric Propagation and Radiometeorology is published in Volume 2 of the Summary Technical Report of the Committee on Propagation. 92 ATMOSPHERIC STRATIFICATION From the meteorological viewpoint it is convenient to distinguish three factors which tend to affect the temperature and moisture distribution in the lower part of the atmosphere. These factors are known to meteorologists as (1) advection, (2) nocturnal cooling (over land) and (3) subsidence. Advection is a term that designates the horizontal displacement of an air mass of specific properties over an underlying surface which tends to modify the structure of the mass. Thus one speaks of the advection of dry polar air over a warm water surface. Advection is not the modification of air mass proper- ties but merely a preliminary to such modification. Advection changes the physical characteristics of the lower strata of the atmosphere through transfer of heat or moisture between the air and the under- lying ground or sea surface. The operating factor in this exchange is turbulence, and a brief review of its effects in the atmosphere will be given. Nocturnal cooling over land is caused by a loss of 75 76 GENERAL heat from the ground by infrared radiation. The cooling thus effected is communicated to the lower strata of the atmosphere by means of turbulence. Nocturnal cooling occurs to an appreciable degree only if the sky is clear. Any layer of clouds will exert a “blanketing”’ effect which reduces the cooling of the ground to a small fraction of that for clear nights. Subsidence is a meteorological term for the slow vertical sinking of air over a very large area. It is usually found in regions where barometric highs are located. By a dynamic process, too complicated to be described here, subsidence often produces a temper- ature inversion, the air in a subsiding stratum being, as a rule, very dry. Subsidence is usually strongest in a layer somewhat elevated from the ground, and when the dry subsiding mass overlies a moist stratum near the ground, a sharp moisture gradient is created which is favorable for the formation of the duct. The elevated ducts at San Diego are of this type. Convection occurs whenever the vertical tempera- ture gradient exceeds in absolute value the critical gradient of about —1 C per 100 m. It is usually the result of the heating of the ground by the sun’s rays, and over land on a hot summer day it may extend to great heights in the atmosphere. Since convection mixes the air thoroughly, it establishes small and constant moisture gradients throughout the lower atmosphere, resulting in a very nearly linear Mecurve. Consequently standard conditions of propagation prevail on summer days over land from late morning until late afternoon, this being the time when con- vection is most likely to be present. Often this applies also to summer days with a light overcast. Frictional turbulence occurs normally in the lowest 1,000 m of the atmosphere even when convection is absent. It is caused by the wind, requires at least light winds, and is fully developed with moderate or strong winds over land. Since turbulence is caused by the roughness of the ground it is less well developed over the sea surface. It can safely be assumed that over land with moderate or strong winds standard propagation conditions prevail because of the reg- ularizing action of turbulence. Temperature inversions occur when the temperature of the sea or land surface is appreciably lower than that of the air. The temperature transition from the ground to the free air takes the form shown in Figure 1. The heat and moisture transfer caused by turbu- lence in a temperature inversion is less simple than that in a frictional layer. The turbulent processes in inversion regions are highly complex and, as yet, are METEOROLOGY AND FORECASTING T GROUND T Ficure 1. Air temperature versus height for a tempera- ture inversion. not very well explored. It is known, however, that the intensity of the vertical transfer of heat and moisture is much less than the rate of transfer with frictional turbulence and decreases with the vertical increase of temperature. In a steep inversion the rate of transfer may be many times less than in a fric- tional layer. This tends to produce a vertical stabiliz- ation of the air layers in the inversion region. As soon, therefore, as a temperature inversion has begun to form, the rapid mixing in the lowest layers, usually effected by frictional turbulence, stops and is re- placed by a much more gradual diffusion. Assuming that the rate of diffusion has become so slow that the transfer of moisture over a height of a few hundred feet takes many hours or, perhaps, a day or two, when the air in the inversion is dry to begin with and flows over the sea or moist land there will be established, in such an air mass, a steep mois- ture lapse, since the water vapor that has been taken up by the air near the ground will only gradually diffuse into the dry air aloft. Conditions are then favorable for the formation of an evaporation duct, in addition to whatever tendency toward duct forma- tion may be caused by the temperature inversion itself. os CONDITIONS OVER LAND Because of the considerable variation of the ground temperature by cooling at night and heating during the day, there is to be found over land an alternation COASTAL AND MARITIME CONDITIONS Hi of convection during the day and conditions of a tem- perature inversion during the night. There is some phase shift in that the atmospheric conditions lag about three to four hours behind the sun. The amount of nocturnal cooling caused by infrared radiation of the ground is very nearly independent of its constitu- tion. It is, however, strongly reduced by the presence of clouds which in turn radiate toward the ground, canceling part of the cooling effect. High moisture content in the lower atmosphere acts partly in the same way and somewhat reduces the heat lost by the ground. With a full overcast, nocturnal cooling is negligible and normally no temperature inversion will be formed. In temperate climates temperature inversions alone can produce only weak ducts because the effect of temperature upon the refractive index is relatively small. In the fairly common case, however, where the inversion is accompanied by sufficient moisture gradient, a strong duct will result. This occurs when the air is dry enough to allow evaporation into it from the ground. In warmer climates where the transi- tion between night and day is rapid, evaporation may set in early in the morning before the nocturnal in- version has been completely destroyed by the action of the sun. A strong duct will then be formed for a short period. Fog. Contrary to what might perhaps be expected, the formation of fog results generally in a decrease of refractive index. For instance, when fog forms by nocturnal cooling of the ground, the total amount of water in the air remains substantially unchanged, although part of the water changes from the gaseous to the liquid state. It is found that water suspended in the air in the form of drops contributes less to the refractive index than the equivalent amount of vapor. The formation of fog, therefore, reduces the effective contribution of the water vapor to the refractive index. If there is a temperature inversion in the fog layer, the vapor pressure required for saturation increases with height, and a substandard M curve usually results. With a substandard M curve the electromagnetic field near the earth surface is diminished instead of increased, a case opposite to that of superrefraction. In practice this weakening of the field not uncom- monly leads to a more or less complete radio blackout. Fog, however, does not always produce a sub- standard M curve although that is usually the case. In certain less frequent types of fog, the temperature and saturation vapor pressure may be constant or increase with height through the fog layer. In this event propagation will be standard, or ducts may even form occasionally within the fog layer. "4 COASTAL AND MARITIME CONDITIONS Advection is of prime importance near a coast where the wind may blow the air from land to sea or vice versa. The former case, which is the more important in practice, will be considered. A tempera- ture inversion is formed, if the air from above a warmer land surface flows out over a cooler ocean surface. Over the land the air will usually have attained a state of convective equilibrium with correspondingly slow variations of temperature and humidity with height. When this air comes in contact with the cold water surface a temperature inversion is formed which increases gradually as the air proceeds over the water. Thus the inversion is the more pronounced, the greater the distance from the shore. Eventually, however, at very large distances, equilibrium between the air and the water surface will again be reached. The temperature inversion formed during this process would in itself give rise to only a compara- tively weak duct. When, however, the air is dry, evaporation from the sea surface takes place simul- taneously with heat transfer, and a fairly strong negative humidity gradient is established in the lowest layers. This combination of temperature inver- sion and moisture gradient is very favorable for the formation of a pronounced duct off shore. To=32G Eo= 12.3 MILLIBAR Tw=22 GC E\y= 26.5 MILLIBAR ais — 600 500 Ww = is z E & 300 rm INITIAL 4HR 6HR IOHR| 20HR 200 100 | 0) 310 320 330 340 350 360 370 380 M Ficure 2. Successive M curves resulting from modifica- tion of warm dry air over cool moist surface. Zero time corresponds to the coastline; 1/4 hr, 1/2 hr, etc. refer to the time the air has been over water. The progressive formation of an advection duct, created by the mechanism just outlined, is shown 78 GENERAL schematically in Figure 2. The successive M curves correspond to a series of time intervals measured from the passage of the air over the shore line. The increase of the duct toward the maximum and the subsequent flattening of the M curve as the air approaches a new state of equilibrium is clearly seen from the figure. Duct formation in such a case depends on two quantities: (1) the excess of the unmodified air temperature above the water temperature, and (2) the humidity deficit, that is, the difference between the saturation vapor pressure corresponding to the water temperature and the actual water vapor pres- sure in the unmodified air. The problem can be treated by means of the mathematical theory of diffusion in a turbulent medium, and a considerable amount of effort has been spent in investigating this type of advective duct. Extensive mathematical work has been carried out in England?°° based primarily on the large body of data on atmospheric diffusion gathered in connection with chemical warfare problems.!°7 In the United States such ducts have been studied very extensively in con- nection with the propagation experiments in Massa- chusetts Bay where conditions are favorable for their formation.?%?% Another phenomenon often responsible for ducts in coastal regions is the land and sea breeze. This type of wind is of thermal origin and is produced by temperature differences between land and sea. During the day, when the land gets warmer than the sea, the air over the land rises and that over the sea descends, thus causing a circulation in which the air in the lowest layers flows from sea to land. This is the sea breeze. Vice versa, during the night the land becomes colder than the sea, and circulation is in the reverse direction, creating the land breeze. As a rule this type of phenomenon is extremely shallow, and the winds do not extend above a few hundred feet at the most. A sea breeze modifies the advective conditions described above in various ways, and extremely strong ducts have occasionally been observed under sea breeze conditions. The land and sea breezes are of a strictly local nature and in some cases will extend only a few miles to land or sea from the shore. Nevertheless this region may be an important part of the radiation trajectory of coastal radars. These breezes develop only under fairly calm conditions; they are wiped out by a moderate or strong wind. The advective ducts of the types described here METEOROLOGY AND FORECASTING are by their very nature of only limited horizontal extent. The horizontal variation of refractive index presents a problem that till now has not been sys- tematically studied from either the experimental or the theoretical angle. A particular type of duct has been discovered in purely maritime air, that is, air which has had an extremely long sea trajectory and thus should have reached an approximately steady state of diffusion relative to the underlying sea surface. The Antigua experiments described in the preceding chapter reveal the existence of a type of low duct which seems to be characteristic of maritime air. It appears probable that similar ducts are permanent in the oceanic regions of many parts of the earth. The relative humidity of the air at Antigua was found to be 60 to 80 per cent, indicating that a continuous upward diffusion of moisture must take place, since the air immediately adjacent to the water surface is always practically saturated. On the other hand, there is little difference between the air and sea tempera- tures in this case, the ocean being about 25 C while the air temperature varies between 23 and 26 C. The ducts are therefore caused solely by the varia- tion of water vapor in the lowest layers and are much lower than the advective ducts described before, their height rarely exceeding 40 ft. Typical M curves have been shown in Chapter 7, and, for the particular effects caused by the low height: of these ducts, we refer to the discussion of the experi- mental results. The diurnal change of ocean temperature is insignificant, except in extremely shallow water, and therefore, at some distance from the coast, propaga- tion conditions do not show any appreciable diurnal variation. 9.5 DYNAMIC EFFECTS The physical processes in the lower strata of the atmosphere which determine the formation of ducts are to a considerable extent controlled by the large- scale dynamics of the atmosphere. It is therefore often possible to make at least a qualitative forecast of propagation conditions on the basis of a knowledge of the synoptic weather situation. An example in point is the diurnal variation over land in clear weather from standard conditions during the day to duct conditions in the latter part of the night and the early morning hours. Conditions in a barometric low pressure area WORLD generally favor standard propagation. Winds are usually strong or at least moderate resulting in a well-mixed layer of frictional turbulence. Local thermal stratifications are destroyed, and abnormal moisture gradients will not develop because of the intense turbulent mixing. The sky is frequently overcast in the low pressure area and nocturnal cooling therefore is often negligible. On the other hand, meteorological conditions in a high pressure area are frequently favorable for the formation of ducts. The sky is commonly clear, thus giving rise to pronounced nocturnal cooling of the ground and to the attendant formation of a temperature inversion in the lowest layers. This, again, often gives rise, by evaporation, to steep moisture gradients within the inversion layer result- ing in the formation of ducts in the manner already described. Winds in high pressure areas are often slight, or a calm prevails, resulting in a formation of local thermal stratifications and of land and sea breezes. One of the prime phenomena conducive to non- standard propagation conditions in a barometric high is subsidence, already described. Subsidence is closely connected to high pressure areas on the weather map and is always found in such areas, but it is not always intense enough to produce an inversion. The typical pattern of air flow in a baro- ILLUSTRATING SUBSIDENCE (SINKING) IN HIGH PRESSURE AREA AS IT APPEARS JON THE WEATH- ER MAP HIGH PRES- SURE AREA THE AIR AS mM RAS GETS WARMER—MORE SO IN THE HIGHER LEV ELS-AND A TEMPERATURE INVERSION IS CREATED ee nee \ “a. VERTICAL GROSS A ae en eS RS RY SR ~e Pa INVERSION REGION —>~—___ SECTION ‘Ss —_— ~ EE re ee ~ ie UNAFFECTED AIR ew as SURFACE Figure 3. Schematic diagram illustrating subsidence in a region of high barometric pressure. metric high is shown in Figure 3 in both horizontal projection and vertical cross section. The air in the lower parts of a region of subsidence is very dry because it has descended from a high level in the atmosphere where the temperature is low and hence the saturation vapor pressure is small. SURVEY 79 If such air is located over a surface capable of evap- oration such as the ocean, a steep moisture gradient may be established at some level above the ground. This is the most common mechanism for the forma- tion of elevated ducts. Quite often subsidénce com- bines with some or the other effects mentioned earlier enhancing their tendency toward the forma- tion of the duct. The elevated ducts found in the San Diego region are perhaps the most outstanding exam- ple of this type of dynamically induced stratification. The effect of fronts in the atmosphere upon propa- gation does not seem to be very pronounced. This is probably due to the fact that in a front the transition between warm and cold air is comparatively gradual extending over a height of perhaps 1 km. In the Eng- lish propagation experiments some effects of fronts have indicated slightly substandard conditions with warm fronts and slightly superstandard conditions with cold fronts. Often, however, the effect of fronts upon radio propagation is negligible. This, of course, refers only to the frontal region itself and not to the change in air mass and attendant propagation con- ditions connected with the passage of a front. 9.6 WORLD SURVEY It clearly appears from the preceding sections that climate has a fundamental influence on the nature of propagation conditions. A systematic attack on the problem of the occurrence of ducts over the ocean has been made in England on a world-wide seale.2°° Monthly maps based on estimates. drawn from general low-level weather data, giving regions of the most frequent occurrence of superrefraction and substandard refraction, were issued. However, these need much further checking by actual observa- tions. The propagation features of some important parts of the world where some knowledge has been accumulated is outlined briefly below. Atlantic Coast of the United States. Along the north- ern part of this coast superrefraction is commonin summer, while in the Florida region the seasonal trend is reversed, a maximum occurring in the winter season. Western Europe. On the eastern side of the Atlantic, around the British Isles and in the North Sea, there 1S a pronounced maximum in the summer months. Conditions in the Irish Sea, the Channel, and East Anglia have been studied by observing the appear- ance or nonappearance of fixed echoes. Additional 80 GENERAL METEOROLOGY AND FORECASTING data based on one-way communication confirmed the radar investigations. Mediterranean Region. The campaign in this region provided good opportunities for the study of local propagation conditions. The seasonal variation 1s very marked, with superrefraction more or less the rule in summer, while conditions are approximately standard in the winter. An illuminating example 1s provided by observations from Malta, where the island of Pantelleria was visible 90 per cent of the time during the summer months, although it lies be- yond the normal radar range. Superrefraction in the Central Mediterranean area is caused by the flow of warm, dry air from the south (siroeco) which moves across the ocean, thus pro- viding an excellent opportunity for the formation of ducts. In the winter, however, the climate in the Central Mediterranean is more or less a reflection of Atlantic conditions and hence is not favorable for duct formation. The Arabian Sea. Observations covering a con- siderable period are available from stations in India, the inlet to the Persian Gulf, and the Gulf of Aden. The dominating meteorological factor in this region is the southwest monsoon which blows from early June to mid-September and covers the whole Arabian Sea with moist equatorial air up to considerable heights. Where this meteorological situation is fully developed, no occurrence of superrefraction is to be expected. In accordance with this expectation, all the stations along the west side of the Deccan report normal conditions during the southwest monsoon season. During the dry season, on the other hand, conditions are very different. Superrefraction then is the rule rather than the exception, and on some oc- casions very long ranges, up to 1,500 miles (Oman, Somaliland), have been observed with fixed echoes on 200-me radar, based near Bombay. When the southwest monsoon sets in early in June, superrefraction disappears on the Indian side of the Arabian Sea. However, along the western coasts conditions favoring superrefraction may still linger. This has been reported from the Gulf of Aden and the Strait of Hormuz, both of which lie on the outskirts of the main region dominated by the monsoon. The Strait of Hormuz is particularly interesting as the monsoon there has to contest against the “‘shamal” from the north. The Strait itself falls at the boundary between the two wind systems, forming a front, with the dry and warm shamal on top, and the colder, humid monsoon underneath. As a consequence, conditions are favor- able for the formation of an extensive radio duct, which is of great importance for radar operation in the Strait. The Bay of Bengal. Such reports as are available from this region indicate that the seasonal trend is the same as in the Arabian Sea, with normal condi- tions occurring during the season of the southwest monsoon, while superrefraction is found during the dry season. It appears, however, that superrefraction is much less pronounced than on the northwest side of the peninsula. The Pacific Ocean. This region appears to be the one where, up to the present, least precise knowledge is available. There seems, however, to be definite evidence for the frequent occurrence of superrefrac- tion at some locations, e.g., Guadalcanal, the east coast of Australia, around New Guinea, and on Saipan. Along the Pacific coast of the United States, observations indicate frequent occurrence of super- refraction, but no statement as to its seasonal trend seems to be available. The same holds good for the region near Australia. In the tropics there is a very strong and persistent seasonal temperature inversion, the so-called trade wind inversion. It has no doubt a very profound influence on the operation of radar and short wave communication equipment in the Pacific theater. 9.7 RADAR FORECASTING The forecasting of propagation conditions for early warning radars is of great operational significance be- cause ranges for airplane as well as ship targets often vary by as much as a factor of 2 or more depending on the weather conditions. Forecasting is based on the general meteorological principles presented above which can be organized into a system of standard procedures for the prediction of propagation in a given area.744/253,299 Tt is usually quite difficult to make a quantitative forecast of such parameters as duct height, but this has been tried with a fair degree of success. A radio forecast is made by first taking the general synoptic weather situation as presented on a weather map and including such upper air data as may be available. Usually one forecast cannot be applied to more than-a limited area of specific local conditions; fortunately such a forecast is in general adequate for the area covered by one or a few radar sets. The RADAR formation of ducts depends principally on the tem- perature difference between the air and the ground or sea surface and on the humidity of the air. Data on sea temperature, which is usually fairly constant, are collected while over land it is necessary to obtain data on the diurnal variation of the soil temperature. Wind velocities may be gathered from the weather map, and the trajectory of the air previous to and during the forecast period can then be determined. If the relative humidity of the air is known, it is possible from the theories at hand to draw estimated curves of the temperature and moisture variation in the lowest layers. From these an estimated M curve is obtained. The success of this method depends to a large degree upon the familiarity of the forecaster with local conditions. The forecasting of advective ducts over the ocean FORECASTING 81 is the main problem in which radio forecasting requires other tools than those used for ordinary weather forecasting; but most other problems are closely similar to those presented by conventional practice, among which are the forecasting of subsi- dence from upper air meteorological data, the forecasting of nocturnal temperature inversions in dry climates, and the forecasting of standard propagation conditions. In order to facilitate weather forecasting in the Pacific, where data have been very scanty during the war, a system has been worked out whereby localities in the Pacific area are compared to those of closely similar climatic and meteorological charac- ter in the Atlantic. A rough estimate of propagation conditions to be expected may be derived there- from. 2°75 Chapter 10 SCATTERING AND ABSORPTION OF MICROWAVES HE OBJECT of the present chapter is to summarize the status of absorption and scattering of micro- waves by different solid obstacles, by liquid water or ice particles floating or falling in the atmosphere like those present in clouds, fog, rain, hail, and snow. The absorption of microwaves by the atmospheric gases as well as the aforementioned meteorological elements will also be summarized here. The following grouping of the material included suggests itself naturally: absorption and radar cross section; targets (planes, ships); absorption and scat- tering by rain, hail, snow, clouds, and fog; and absorption by the atmospheric gases, oxygen, and water vapor. HAO ABSORPTION AND RADAR CROSS SECTION Any object irradiated by electromagnetic waves will in general remove energy from the incident beam both by absorption and by scattering. The absorbed energy is transformed into heat in the body, while the scattered energy appears in the form of radiation propagated generally in every direction around the scatterer as the source. Let us call P. the power removed from the beam through the internal absorption of the object. Its absorption cross section is defined by Pa A= W.’ (1) where W, is the power density in the incident beam, that is, the power passing a unit cross-sectional area. Similarly, if P, is the total power removed from the beam through scattering in every direction, then the scattering cross section associated with this object: is P, S=—- (2) The value of S gives information about the total scattered energy, but this is not directly useful in radar work because one is interested only in that fraction of the total scattered power which travels in the direction of the receiver. One wants then a 82 parameter involving the scattered power per unit area W, at the radar receiver instead of the total. If the target is an isotropic scatterer, Ps ~ 4nd?’ W, (3) d being the distance from the target to the receiver. The scattering cross section can thus be written as , WwW, Salah. (4) For targets other than isotropic scatterers, however, this procedure fails since one cannot say that the power per unit area at the radar is P,/4ad?. Never- theless, it is useful to define a parameter, 9 W, = 4nd W, ) (5) which is called the radar cross section in analogy with the scattering cross section S of an isotropic scatterer. This cross section « may be thought of as the scattering cross section which the target in question would have if it scattered as much energy in all directions as it actually does scatter in the direction of the radar receiver. For an isotropic scatterer ¢ = S, but in general it does not. It can be shown’ that the ratio of the received power P, to the output power P; is given by Pe ye ees 3d : 4 O03 TP (= AbD» (6) Aa The gains G,, G. and path factor A, are defined in Volume 3, Chapter 2, and ) is the wavelength of the radiation used. (See also Volume 3, Chapter 9.) This formula can be used for the determination of o. Or if o is known, it may serve to calculate the possible range. (It may be noted here that sometimes cA} is called radar cross section.) Also, a characteristic length Z, sometimes called the scattering coefficient, is occasionally defined in relation to o by o = 4rL?. (7) For simple targets o may be calculated. Table 1 contains a few calculated radar cross sections. ®8See Volume 3 of the Summary Technical Report of the Committee on Propagation. AIRCRAFT TARGETS 83 Tasie 1. Radar cross sections. Radar Targets Condition cross section Conducting j<> 2 Cylinder, Axis of eylinder wdl? diameter = d__ parallel to =H length =J1 _ electric field, \ KGL IN SKU Matched load Oriented parallel 9? dipole to the incident 16x electric field Shorted dipole Oriented parallel 9d? to the incident Aor electric field Corner reflector 4S? 2 S = cross section of triply reflected beam Triangular L = length of 47L4 : corner reflector’s edge. 32 (1 —0.0076 6") reflector 6 = angle between direction of incidence and axis of symmetry of reflector Square corner 1271 Sena 57 (1 —0.02748) 10.2 AIRCRAFT TARGETS Diagrams showing the dependence of c on the orientation of the aircraft indicate very large and irregular fluctuations. The radar cross section can change by 100 to 1 with a change of aspect of only a few degrees. These varying values of the radar eross section are dependent on wavelength, polari- zation, details of plane design, ete. Reflection pat- terns such as shown in Figure 1 have been measured _ in the laboratory for a few simplified models. Actually an observer would see only the time average of the radar cross section of a plane, and it is only this average value which is of operational importance. Table 2 gives measured values of co for various aircraft. These are the values to be used in equation (6). As far as is known, these empirical cross sections f=100 MC POLARIZATION HORIZONTAL Er=SCATTERED FIELD STRENGTH IN ARBITRARY UNITS @=CORRESPONDING RADAR CROSS SECTION IN SQUARE METERS 310 Pp 320 340. «35020. +10 20 30 Figure 1. Aspect diagram of a B-17E at 5 degrees above horizon. are independent of wavelength. This result may be interpreted to mean that a plane in motion behaves more or less like a collection of good reflecting surfaces oriented at random. It is worth noting in this connection that the radar cross section of a circular plate of radius a, whose normal is at an angle 6 with the direction of incidence, is co = 7a" | eot 6X Ji (= sin a) | : (8) Tasue 2. Airplane radar cross sections. Airplane co, sqm oc, sq ft SNC 3.9 42 SNJ 5.0 54 OS-2U 9.5 100 Taylorcraft 9.5 100 CESSNA 9.5 100 0-47 10 110 AT-11 11 120 SWB 13 140 15-D (Curtiss Wright) 23 250 J2¥ 25 260 JRE 30 320 PBY 31 340 B-18 36 380 B-17 45 480 B-29 67 710 84 SCATTERING AND ABSORPTION OF MICROWAVES where J; is the first order Bessel function of the first kind. The maximum of o occurs for @ = 0, when equation (8) reduces to 4ra4 c=. 2 (9) This sharp maximum of o at 6=0 is the phenom- enon of specular reflection. The average value of o over all values of 6 turns out to be 1 Go = gma” 5 (10) This result is independent of wavelength and suggests that a large number of specularly reflecting surfaces oriented at random will have a cross section inde- pendent of A, or that a few surfaces of rapidly chang- ing orientation may have this property. The lack of dependence of wavelength of aircraft radar cross sections might be understood on the basis of these results. 10.3 SHIP TARGETS A ship being a collection of both complicated and flat surfaces, a rigorous computation of the radar cross section of any given ship of known design is not feasible. Nevertheless, the Naval Research Laboratory workers have been able to give a good account of these problems.?743763838-392,417,421 The path factor in the formula (6) raised to the fourth power is (e=6 E = a @ = es io |, (1) where 4h WH madi h, = antenna height, H = height of ship above water including superstructure. The above result follows by integrating the received power over the height H, assuming perfect reflection from sea. Tt is seen in equation (11) that whether 6) < z, the region called the “far zone,” or 6) > 7, the ‘‘near zone” (short ranges), materially affects the qualita- tive behavior of the factor A4. In the latter region A, =6. The radar cross section of a ship which does not exhibit marked specular reflection is given roughly by where a = dimensionless constant dependent on ship design, the breadth of the aspect under observation, height of ship above water including superstructure. B= H = The approximate values of a to be used are indicated in Table 3. Taste 3. Ship targets. Type of ship a Remarks Battleship 0.1 Cruiser 0.1 ; Aireraft carrier 0.05 Except at direct broadside aspect Submarine 0.01 In Tables 4 to 7, values of o computed from equation (12) are called theoretical values. Experi- mental values are computed from observations made by the Naval Research Laboratory workers with each quantity the mean of several observations. The 200-me experimental result is unexpectedly low while the values at the higher frequencies are a little higher than would be anticipated. This points to the existence of some specular reflection for this ship, which would not be surprising in view of its great size. Considering the uncertainty in the experimental values, the agreement with the theoretical results is not unsatisfactory and bears out the assumed dependence on wavelength. The aircraft carrier shows pronounced specular reflection at the direct broadside aspect, particularly at the higher frequencies. These values of o are TasLe 4. Radar cross section of a battleship (BB-63), broadside aspect. a = 0.1, B = 270 m, H = 24 m. f(me) o (exp), sqm __ a (theory), sq m 200 0.12 * 10° 1.9 X 10° 700 10.2 x 10° 6.8 X 10° 970 15. xX 10° 9.4 X 10° 3,060 110. xX 10° 30. x 10° TasLe 5. Radar cross section of a cruiser (CL-87), broadside aspect. a = 0.1, B = 180 m, H = 24 m. f(me) o (exp), sq m o(theory), sq m 100 2.45 X 104 2.6 X 104 200 5.06 < 104 5.2 < 104 700 7.79 X 104 18.1 X 104 970 ‘28.4 x 10! 25.1 X 104 3,060 102.2 x 10! 79.3 X 104 ABSORPTION AND SCATTERING BY Tasie 6. Radar cross section of submarine (SS-171), broadside aspect. a = 0.01, B = 838m, H = 7.6 m. JS(me) o(exp), sq m o(theory), sq m 200 3.0 x 10° 3.5 & 10? 700 18.7 X 10? 12.2 < 10? 3,060 71.4 X 10? 53.4 < 10? Tasue7. Radar cross section of aircraft carrier (CV-36), near broadside aspect. a = 0.05, B = 250 m, H = 46 m. f(me) o(exp), sq m o(theory), sq m 200 0.22 < 105 0.96 105 700 2.6 X 105 3.4 x 10° 970 6.3 X 10° 4.6 X 10° 3,060 11.3 X 10° 14.4 xX 10 typical of the ship for aspects other than direct broadside. In Table 8, the same ship is analyzed at direct broadside. No theoretical calculation of « has been attempted because of a lack of sufficient data from other ships of this type. The column )?o is near TABLE 8. Radar cross section of aircraft carrier (CV-36), direct broadside aspect. f(me) o(exp), sq m 2 o(exp) 200 0.055 x 107 1.2 < 10° 700 10 x 107 1.8 < 10° 970 5.0 X 107 4.8 X 10° 3,060 Wall d< 1@¢ 7.1 X 10° enough to a constant to indicate the existence of specular reflection. Since the hull at broadside can be considered as a flat surface, specular reflection is to be expected under normal incidence with a radar cross section proportional to 1/\? as indicated by equation (9). In view of the complicated reflecting properties of targets of operational interest, it may be said that the experimental results can be considered as being in fair agreement with theoretical predictions. 04 ABSORPTION AND SCATTERING BY CLOUDS, FOG, RAIN, HAIL, AND SNOW The theory of the scattering and absorption of microwaves by a collection of spherical particles of known concentration, size, distribution, and given dielectric properties was completely worked out before systematic experimental work was done on these phenomena.?°*?7"?79 The electromagnetic theory predicts that the total scattering cross section of a sphere of given electrical properties is CLOUDS, FOG. RAIN, HAIL, AND SNOW 85 Ss = ue 2 (2n + 1) (ja, |? ++ |b, |?) em? , (18) 2r sae where A is the wavelength in centimeters of the incident radiation in air and a, and b, are the so- called scattermg amplitudes associated with the magnetic and electric 2-poles induced in the sphere by the incident electromagnetic field. Similarly the absorption cross section of a sphere defined as the ratio of the total power removed from the incident beam both by “internal absorption” (heating) and by seattering is nV? ate ars A = 5 (—Re) 2a) + 1) (Gn + 6,) em?. (14) Here Re means “Real part of ... .”” The complex scattering amplitudes depend on the dielectric con- stants of the sphere, its diameter, and the wavelength of the incident radiation. The observations which are available seem to indicate that a collection of spherical particles with random distribution scatter microwaves incoherently, although under certain circumstances, existing for very short time intervals, they may scatter coherently.“° On the assumption of incoherent scattering, given a collection of spherical particles of diameters Di, De, ---, Dy, ---, D,,, whose number per unit volume or ce 1s m1, Ne, -*-, Ny, *** , Nn, the scattering cross section of such a collection per unit volume or the absorption coeffi- cient due to scattering is a, = 4.343 X 10° yy n; S; db/km , 1=1 where S, is the scattering cross section of one drop of diameter D; centimeters, and the summation extends over all possible drops present in the col- lection. Similarly, the “absorption coefficient” or “attenuation”’ associated with the absorption cross section A, (sphere of diameter D,) defined by equation (14) is (15) Pee ARV) SZ TO ys i=1 n, A; db/km . (16) Rain anp Hart ABSORPTION In order to compute the theoretical absorption coefficient of a rain or thunderhead (heavy storm cloud) one has to know the raindrop size distribution, since the computation of the cross sections for one spherical drop is straightforward provided its dielec- tric properties are known. The greatest uncertainties 86 SCATTERING AND ABSORPTION OF MICROWAVES in the theoretical predictions of scattering or absorp- tion by rain are due to the relatively limited knowl- edge of drop size distributions in rains of different rates of fall. There is no evidence that a rain with a known rate of fall has a unique drop size distribution though the latest studies on this problem seem to indicate that a certain most probable drop size distribution can be attached to a rain of given rate of fall.*4° Results of this study are included in Table 9. On the basis of these results the absorption cross TaBLE 9. Drop size distribution. Dp Percentage of total volume mm/hr O75 175} D5 eb Bs 50 100 150 D, em 0.05 70) OM 43 BO iv” 12 10 1 0.10 HOM sell 273 ils 7G Ae Ag Al 0.15 18.2 31.3 32:8 245 184 125 88 7.6 0.20 3.0 13.5 19.0 25.4 23.9 19.9 13.9 11.7 0.25 0.7 #49 7.9 17.3 19.9 20.9 17.1 13.9 0.30 15 33 10.1 12.8 15.6 18.4 17.7 0.35 0.6 11 43 82 10.9 15.0 16.1 0.40 0 O00 78 38th O77 O80 ile 0.45 OA iA Bl 83 B88 27 0.50 OG il Ig Bi) 8G 0.55 0.2 0.5 1.1 If BB 0.60 0.3 #05 10 41.2 0.65 0.2 O7 1. 0.70 0.3 section of raindrops of different size has been com- puted for use in Table 10. This table gives the decibel attenuation per kilometer in rains of different rates of fall and for radiation of wavelengths between 0.3 and 10 em. In Table 11, similar to Table 10, another set of results is contained for rains of measured drop size distributions. This table is extended to include radiations of wavelengths up to 100 cm. It seems equally interesting to give a graphi- cal representation of those results. Figure 2 corres- ponds to Table 10 and Figure 3 to Table 11. All these data refer to raindrops at 18 C. 35 - {00 MM/HR: = 20 = || S SB 20 = P =50MM/HR S piso ese 15/g ny 100! ~~_| 25miM/HR ' 10 le<| i b- 50 | 12:5 MM/HR Ow Si-ak25 = -i2s|--_| 25 mmr a bas {o) Ol 02 03 05 O7 1 2 s 8 w 0 20 FiGcure 2. Graphical presentation of data given in Table 10. Since the scattering coefficients a, and b, depend on the temperature, because of its effect on the dielectric properties of water, it seems important to evaluate the attenuation of rains whose drops are at temperatures different from those included in the preceding tables. Table 12 contains the necessary data relative to the changes of attenuation with temperature and is to be used primarily in connec- tion with Table 10. It will suffice to mention here that, for waves larger than about 38 cm, the attenuation produced by hail of the same water precipitation rate as a rain will be but a few per cent of the rain attenuation. At shorter waves, in the millimeter region, hail attenuation may become larger than that of rain. Similarly the attenuation of snow should be con- siderably less than rain; however, Canadian reports indicate approximately the same value for the same water content. As mentioned above, the whole theory of attenua- tion is based on equation (14). The formulas giving Taste 10. Attenuation in decibels per kilometer for different rates of precipitation of rain. Temperature 18 C, ) in em.277 Attenuation, db/km. P; mm/hr A= 0.3 = 0.4 = 0.5 = 0.6 A=10 AH 1.25 A= 3.0 dX = 3.2 = 10 0.25 0.305 0.230 0.160 0.106 0.037 0.0215 0.00224 0.0019 0.0000997 1.25 11116} 0.929 0.720 0.549 0.228 0.136 0.0161 0.0117 0.000416 2.5 1.98 1.66 1.34 1.08 0.492 0.298 0.0388 0.0317 0.000785 12.5 6.72 6.04 5.36 4.72 2.73 1.77 0.285 0.238 0.00364 25 11.3 10.4 9.49 8.59 5.47 3.72 0.656 0.555 0.00728 50 19.2 17.9 16.6 « 15.3 10.7 7.67 1.46 1.26 0.0149 100 33.3 31.1 29.0 27.0 20.0 15.3 3.24 2.80 0.0311 150 46.0 43.7 40.5 37.9 28.8 22.8 4.97 4.39 0.0481 ABSORPTION AND SCATTERING BY CLOUDS, FOG, RAIN, HAIL, AND SNOW 87 oa Tasie 11. Attenuation in rains of known drop size distribution and rate of fall (decibels per kilometer). Wavelength \, em mm/hr 1.25 3 5 8 10 15 Distribution 2.46 1.93 107 4.92 107 4.24 1073 N23 LOs 7.34 1074 2.80 10-4 A 4.0 3.18 107! 8.63 1072 Collil — iN(a}=s' 2.04 1073 Iile) alae 4.69 1074 Cc 6.0 6.15 102 1.92 107 E25) Om 3.02 107% 1.67 107% 5.84 1074 D 15.2 PY?) Coen Ke Oe 5.91 10>2 ihe, ir 5.68 107% 1.69 107% H 18.7 2.37 8.01 107! 5.13 1052 1.10 10-2 6.46 107% 1.85 1073 Fr 22.6 2.40 7.28 107 5.29 10-2 1.21 10-2 6.96 107% 2:27 LOx G 34.3 4.51 1.28 Li 10—: 232) Om tle? = 3.64 107% H 43.1 6.17 1.64 1.65 107 3.33 1072 1.62 107? 4.96 107% I Wavelength A, em mm/hr 20 30 50 75 100 Distribution 2.46 1.52 1074 6.49 1075 2.33 107° 1.03 107° 5.85 107% A 4.0 2.53 1074 1.08 10~4 3.88 107° 1.72 10% 9.75 105% Cc 6.0 3.02 1074 1.25 1074 4.34 107° 1.93 107° 1.09 107° D 15.2 7.85 1074 2.95 1074 9.23 10-5 4.15 10% 2.385 107° H 18.7 9.09 1074 3.60 1074 1.20 1074 5.36 107° 3.03 107% F 22.6 1.17 10% 4.81 1074 1.66 1074 7.41 107° 4.19 10% i 34.3 1.75 10° 6.83 10-4 2.24 1074 9.95 107° 5.63 107° H 43.1 2.29 107% 8.71 1074 2.78 1074 1.23 1074 6.98 10° I the amplitudes a, and b, are too complicated to be reproduced here. Their numerical evaluation for spherical drops of given size and temperature 1s LOG 4a DISTRIBUTI 40 50 60 AIN CM 70 Figure 3. Attenuation in rains of known drop-size dis- tribution as a function of the wavelength \ in centi- meters. The ordinate scale gives logio @&, where the attenuation constant @ is expressed in decibels per kilometer. The letters on the curves refer to the drop size distributions given in Table 11. quite laborious except for small meter mD/\. They involve Bessel and Hankel func- tions of half-integer order of the parameter tD/). A series of experimental results are given in Table 13. These results are to be regarded as maximum attenuation values. If these results are compared with those of Table 10 and Figure 2 one sees that, in view of the uncer- tainty in the temperature of the raindrops and their size distribution, the agreement between theoretical values of the para- TABLE 12 Rate of Correction factor 6 (T) precipitation, oN f= T= T= T= T= mm/hr m OC 10C 18C 30C 40C 0.25 0.5 0.85 0.95 1.0 1.02 0.99 1.25 0.95 1.0 1.0 0.90 0.81 3.2 1.21 1.10 1.0 0.79 0.55 10.0 2.01 1.40 1.0 0.70 0.59 2.5 0.5 0.87 0.95 1.0 1.03 1.01 1.25 0.85 0.99 1.0 0.92 0.80 3.2 0.82 1.01 1.0 0.82 0.64 10.0 2.02 140 1.0 0.70 0.59 12.5 0.5 0.90 0.96 1.0 1.02 1.00 1.25 0.83 0.96 1.0 0.93 0.81 3.2 0.64 0.88 1.0 0.90 0.70 10.0 2.08 1.40 1.0 0.70 0.59 50 0.5 0.94 0.98 1.0 1.01 1.00 1.25 0.84 0.95 1.0 0.95 0.83 3.2 0.62 0.87 1.0 0.99 0.81 10.0 2.01 140 1.0 0.70 0.58 150 0.5 0.96 0.98 1.0 1.01 1.00 1.25 0.86 0.96 1.0 0.97 0.87 3.2 0.66 0.88 1.0 1.03 0.89 10.0 2.00 140 1.0 0.70 0.58 88 SCATTERING AND ABSORPTION OF MICROWAVES TaBLE 13. Experimental values of the maximum attenuation per unit precipitation rate. References », em (a/p) db per km/mm per hr 0.62 0.37 269 0.96 0.15 256 1.089 0.2 262 0.19 176 1.25 0.09-0.40 276 0.63 281 3.2 0.032-0.042 261 and observed values is, on the whole, satisfactory. It will be seen that the results reported on K-band rain attenuation in Hawaii by the U.S. Navy Radio and Sound Laboratory workers! are higher than those observed by other workers on the same wave- length. The orographic character of these Hawaiian rains which were made up of drops falling about 300 m instead of ordinary rains falling 1,500 to 2,000 m may be one of the reasons for this divergent result. CLoups anp Foe Observations indicate that fair weather clouds and fog are composed of droplets whose diameters do not seem to exceed 0.02 cm. Under these conditions the attenuation formula takes on a remarkably simple form since it becomes independent of the drop size distribution. The attenuation formula in this limit of very small values of the parameter 7D/) is 4.092 mc, x (17) Chy = db/km , where m is the mass of liquid water per cubic meter, d is the wavelength of the radiation in centimeters, and 6e1 ) GaPoP aa?” C1 (18) where ¢, and ¢, are the real and imaginary parts of the dielectric constant of water at the temperature in question and for radiation of wavelength \. Figure 4 represents the attenuation in clouds and fog in the range 0.2 to 10 cm. This graph corresponds to a TasBLeE 14. Attenuation in decibels per kilometer for ice crystal clouds. —40 C 0.00044 m/ 0.00062 m/X 0.00087 m/d T=0C 0.0035 m/r 0.0050 m/ 0.0070 m/X Shape of crystals i Spherules Needles Disks ° , M,°°° ) Mn drops per cubic meter, the cloud or rain cross section for scattering is Se) = )) neon) AV (19) where AV is the scattering volume of the cloud, on the assumption of incoherent scattering on account of the random character of the drop distribution. The summation includes all the drop groups. The ABSORPTION AND SCATTERING BY rain front is usually wider than the irradiated area so that the radar beam intersects it. Under these conditions, taking AV approximately as a spherical shell of thickness Ad, at a distance d from the radar set, and denoting by 2@ the half-power beam width of the radar beam, one gets AV = 2rd? (1 — cos 6) Ad. (20) The rain echo cross section is then S(m) = 2rd? (1 — cos a)(aa » ich f)) . (21) Remembering that o;,(z) or S(r) is precisely the cross section per unit solid angle in the direction of the radar set, one gets instead of equation (6) for the ratio of received to transmitted power BGG: (3N\ 5 for small angles @ which must be given in radians. Tasie 15. Fraction of incident power scattered back- ward by a layer of 1 km of rain in different types of rain. (Decibels) Drop size distri- PD, Wavelength in centimeters bution* mm /hr 3 5 8 10 15 20 30 50 A 2.46 —45 —54 —61 —65 —72 —77 —84 —93 D 6.0 —38 —46 —54 —58 —65 —69 —76 —85 E 15.2 —32 —37 —45 —48 —55 —61 —68 —77 H 34.3 —29 —35 —42 —46 —53 —58 —65 —74 I 43.1 —27 —33 —40 —44 —51 —56 —63 —71 *See Table 11 for drop size distributions. The quantity [Adz,n,0;()] or its value in decibels for known drop size distributions has been tabulated in Table 15. With this table and the known characteris- ties of a radar set the ratio P;/P2 can be computed at once. In the table Ad is taken as 1 km. Since the maximum thickness Ad cannot exceed the pulse length, the values found in the table can be adapted immediately to any pulse length J by adding to it (10 logio 1), 1 being expressed in kilometers. Using equation (22) for particular radar sets it is found that the theoretically computed’ echo powers from rains agree well with the observed values, if the uncertainties of the meteorological knowledge of the echoing elements, which are mostly rains and storm clouds, is kept in mind. As expected, the echoing power of snow is very much less than that of rain. The systematic observations on S band by the CLOUDS, FOG, RAIN, HAIL, AND SNOW 89 Canadian group?” and on X band by Bent‘*4 clearly indicate that precipitation either in the form of rain or snow is necessary to produce an echo on the scope of the radar set. ABSORPTION BY THE ATMOSPHERIC GASES It was predicted that oxygen and water vapor will absorb electromagnetic waves in the microwave range.?>*?7° In particular, oxygen was predicted as having a resonance band around 5 mm and one line at 2.5mm, while the water vapor absorption is caused mainly by a single rotational line of relatively small strength around 1 em. Experiments have confirmed both these absorption effects.?7”273 In Figure 5, the N ABSORPTION IN DB PER KM ESPNS ase rare ae Po i z oe 3.0 6 0 9.0 15 30 60 90 150 FREQUENCY IN 10° MC——> 10 5 4 3 215 108 050403 02 ——_———-) INCM Ficure 5. (1) Absorption due to water vapor in an atmos- phere at 76-cm pressure containing 1 per cent water molecules, or 7.5 g per cu m. The water resonance line is assumed to be at 24,000 me, and its half width at half maximum (line breadth) is 3,000 me. (2) Absorption due to oxygen in an atmosphere at 76-cm pressure whose resonance band at 60.10% me is supposed to have a line breadth of 600 me. 90 SCATTERING AND ABSORPTION individual oxygen and water vapor attenuation curves have been plotted in the 0.2- to 10-em wave- length range. Any change in the water vapor content from the one adopted for this graph (7.5 g per cu m or 6.5 g per kg of air) or the total pressure can be taken into account in computing the combined oxygen and water vapor attenuations, since these ATTENUATION IN DB/KM N 150 90 50 3024 15 10 60 3.0 15 10 0.6 0.3 <4— FREQUENCY IN 10° MG 0.2 03 O7 25 2 3 5 7 10 15 2030 50 100 A IN CM —oe Figure 6. Atmospheric one-way attenuation. (1) Oxy- gen and water vapor (total for p = 76 cm Hg, T = 20C, water vapor. = 7.5 g per cum). (Van Vleck.) (2) Moder- ate rain (6 mm per hr) of known drop size distribution. (3) Heavy rain (22 mm per hr). (4) Rain of cloudburst proportion (43 mm per hr). are proportional to the partial pressures of oxygen and water vapor. For practical purposes the effect of temperature variations can be neglected. In Figure 6, curve 1, is plotted the total attenua- tion of oxygen plus water vapor in an atmosphere OF MICROWAVES at 76-cm pressure, with the same water vapor content as the curve of Figure 5. Curves 2, 3, and 4 are additional rain attenuation curves computed for a moderate rain of rainfall 6 mm per hr, a heavy rain of 22 mm per hr and an excessive rain of 43 mm per hr, which is of cloudburst proportions. In any rain the result of total attenuation is the sum of the oxygen, water vapor, and liquid drop attenuation. It is thus seen that for waves of 3 em or shorter the rain attenuation may become prohibitive, whereas the gaseous attenuation loses its practical import- ance at waves longer than about 2 cm. In this connection it is to be noted that for millimeter waves the rain attenuation begins to level off at waves of a few millimeters, as Table 10 indicates, and would actually decrease at waves shorter than 1 mm. However in this range, the water vapor absorption due to the strong water lines situated at much shorter waves becomes more and more intense, and communication or radar on these bands is almost totally excluded. It is worth noting in this connection that using radiation which is strongly absorbed might, in certain cases, be of great operational interest. In the oxygen band, for example, short- range communication could be achieved without any likely interference by the enemy. Electromagnetic theory thus gives a satisfactory picture of the absorption and scattering phenomena of microwaves both by floating or falling water drops, or their equivalent in hail and snow, and by the oxygen and water vapor of the atmosphere. Of the approximately 100 reports which were prepared by the Columbia University Wave Propa- gation Group or were presented at the second, third, and fourth conferences on propagation held in February 1944, November 1944, and May 1945, 61 have been selected for publication in the Summary Technical Report. Of these, 18 reports, covering standard and nonstandard propagation, are published in this volume; the remainder are published in Volume 2. The reports not included in these two volumes were omitted chiefly because their material was superseded by later documents. The reports in the remainder of this volume appear in two sections. Chapters 11 through 15 are concerned with standard propagation; Chapters 16 through 27, with nonstandard propagation. PART Ill CONFERENCE REPORTS ON STANDARD PROPAGATION Chapter 11 A GRAPHICAL METHOD FOR THE DETERMINATION OF STANDARD COVERAGE CHARTS* Ne POWER DENSITY at distance S from a trans- mitter of unit power depends upon hf; and hg, the heights of the transmitting and receiving anten- nae, and upon X, the wavelength of the radiation. For the high frequencies under discussion, we assume the earth to be a perfectly conducting sphere, of effective radius r, equal to 43 that of the earth. We are to take into account the so-called divergence factor D resulting from the earth’s curvature. Even with the simplifying assumptions above, one cannot express the power as a simple function of S, hy, he, and ) in a single equation. Accordingly, most workers on this problem have introduced various arbitrary parameters, as intermediate steps. Differ- ences in procedure he primarily in the choice of parameters. Whether a method is simple or difficult depends upon the character of the parameters. Certain procedures suggested are satisfactory for determining the number of decibels by which the signal is below the adopted standard of 1 nw per square meter, designated here by A; but if we are given A, fy, and f and then are asked to compute he as a function of S, as for a coverage diagram, some of the methods become very unwieldy. The present method works satisfactorily for either case. TRANSMITTER _S Rc a RECEIVER Figure 1. Geometry for determination of standard cov- erage. In selecting a parameter we have been guided by the following conditions. The number of parameters should be kept to a minimum; the remaining vari- ables fi, he, and S should appear in the final equa- tions, if possible. Also it should be unnecessary to interchange transmitter and receiver according to *By Lt. Comdr. D. H. Menzel, USNR, Office of the Chief of Naval Operations. the condition that he is or is not greater than hy The arbitrary parameter a is defined as follows. Let d; be the distance from the transmitter to the point at which the ray is reflected and d) the distance to the point where a ray is tangent. Then ai = (1 — aw) = 2hyr(1 — a). (1) a, therefore, is constant along a reflected ray; a = 0 corresponds to the continuation of the tangent ray; a = %% corresponds to a reflected ray perpendicular to the mast of the transmitting antenna; a = 1| is the vertical ray. Thus QOSs@ 24 over a large portion of the range of interest for the frequencies involved. Equation (1) leads to the following relationship (—2 + 3a) S? a: (1 — @)3 SV 2rh;y + 2rh, - (1 — 2a) — 2rh, = 0, (2) an irreducible cubic in a. It is this fact that makes the problem mathematically difficult and makes impossible the explicit elimination of a. Additional equations are Db — #2 =. 4A — 8a — 4V/ 27h, S-!(1—a): 4 — 3a ) an approximation holding well over the region of interest since a > 24. The phase difference 4, result- ing from the difference in optical path between the reflected and direct rays, is we oie | 1 | (4) Xr V 2rhy (1 = a) S|? and for the transmitted power ® P Here we have four equations. If hy, \, and A are specified, there remain five unknowns: D, 4, a, ho, and S. Thus we should be able theoretically to elimi- 6 = ey 10 =[o D)* Dp sin? —A/10 — He TT iS? 4 93 94 DETERMINATION OF nate all but he and S, defining our coverage diagram. We may substitute the approximate value for D into equation (5) and also use equation (4) to elimi- nate S from the equation 10-4/20 = =a I _ dhe |x Vk; (1 —a) 4mhjo? it 3 lc = | lass | sin? ( no) | 4 wo \ We may now set w= (n—5)m; = Il, 2 B 22° which correspond to the maxima of the lobes. We may alternatively take T (7a) (7b) @-n7r, corresponding to lobe minima or, more generally ’=(n+b)r (7c) to represent any specific position on the lobe. With A, hi, \®, and @ as variables, we may throw equation (6) into the form of a nomogram, from which we determine a, first for the lobe tips, second for the minima, and third for as many intermediate points as are necessary. With the a’s so determined, proceed to equation (4), also in nomographie form, to get S. Finally, use STANDARD COVERAGE CHARTS equation (2), to determine he. This equation can also be thrown into nomographic form if we set S pr = ho =h 2 (8) where h’. is measured vertically from the line tangent to the base of the transmitter. Another somewhat simpler type of coverage dia- gram is possible. If we take 106 1Q=4270 = ies? (9) as defining the intensity for a transmitter in free space, we get for the ratio of the two i772 10-(4-4*)/10 = 4QB8/10 = a @ 0 0 E G aA =F (10) where B is the number of decibels by which the actual field exceeds the free space value. Coverage diagrams of this type consist of lines radiating from the transmitter, rather than contours. For non- standard propagation the drawings have some com- plications, but the procedures are clear. This method has the additional advantage of fitting in with the theory used for surface targets, for which it is simpler to use free space intensities and lump the field strength integrated over the target area as an “effective” target area in a uniform field. Chapter 12 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE* HE EQUATIONS GIVEN in the preceding chapter have now been thrown into nomographic form. When these nomograms are employed a rapid method for constructing coverage diagrams results. Let h, denote the height of the transmitter in feet, fm. be the frequency in megacycles, n be an integer (1, 2, 3, ---) specifying the number of the lobe, b(0 S b < 1) a “phase” factor specifying the position on the lobe, and r the radius of the earth. Introduce the quantity B defined as follows. 150 (n — b) V/2N (3.281)? B hife Bynes 10° (n — b) = 3.676 X Te ) (1) where we have taken r = 8.50 X 10° m, as the approximate 4% earth value. We have to decide on the interval for b. By taking b = 0, %, %, %, %, %, we actually obtain seven points on each lobe, which should be sufficient for the purpose of drawing a coverage diagram. Hence, n — b = 0, \%, %, %, %, %, 1, %, ---, etc., spaced at intervals of \. Equation (1) is represented in the nomogram of Figure 1. We are given h; and f,,, the height and frequency of the transmitter. Connect the appro- priate values on the scales by a straight line and mark the point of intersection on the central vertical line. Define a quantity k by the equation n—b= a so that k = 3 corresponds to the maximum of the first lobe, k = 6 to the minimum, & = 9 to the next maximum, k = 12 to the minimum, etc. & = 15, 21, and 27 correspond to the third, fourth, and fifth maxima, respectively. Other values of k determine intermediate points on the lobe. Now draw a straight line from & = 1 through the point previously determined on the central vertical line until it intersects the left-hand axis of B. Read off B or 1/B, whichever is given. Repeat the process for k = 2, 3, -- -, etc., until a value of B is obtained 2By Lt. Comdr. D. H. Menzel and Lt. A. L. Whiteman, Office of the Chief of Naval Operations. that exceeds 10; in other words, continue until the straight line runs off the lower edge of the left-hand scale. There will be cases, however, usually involving large values of h; or fm, where B will still be small (1/B large) even for k = 27. When this condition exists, the lobes tend to be so closely spaced that the individual maxima are difficult to define and even more difficult to draw on a coverage chart. For such conditions an alternative procedure is recommended, which will be given later. If no difficulty is encountered, however, enter the values of B or 1/B (designate the latter with an asterisk) in a table such as Table 1. TABLE 1 Jme = Frequency in me h, = Height of antenna in ft k= B* n b 1 1 a 2 1 z 3 1 3 max. 4 1 z 5 1 3 6 2 0 min 7 2 t 8 2 4 9 2 3% max. 10 2 3 11 2 5 12 3 0 min 15 3 4 max. 21 4 3 max. 27 5 3 max. *Put an asterisk after an entry if the value read off is equal to 1/B. The corresponding values of n and b are entered in columns 3 and 4 of the form sheet. It should be noted that equation (1) is easy to solve, and the operator familiar with mathematical procedures may prefer to use direct calculation, by slide rule or logarithm tables, as much more accu- rate. In general, however, the nomogram values are sufficiently accurate for the work. Next, for the five or six assumed values of decibels for which contours are desired, we solve a subsidiary equation for Y by means of a nomogram (not repro- duced here). We note that Y = db + 60 — 10 log (2arhi) , 95 96 B 10800000 4000000 400000 40000 1000 100 10 hy IN FEET 100000 410000 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE Figure 1 EXAMPLE SHOWN BY DASHED LINES h,=4 a 7 Ye Cc 27 20 40 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 97 and slide-rule calculation is extremely convenient. For each of the selected values of b, we have pre- pared a nomogram connecting Y, B, and a. Although there are six adopted values of b, the expressions for b = \%, %, 1's, % coincide, so that four charts suffice. A representative sample of these charts, for b = 0, Is given in Figures 2 and 3. Connect each value of Y, for which a contour is desired, with the value of B on the appropriate chart, according to the value of b (or k). Read off the corresponding value of a. Having determined a for a given point on the coverage chart, we now calculate S from the nomo- gram in Figure 4, with a, db, and S as variables. For S measured in units of 1,000 yd, we have 10-#/20 = (sq ) 7 Ve \OIes er 472 2 Bee) |). pane al + 4—3q/ SD'™ f : A typical example for the selected values of b is shown, as before. Finally, we must calculate he. For heights we have (3.281) (914)? 2r ie H=hz+ 1—a)h = (3.281)? (914) (150) (n — b) (— 2 + 3a) sg ae 2) + 5 a? This equation, unfortunately, has too many variables for nomographic solution in a single step. We first define a quantity C, such that _ (3.281)? (914) (150) (n — 6) (— 2 + 8a) e hy ime 9 az Obtain the simple product /if,,,, which is a charac- teristic of the set. Then use the nomogram of Figure 5 to obtain the values of C for the selected ranges of k and a. Then we can determine H from the nomo- gram of Figure 6, for each value of S and C. Finally, from a nomogram (not shown here), representing the equation H =. @l ma a)hy ho = we determine hy. Actually, for much of the range, a~landh, ~ H. For the upper lobes considerable simplification is possible. We may omit all the steps involving cal- culation of a. We determine the various B’s as before. Then, as long as B > 1 we employ the equation 10° / 1 \? —2b/10 — = =— id = (sas) “ 1 1 Ae E + € — = sin? n| f This equation gives S directly for each decibel value and assumed value of b. The nomogram for this problem appears in Figure 7. We then obtain H from equation (2), with aset equal to unity. _ (3.281) (914)? 5 iS? H ~ S 3.281)? (914) (150 a | niet ) ee. (3) In equation (3) we have written C’ instead of C. For much of the range, wherever B is very large, we may take C’ ~ C. If greater accuracy is desired, we may compute C’ directly by the equation = It is interesting to note that equation (3), apart from the correction factor (1 — 1/B?), which merely serves to improve the accuracy of the result, is familiar to many in the construction of so-called “fade charts.” These diagrams depict merely the lobe minima (and sometimes also the maxima). If we set b = 0 we get the former, and if we take b = Y% we determine the latter. The total number of lobes N is approximately = (3.281)? (914) (150) k e 6 fine hy 2Qhi hy ile NW = = Ge) ©) = 2.08 X 10-1 fine for fh; in feet. These will be distributed over an angle of 90 degrees. Hence A, the average angle per lobe, is 7 OUP 8 <1 ir N a ih mc hi ; Near the horizon, however, the angle per lobe Ap is somewhat smaller, to wit: _ 360° — 5°64 XK 10? ae ye 98 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE - oe a io) © EXAMPLE SHOWN BY DASHED LINE B = 0.112 Y = 12.2 QL, = 0.465, &, = 0.910 TVigure 2 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 99 2.0 7 1.6 L4@ b=0 EXAMPLE SHOWN BY DASHED LINE B= 0.112 V/s [BoB OL, = 0.47,0,= 0.91 Ficurn 3 100 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 80 by ; ' i 70 Bee cam 300 severe 250 eee 65 200 _----~ __--E150 pe 125 ee 100 pee ae 75 60 eee ae eee 50 25 55 20 1S 10 50 5 4s 1 40 EXAMPLE SHOWN BY DASHED LINE b=0 a=,3 3s DB=57 S= 150 S IN THOUSANDS OF YARDS 30 25 20 Figure 4 c 1000000 - 500000 400000 300000 200000 100 000 10000 r bP wan bb w au » NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE EXAMPLE SHOWN BY DASHED LINES k=3 = 0.48 h, fm = 100,000 C218 NOTE: WHEN ©<¢ 273, C IS NEGATIVE WHEN ©) 273, C IS POSITIVE h, IN FEET | FIGureE 5 if mc IN MEGACYCLES 500 000 1000 10] 200 "98 -80 75 -60 70 69 -65 .68 -66 67 102 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE es +2 a is 7: 7500 + n 5000 x EXAMPLE SHOWN BY DASHED LINE So S$=220 2500 hs S C=+10 H=10,000 ° H IN FEET : % ot S IN THOUSANDS OF YARDS ' ne cpio can leben —10 ul ' 3 beeen ( a 1 is) ° FIGureE 6 NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE 103 ee 35 40 45 5.0 20 — EXAMPLES SHOWN BY DASHED LINES { b =O b = Ve eo _ B=3.75 428410 $=70 S=7 : DB=64 DB=27 4 10 ; Oo if =— 10.0 FIGURE 7 104. NOMOGRAPHIC SOLUTIONS FOR THE STANDARD CASE HEIGHT IN FT 7 COVERAGE CHART it DS po bmnSooIo Sasa Ser = SSnooSsoSSSs5o5 {cst [a | a | B [e) [5 a a a eae a ff a |e a a a [ss es | fe fc fe ice] lo] ae ae [ea ee || | | | ps [ia | | a fe ea) fas [ef | a Ff (A || | ea | ec a [| es | | a | fa 20,000 a | a a a a (a ff na rae ta] (eff | | Ff | ce nr [ae] : fee a fe Yio |e ae | ea SSS es (a | =a Bi a [a [au p+ tif tf tt tt BES a BB = ff a | a a] [a a (Se |e ce Pa | [fea (al = GEOS0es9S0Sss000C055005 fe Beeo nem SOURS es] a a | | a a || Riba as [el ) 72s a Be eg ee ge ee 2 ee ee cee EEEEEEEEEEEE EEE EE EERE EEE EEE EEE EE are | a | | EES HAS (a Bea ee a a a eee H-HH--H-EH JB2 2208 epee = | || | a a BERREZ22s°Za0 =| 8 | | = 0000 | nee BSH E SEDER eee tee sone JUDE : gee272ZaGRREEeZaes PEECEPEEEEC CCE Z 2222082 Ape 660 = Geo Ooo oOoIoSeoe Eee eocesoecegaeuaeeeeee Bis EEE et ee a SOG OOO GGnnnbeseeese:cablabcaae DED eSeo eee =AR AEE H-He BB eee re Bee Bee Go oe eee BRRERBRES2 522" 2o20Ze0 2 aRnn8 i Loe CORaonbe22 ECB CURT ER USE = ES a ES GS SS SS a a SSS SSSSSSqq SS SS SS oS aS SS a Se SeeSeooSeCeeor SSCS SSS = === === SSSsSs=sS==o ea ee SSeS SSSooS Zee SSSSss BSeesccsc =~» JGBESSSSb2een0RS05000o Beoee SSS leet een es SBBabea | LEN Scant AAHAABAEADGRABAGOARAGETROAROAE THOUSAND YARDS FIGureE 8 TasiE 2. Work sheet for coverage diagram calculations. db = 46 (MIT — 95 db) fme = 3,000 , Y = 13.9 hy = 100 ft hifme = 300,000 > & — R Rm Q qy > CONOUrPWNH = (=) iw) — (o,0} or TRWWNHNNNNNPR REE [HE alee Role CO PIM alto pale cole Je CD alercs|to wale! cole oe i=) i) (SS) or Wo) ms = > aI (=) — (e,2) or (=) i (e,2) ie) TSS NOMOGRAPHIC When Ay < 0°.1, the lower lobes are so closely packed that the drawing of a coverage diagram becomes almost impossible. For such cases one should determine, for a given decibel value, the lower edge of the lowest lobe. Then, with the aid of the nomograms for b = 1%, calculate merely the posi- tions of maxima of the other lobes. A work sheet for coverage diagram calculations is shown in Table 2. As an illustrative example we have selected the case in which hi = 100 ft, fc = 3,000 me, db = 46. Here db stands for the number of decibels that the power density is below standard, where we have assumed a power of 1 w for the transmitter. The symbol db is defined differently by the MIT group. The correspondence is: SOLUTIONS FOR THE STANDARD CASE 105 db <—> — [dbyrr + 49] . The value of \, which depends only on db and hy, was obtained from the nomogram of Figure 4 and equals 13.9. The product hif,,. is, of course, 300,000. The rest of the table was filled out by the methods just described. The lobes corresponding to this data were also computed by the MIT method and are shown plotted in dotted lines in Figure 8. In general, these lobes agree completely with our own. In the cases where there is some slight variance, we have also drawn our lobes in heavy lines. Note that the MIT db of 95 corresponds to our db of 46. The nomograms presented herein correspond to a reflection coefficient of —1. For any other value they would have to be redrawn. Chapter 13 THEORETICAL ANALYSIS OF ERRORS IN RADAR DUE TO ATMOSPHERIC REFRACTION: el PURPOSE HIS REPORT is a theoretical evaluation of errors in altitude, azimuth, and range caused by atmos- pheric refraction. These errors are compared with the error tolerance specified in military characteris- tics for fire control radar equipment. Regional climatological data are utilized to determine probable refractive index gradients used in the determination of the error. Errors in heightfinding resulting from ducts are also treated. An Evans Signal Laboratory [ESL] report now under preparation discusses errors which may occur during specific meteorological situations and which may exceed the errors indicated in this report. Tee PROCEDURE The variation of the index of refraction perpen- dicular to the path of a radio wave results in a curvature of the ray toward the higher index. The curvature of the ray is approximately equal to the rate of decrease of the index of refraction with altitude. Errors due to atmospheric refraction will therefore depend on the rate of decrease of the index of refraction perpendicular to the ray path and to the range. A simplified equation for the error in azimuth and altitude is derived below and is utilized in this report. This method has been found to check to within a thousandth of a degree with more accurate methods” of ray tracing.° The rate of decrease of the index of refraction in~ a standard atmosphere is 12 X 10° unit per 1,000 ft up to 4,000 ft above mean sea level. This corres- ponds to a curvature of the path of the ray approxi- mately one fourth the curvature of the earth. The standard atmosphere represents average conditions in temperate zones. In tropical air such as exists in equatorial regions and southeast Asia and southeast “By Raymond Wexler, Signal Corps Ground Signal Agency, >Errors in angle of altitude due to a duct with a standard atmosphere above the duct have been computed by members of Group 42 of the Radiation Laboratory. Values computed by the method outlined below under Derivation of Formulas have been found to agree with their results. °For a more detailed analysis of ray tracing methods, see reference 75. 106 United States in summer, the average rate of decrease of the index of refraction is approximately 18 K 10°° unit per 1,000 ft up to 6,000 ft corresponding to a curvature of the ray % that of the earth. Over trade wind regions of the ocean (latitude 10° to 30°) dry subsiding air exists over a moist tropical layer. The rate of decrease of the index of refraction in these regions 1s approximately 24 & 10° unit per 1,000 ft corresponding to a curvature of the ray one-half that of the earth. Within layers of atmosphere designated as “ducts” the curvature of the ray may exceed the earth’s curvature and may result in a trapping of the ray within the duct. Errors due to atmospheric conditions in each of the above atmospheres are analyzed. In Table 1 are tabulated values of the index of refraction at selected levels for the standard atmosphere, tropical atmosphere, and tropical dry atmosphere as utilized in this report. TasiE 1. Values of the index of refraction for selected levels in different air masses.* (n — 1) 108; nm = index of refraction. Elevation above mean sea level Standard Tropical Tropical air (feet) atmosphere atmosphere dry air above 0 324 394 348 2,000 300 358 300 4,000 276 322 260 6,000 255 286 242 8,000 236 255 227 10,000 219 234 216 15,000 191 195 179 20,000 151 159 146 30,000 105 107 105 *Aerological data for Miami and San Diego for July 1943 were utilized to compute the indices of refraction for the tropical atmosphere and the trop- ical atmosphere with dry air above, respectively. 13.3 APPLICATION TO GROUND RADAR EQUIPMENTS GUNLAYING (ANTIAIRCRAFT) RADAR Military characteristics for gunlaying radar call for a tolerance of 50-yd error in a range of 29,000 yd and an angle of 1.5 mils in azimuth and elevation. Initial angles of sight are between 10° and 90°. RESULTS In a standard atmosphere, errors in angle of eleva- APPLICATION TO GROUND RADAR EQUIPMENTS 107 TROPICAL ATMOSPHERE ORY AIR ABOVE TROPICAL ATMOSPHERE STANDARD ATMOSPHERE Wa yi ERROR IN ALTITUDE IN 10° FT fo (°) 25 50 75 100 RANGE IN MILES APPARENT ALTITUDE TRUE ALTITUDE HORIZON PLANE TRUE EARTH TROPICAL ATMOSPHERE DRY AIR, ABOVE TROPICAL ATMOSPHERE (°) 25 50 75 100 RANGE IN MILES Figure 1. Maximum errors in absolute altitude due to atmospheric refraction. A. True earth radius. B. 4/3 earth radius. Target assumed to be at true angle of zero degrees. tion for a range of 29,000 yd and an initial angle of sight 10° are 0.5 mil. A maximum error is obtained at 0.9 mil. For an initial angle of sight of 20° the maximum error is about 0.6 mil as compared to an error in a standard atmosphere of 0.4 mil. Errors in azimuth and range are negligible. Harty WARNING HEIGHTFINDING RADAR Military characteristics call for the following tolerances in heightfinding radars. Set Freq. Band Accuracy Required AN/CPS-4 S 1,000 ft in absolute altitude and 500 ft in relative altitude at 45 miles range, preferably 90 miles. AN/CPS-6 S 1,000 ft in absolute altitude and 500 ft in relative altitude at 75 miles range, preferably 100 miles. AN/TPS-10 xX 1,500 ft in absolute altitude and 500 ft in relative altitude at 50 miles range. ABSOLUTE ALTITUDE Figure 1A indicates the errors in absolute altitude for different air masses on the assumption that the target is at a true angle of zero degrees. Thus at a range of 75 miles the error in elevation is 940 ft in a standard atmosphere and 1,880 ft in a tropical atmosphere with dry air above. Figure 1B depicts the errors on the assumption that the standard atmosphere correction (% earth radius) is applied. Thus with the “4 earth radius correction the error remains under 1,000 ft at 75 miles. However, these atmospheric conditions represent normal conditions so that in specific meteorological situations the error may exceed 1,000 ft im 75 miles especially in the trade wind regions. Since the maximum error occurs at a true angle of 0°, these errors in absolute altitude for a range of 75 miles are tabulated for true angles of 0° to 3°. 108 TaseE 2. Errors in absolute altitude for early warning heightfinding. Range 75 miles. True Angle of sight (degrees) Errors in altitude (feet) angle Standard Tropical Standard Tropical 0 0.14 0.20 941 1,412 1 1.12 1.17 823 1,332 2 2.10 2.14 705 970 3 3.09 3.12 626 845 Ducts in the lower layer of the atmosphere will cause errors to exceed those specified by military characteristics. For a duct depth of 25 ft and 1-unit decrease in the modified index of refraction, errors in absolute altitude may exceed 1,000 ft within ranges of 50 miles. A 200-ft duct, in which the modified index of refraction decreases 10 units, may cause an error of more than 2,000 ft in 50 miles range. Figure 2 depicts errors in absolute altitude 4 ou ERROR IN ALTITUDE IN 10° FEET fo} 25 50 75 100 125 — RANGE IN MILES Figure 2. Maximum errors in absolute altitude due to surface ducts with standard atmosphere above. for ducts of various depths on the assumption that the ray just escapes the top of the duct into a stand- ard atmosphere above. The rate of decrease of the modified index of refraction in the duct is 1 unit per 20 ft (corresponding to a curvature of the ray about twice that of the earth). RELATIVE ALTITUDE As an exmple, let us assume that five aircraft are located at altitudes of 3,000, 8,000, 13,000, 23,000, and 33,000 ft above mean sea level. Suppose that these planes are detected by radar at ranges of 50, 75, and 100 miles. Errors in relative altitude occur because of differential refraction at high and low RADAR ERRORS DUE TO ATMOSPHERIC REFRACTION levels. Even in a standard atmosphere errors in relative altitude arise since the rate of decrease of the index of refraction near sea level is 12 X 10° unit per 1,000 ft, while at 15,000 ft it is only 6 X 10° unit per 1,000 ft. In a tropical atmosphere with dry air aloft the errors are likely to be considerably greater since the rate of decrease of the index of refraction with height is greater. TABLE 3. Errors in altitude relative to lowest plane located at 3,000 ft above mean sea level. Separation Standard Tropical Tropical of planes atmosphere atmosphere dry (feet) (feet) (feet) (feet) Range 50 miles 5,000 35 24 317 10,000 73 107 380 20,000 131 243 514 30,000 171 306 572 Range 75 miles 5,000 78 54 713 10,000 164 242 924 20,000 287 539 1,158 30,000 389 693 1,290 Range 100 miles 5,000 139 97 1,270 10,000 376 431 1,644 20,000 527 960 2,061 30,000 673 1,237 2,296 Thus in a tropical atmosphere with dry air aloft such as exists in the trade wind areas over the ocean errors of some 500 ft relative altitude for planes separated by 20,000 ft would occur in a range of 50 miles. For 100-mile range, errors can be as much as 2,000 ft. Even in a standard atmosphere errors are more than 500 ft for ranges of 100 miles for the higher level planes. AZIMUTH AND RANGE Errors in azimuth are negligible for all meteoro- logical conditions except possibly for propagation parallel to a sea coast or sharp cold front (see para- graph below). Errors in range are likewise negligible for all possible meteorological conditions. SURFACE SURVEILLANCE RADAR Military characteristics for sets AN/MPG-1 and AN/FPG-2 specify errors up to 0.05° in azimuth at 28,000 yd and 50,000 yd respectively. Range error toleration is 20 yd in 50,000 yd. CONCLUSIONS AZIMUTH Errors in azimuth arise from horizontal variations in the index of refraction in the atmosphere. Generally these variations are of insufficient magnitude to cause such errors to be appreciable. In order to obtain an error of 0.05° in 50,000 yd it can be shown that a change in the index of refraction of 1.5 X 10° unit in 44 yd perpendicular to the path of propagation is required. This corresponds to an increase of 1C temperature and a decrease of 0.1 mb in vapor pressure. Such changes within 44 yd may occur ia propagation parallel to a sea coast or to a sharp cold front, or in isolated regions such as between forest and meadow, valley and plain, or land and water surfaces. Except in the vicinity of a cold front or sea coast it is unlikely that such horizontal gradi- ents of the index of refraction exist along the entire path of the ray. RANGE Errors in range due to vertical refraction within a duct are approximately of the order of 1 yd in 50,000 yd. The error in range corresponding to an azimuth error of 0.05° is estimated at less than 0.2 yd in 50,000 yd. WS CONCLUSIONS 1. For gunlaying (antiaircraft) radar, the maxi- mum error in angle of elevation at 29,000-yd range is 0.9 mil, as compared to a military tolerance of 1.5 mil. 2. In early warning heightfinding radar, errors of 1,000 ft absolute altitude at 75 miles range may be exceeded even with the application of a standard atmosphere (% earth radius) correction. Because of ducts, errors may be as much as 2,000 ft at 50 miles. Errors in relative altitude may likewise exceed 500 ft in 75 miles. 3. Errors in azimuth may exceed 0.05° in 50,000 yd in propagation parallel to a sea coast or a cold front. Errors of this magnitude will, however, be rare. 4. Errors in range are negligible for all possible meteorological situations. DE=ERIVATON OF FoRMULAS Let the origin of the coordinate system be the point where a ray is initially tangent to a line of constant index of refraction %o, and let the Y axis 109 coincide with this line. Since the ray curves toward higher index of refraction ”, according to Snell’s law: ncosp =n, (1) where @ is the angle the ray makes with the line 7. Then from trigonometric relations: dX _W/n® — n2 ayy no , AVA n— No V n+ No No tan oa (2) Since 7 and 7 are extremely close to unity no appre- ciable error will result if we assume that n + np = 2, hence dX _ V2, n— 1. dy No As ssuming a linear variation of the index of refraction the X direction, m = m) + wX, and No =l2 aa a ng M2 2. ss 2ne X (2) y?2= Equation (3) indicates that the ray follows a para- bolic path. Let us convert into polar coordinates by the transformation X =r sin ¢ and Y =r cos 4, where r is the actual range. Then the equation of the path becomes ae Zilli tan @ sec ¢ . (4) Since in actual practice, ¢ is extremely small and no is extremely close to unity, equation (4) can be written as or tan ¢ = Gy (5) Here w represents the rate of change of the index of refraction perpendicular to the ray, and @ is the error. If the ray were initially at an angle @ to the line of equal index of refraction, then the rate of change of the index of refraction perpendicular to the ray would be w cos a. Hence, more generally, the equation for the path of a ray at a mean angle a to the lines of index of refraction can be written as jam & = = @O8@. (6) 2 Equation (6) has been utilized to compute errors in azimuth and angle of elevation. Chapter 14 DIFFRACTION OF RADIO WAVES OVER HILLS’ XPERIENCE HAS SHOWN that frequencies in the VHF (very high frequency) range and higher are propagated over hills and behind obstacles more easily than has been commonly expected. Hills or other obstacles in the transmission path cast shadows which may make a radio system unworkable when either antenna is located close to the obstacle, but recent experiments, notably the work of Jansky and Bailey,*** have shown that hills and mountains can cause constructive interference as well as destructive interference. In other words, with proper antenna siting, the field intensity beyond the line of sight may be higher than is expected for the same distance over plane earth. This 1rmprovement in field intensity may be 5 to 10 db or more. One attempt to develop a theory for radio trans- mission over hills is based on the computed field intansity over the solid triangle shown in Figure 1. P(0,Y,Z) S X AXI Vn (x,0,0) s an eee BC Z AXIS 1S PERPENDICULAR TO a THE PLANE OF THE PAPER > B(Xp,0,0) Ficure 1. Analysis of field intensity over a solid triangle. It was reasoned that a good approximation to the field over any profile might be obtained from a knowledge of (1) the field over a perfectly smooth earth, (2) the field over the solid triangle that encloses the actual profile, and (3) the field over a knife edge equal in height to the highest point in the profile. The theory of propagation over a perfectly smooth earth is well known; it is the basis of all the published theoretical curves on radio propagation. The corresponding expressions for the field intensity “By K. Bullington, Bell Telephone Laboratories. 110 over a solid triangle and over a knife edge are indi- cated in a paper by Schelleng, Burrows, and Ferrell,*47 but some effort is needed to place these expressions in a convenient form for computation. The method of obtaining an expression for the field over a solid triangle is indicated in Figure 1, and the same analysis applies to each of the ideal profiles shown in Figure 2. The field intensity at any Ficure 2. Analysis of field intensity over various tri- angular profiles. point P in the vertical plane through the apex of the triangle is assumed to be the sum of a direct ray and a ray reflected from the ground which is equivalent to a ray from an image antenna. In a similar manner the field at point P is propagated to the receiving antenna by means of a direct ray and a ground reflected ray. By integrating over the plane above the apex of the triangle (that is, from y = H to y = o and from z = — o to 2 = o) am expression for the total received field is obtained. The complete expression is not as complicated as the expression for propagation over a smooth sphere, but two simple approximations will be sufficient for the present discussion. When the height of the hill H = 0 and when the ground reflection coefficient is —1, the complete expression reduces, as it should, to the well- known formula for VHF propagation over plane earth. Qh ihe ae, 1 dN (@1 + 22) (1) When the height of the triangle H is greater than three to five times the average height of the antennas and when the reflection coefficient is :—1, the com- plete expression reduces to 2rHh, AX H= 2K sin ae 2rHhe . AX s EH = 4£,S sin (2) DIFFRACTION OF RADIO WAVES OVER HILLS 11] 20 20 LOG S ol io} 40 50) \[_2x% UH Vai Xe) Figure 3. Shadow-loss factor S. The factor S is the shadow loss shown in Figure 3 as a function of 2210 Vi (Gi SE a) The other symbols in the above expressions have the following meanings: mw = Lal FE = field intensity in microvolts per meter, Ey = free space field intensity in microvolts per meter _ BVP X< 1 | Ge” P = radiated power in watts, \ = wavelength in meters, = height of the obstruction in meters, hyi,ho = antenna heights in meters, 21,02 = distances as shown in Figure 1 in meters. The approximate expression given in equation (2) indicates that the field intensity for points well beyond the line of sight may be greater than the field over a plane earth which is given in equation (1). The sine terms in equation (2) indicate interference patterns beyond the line of sight which seem to offer an explanation for the experimental fact that behind hills raising the antenna may cause a loss, or lowering the antenna may result in a gain, in signal intensity. A comparison between theory and experiment is shown in Figure 4. These data, which were taken from the previously mentioned NDRC report pre- pared by Jansky and Bailey, show measured values at 116 me for horizontally polarized waves propa- gated over the profile shown in the bottom of the ovPUTED FOR = ho 29FT COMPUTED FOR) a fo} 30 ee ! ms Ge} Pee EL 2.7 MILES FROM 660-FT RIDGE @ heh, =29 FT oa |iene) eee he «19 FT nen ke Be bee # b. 80 co 800 1: 2 3 4 DISTANCE FROM TRANSMITTER IN MILES H/ELD INTENSITY IN DECIBELS BELOW INVERSE DISTANCE FIELD Figure 4. Theoretical and experimental results in meas- uring field intensity of horizontally polarized waves. Frequency 116 me. drawing. The open circles show the field intensity in decibels below the free space value when both antennas are 29 ft in height, and the dots give similar data for 19-ft antennas. The two dashed lines running from upper left to lower right are the computed values for smooth earth for 29-ft and 19-ft antennas, respectively. The solid line with the inter- ference fringes is obtained from equation (2) for the case of 29-ft antennas. The correlation between theory and experiment is not complete, but at least the theory may be a step in the right direction. Similar theoretical and experimental results are obtained with vertical polarization. Thus far the only type of profile considered has been one with a single prominent hill, and it is natural to ask what happens over profiles containing several hills. There are less experimental data avail- able on this point than for propagation over a single hill, and consequently the remainder of this discus- sion is more speculative than the preceding part. An ideal profile consisting of two hills of equal height is shown in Figure 5. The complete mathe- matical solution for this case is difficult, but an approximation can be obtained in the following manner. The field at any pomt P midway between the two hills can be obtained by means of the expres- sion for the diffraction over a single hill. The field at this point is then propagated over the second hill to the receiver. The total received field is obtained by mechanical integration, that is, by adding the effect (magnitude and phase) of many evenly spaced points in the vertical plane midway between the two hills. 112 The net result is that the total received field is represented more closely by the path ACB than by the path A DEB. The energy received over any given Fieure 5. Field intensity computation for a profile of two hills by a solid triangle. path such as path ADEHB decreases rapidly as the number of diffractions in that path increases. How- ever, for any profile there is always at least one path between transmitter and receiver such as path ACB that requires no more than one diffraction, and the field intensity over this path is usually controlling. In other words, the profile consisting of two hills can be approximated for computation pur- poses by a solid triangle which is formed by a line from the base of the transmitting antenna to the base of the receiving antenna and lines from the base of each antenna tangent to the hill that blocks the line of sight. By the same reasoning it appears that a profile which includes any number of hills can be represented approximately by the circumscribing triangle. The principal assumptions that are basic to this method of treating radio propagation over hills and other obstructions are as follows: (1) the height of antennas is greater than about one-half wavelength, | (2) the size of obstructions is large compared with the wavelength, and (3) the distance between anten- nas is large compared with either the antenna height or the size of the obstructions. These assumptions DIFFRACTION OF RADIO WAVES OVER HILLS limit the application of this theory to wavelengths shorter than a few meters. The principal differences between the diffraction over an irregular earth and the diffraction over a smooth sphere is illustrated in Figure 6 for trans- 60 40 20 FIELD INTENSITY S BAND 50-FT ANT 1 WATT RADIATED REFLECTION GOEFFICIENT=~-1 DB ABOVE 1pV PER METER n fe} {eo} N S N -40 MAXIMUM VALUES/ FALL ON THIS LINE “eo 5 10 50 100 500 1000 MILES Fiaure 6. Comparison of diffraction over irregular earth and over a smooth sphere for S-band waves over sea water. mission of S-band waves over sea water. The dashed line shows the field intensity versus distance over a perfectly smooth earth. The solid line shows diffrac- tion over a solid triangle which represents what is expected when the sea is rough, that is, when the height of the water waves is large compared with the S-band radio waves. It will be noted that there is little difference between the two methods for distances less than about twice the optical range, but at greater distances the solid triangle theory indicates that some energy will be received at appropriate distances. These views on the transmission of meter and centimeter radio waves over multiple obstacles are speculative. There is little experimental evidence to support them, but also there appears to be even less experimental evidence to contradict them. Chapter 15 SITING AND COVERAGE OF GROUND RADARS* 15.1 INTRODUCTION Bi ISAGENERAL discussion of the effects of terrain on the operation of ground radar systems. Written to supplement a Signal Corps publication Radar Performance Testing, it is intended to provide a practical, engineering type of solution of siting problems. The principal emphasis is on early warn- ing and other very high frequency [VHF] systems although application may be made to microwave and other types of radio equipment. The objective has been to enable field personnel to compute coverage and other characteristics of a given site and radar and reduce the number of test flights required to a minimum. Thus the terrain factors may be evaluated, and a definite, numerical description of the capabilities of a site may be stated. Since it is not possible to anticipate all problems that may arise in the field, sufficient theory has been included to cover a fairly wide scope. In most cases several types of solutions are provided so that the accuracy and detail required may be related to the labor involved. A number of fully worked examples are included with a discussion of significant features. The drawings are made to scale and to fit practical situations. 15.2 RADAR SYSTEMS 15.2.1 Types of Ground Radar Tactical requirements and intensive technical development have led to the introduction of numer- ous types of ground radar equipment. The charac- teristics and descriptions of these units are given in several Service publications. Ground radars may be divided into two classes: (1) those which utilize ground reflection; (2) those which use only the direct ray. Sets which are sited so that ground reflection influences their performance usually have stringent siting requirements and the coverage is dependent on the site. This report is concerned chiefly with this type of radar. Equipment that uses only direct rays is relatively free from site ®By Capt. E. J. Emmerling, detailed by Signal Corps to the Columbia University Wave Propagation Group. restrictions, and the terrain has little effect on the coverage. 622 Radar Systems—Tactical Aspects In most cases radar stations are operated in groups for the defense of a region of considerable extent. The several stations are assigned sectors in which searches are conducted for designated targets, and these, when located, are reported to a central agency for tactical disposition. Technical operation of such groups requires close study of the topography of the region so that available equipment and personnel may be used to the best advantage. In this way adjacent stations may support each other in the event of outage due to maintenance or enemy activ- ity, and other factors may be taken into account, such as jamming, atmospheric effects, and perma- nent echoes. The nature of the region to be protected and the type of application for which the radar equip- ment is to be employed are controlling factors determining the number, location, and kind of sets which must be used. Thus, harbors, islands, and inland mountainous regions present problems with widely differmg operational characteristics. Early warning [CHL], fighter control [GCI], gunlaying (coast defense), gunlaying (antiaircraft), and search- light control radars all have different siting require- ments. This report deals mainly with the first three types of equipment listed above, but the methods have general application to other problems such as the siting of direction finding sets [DF]. The early warning radar usually has the mission of reporting and identifying enemy aircraft (at say 20,000 ft) 45 minutes before they can reach the vital defense area. This is based on the time required to alert the area and to give the defense aircraft time to take off and make their attack. Other missions may be assigned, such as detection of ships or obser- vation of friendly aircraft for purposes of control and air-sea rescue. Using the moderate plane speed of 240 miles per hour it is apparent that the early warning radar must have a range of 180 miles if located near the defense area. Sometimes suitable outlying sites, such as islands, are available, and the 113 114 coverage may be extended accordingly. The disad- vantages of outlying sites presented by communica- tion and supply difficulties, exposure to enemy attack, etc., should be carefully considered. More often, however, the success of the warning system depends on effective long-range operation of radars located relatively close to the defense area. The early warning stations give periodic reports of the grid position of an aircraft and its response to interro- gation signals. The GCI radar is used to direct from the ground the operation of friendly fighters against enemy aircraft. It has a range of about 50 miles and is capable of handling a large volume of traffic. In addition to the grid position and identification of the target it also determines the height. Surrounding the defense area is a region whose width depends on the time required to make an interception on an incoming enemy plane. The siting objective of the GCI stations is the continuous and effective cover- age of the interception region. Close coordination is maintained between early warning and fighter sta- tions, and the coverage deficiencies of one station are counteracted by favorable characteristics of the other stations. The coast defense gunlaying radar is concerned primarily with accurate location of ships. It has a range up to 100,000 yd and must be sited fairly high and within a few miles of the coast defense guns which it directs. This radar supphes accurate data on the azimuth and range of the target. The antiaircraft gunlaying radar is used primarily for directing the guns. Long-range search features are usually provided so that they may function also as early warning radars, at least to a limited extent. They are sited near the guns which are located to meet artillery requirements. These units provide a continuous flow of data to the gun director giving the azimuth, elevation, and range with great accuracy. The searchlight control radar is a short-range high angle set which is located near the light it directs. It furnishes the azimuth, angular elevation, and altitude of the target. %23 Radar Siting—Technical Aspects In the past some elaborate air warning systems have been set up without a competent analysis of terrain effects. This resulted in a waste of time and money and in failure to adequately provide urgently needed radar screens. This failure was caused in SITING AND COVERAGE OF GROUND RADARS many cases by the use of prepared coverage diagrams, furnished with the equipment, which were computed for idealized sites. In mountainous regions where only limited reflection areas occur and where the sites are very much higher than those used in labora- tory tests, such diagrams are likely to be very misleading. A result of this experience is an unfor- tunate tendency to explain variations from expected coverage by resort to various abstruse speculations, with weather not infrequently bearing the brunt of the odium. It is the purpose of this report to provide an engineering type of solution for the bulk of the problems that arise in siting and in field computa- tion of coverage. A more accurate analysis, with increased attention to detail, probably is not war- ranted at this time in view of the relatively rough measurements which now are made in the field of radar. The common early warning radar uses horizontal polarization and operates in the VHF band. It must be sited from several hundred to several thousand feet high in order to obtain sufficiently low angles for the range and low coverage desired. Suitable sites of the required height may be far inland so that an important part of the reflecting surface may be rough land or sloping flat areas. Such features and also cliff edges, ridges, hills or other obstacles, nearby towers and structures will, in general, produce a marked effect on the coverage pattern. The GCI radar uses horizontal polarization, operates in the VHF band and should be sited on a large, flat area. The determination of the height of an airplane is accomplished by comparing signals from two antennas of different heights. If reason- able accuracy is to be attained the lobe structure in the vertical plane must be known with considerable precision. Best results are obtained by using a site of the extent and flatness prescribed in the instruc- tion manual. In practice it may be necessary to operate on rough ground or limited areas. The ques- tion may then arise concerning the benefit that will be obtained by grading the surrounding areas, or how much forest or vegetation should be removed for acceptable operation. Similar problems arise in siting DF stations. Large errors may be introduced by reflection from sloping land or other terrain features. The effects described above, involving reflection from limited areas or rough land or passage of waves past an edge, may all be treated as problems of TOPOGRAPHY diffraction, for which solutions are well known or may be readily computed. This subject is unfamiliar to most Service personnel; but a working knowledge of the methods of computation may be obtained by anyone who has the usual engineering education. Since it is not possible to anticipate all problems which may arise in the field, a fairly comprehensive discussion of diffraction has been included in this report so that even in the absence of other references the majority of problems may be treated. Other important considerations such as orienta- tion, visibility, permanent echoes, interference, and test methods are discussed. There have been many ingenious developments in these subjects in different theaters, and where available they have been included in this report. Only standard atmosphere propagation has been considered. Those who are interested in nonstandard propagation should refer to the articles on this subject published in this series. 15.3 TOPOGRAPHY OF SITING 15.3.1 Introduction The performance of equipment which utilizes radio propagation depends upon the character of the inter- vening Jand or sea and in particular upon the local terrain at the terminals of the propagation path. Siting refers to the general problem of selecting and utilizing available locations for the best operation of the equipment involved. With some types of _ equipment the effects of local conditions are minor, and with other types the requirements are most exacting. In many cases practical and tactical con- siderations will compel the use of unfavorable loca- tions. Performance may then be considerably below that obtained in the laboratory or under ideal condi- tions, and familiar characteristics may be drastically modified. Field personnel are frequently called upon to predict or explain abnormal operation, to devise methods of improving poor performance, and to make modifications to fit local requirements. This discussion will be limited to general principles, and reference is made to the instructions furnished with the individual equipment for specific details. Elements of a communication or radar network should ordinarily be viewed as parts of a system and not as isolated, self-sufficient units. From this point of view a site that gives outstanding results would not be satisfactory if it did not help achieve the OF SITING 115 mission of the system. This interrelation between various parts of a system, which may extend over hundreds of miles, raises numerous problems of orientation, visibility, and coverage. nie Maps and Surveys Where available, topographic maps of a scale on 1 or 2 miles to the inch and contour intervals of not more than 100 ft, preferably 20 ft, should be secured. Hydrographic charts are valuable in coastal areas. If there are no reliable maps, aerial photographs may be used to a limited extent. Due consideration should be given to the suit- ability of the map projection for the purposes for which it is to be used. The grid system used for reporting should be based on the Lambert polyconic projection, and not on the Mercator projection. Otherwise important errors in azimuth may occur. This is especially true at high latitudes. If in coordi- nating with other services, such as the Navy, it is required to use the Mercator projection, the transfer from the Lambert projection may be made with a transparent overlay of one grid system on the other. A transit and a stadia rod are most useful for orientation, surveys, profiles, etc. Compasses, clinom- eters, and other surveying instruments should be provided. In the absence of some of this equipment much may be done with improvised devices made with plumb bobs and protractors. Rough surveys may be made with only a sketching board and by pacing off distances. Navigation instruments may be used for approximate determination of position. Engineer and artillery publications describe orien- tation methods in detail. Close attention should be given to the grid system used for reporting nets so that all stations are accurately located. Grid errors may be minimized by making all charts from a master copy. 15.3.3 Profiles The height of the center of the antenna should be determined to within a few per cent. The reference level is the main reflecting surface, which is normally the sea. Heights given on maps should be checked against available bench marks and the terrain. Barometers or airplane altimeters are useful for height determinations, but their readings should be corrected for temperature. Where the reflection surface is part or all land, a 116 SITING AND COVERAGE OF GROUND RADARS profile is usually necessary for estimation of the effective antenna height and the reflection charac- teristics of the terrain. Profiles should be prepared of several representative azimuths in the operating sector. The accuracy required decreases with the distance from the transmitter. In most cases suffi- cient detail is not available on maps so that a personal inspection of the terrain should be made to become familiar with the nature of the soil and the degree of roughness. Special attention should be given to ridges, flat areas, bodies of water, distance to the shore, hills to the rear, obstacles in the operat- ing area and at the boundaries. A knowledge of the antenna pattern in both the vertical and horizontal planes is necessary for judging what parts of the terrain should be more closely examined. 15.3.4 Orientation Where long distances and directive beams are involved fairly accurate orientation is required. This is especially true of the narrow beam, precision type radars. Of the many ways of determining the direc- tion of north, one of the most convenient is observa- tion of the azimuth of the sun. Care must be taken when using compasses because of local attractions or inadequate information of the declinations. Star observations are capable of good accuracy, but where Polaris is not visible they require the same procedure as solar shots. Caution must be used in aligning on permanent echoes because nonstandard refraction may bring in confusing distant echoes, or side lobes may give false echoes. In general several methods should be used in order to obtain independent checks. When an accurate orientation has been obtained reference marks should be provided so that the ~ azimuth may be readily checked. Solar azimuths, correct to the nearest quarter of a degree, may be determined from the date, time to the nearest minute, and the latitude and longitude to the nearest degree. Two methods will be given for obtaining the azimuth of the sun: (1) by calcu- lation, (2) from tables. A third method gives true south only. The azimuth of the sun may be calculated from the formula: sin HA ta = — = ; pate cos ® tan 6 — sin ® cos HA (1) B = bearing of the sun. The bearing is east or west of south when ¢-6 is positive. The bearing is east or west of north when #—6 is negative. The bearing is east in the morning (6 will be negative), and west in the afternoon (8 will be positive). HA = hour angle of the sun. During the morning hours when the hour angle is greater than 12 hours, its value should be subtracted from 24 hours for use in the formula. @ = latitude of the place of observation. 6 = declination of the sun at the time of observation. The signs of # and 5 are important and each is positive when north of the equator and negative when south. The hour angle HA is the local apparent time [LAT] minus 12 hours. To convert the observed time into LAT the civil time at Greenwich [GCT] must be found and combined with the equation of time to correct for the apparent irregular motion of the sun. This gives Greenwich Apparent Time [GAT] which is converted to LAT by allowing for the lon- gitude. The equation of time and the declination of the sun are plotted in Figure 1 for 1945. The annual change is small, and these curves may be used for radar work without regard to the year. Standard time meridians are every 15° east or west of Greenwich, each zone corresponding to 1 hour. Care should be used to take daylight saving, or other changes from standard, into account correctly. Example 1. It is desired to compute the azimuth of the sun. Given: Date March 16 Time 1345 hours PWT Latitude 40° North Longitude 118° West Solution: The hour angle will be determined first: Observed time PWT 13" 45” Zone difference + 7 Greenwich civil time 20" 45” Equation of time (Figure 1) — gm Greenwich apparent time 20" 936” Longitude difference for 118° W = oo Bye Local apparent time 12?) 44 LAT — 12 = HA — 12" Hour angle of sun + oF 44m HA in are.(4" = 1°) + 11° Latitude ® + 40° Declination of sun 6 (Figure 1) = Substituting in equation (1): sin 11° cos 40° tan (—2°) — sin 40° cos 11° tan B = — 0.19 0.766 X (—0.0349) — 0.643 x 0.982 TOPOGRAPHY OF = 0.29, B = 16°10’. Since #@ — 6 is positive, 8 is the bearing from the south. The bearing is west of south since £ is positive (p.m.). The azimuth of the sun is 180° + 16°10’ = 196°10’. A quicker solution may be obtained from a book Azimuths of the Sun, H. O. 71, published by the U. 8. Navy, Hydrographic Office. The equation of time may be obtained from a current copy of The American Nautical Almanac, United States Naval Observatory, Washington, D. C. This method will be illustrated by the data from Example 1. The LAT is obtained as before. Between September 23 and March 21 the sun is in south declination and since the latitude in this case is north, the second part of the book labeled “‘Declina- tion Contrary Name to Latitude” is used. For latitude 40° an interpolation is made between 12:40 and 12:50 obtaining 164°. The table is marked ‘‘the angular departure of the sun west of north” for readings in the afternoon, and the tabular value is therefore subtracted from 360°, giving 196° as the azimuth of the sun. It is usually more convenient +24 ee oo oa TS SOR SS See Babee rag aey Ger oo se eaeseran -, JUDD SESS UooRooSo0S Bice i ce i Nia Page Vlog _ , HODDER Sooeoee ZOOS oe 8 “hUGtnnERere CSS aNoo 25 Rtas onee be CESS 22 ORE HSSoooNo 2 pls ee sos ses i <2 “ (DEREoRe yey afi NS *— jue saya i a gow HCeosos 25 . Ene oeeag is ta 22 | NODOeooMm HeSoeeeo g _,|SODooDaa NESDGEoo 25 PN SoDveZo NIE 2oS0 4 _ |ONGopaZoo SENT e noe HoSeaZdoo COD SUGSooS | nn oe ee DESEO oNeo eo oy a a a a _o =, Gp DOE ene an eS eaeeeae sera. 2 eo i i | Bede See ee eee 4 il 2l 3) lo20 2 12221 I el fd JAN APR FEB MAY a a SO | a SITING 117 to plot a curve of azimuth against time for the hours during which it is expected that the observation will be made. Such a curve may be used for several days without much error. A method that is less convenient but requires no calculation is the equal altitude method. This con- sists’ in measuring the horizontal angles between the sun and a mark, when the sun is at the same altitude on both sides of the meridian of the observer. The bisector of the horizontal angle between the two equal altitude positions of the sun during the obser- vations is very close to true south, and the azimuth of the mark may be determined. A horizontal radiation pattern should be obtained to determine whether the electrical and mechanical axes of the antenna coincide and to discover any abnormalities in the main or secondary lobes. Defec- tive patterns should be corrected by appropriate maintenance. 15.3.5 Visibility Problems It is frequently necessary to estimate the effect on rays of intervening obstacles or the curvature of the MW 20309 1929 8 18 28 8 18 287 17 27 7 2I 31 10 20 30 10 8 17 27 JUN —_— JUL AUG SEP NOV DEC SUN DATA FROM NAUTICAL ALMANAC 1945 Figure 1. Sun data from nautical almanac, 1945. 118 earth, or to compute the distance to the horizon, or the amount a ray would have to be diffracted to clear an intervening hill. The methods described here enable one to solve such problems quickly and simply. DISTANCE TO THE HoRIzOoN The distance d of the horizon on a spherical earth as seen by an observer at elevation h is given by the well-known formula: _ |B d= eae ap. (2) is: 3 with din statute miles and h in feet. This expression makes no allowance for refraction and is commonly used in visual work. In radio propagation work the refraction of the standard atmosphere is sufficient to increase the distance of the ‘‘radio horizon” to d= V/2h or h=-—d@, (3) Nl Re where d is expressed in statute miles and h in feet. This corresponds to the use of an effective radius of the earth equal to ka where k is 4% and a is 3,960 miles. This value of k will be used throughout this report. If it is desired to use other values of k, equation (8) may be written as d= a oF f= ie : Points at heights h; and he which are separated by the sea or smooth earth are visible from each other if the distance between them is less than dy = V2hy + V/2h2 . (4) SITING AND COVERAGE OF GROUND RADARS Dre anD RISE Over land, visibility is determined by the profile of the path involved. Elevations obtained from map contours may be plotted on a profile so as to take the effective earth curvature into account, and visi- bility can then be determined by graphical means. However, construction of such profiles on a curved datum line is tedious, and it is easier to compute the earth curvature and the visibility directly from the map by methods given below. In Figure 2 is shown the relations between various heights on the earth’s surface. In considering the reference line (sea level) flat as on a map or ordinary profile diagram, use is made of the line H;TH>,T’ instead of the curve H,HH2H’. This will be com- pensated for by using a fictitious ray path P:PP2P’ instead of the line P,QP:Q’. The deviation of this fictitious path from P,QP.Q’ at P is QP = HT and is called the dip. The deviation at P’ is Q’P’ = H’T’ and is called the rise. In the figure on the left the triangles HH2T and H,KT are similar and ely _ TRUE Te (Tae or approximately (right-hand figure) HT X 2ka = did2. Therefore the dip, _ 5,280 X dids X 3 dydy é C= CRC Ca HS ) Similarly for the rise ee dy'do! Qe’ = omc Ficure 2. Relations between various heights on earth’s surface. Dip and rise. TOPOGRAPHY The application of these formulas will be shown by a number of examples. Example 2. Intervening Obstructions — Graphical Solution. In Figure 3 is shown a profile as may be Figure 3. Intervening obstruction of radiation between two points. obtaied from a topographical map. It is desired to ascertain whether P» will receive radiation from P, without being obstructed by the intervening hill P. Owing to the curvature of the earth the line marked “datum level” is actually curved instead of being straight as shown. To compensate for this distortion the line of sight of the radar is taken as the parabola P,X Pz, (shown dashed) instead of the straight line P,QP»2. If X lies above the top of the intervening hill P, the ray is not obstructed. The distance QX is from equation (5). QX = ae = oe = 300 ft. Scaling this distance down from Q, it will be found that X lies above P and there is no obstruction to the radiation. It will be noted that QX is a maximum midway between P; and Pp». One 5 (a 4 in) (6) Where there are several obstructions to be con- sidered the work may be speeded by drawing a line SS (Figure 4) parallel to P:P2 at a vertical distance WILL NOT. Py OBSTRUCT MAY OBSTRUCT. ad Figure 4. Several obstructions of radiation between two points. below it equal to the maximum dip. Then intervening hills which do not rise above S,S_ will not have to be considered, and those that do cut the line may OF SITING 119 be checked for obstruction by equation (5) as before. Hxample 3. Remote Shielding—Graphical Solution. It is frequently desired to know from a position as P, what degree of shielding will be obtained from a given profile. In Figure 5 the rise Q’X’ is computed Fieaurr 5. Remote shielding obtainable from a given profile. by equation (5). Since P’ lies below X’ it is shielded from P, and the minimum height of radiation is indicated by the dotted lines did’ _ 90 X 80 ate Ox = = 3,600 ft . Example 4. Visibility Determined by Computation. In many cases it is not necessary to construct profiles, as visibility may be determined by a simple compu- tation. The critical height, ,, which an intervening hill must equal or exceed to obstruct the line of sight, may be computed from Figure 4. Let the height of the line P;P, at d; be h’. Then hy — h’ h’ — ho dy Fe ds or hide + hod = —— dy alt do But the height h’ exceeds h, by the dip (didz)/2; therefore hide + hedi dds d; + ds 2 a (7) For the values given in Figure 4 the eritical height at d; is 3,000 X 35 + 1,500 X 15-15 X& 35 15 + 35 2 — 228 ont Since the hill P is 2,300 ft high it will interfere with radiation to Pe. Example 5. Remote Shielding—Computation. An important problem is illustrated in Figure 5. A trans- mitter is located at P,, and it is desired to know if the nearby hill Pe shields the distant mountainous island. The height of the line PiQ’ at a distance of — 120 d;’ from P; is denoted by h’ and may be obtained from the relation: lip = Ie hon = Ie! da! x dy’ : giving pe = tile = dies i dy! — da! For this case the rise Q’X’ due to earth curvature must be added to give the elevation X’ of the line of sight. The height of the lowest ray is therefore dy/he = do'hy dy'do! h= a = ae =F oman (8) For the values given in Figure 5 90 X 2,200 — 80 X 2,400 tL 90 X 80 oy 90 — 80 2 = 4,200 ft . h It is apparent that the hill P’ is shielded from P; by the nearby hill P2 except by diffraction. 50 MILES Ficure 6. Vertical angle computation. Example 6. Vertical Angles. The slope of the line of sight at the near end (Figure 6) is given by On = ho = hy a d *— 5,280d ~ 10,560 ° (9) 6, is in radians and is measured from the horizontal at hy. The angle with respect to the horizontal at the . far end is given by Aas h; — ho ie d * 5,280d ~ 10,560° Thus for the values shown _ 160 =4000 OM _ 5,280 X 50 10,560 62 = 0.00474 radian . A, 0.0142 radian , and Example 7. Angle of Diffraction. One of the principal problems in connection with intervening obstacles is the computation of the angle of diffraction. In Figure 7 the angle of diffraction is 6,. The line P,P is the geometrical shadow line; h, is the height of the SITING AND COVERAGE OF GROUND RADARS 30 MILES 20 MILES Freure 7. Angle of diffraction computation. direct line P,P: at the distance d; and is given by equation (7). — hhe = Jal fa 5 980d; am For the values shown in Figure 7 ] 4,000 < 30 + 1,500 « 20 20 X 30 20 + 30 2 = 2,700 ft , 2,700 — 2,500 o 6a 5,280 X 20 0.00189 radian . P» is therefore in the illuminated region. Had hz been 100 ft instead of 1,500 ft, h, would be 2,140 ft and _ 2,140 — 2,500 bu = Say Cap =~ 0.00341 radian , and P, would then have been in the shadow region. 154 DIFFRACTION OF RADIO WAVES 15.41 Introduction Whenever interference effects are important, the reflecting surface must be examined to determine to what extent the assumption of an ideal plane or spherical surface with uniform values for the ground constants is valid. This uniformity holds when the reflecting surface is the sea; but it is often not true over land areas, and especially at the coastline. More important deviations from the ideal case are roughness of the reflecting surface, such as waves on the sea, or irregularities of the land, such as hilly or broken terrain. This frequently causes diffuse reflection and virtual elimination of useful reinforce- ment of the direct ray. To deal with these practical terrain problems the methods of physical optics are employed. DIFFRACTION OF RADIO WAVES 12] ce Wave Propagation For most purposes the antenna may be considered as a point source of radiation. Near the antenna the wavefront (the locus of points of constant transit time) is spherical, but at great distances it is prac- tically plane. According to Huyghens’ principle each point of a wavefront may be considered as a source emitting wavelets whose envelope at a given time is the new wavefront. In Figure 8A, O is the source a! A Figure 8. Radiation wavefronts. A. Spherical wave- front. B. Plane wavefront. of radiation, and AB a portion of the spherical wavefront. From centers a, b, and c, secondary waves spread out as shown by the dotted lines and are enveloped in the new front A’B’. A similar construc- tion is made in Figure 8B for a plane wavefront. Another example showing how waves are reflected from a plane surface is given in Figure 9. A wavefront AB is descending in an oblique direction on the reflecting surface AB’. Points ACDEB’ are struck successively and in turn become centers of new wavelets. In the time required for B to reach B’ the wavelet from A spreads to a radius AA’, the distance it would have traveled if there were no reflector. Other wavelets have lesser radii which, in spreading, form a new wavefront. This is the reflected wavetront, and its angle with the reflecting surface is the same as that of the incident wavefront. The secondary wavelet from a point on a spherical wavefront (AB in Figure 10) does not produce the same effect im all directions. The field strength in a direction ac varies in proportion to (1 + cos @). The field strength drops from a value 2 in the forward direction to 1 along the line zy and to zero in the backward direction (@ = 180°). While in Figure 8A an envelope of secondary wavelets can also be drawn Ms TFicure 9. Reflection of waves from a plane surface. Huyghens’ construction. x B ") Dh NaeaAG * SOURCE 5 NS Li | Vi A / Cc | | Ficure 10. The secondary wavelet. to the right of AB so as to produce a convergent wave traveling back to zero, it can be shown that this backwave does not exist. Only waves in the forward direction should be considered. Be Fresnel Zones In Figure 11, BC denotes a plane wavefront moving from a distant source on the right toward SITING AND COVERAGE OF GROUND RADARS Figure 11. Fresnel zones. a point P to the left. It is desired to know the effect at P of the secondary wavelets emanating from the wavefront. A straight line is drawn from the distant source to point P cutting the wavefront at C. In the wavefront with C as a center are drawn circles such that the first is a half wavelength further from P than C is, the second is 2 half wavelengths, ete., so that . the secondary disturbance from any circle will reach P half a wavelength ahead of those from the circle enclosing it. If PC = b, the radius 7; of the first zone may be obtained from (3 +3) —b=r?. y/o and the V/2tX, r3 = V/3bx, ete., and in general rm = Vmbo . (11) The corresponding areas are approximately bd, 2rb\, 3rb\, and mzbd. The area of the central zone Neglecting \?/4, the radius m = radil, ro = is rb, and each succeeding ring or zone is slightly greater. The effect which one of the zones produces at P is proportional to its area and inversely proportional to its distance from P. These factors compensate as the radius increases, so that the successive zones may be regarded as producing equal and opposite effects at the point P. The zones become less effective further from the center owing to the increased obliquity, since the effect at P is proportional to 1 + cos @ (see Figure 10). The resultant effect may be represented by a series of terms of alternate sign which decrease slowly at first and then more rapidly, eventually becoming zero, thus: S = m, — mz + ms, etc., 1 il u = a ar (Gm = 102 7 3s) =F ( m3 — 5) ma + 3") = = = =p « DIFFRACTION OF It can be shown that all terms except the first cancel so that ; I Ss = 5m - “= (12) The resultant effect of the entire wavefront is equal to one-half of that due to the central zone. The secondary wavelets from the central zone unite into a disturbance whose phase is midway between the center and the rim. This may be shown by dividing the first zone into rings such that the effect of each ring at the point P is equal in ampli- tude, and the phases range over half a complete period. The electric vectors corresponding to these subdivisions may be combined to obtain the resultant phase as in Figure 12. The vector for the central RESULTANT A B Figure 12. Phase of a zone. area of the first zone is AB with succeeding sur- rounding rings represented by BC, CD, etc. These vectors fall along the perimeter of a half circle, as a consequence of which the resultant amplitude is 2/x times the sum of the amplitudes of the individual vectors. The vectors for the second zone are shown dotted. In Figure 13 1s shown the first six half-wave zones and the phases relative to the center of the first zone are indicated. A set of alternate black and white zones as shown at the top is known as a zone plate. If a sereen is provided which has an aperture of the same diameter as the first zone, it will be found that the electric intensity of the wave at the point P is doubled (m, = 2S) and the power intensity is four times as great as for the unobstructed wave. If the aperture is increased to include the second zone, the intensity at P will be reduced nearly to zero. The RADIO WAVES Fiaure 13. Polarity of zones. disturbances from the second zone are out of phase with those of the first zone and equal in magnitude and therefore cause cancellation. 44 Reflection from Rough Surfaces— Rayleigh’s Criterion A rough surface may destroy all phase relations between the elements on the wavefront. The second- ary wavelets start from the elevated portions of the surface first, since these portions are struck first by the incident wave, and the lower portions send out secondary disturbances at various other times in random phase. It is impossible to arrange any zone system on such a surface for there are all possible phase differences irregularly distributed over the reflected wavefront and each point on the surface acts as an independent source radiating in all directions. In Figure 14 is shown a plane surface xy with incident rays SB and SA falling on a raised portion and a crevice respectively and being reflected to P. The path difference is SA + AP — (SB + BP). Since BP and AP are practically parallel, the path difference may be taken as BA — BK. H sin W ’ BK = BA - cos 2W. BA = 124 TO DISTANT POINT P ya == ——— by, TITITITITT I 1117 777 Ficure 14. Reflection from rough surface. The path difference H sin V = 2H sinw. A= (1 — ccs 2) (13) The corresponding difference in phase is r d 27rA : ul = a! oe (14) Since the path difference increases as the grazing angle increases, the diffusion is greatest when the rays are perpendicular. When the angle is small, near zero, regular reflection may be obtained. It was suggested by Rayleigh to take as an upper limit for the grazing angle, giving regular reflection, the value corresponding to a phase difference of 7/4. By equation (14) this angle is given by i eget sn WV , or X sin VW = 16H: (15) For a given wavelength and lobe angle the terrain at the reflection point may be examined to determine the limiting height of the roughness for regular reflections. Equation (15) may also be given in a more convenient form using the approximation sin YW = W radians for small values of V: 3,520 with H in feet, f in me, and W in degrees. Thus for 100 me regular reflection may be obtained over ridges as high as 35 ft for a grazing angle of 1°, but for 3,000 me the roughness could not exceed 1 ft in height at this angle. SITING AND COVERAGE OF GROUND RADARS ee Diffraction at Obstacles The preceding considerations of Fresnel zones in a wavefront will now be applied to the problem of radio wave diffraction past hills, ridges, or nearby objects. These obstacles will be treated as though they were straight edges, narrow screens, or rec- tangular slits. In Figure 15 is shown a distant source of radiation DISTANT SOURCE Fraure 15. Interference of waves at an edge. and a diffracting edge. The illuminated edge is considered to send out secondary cylindrical wavelets which interfere with the plane waves which are not shielded by the edge. The dotted and solid lines are spaced a half wavelength apart. In the unshaded region the intersection of two dotted or two solid lines indicates reinforcement and the intersection of a dotted and a solid line indicates cancellation. The loci of maxima and minima are parabolas along which the relative intensities are practically constant. In the shadow region, where only the wavelets from the edge are propagated, the relative intensity falls off continuously as the angle of diffraction is increased, since the angle 6 (see Figure 10) approaches 90°. In Figure 16 is shown the zone system obtained - because of a diffracting edge with the source of radiation at a distance behind the paper and with the edge viewed from a screen on which diffraction fringes are formed. The observer is within the shadow region a distance bc, and the zone system is largely obscured as indicated by the dotted lines. The radiation received at c comes from the exposed zones, and its intensity is equal to a series of the form m,— m2+m3--:-, ete., where m is the electric intensity due to the exposed portion of the first uncovered zone, etc. The sum of this series is a fraction of m; since the outer zones tend to cancel. As c is moved to the right, that is, further into the shadow, m will decrease very rapidly without passing through maxima and minima. DIFFRACTION OF b Figure 16. Fresnel zones in the shadow region. Figure 17. Fresnel zones on the shadow line. In Figure 17 the observer is at the geometrical edge of the shadow. Only one-half of the wave is effective and the electric intensity is reduced to one-half, considering the unobstructed wave as unity. Outside the edge, Figure 18, at a distance ab the electric intensity is that due to the half of the wave, plus such portions of the zones between a and b that are uncovered. If an even number of zones is uncovered there is approximately a minimum of radiation received at the line a, that is, the half RADIO WAVES | a b Ficure 18. Fresnel zones in the illuminated region. wave plus the effect of the two zones, 44 + m: — mz, for the case shown. If a were moved to the right so that slightly less than one zone were uncovered there would be a maximum, 44 + mj, in which case m, is greater than one-half owing to the partial screening of the other zones, which, if allowed to operate, would reduce the effect due to the right-hand half of the central zone. For this reason the fringes formed outside the shadow may exceed the electric intensity of the unobstructed wave. As a is moved to the left, more zones are uncovered, and the maxima and minima are spaced approximately according to the radii of the zones; that is, the distances are proportional to the square roots of I, 2, 3, ete. 15.4.6 Fresnel Integrals The preceding discussion is approximate and provides a qualitative picture of diffraction phenom- ena. The problem will now be formulated quanti- tatively by the method of Fresnel. Since the applica- tions in view all have to do with diffraction by straight edges, slits, etc., the theoretical approach will be limited to diffraction of cylindrical waves by long edges parallel to the axis of the cylinder. The diffraction images of the source will then be bright bands also parallel to this axis, and the whole prob- lem may be reduced to the consideration of rays in a plane perpendicular to the axis. The fact that in the applications to be discussed later the illumina- tion is due to a point source rather than a line source is probably of little importance provided the distance 126 from the source to the diffracting edge is sufficiently large. In Figure 19 is shown a cylindrical wavefront AB Ficure 19. Effect at point P of wavefront AB. with its axis at the line source S’ (say an illuminated narrow slit). The secondary wavelets from the various line elements ds of the wavefront arrive at P with different phases, having traveled different distances MP. It is desired to find the resultant field strength MP due to wavelets from any given finite part of the front. Let the electric field strength at a point in the wavefront be given by the expression E = E, sin 2rft , (17) where ¢ is the time, f the frequency, and H, the amplitude of #. The phase has been adjusted so as to make H = 0 when t = 0. Consider next the secondary wayelets spreading from the front in the direction of P. The field intensity at P due to the secondary wavelet emanat- ing from the line element ds at the point M (see Figure 19) is proportional to dsH and is inversely proportional to the square root of the distance MP = d (since this is a cylindrical wave). Further, the field intensity must show a phase retardation _ corresponding to the distance d, that is 2rd/. Hence the field strength of the wavelet at P is given by an expression of the form 2rd dH = kE, ds sin (2xft — — ), x (18) where k is a factor of proportionality which depends to some degree on the angle MPM), and the distance d, but which will be considered constant here, as the dependence of the phase on d is of much greater importance. To obtain the intensity due to wavelets emanating from a finite part of the front, equation (18) must be integrated over the corresponding region of s. For this purpose we need a relation between d and s. This is obtained by applying the SITING AND COVERAGE OF GROUND RADARS cosine law to the triangle MSP, which gives at once d? = (a +b)? + a? — 2a (a + b) cos —, (19) or after a simple reduction, using the identity cos (s/a) = 1 — 2sin? = then g d? = b? + 4a (a + BD) sin? a ° (20) For the present purpose it is sufficient to consider the case when angle s/a is so small that powers of s/a above the square may be neglected in comparison with unity. This means that d= Jie + 4a (a + b) sin? 5 ~b (@sF 0) oo» 8 (a + b) : + 20 re sin” 55 b+ Dab se, (@) or again, on writing @aeo) | a 8 D9 (22) the phase lag 2rd/) assumes the form 2nd 2nd, | , . Dy oa ce) Using equations (22) and (23), expanding the sine expression of equation (18), it follows that dK = ae Bi] eos (§ r) - sin 2n( = 3) — sin( o) - cos 2r( st — °)| dv. (24) This expression may now be integrated over a certain region of the wavefront, say from v = vp to v = v, corresponding to s = s to s = s, giving the following expression for the electric field strength at P: ; aby . b H = aS B fos) sin 2n( = 3) — g(v,v0) cos 2r( i = °) | (25) where » = f(v,vo) = il cos é 7) dv, (26) 0 and v m g(v,V0) =| sin e *) dv. (27) 0 DIFFRACTION OF Equation (25) may be brought into a more con- venient form by writing _ g(v,vo) 3 f(v,r0) / i = V f2(v,v0) ae g?(v,o) : It then follows that equation (26) assumes the form ae abd maa: eb : j— ee ER sin | 2x(1 | | ‘ (30) For tabulation purposes the quantities f(v,vo) and g(v,¥o) are replaced by the Fresnel integrals, defined tan 0 (28) and (29) by: Y T 9 « C@) = i cos G “) dv (31) and S(v) _|| sin e ) dv . (32) Evidently f(@,v0) = Cw) = Co) , (33) and gvjvo) = S(v) — Sv) . (34) In the sequel the arguments will be omitted wherever it can be done without causing misunderstandings, and the above symbols will be written simply as f, g, C, and S. TaBLE 1. Fresnel integrals. v C S v C S 0.00 0.0000 0.0000 2.50 0.4574 0.6192 0.10 0.0999 0.0005 2.60 0.3889 0.5500 0.20 0.1999 0.0042 2.70 0.3926 0.4529 0.30 0.2994 0.0141 2.80 0.4675 0.3915 0.40 0.3975 0.0334 2.90 0.5624 0.4102 0.50 0.4923 0.0647 3.00 0.6057 0.4963 0.60 0.5811 0.1105 3.10 0.5616 0.5818 0.70 0.6597 0.1721 3.20 0.4663 0.5933 0.80 0.7230 0.2493 3.30 0.4057 0.5193 0.90 0.7648 0.3398 3.40 0.4885 0.4297 1.00 0.7799 0.4383 3.50 0.5326 0.4153 1.10 0.7648 0.5365 3.60 0.5880 0.4923 1.20 0.7154 0.6234 3.70 0.5419 0.5750 1.30 0.6386 0.6863 3.80 0.4481 0.5656 1.40 0.5431 0.7135 3.90 0.4223 0.4752 1.50 0.4453 0.6975 4.00 0.4984 0.4205 1.60 0.3655 0.6389 4.10 0.5737 0.4758 1.70 0.3238 0.5492 4.20 0.5417 0.5632 1.80 0.3337 0.4509 4.30 0.4494 0.5540 1.90 0.3945 0.3734 4.40 0.4383 0.4623 2.00 0.4883 0.3434 4.50 0.5258 0.4342 2.10 0.5814 0.3743 4.60 0.5672 0.5162 2.20 0.6362 0.4556 4.70 0.4914 0.5669 2.30 0.6268 0.5531 4.80 0.4338 0.4968 2.40 0.5550 0.6197 4.90 0.5002 0.4351 RADIO WAVES st The Cornu Spiral In Figure 20 the two Fresnel integrals are plotted against each other, S being the ordinate and C the abscissa, for different values of v. The resulting curve is known as Cornu’s spiral. The upper positive branch (C and S positive) corresponds to points on the wavefront above the line. S’P in Figure 19, and the lower or negative branch corresponds to the wave- front below the line S’P. By their definition f and g signify the coordinate differences between any two given points on the Cornu spiral, and it follows that R, as defined by equation (29), represents the corresponding distance between these points. Differentiating equations (31) and (32) for C and S, squaring and adding, it follows that (GC)? s— (GSP = GDP , so that dv is the line element of the spiral, and v measures length along the curve from the origin. In order to see more in detail how the Cornu spiral is built up of contributions from different zones we may suppose the half-wave zones on the wavefront to be divided into equal areas and the contributions of these areas to the field strength vectorially combined to obtain the resultant effect as in Figure 22. Then as smaller areas are used and more zones are summed up the vector diagram becomes in the limit the Cornu spiral. This is shown in greater detail in Figures 21 and 22. Here the first half-period zone of Figure 21 is divided into nine parts and the resultant is AB (Figure 22). The second half-period gives a resultant BC. The sum of the first two half-periods is AC. The sum of all half-periods is AZ, which is thus the resultant effect at P of the upper half of the wavefront. A similar result is obtained for the lower half. It may be remarked that the superiority of the dimensionless variable v over s shows itself in the fact that one Cornu spiral suffices for all situations of the diffracting edge, while the use of s would have necessitated the construction of a special spiral for each specific set of values, a, b, and X. In Figure 20 the values v = 1 and v = 2 are marked and corres- pond to path differences A = \/4 and A =), respectively. Equation (380) shows that the electric field strength in the diffraction region which is due to a certain section of the wavefront is proportional to the corresponding value of R. Hence, it follows that the SITING AND COVERAGE OF GROUND RADARS Figure 20. Cornu spiral. power per unit area is proportional to R?. Let W denote peak power per unit area at the point P for a certain arbitrary value of Rk. Then WY = Io 1? (36) where K is a certain constant. When the whole wave is acting, the integration limits extend from v = | — «tov = + ©, that is, along the full length of the Cornu spiral. The coordinate difference between the foci of the spiral being (1,1) (see Figure 20) it follows that their distance is R = 1/2, so that the corresponding peak power per unit area Wo is, by equation (36), Wy = 2K which defines K as 144Wo. Hence it follows that equation (36) may also be written as 16? (37) 15.4.8 Straight Edge Diffraction Using Cornu’s spiral the diffraction pattern due to au straight edge may be obtained. In Figure 23 is shown a diffracting edge at Mo. At P the upper half of the wave is effective, and on Figure 22 the amplitude is AZ of length 1/+/2. The square of this is one-half, which by equation (37) is multiplied by ¥% to get % for the power intensity at the edge of the shadow. The electric field intensity is 14. Consider next a point such as P’ at a distance x above P (see Figure 23). To be specific, the point FIRST HALF PERIOD ZONE SOURCE Figure 21. Division of wavefront into half-period zones. DIFFRACTION OF RADIO WAVES x6 FicurE 22. Vector sum of subzone contributions. P’ is chosen in the direction of SM, of Figure 23, where M, is the upper edge of the first half-wave- length zone. The illumination at the point P’ is, firstly, due to all wavelets emanating from the half wavefront above P’S. In addition, there is the contribution from the lower half of the wavefront extending from M, to Mo). The situation is, in fact, the same as if P’ were brought down to P and the diffracting edge were lowered from M,) to M’ (see Figure 24). The resultant amplitude R is represented Ss SOURCE Figure 24. Diffraction in illuminated region. 129 on Figure 25 by ZB. Starting at the point P at the edge of the shadow (Figure 23) where the amplitude is AZ, if the point is moved upward, the tail of the amplitude vector moves to the left along the spiral while its head is fixed at Z. The amplitude goes through a maximum at b’, a minimum at c’, ete., approaching a value ZZ’ for the unobstructed wave. Moving in the other direc- tion, into the shadow, the vector moves to the right from A, decreasing steadily to zero. The power intensity versus v is plotted in Figure 26, and the points B, C, D, etc., corresponding to those in Figure 25 represent the exposure of 1, 2, 3, etc., half-period zones below Mo. The maxima and minima occur a little before these points are reached. This curve may be plotted from the table of Fresnel integrals with the equations f=05-+C, g=05+S, g— Wass 2 where 2? is the relative power intensity compared to the unobstructed wave. The relative electric inten- sity 18 7 am Equation (89) is plotted in Figure 27. The portion of the curve for —v has been drawn to the right and is to be used with the right-hand ordinate. The phase lag ¢ due to diffraction may be deter- mined from the angular position of the vector R in Figure 25. In the illuminated region the phase lag oscillates about the reference value, Z’Z, and is given by (38) (39) © teat o q tan 7 At the shadow line the relative value is the same as Z'Z. \n the shadow region the phase lag varies continuously along a parabolic curve and is given by Oy as The phase lag relative to that of the shadow line is plotted in Figure 28. The portion of the curve for —v is drawn to the right, and its ordinate, on the right, has a different scale from that used with the +v portion of the curve. : 1549 Location of Maxima and Minima When the source is close to the diffracting edge, the positions of the maxima and minima in the 130 SITING AND COVERAGE OF GROUND RADARS Freure 25. Method of using the Cornu spiral. illuminated region may be determined by the follow- elements is odd the intensity is a maximum. That is ing analysis. The effect of the wave RM (Figure 29) a at P’ may be considered to be due to the upper half MF’ — RP’ = cone (40) of the wave (above R), which is unaffected by the edge, and the lower half of the wave (below R), - where m is an integer with values 1, 3, 5, ete., for which is partly shielded by the edge. If RM contains 1.2 0.7 an even number of half-period elements the intensity 9 ey at P’ is a minimum. If the number of half-period > z we 1.0 5B Wd Ww = Ee = 09 az w LEFT SCALE (+v) y E 0.8) .3E =} — Ww ire} = Or 2% aA RIGHT SCALE (-v) . 2 =I 0 1 2 3 4 5 %O 1 eit ee) 4 5° v Ficure 26. Relative power intensity—straight edge FicurE 27. Relative electric intensity—straight edge diffraction. diffraction. DIFFRACTION OF RADIO WAVES 131 05 = e 25 04 = L 20 IGHT SCALE| 7) (-v wo = 03 Is Zz ra) fa) a © o2 | 10m : z LEFT SCALE o < 04 (ty) 5 | w ro) fe} 0° Ww = 3 9° z =-01 z w w -0.2 Ficure 28. Phase lag—straight edge diffraction. maxima and 2, 4, 6, etc., for minima. The difference MP’ — RP’ is a constant, and the locus of the point P’ is a hyperbola having. M and S for loci. That is, SP) — MP! = SK — (MiP? — RP’), (41) and SR is constant; therefore, the difference of the distances of P’ from the fixed points S and M is constant. P’ describes a hyperbola, but its curva- ture is so small that it almost coincides with its asymptotes. The distance x to a maximum or minimum may be computed as follows ae ne 2 SP! = (@ + [i 2 GREGE =| Since x is small compared to a + 6 ‘= ae SE = Gar OF ae a by b) also (m= ae" Via b+ 5 - Ficure 29. Path differences at a straight edge. Therefore from equations (40) and (41): ea te, ae TON 4 eke -5(; at a es b(a + b) mx - a d where 7 is odd for maxima and even for minima. MP’ hence (43) A , SOURCE Ficure 30. Rectangular slit. 15.4.10 The Rectangular Slit A problem similar to the straight edge is the rectangular slit (see Figure 30). Cornu’s spiral will be used to determine the field intensity along the plane PP’. With the slit in the central position, the only radiation at the plane is due to the wavefront in the interval As = MN. Equation (31) is used to determine what length Av corresponds to As. The resultant field strength at P is given by the chord of the spiral which has a length Av. Since the point of observation P is centrally located, this chord will be centered on the spiral. Thus, if Av = 0.5 the chord (see Figure 20) will extend from approximately C = —0.25 to C = +0.25. The resultant R = 0.5 substituted in equation (37) gives a power intensity of % relative to the unobstructed wave and a field strength of 0.353. The field intensity at P’ is due to the same length Av but taken over a different portion of the spiral. For this purpose, it is desired to use distances along the plane PP’, x, instead of s (Figure 30). a+b br (a + b) oP =r Oa ; (44) a Thus the portion of the spiral nO in Figure 31 from v = 0.9 tov = 1.4 has an average value of v = 1.15 which multiplied by the radical term of equation (44) gives x. The chord connecting these points is 0.43, x= 132 SITING AND COVERAGE OF GROUND RADARS SS" FicureE 31. The Cornu spiral applied to obstacles and slits. and the relative power intensity is 0.092. This same result may be computed from the table of Fresnel O ZL n R' m —_——}————————————— Av=b5 . bv: 4.6 i a -5 Oo +S -3 (0) +3 integrals by obtaining the values of AC and AS for v = 0.9 and v = 1.4. The sum of the squares of AC and AS is R?. Typical patterns for slits of several widths are shown in Figure 32. It will be noted that ~ there is little radiation outside the slit. ®<™ Diffraction by a Narrow Obstacle The effect of a narrow object with parallel sides may be determined with the Cornu spiral. In the case of the slit only a fixed length slid along the spiral is effective, the remainder being shielded by the edges of the slit. With an obstacle, however, a fixed length slid along the spiral represents the ineffective portion. If the obstacle is of such size that it covers an interval Av = 0.5 on the spiral, Vigure 31, the segment Av may be located as JK. The radiation at the point considered will be due ao Av =5.2 ae -4 0+4 -3 Oo +3 Ay=3.9 Av=6.2 -3 Oo +3 -3 Qo +3 4vi2 Figure 32. Diffraction patterns of slits. DIFFRACTION OF to the two parts of the spiral Z’ to J and K to Z. The resultant amplitude is obtained by adding the two vectors Z’J and KZ. The sum is R for a point midway between J and K. The head of the vector is always in the direction Z along the spiral. Typical patterns for narrow obstacles are shown in Figure 33. 2) (0) cs) =" — Ficure 33. Diffraction of narrow obstacles. 15.4.12 Multiple Slits and Obstacles Slits or obstacles with parallel sides may be treated by means of the Cornu spiral and the resultant sum of the vectors obtained. Thus, with two slits of a width such that Av = 0.5 and spaced so that Av =0.5 may be located on the spiral as JK and Im in Figure 31. The total R is the vector sum of R and R’’. The field strength pattern is then obtained by sliding the two lengths along the spiral holding their spacing fixed. In similar fashion two narrow obstacles would cause two absent sections such as JK and Im and three open sections Z’J, Kl, and mZ. The three vectors, obtained by joining these three latter pairs of points, are combined to give the resultant ampli- tude R. 413 Limitations of Fresnel’s Theory Neither Huyghens’ principle nor Fresnel’s theory, on which the above treatment is based, is rigorous, and their limitations must be kept in mind when making applications to radio and radar problems. In the development of the theory no mention was RADIO WAVES 133 made of the effect of the shape and composition of the edge. Actually within a region of about one wavelength around the edge the wavefront is affected by the presence of the edge. In Figure 34 the region of the edge disturbance is DE, and first half period of the wave front is DF. The first half Ficure 34. Edge effects. turn of the Cornu spiral is due to DF. The position of F depends on the point considered. When DE is an appreciable part of DF, the simple Fresnel theory should not be depended upon. This occurs when the field point is at Q, lying at a large angle of diffraction, or at R, close to the edge. Near the diffracting edge, a certain amount of re- flection occurs, especially near R. This reflection is divergent and decreases rapidly in intensity as one recedes from the edge. When the edge is blunt or has a large radius of curvature, the amount reflected is Increased and the field is affected over a greater distance. Since the angle is near grazing, the nature of the reflecting surface is not important. If Fresnel’s theory is applied to spheres and cylinders, the results may be only approximate. When the edge and the electric vector are parallel, the theory gives good results. When the electric vec- tor is perpendicular to the edge, the field strength in the shadow region may be several times larger than that obtained with the electric vector parallel, and the theory should then be used only for small angles of diffraction. Other discrepancies are due to ignoring the ob- liquity factor and the effect of the inclination of the wavelets with respect to each other. The theory does not give the correct phase angle for the diffracted wave. The same objections may be raised for apertures and obstacles whose dimensions are of the order of a wavelength. 134 It should be noted that 1. Fresnel’s theory vs valid when the wavelength is small compared to the dimensions of the diffracting object (as in optics). 2. Fresnel’s theory should not be used: a. For large angles of diffraction. b. Close to the diffracting edge. c. For apertures or obstacles of the order of a wavelength. d. When the diffracting edge is not parallel to the direction of polarization of the wave. In spite of these shortcomings the theory is useful because it provides simple solutions for the majority of the diffraction problems encountered in the field, and, considering the difficult nature of the general problem, it is still the most manageable treatment that has been developed. 15.5 PERMANENT ECHOES 155.1 Introduction Permanent echoes are due to reflection from terrain features such as mountains, islands, or even smooth surfaces near the antenna (ground clutter). Nearby hills and surfaces produce strong echoes which obscure the indicator and widen the main pulse so that the minimum range of detection is increased. More important are the distant hills, especially those in the operating sector which obscure areas of tactical importance. Permanent echoes are a prime considera- tion in siting, as many otherwise excellent sites are rendered worthless by excessive fixed echoes. A care- ful analysis of the terrain will enable an approximate prediction of such echoes. In this section is presented a systematic method of preparing permanent echo predictions so that the suitability of sites may be determined without actual field tests. Several factors combine to make permanent echoes more troublesome than might be expected on first thought. 1. Hills and land surfaces are so much greater in extent than the target which the equipment is designed to detect, that strong echoes may be obtained from distances where an ordinary target would give an echo far below normal detection levels. 2. The low elevation of the land surfaces places them in regions most subject to nonstandard propa- gation effects where extreme ranges and large responses are frequently obtained. 3. Side lobes of the horizontal pattern of the SITING AND COVERAGE OF GROUND RADARS antenna cause permanent echoes to appear at several other azimuths in addition to that of the main lobe. Although the signal intensity of the side lobes is much reduced, the echoes may still be strong enough to obscure targets. 4. Strong permanent echoes causing considerable trouble may be obtained from distant mountains in the rear as a result of back radiation. Again, the weakness of the radiation and distance of the moun- tains are often compensated for by the large extent of the reflecting surface. 5. Antennas with wide beams cause permanent echoes to be much wider than the object that produces them. 6. Diffraction over intervening ridges is often sufficient to nullify their screening action so that objects behind the ridge are visible. Permanent Echo Diagrams The permanent echoes associated with a radar station may be plotted on a chart and their extent, location, and strength represented. Permanent echo diagrams should be prepared for each unit of a radar system using a standard procedure for the taking and presentation of data. These diagrams are very useful for: 1. Indicating blind areas in a station’s coverage. 2. Assigning the operating area of a station. 3. Checking the range and azimuth accuracy. 4. Checking the transmitter output and receiver sensitivity. 5. Estimating nonstandard propagation. 6. Planning test flights. While methods used in different theaters vary as to detail, the typical permanent echo diagram is prepared about as follows. The equipment should be in normal operating condition: that is, the trans- mitter output and receiver sensitivity should be as recommended by the instruction manual; the range and azimuth calibrations should be accurate; and the weather conditions that affect propagation should be average. The receiver gain should be set to some standard level, usually maximum, or to some definite noise height. The value of the data taken will depend to a considerable extent on the skill and judgment of the operator. The station would normally be taken out of operation for about an hour while data are taken, although it is possible to take observations during normal scanning by stopping momentarily. Where antenna switching is provided, the low-angle, PERMANENT long-distance beam should receive the most atten- tion although the other combinations should be checked also. If the beam is highly directive and can be changed in elevation, a low angle such as would be used for distant search should be used for recording perma- nent echoes. In some situations several elevations should be used. On plan position indicator [PPI] scopes it may be more convenient to photograph the screen if proper equipment is available. Care should be taken not to confuse storm and fog echoes with permanent echoes on microwave sets. A more detailed procedure 1s required where A- scope presentation is used. After the initial adjust- ments have been made the next step is to decide on the intervals in azimuth at which readings are to be made. The definition of the echoes will depend in part upon the beam width so that the narrow beam radars should be checked at closer azimuth intervals. Readings may be taken at intervals of 10° or 5° or even less depending upon the detail desired; in general an interval of about a fourth of the beam angle is sufficient. Permanent echo readings should be taken through 360° regardless of the sweep sector used, so that back and side echoes may be investi- gated also. At each azimuth the range of all permanent echoes is recorded from zero out to the extreme range. The width of the main pulse and local ground echoes should be noted as well. Echoes one mile or less in width are recorded by a single reading at the center of the echo. Wider echoes are recorded by two read- ings, one at the left of the echo where the trace leaves the baseline and a second at the right where the trace returns. Adjacent echoes less than 1 mile apart are recorded as a single echo. Where the separation is greater, care should be taken not to lump echoes together. For most purposes variations in amplitude may be disregarded. Amplitude is, however, sometimes recorded for a few azimuths of special interest such as those used for test flights or in tactically important regions. To plot the data an overlay of a regional aero- nautical map or other chart with a scale of 1 to 1,000,000 may be made showing some of the signif- icant features as coastlines, islands, and cities. On this should be drawn radial azimuth lines every 10 degrees and range circles every 10 miles. The data are then marked on the chart as short lines, and these lines are connected as indicated by inspection. ECHOES 135 The enclosed areas may then be shaded lightly. If it is desired to represent amplitudes, a few equal amplitude contours may be shown within an echo area. More detail may be shown by plotting ampli- tude versus range on a rectangular graph for each azimuth. The completed permanent echo diagram should be compared with a topographical map to check the degree of shielding obtained and the range and azimuth accuracy of the equipment and back and side lobe radiation effects. Care must be exercised in identifying the cause of an echo, as distant echoes may come in on the second or third sweep on the scope after the main pulse. In Figure 35 is shown a permanent echo diagram which was selected for purposes of illustration rather than as an example of a good site. A few miles from the coast is an extensive range of mountains which are poorly shielded to the north. The large echo at 200° is due to a mountainous island 260 miles away. *°3 Use of Permanent Echoes in Testing Permanent echoes are useful for tuning the equip- ment, estimating the output and sensitivity, and checking the range and azimuth accuracy. While such observations may be used as an overall test of performance, care should be used in selecting the test echo and in interpreting the indications. Careful tests have shown that, even though equipment performance is closely controlled, the strength of permanent echoes varies over a consider- able range. It is noted further that indications from aircraft also vary, but there is little correlation with the changes in permanent echoes. Other tests show that, as the performance of the set is reduced, the maximum range for small targets is reduced at a much faster rate than for large targets. Thus a reduction of receiver sensitivity may cause weak echoes to disappear entirely without a noticeable effect on strong permanent echoes. Permanent echoes vary for the following reasons: 1. Atmospheric changes affect both the direct and reflected rays. This may be due to a change in the amount of refraction from standard or in the degree of trapping. Under some conditions marked absorp- tion may occur. The changes may occur slowly or fluctuate erratically, being most marked in connec- tion with microwaves. 2. If the reflecting surface is the ocean, variation of the reflected ray may occur if the tide changes 136 SITING AND COVERAGE OF GROUND RADARS Ficure 35. Permanent echo diagram. or the roughness of the surface becomes excessive. 3. Frequency variations will affect the echo from complex reflectors such as rugged terrain. Peaks which are separated in distance such that the returns from a single pulse overlap are said to be frequency sensitive. In the overlap portion the echo strength will depend upon the relative phase of the two returns. Thus if the pulse width is 10 usec the wave train will be about 2 miles long. If there are peaks at 10 miles and 1014 miles their echoes will appear as follows on an A scope: 10 to 10% miles near peak echo only 101% to 12 miles 12 to 121% miles combined echo of both peaks far peak echo only The combined portion of the echo may have a height from zero to twice that of the individual echoes and usually fluctuates rapidly as the frequency drifts. A change of a half wavelength in the separation of the peaks will change the combined echo from maximum to minimum. This means that a frequency stability of the order of one part in a million is required for a steady combined echo. Permanent echoes used for testing should therefore be (1) nearby but distinct from ground clutter and PERMANENT other echoes, (2) separated from the transmitter by rough nonreflecting land, (3) a single distinct target such as a steel tower, (4) weak in response, that is, comparable to that of a distant aircraft. The range of echoes which come in on the second or third pulse may be estimated by adding one or two times the length of the range scale to the observed range plus an allowance for the return trace time, usually several miles. To determine by test which sweep an echo is associated with, the pulse repetition rate should be changed, and the shift in range of the echo observed. Thus if the range scale is 200 miles long and the pulse rate is reduced 10 per cent, then a target at 250 miles which had been appearing at 48 miles would shift to an indi- cated range of 23 miles and could thus be distin- guished from a 48-mile target that would shift to 43.2 miles. Frequency-sensitive permanent echoes are not suitable for checking range accuracy. The frequency changes from maximum to minimum return are usually too small to be detected on a frequency meter, so that frequency-sensitive echoes are recog- nized chiefly by their unsteady appearance. Azimuths may be determined to best accuracy by “beam splitting.” This consists in turning the antenna slightly to one side of the maximum until the signal decreases to a predetermined level. The antenna is then turned past the maximum until the same level is reached and the two azimuths are averaged. When checking azimuth accuracy the possibility of horizontal diffraction due to a nearby hill should be considered. poet Shielding The principal device for control of fixed echoes is shielding. This means that the antenna is to be sited in such a way that distant hills are screened by a local obstruction. A local echo at say 3 miles, is combined with the main pulse or ground return, and the distant echo is weakened or eliminated entirely. In operating regions the loss of coverage may be more serious than the permanent echo, so shielding should be used with caution. Rear areas which are not scanned should be well shielded so that back and side echoes do not interfere with targets in important tactical regions. Operation over such shielded sectors would be limited to high targets. Construction of artificial shields made of poultry ECHOES 137 netting has been suggested in some cases, where the back radiation and side lobes were relatively strong. The very large size of such structures ordinarily renders them impractical. Most of the antennas using parabolas have a small back radiation, and permanent echo problems are much simpler. In special cases it may be desirable to eliminate a particular echo from some obstacle without using shielding. This may be done by constructing a target of sheet metal on the side of the obstacle, spaced so that the target echo and obstacle echo are about 180° out of phase. This requires accurate alignment of the target (so that it is normal to the radiation to within 5° or less) and close control of the frequency. It is also necessary that the area be adjusted so that the response of the target and obstacle are equal. 155 Prediction of Permanent Echoes Permanent echoes may be determined by several methods: 1. Tests with the radar at the site. 2. Profile method. 3. Radar planning device [RPD]. 4. Supersonic method. The feasibility of moving the radar to the site to determine the permanent echoes is dependent on portability, accessibility, etc. Echoes obtained with one type of equipment may be very different from those from another type of radar with different directivity, frequency, and range. The profile method, which will be described in detail below, involves a study of topographical maps and plotting the echoes according to their visibility and the amount of diffraction. A fairly difficult site may be handled in perhaps 8 man-hours. This method is adapted to long-range, low-frequency radars where diffraction and side and back lobe radiation are important. On microwave equipment fixed echo prediction is simpler and the profile method may be worked out in a few hours. The RPD technique requires construction of a relief model of the terrain considered. A small light source is used to simulate the radar and the echoes are plotted as a result of a study of the areas illu- minated. This method is adapted for short ranges and microwaves where the diffraction and side and back lobe radiation are small. Construction of a fairly difficult model may take a crew of men several days to a week, as a model should be accurate. 138 SITING AND COVERAGE OF GROUND RADARS Once completed, all possible sites or aspects from a plane or ship may be readily examined. Models of enemy areas may be used to predict the coverage of possible enemy sites, and evasive action may be planned. The RPD is well suited for training and briefing of air personnel. Kits are provided contain- ing the light source, supports, etc. Darkroom facilities are required, and special processing of films is used to secure more realistic pictures. The supersonic method requires a model made of sand, glass beads, ete., to be used under water. Such models are much easier to construct than the RPD type. Supersonic gear is used to send out pulses which are reflected like radar pulses and the echo is picked up and presented on a PPI scope. Photos may be taken of the scope picture, and the method may also be used for training and briefing. Special equipment is required, but the models may be made easily and the presentation is obtained direct on the PPI scope without further processing. This method is well adapted for training, as flight, changes in altitude, etc., may be simulated readily by movement of the sonar head. In general the profile method should be used on long waves or on microwaves where only a few sites are being considered. It is well adapted for the estimation of nonstandard atmospheric effects. For alr- or ship-borne radar the RPD or supersonic methods are convenient because of the large number of aspects involved. It may be noted that the latter two methods should not be considered more exact than the profile method, as the principle of similitude does not apply unless all elements including the wavelength are changed in proportion. The principal difficulty is to secure a source which has the same radiation characteristics as the antenna system. 15.5.6 Prediction by Profile Method The profile method will be described in detail. The discussion will refer chiefly to VHF radars in a mountainous terrain, but the methods have general application. The principal requirements are topo- graphic maps of the surrounding area with a scale of 1 or 2 miles to the inch and a contour interval of 20 ft, although intervals up to 100 ft may be used. Maps with a scale of about 20 miles to the inch are needed for checking distant echoes. Regional aeronautical maps, with a scale of about 1 inch to 16 miles and 1,000-ft contours, are suitable as the height of prominent peaks is indicated. From the maps, profiles are prepared for various azimuths about the radar station. The first mile or so should be plotted accurately, and at greater distances the critical points such as hills and breaks should receive the most attention. A convenient scale is 2 miles to the inch for range and 500 ft to the inch for elevation. The distances to which the profile should be plotted is a matter of judgment, but it should be extended to perhaps 20 miles, or further if there is doubt. On each profile is drawn the tangent line from the center of the antenna to the point on the profile which determines the shielding, as in Figure 36. FEET 6 RANGE IN MILES Fiaure 36. Typical profile. (Note: Y in degrees). This is the line-of-sight curve; it is drawn for each azimuth, and the vertical angle y is marked on the profile. If the angle is below the horizontal it is negative, and caution must be used on high sites not to exceed the limiting shielding angle of the radar horizon. This is given by the expression + = —0.0108 ~/ 2h, , (45) where y is the angle between the effective horizon and the horizontal at the antenna in degrees and hy is the height of the center of the antenna in feet. The line of sight is actually curved, as explained in the section on visibility problems, but for ranges up to 10 miles the error in using a straight line is small. For longer distances the dip QX as computed from equation (5) should be considered. More con- venient for this purpose are the curves of the line of sight for various angles which are calculated from Figure 37. Standard refraction is taken into account by use of 4 a@ instead of a for the earth’s radius, 1.33 X 3,960 = 5,280 , gn (46) he — hy = 5,280d tan y + 9? ae 3 = with h, and he in feet and d in miles. Above 10°, or where the shielding is distant, equation (8) should be used. PERMANENT ANTENNA TARGET a hy Ce) CENTER OF EARTH Fiaure 37. Line-of-sight geometry. These curves are plotted in Figures 38 and 39, and their use is illustrated in Figure 36. The center of the antenna is at 200-ft elevation, and the height of the shielding ridge 4 miles away is 400 ft. For a a @_IN DEGREES 15 10 Z 6 7 5 6 4 5 ci 3 Ww uw Mm ° = s = 2 = ‘ou i = 2 13 1 1 i 2 a 4 ) e. “4 ail 2 3 4 -2 -1 4h 4 1 -2 miei 2 4 6 8 10 12 14. RANGE IN MILES Figure 38. Line-of-sight curves. ECHOES 139 2% IN DEGREES ——— 30 10 76S S 4 3 2 28) 24 20 IN 10° FEET nD hooh, SS 10 30 70 90 RANGE IN MILES 50 Ficure 39. Line-of-sight curves. 200-ft rise in 4 miles the angle is found from Figure 38 to be 0.5 degree. This curve can then be used to determine the height of the shielded region at other ranges. Thus the range at which the shielded region is 4,000 ft high for the case considered is found from Figure 39 by using he — hi = 4,000 — 200 = 3,800 ft for height and the 14-degree curve, giving 53 miles. It is desirable to be able to estimate diffraction effects in a simple fashion suited to the approximate nature of this kind of work. As shown in Section 15.4.8 the field intensity varies in a rather compli- cated manner with the diffracting angle 9, and the distance of the shield d, [Figure 7 and equation (10) ]. In Figure 40 is plotted the relative field intensity compared to that obtained without a shield for shields at several distances. This graph is intended for 200 me but may be used on other frequencies by changing d, in proportion to the change in X. It enables one to make an estimate of the effectiveness of a shield. Thus if a shield is 1 mile away it may be neglected for values of 6, in excess of +3°. Likewise 140 SITING AND COVERAGE OF GROUND RADARS fee rage MILE fears Wit an ee WG os = = 0.8 z a = Ww > = 06 s INTENSITY RELATIVE TO THE a INTENSITY WITHOUT THE RIDGE VHF- 200 MG 0.4) 0,2 0 “10 “8 6 2 @4 IN DEGREES Ficure 40. Diffraction over a ridge. (200 mc) (For other frequencies change d; in proportion to the change in wavelength.) objects below —3° in the shadow region would give weak echoes in most cases. For intermediate angles the relative intensity may be read from the curve. For shields closer than 0.1 mile the methods of Section 15.4.8 should be employed. Figure 15 shows that the relative intensity of a diffracted wave is virtually constant for a given angle when the distance from the edge is large. Equation (22) may then be written in the form (47) where 6, is in radians (1 radian = 57.3°) measured from the geometrical shadow line (Figure 7) and d; is in the same units as \. This equation is approxi- mate, and the error is of the order of a/b. Where the shield consists of several ridges close together, an equivalent shield is used instead of successive shields. The height and distance of the equivalent shield is found by constructing a triangle between the radar and the reflecting object which encloses the shielding ridges. The apex of this triangle is then treated as though it were the diffracting edge. In Figure 41 H and d; are the quantities to be used in equations (10) and (47). The general procedure to be followed in preparing aay — Cite = RADAR__-<( TO DISTANT = OBJECT — Ficure 41. The equivalent shield. a prediction of permanent echoes will now be out- lined. By examining a topographical sheet the azi- muths are determined at which profiles should be prepared. This will normally be about every 10 degrees. Where the shielding is obviously good the interval may be 20 degrees, but where the terrain -is questionable such as a region of low hills the profiles should be taken at 5-degree intervals. The profiles are prepared and the angle of the line of sight determined as described above. _ The next step is to make an overlay of a map of scale 1 to 1,000,000. The principal features as coast- line, towns, and rivers are sketched in to aid in reading the completed chart. On this is drawn a polar coordinate system with azimuths marked every 10 degrees and range circles every 10 miles out to the full range of the indicator. On the overlay are now drawn the coverage contour lines. These lines represent the limits of the heights of the shielded regions. Targets or mountains below these coverage contours will not PERMANENT be visible except by diffraction, and targets above the contours are in line of sight and receive direct radiation. For each azimuth and the corresponding angle of sight (Figure 36) the ranges are plotted for various contour heights as 1,000, 5,000, 10,000, and 15,000 feet. Where these coverage contour lines are close together the shielding is good but the coverage is poor; where the lines are widely separated, the shielding is weak, and toward the sea there is no shielding except by the horizon. With the coverage contour diagram superimposed on a map, the peaks exposed to radiation may be noted. The extent of the echoes due to these peaks depends on the horizontal radiation pattern and pulse width. The horizontal beam width is only a very rough measure of the width of an echo, and some other angle usually between the half-power points and the nulls will determine the echo width. The angle may be estimated by considering the range and size of the peak. The extension of the echo in range will be at least as great as the pulse width in miles, which as it appears on the indicator is about 0.1 mile per usec. Actual echoes are usually much wider than this, as all of the exposed hill sends back an echo. The echoes are then sketched in, based on inspec- tion of the profiles. The plotter’s judgment is a very important factor, but the following rules may be -used as a guide. 1. Shade in a circle for the main pulse several miles wide, depending on the pulse width and local return. 2. Consider each profile in turn and for each peak or hillside in front of the shielding plot an echo on the main and all sidelobes. 3. A series of sharp hills within the shielding region should be plotted as a single echo rather than a number of echoes. 4. The inner edge of an echo should be at the same range as the hill, and its extension depends on the slope of the hill and the pulse width, which may be several miles with some sets. 5. In case of doubt plot the echo. 6. Peaks beyond the shield may be in the diffrac- tion region and the relative intensity of the radiation at these peaks will then be obtained from Figure 40 as described above. 7. If the mountain is large enough to intercept several lobes, the interference effects may be ignored. The echo strength may be estimated roughly as proportional to the cross-sectional area of the moun- ECHOES 14] tain, the relative intensity of the radiation from Figure 40, and the inverse square of the distance. For side and back lobes an additional factor is required. 8. The 1 to 1,000,000 scale map should be carefully checked to make sure that no peaks are missed in between the azimuth considered or at extreme ranges. In the above method much is left to the judgment of the plotter but it will be found that with experience a reasonably good estimate of permanent echoes may be made from a map. Example 8. Profile Method. A detailed example of a difficult site will be worked out, and comparison will be made with the actual recorded echoes. The site selected is that of Figure 35. The characteristics of the SCR-270B radar are given in Table 2. TABLE 2. pattern. Type SCR-270B. Characteristics of antenna Horizontal pol. _- Vertical pol. Half-power beam angle 26° 6.5° First null angle 40° 14° Secondary lobe angle 45° Secondary null angle 90° Secondary lobe angle 5% Back radiation 4% Other characteristics of this set are as follows: Pulse width 30 usec = 3 miles Nominal range 150 miles Sweep sector 185° to 290° Elevation: center of antenna 387 ft From these data may be calculated the relative echo strengths of mountains at various distances and the relative side and back echoes. A reference value of 1.0 is taken for the main echo from a typical mountain 100 miles distant, and the relative intensity from Figure 40 is taken equal to 1.0. It is estimated that all echoes whose strength compared to the reference value is over 0.25 will be strong enough to obscure targets. Thus the back echo of a mountain 10 miles away in a diffraction region where the relative strength is 0.5 would have an echo value of (100/10)? X 0.5 X 0.04 = 2.0 and should be plotted since it exceeds 0.25. A table may be constructed for the main, side, and back lobes (M, S, B) for various distances and degrees of diffraction to show which echoes should be plotted. Table 3 is such a table, corresponding to a reference strength equal to 0.25. This table will apply only for the conditions of this example. 142 SITING AND COVERAGE OF GROUND RADARS SCALE 1:1,000,000 CONTOUR INTERVAL 1000 FEET Fieure 42. Topographical map for Example 8. TABLE 3. Prediction of permanent echoes.* Relative intensities from Figure 40. Distance inmiles 1.18 1.00 0.75 0.50 0.25 0.10 0.03 1 MSB MSB MSB MSB MSB MSB MSB 10 MSB MSB MSB MSB MSB MSB M 20 MSB MSB MSB MSB MSB M M 50 M M M M M M 100 M M M M M 200 M M : Bo *This table will apply only for the conditions of Example 8. In Figure 42 is shown a topographical map of the area. Contours are drawn for the first few thousand feet, and prominent peaks are indicated. From topo- graphical sheets of a 20-ft interval and a scale of 2 in. to the mile the profiles of Figures 43 and 44 are obtained. From the center of the antenna to the “effective” shielding, the line of sight has been drawn and the angle of the line of sight noted. In some cases, as at 20 degrees (Figure 43) a near sharp ridge is not PERMANENT DISTANCE IN FEET RANGE IN MILES Figure 43. Profiles for Example 8. 80 DEGREES aa CA Speen DISTANCE IN FEET RANGE IN MILES Ficure 44. Profiles for Example 8. considered an effective shield because of the large diffraction around such obstacles. The map is inspected between the azimuths used and the hori- zontal limit of shielding of a ridge noted. Thus the shielding ridge on 120 degrees (Figure 44) is found to drop off at 138 degrees. From the curves of Figures 38 and 39 are read the ranges for hy — hy = 1,000, 5,000, 10,000, and 15,000 ft for the line-of- sight angles at various azimuths. These points are plotted on Figure 42; they are connected by heavy dashed lines and are the coverage contours. In Figure 45 are plotted the predicted echoes. It will be noted that the shielding to the east is very good and most of the mountains are not visible. To ECHOES 143 the north the numerous mountains are unshielded and give rise to many echoes which extend into the search sector to the west. The islands are inherently bad and cannot be shielded without drastic loss of coverage. In some cases, as along azimuth 345°, ridges which cause large echoes shield more distant ridges. The broken terrain in this region is taken to give one large echo rather than a number of small echoes. In most cases the simple rules for plotting echoes may be applied directly. Where diffraction is involved the procedure should be more detailed. In Figure 43 azimuth 20° will be examined to determine the visibility of the hill at 4.65 miles. The following data are obtained from the profile. hy = 387 ft; d’, — d’, = 1.45 miles hy = 550 ft; d’ = 3.20 miles H = 425 ft; dy = 4.65 miles From equation (8): 4.65 X 550 — 3.20 X 387 | 4.65 X 3.20 A 4.65 = 3.20 a ar = OI itt From equation (10): 425 — 917.2 AY ga se Aq = 5,280 X 4.65 X 57.3 = ILLUS? . From Figure 40 the intensity is found to be 15 per cent. At the very short range of this hill a strong echo would be expected at this intensity, and all lobes would be plotted. At 138.5° azimuth and 160 miles is a 10,000-ft mountain (not shown in any figure). The data for this case are: hy = 887 ft; d/: — d's ho = 380 ft; d's 0.27 miles 160 miles approximately H 10,000 ft; dy 160 miles approximately h 160 X 380 — 160 X 387 A 160 X 160 = 0.27 2 = 16,950 ft. Oe Se ee SOS. 5,280 XK 160 From Figure 40 the relative intensity is 43 per cent. A main lobe echo is plotted on the second sweep at 10 miles since the first sweep is only 150 miles. In Figure 35 is shown a large echo at 110 miles from 175 to 242 degrees. This is received only when 144. O OS “HESS ws Pye Lig SEs: CD SITING AND COVERAGE OF GROUND RADARS Rs — = | — U = 50 and 51 ry, 2.46 iG 0 5,280 OY = 97" AE) W= 4h, n hy dy radians radians radians degrees radians 0 0 Ue | 0 —.01466 —.01466 —0°50'24’” 0 1 930 64.3 | .002645 —.01218 —.00954 —0°32/49”” .00082 2 1245 59.2 .003952 —.01121 —.00726 —0°25’ 0” -00164 3 1458 55.5 .005063 —.01051 —.00545 —0°18'44”’ .00246 4 1638 52.2 .006007 —.00989 —.00388 —0°13/20” 00328 5 1788 49.2 .006880 —.00932 — .00244 —0° 8/22” .00410 6 1910 46.7 .007730 —.00885 —.00112 —0° 3/52” .00492 a 2013 44.4 .008550 —.00841 +.00014 -+-0° 0/29” 00574 8 2108 42.4 .009335 —.00803 .00130 0° 4/28” .00656 9 2195 40.6 .01018 —.00769 .00249 0° 8'33” 00738 10 2246 38.8 .01095 —.00735 00360 0°12/22”” 00820 11 2308 37.2 01173 —.00705 .00468 0° 16’ 6” .00902 12 2359 35.8 .01251 —.00678 00573 0° 19/41” 00984 13 2408 34.4 01328 —.00651 00677 0° 23/16” .01066 14 2452 33.1 .01404 —.00627 00777 0°26/44”” .01148 15 2488 32.0 .01484 — .00606 .00878 0°30'10’” .01230 16 2525 30.8 .01558 —.00583 .00975 0°33/31”” 01312 17 2559 29.7 .01635 — .00562 01073 0°36/50” .01394 18 2588 28.7 01712 —.00544 .01168 0°40’ 8” .01476 19 2623 27.8 01782 — .00526 .01256 0°43/10” .01558 20 2638 26.9 .01866 —.00509 01357 0°46'40”” .01640 mull 2662 26.0 .01940 — .00492 .01448 0°49/48”” .01722 22 2685 25.1 .02030 —.00475 01555 0°53/26’” .01804 23 2702 24.4 02093 —.00462 .01631 0°56’ 4” .01860 These equations are plotted in Figure 50. From equation (63): = 4(hy’)? 512801492) X di’ 1-24 — | = —— = a [EN pa] | ere | IN (Iu!)? n = 0.000077 dy n 100 80 ——J EXAMPLE hy FEET i 500 200 DISTANCE dy, IN MILES Figure 51. Reflection area graph. Reading values of hy’ and d; from Figure 50 and sub- stituting in the above equations, curves of n and d; are plotted in Figure 51. From these two curves may be read the values of hy’ and d; corresponding to integral values of n. The calculation of y’ and 6 from equations (60) and (61) are conveniently per- formed by arranging columns as shown in Tables 6 and 7. For purposes of comparison with equation (62) the last column gives values of y computed by means of equation (57). In Table 6 the error in the figures computed from equation (57) is seen to be consider- ably below n = 10; for higher values of n the two formulas tend to show fair agreement. In Table 7 the disagreement is marked even at n = 23 indicat- ing that equation (57) is unsuitable for high sites. The lobe angles are shown in Figures 52 and 53. The lines of constant altitude over the modified earth are plotted from equation (49). The lobe angles are constructed by drawing radial lines from the center of the antenna, while the height in feet at a given distance is obtained by multiplying vy (in radians) by 5,280 times this distance in miles. The lines have not been drawn close in because of the crowding and because they actually start near 40000 20,000 ALTITUDE IN FEET 10000 SITING AND COVERAGE OF GROUND RADARS DEGREE 3 + 3 7 \\ ANG ANS AAA // ily / any a a aS — a DISTANGE IN MILES Ficure 52. Lobe angles for Example 11. the origin rather than at the center of the antenna. The error in the position of the center lines of the lobes near the antenna is a limitation on this method; but this occurs in a region which, because of gap filling, has no nulls and js therefore of little concern. Another difficulty is that the lower lobes are actually curved instead of straight; but as long as the site is not too high, say under 100 ft (100 me), the curva- - ture is small and unimportant. In general the method of equation (62) gives reasonably correct lobe angles for most high sites and with a moderate amount of computation. This is the first step in the preparation of the coverage diagram. Later sections will discuss construction of lobes about these center lines. 15.6.5 The General Lobe Angle Formula For very high sites (over 1,000 ft) and frequencies over 200 me, it is desirable to have a more accurate expression for the locus of constant path difference than is afforded by straight lines. This is of especial interest in the first few lobes as these determine the low coverage which is of great tactical importance. The method described here overcomes the limitations of equation (62) and may be used for the highest sites. In Figure 54 is shown the antenna above a curved reflecting surface whose radius is taken as 4 of the earth’s radius to allow for atmospheric refraction. The tangent plane CH makes an angle 6 with the horizontal at the antenna, and 6 is given by — (d,/ka) as shown in Figure 49. h, = height of the center of the antenna above the earth’s surface, in feet. hi’ = equivalent height of the antenna, in feet — equation (59). ra = distance from the antenna to the target, in miles. A = distance from the antenna to the reflection point, in miles. B = distance from the reflection point to the target, in miles. = path difference, A + B — ra, in miles. = wavelength, in feet. >Ce | THE hy = 3000 FT f = 100 MC LOBES NULLS —-— 40000 30000 20000 ALTITUDE IN FEET 10000 () —<———} ra ae ee ae ee = oe CALCULATION OF VERTICAL COVERAGE DISTANCE IN MILES Ficure 53. Lobe angles for Example 12. 6 = angle between the tangent plane CH and the horizontal at the antenna, in radians. This angle is always negative. ka = radius of the modified earth, 5,280 miles. Wa = angle between the direct ray ra and the horizontal plane CZ, in radians. W = angle between the reflected ray A or B and the horizontal plane CH, in radians. n = number of half-wavelengths path difference. In the triangle A Bra (cosine law) ra = V A? + B? + 2AB cos 2V . (64) From the definition of path difference: mr A= Aa B= a= sao (2) A+B —A = V/A? + B? + 2AB cos QW ; squaring and dropping terms that cancel out gives 2AB — 2AB cos 2V — 2BA = 2AA — A’, or solving with respect to B, AA — 342 = T= as) =A" (66) Substituting mr = TCR OED! into equation (66) gives mr A 1 ( ON ) 10,560 2 \10,560 B= : (67) mr A(1 = cos 2) = 10,560 Several approximations will be introduced to simplify equation (67): A will be taken to equal d; since W is of the order of 3° or less. From Figure 54 it follows that sinW = h,’/5,280A, or for small angles, YW = hi’//5,280A. Substituting for fy’ [equation (59)] it follows that ina Bae = RR Ce Using the approximation cos 2V = 1 — 2W’, SITING AND COVERAGE OF GROUND RADARS rd TO TARGET MODIFIED EARTH SURFACE Ficure 54. Reflection point geometry. and neglecting $(nA/10,560) compared to A, equa- tion (67) becomes TN dy 10,560 2d, y? = md 10,560 From the law of sines sn 2v sin(W+ WW.) — sin (W — W,) Py B a A 4 sin (VW + Wz) = Soi AY : Ta When W and Ware small V+, = ie 2V , a and Gt =Aon, Pa and hence by subtraction VW, = eal a | Ta Since W is a small quantity rz may be taken to equal A + B,and A = dh, that is _ B= th Me = Tae Gh : (70) This is the angle of the target with respect to the tangent plane CH as seen from the antenna. The angle desired however is y, which is measured with respect to the horizontal at the antenna, GH. As shown in Figure 54 y= Was 0. From equation (61) — dy ~ B30 - The line of minimum path difference (A = 0) is along the earth’s surface from the transmitter to the horizon, and beyond it is along the line of sight. tangential to the horizon since the direct and indirect waves are equal in that case. Maximum path differ- ence occurs directly below the antenna and is equal to 2h;. Since the path difference is also n\/2, the maximum value of n is 4h;/X. In practice the vertical directivity of the antenna limits n to a much smaller ) - value. Consider a wave which is reflected from directly under the antenna, and let ha denote the height above the reflector at which the path difference is nd/2. Then hy + ho — (hi — fo) = ug or y= (71) Thus if \ is 10 ft the center of the first lobe will be 2.5 ft high at zero range. For most purposes the lobes and nulls may therefore be considered to start at the origin. THE CALCULATION OF To use this method it is best to arrange the calcu- lations in a tabular form. Points along the lobe center are selected by using various values of d, for the value of n desired. Next WV is obtained from equation (68) and substituted in equation (69), and B and W are substituted in equation (70) yielding Va, which is combined with 6 to obtain y. The curve of constant path difference is then plotted from y and ra, which are now known. Haample 13. The General Lobe Angle Formula. To illustrate this method a radar 3,000 ft high and operating at 100 me will be used. A trial value of 60 miles is arbitrarily selected for d; and substituted in equation (68), giving _ 3,000 — = X (60)? He 9,280 X 60 = (0.003788 radian . In equation (69) using n = 1 and dX = 9.84 ft, 1 X 9.84 iosen B= Toe = 70.85 miles . 2 ; 8)? — ——___ X 60(0.003788) 10,560 70.85 — 60 ; Wa = 70.85 4 60 X 0.003788 = 0.000314 radian . 60 : a 5,280 = —(0.01136 radian . y = 0.000314 — 0.01136 = —0.01105 radian . ra = 60 + 70.85 = 130.85 miles . Laying out the angle y from the antenna and marking off the distance rag gives one point on the curve of constant path difference. Enough other Sal wn VERTICAL COVERAGE L5f points are computed to enable one to draw a smooth curve. The computations may be arranged as shown in Table 8. The values selected for d; should be small enough so that the denominator of equation (69) is positive. These two curves are plotted in Figure 55. For comparison is shown the first lobe as computed from equation (62), and it can be seen that this equation may lead to appreciable error in estimating low coverage. For most purposes it will suffice to calcu- late lobes higher than the first one or two by means of equation (62). 15.6.6 The Calculation of Lobes Three methods of computing lobe angles were given corresponding to low, medium, and high sites, in order to relate the labor of the computations to the complexity of the problem. A similar procedure will be followed in the calculation of the lobe shapes. The lobe diagram represents the locus of all points along a particular azimuth of a definite field intensity, usually the threshold of detection. If the site has horizontal symmetry throughout its sector of opera- tion one diagram will suffice. Usually several dia- grams are required, and it is common practice to prepare a diagram for the central azimuth of the sector and for 10 degrees inside of each limit of scan. 15.6.7 Low Site Lobes The electric field intensity at the target is the resultant of the direct and reflected waves which have the same amplitude and a phase angle which varies continually as the lobe angle y is increased. Tasue 8. General lobe angle formula. (Example 13.) di, WV, B, Wa, — 6, =%5 Td, miles radians miles radians radians radians miles (n = 1) 65 .002800 696.0 .0023220 .0123105 .00999 761.0 62 .003290 141.2 .0012810 .0117450 .01046 203.2 60 .003788 70.85 .0003140 .0113636 .01105 130.85 58 .004800 44.60 —.0005618 .0109850 .01155 102.60 55 .005118 26.32 —.0018050 .0104166 .01222 81.32 50 -006628 13.45 —.0038380 .0094698 01331 63.45 30 -016090 1.91 —.0141600 .0056820 .01984 31.91 (n = 2) 60 .003788 S55 ae .0113636 + . 58 .004300 386.0 .0031770 .0109850 .007808 440.0 56 .004840 137.5 .0020390 .0106060 .008567 193.5 55 -005118 101.0 .0015090 .0104166 .008908 156.0 53 -005700 62.6 .0004733 .0100381 .009565 115.6 50 .006628 36.78 —.0010115 .0094698 .010480 86.78 30 .016090 4.09 —.0122300 .0056820 .017910 34.09 156 30,000 20,000 ’ 10,000 ENTER OF ANTENNA ALTITUDE IN FEET — ——_—— es MODIFIED EARTH'S SURFACE (o} 20 40 60 80 APPROX LOBE BY EQ NO, 62 (n=1) SITING AND COVERAGE OF GROUND RADARS DEGREES NULL (n=2) —— 100 120 \40 160 180 DISTANCE IN MILES Figure 55. Lobe and null lines. (Example 13.) For a perfect reflector and horizontal polarization the phase lag is equal to +a + (2mr/\) X (nd/2) which adds up to nm + 7. Odd integral values of n give lobe maxima, and intermediate values give other points on the lobes. The sum of the two vectors practically parallel and of equal magnitude, H,/d, is _ 2F, TT i = Tt cos | (n + 1) 5. where H, is the electric intensity (microvolts per meter) in the equatorial plane 1 mile from the antenna in free space, that is, without a reflecting surface. H is the electric intensity at the point considered in microvolts per meter. d is the distance (72) to the point, in miles. n is a number related to the - angle of elevation. It is an odd integer for lobe maximums and an even integer for nulls. For a given antenna and radar the electric intensity H will produce at the input of the receiver a voltage, V2 = 21 in (00°n) , (73) where k; is a proportionality factor for the voltage applied to the receiver input. If V2 is set equal to the minimum operating voltage of the receiver equation (73) becomes d= Heald sin (90°n) . if V min The term k,#;/V.i, is usually obtained from test flights on the particular radar or on radars of the same type. The usual form is d = dpax sin (90°n) , (74) where day stands for kiE,/Vmin and is a measure of the performance of the radar set. The lobes will be polar sinusoids and the minima will go to zero only when the amplitude of the direct and indirect waves are equal. These conditions will not obtain if the vertical directivity of the antenna affects the rays unequally, if the reflected wave suffers imperfect reflection or divergence, or the atmosphere or terrain has unequal effects on the two waves. Low sites are generally free from the above effects and equation (74) may be used with acceptable accuracy. Example 14. Low Site Lobes. A radar operating on 200 me is 25 ft high and has a maximum range of 60 miles. The lobes occur at 2.82°, 8.46°, and 14.1° and the nulls at 0°, 5.64°, 11.28°. The method of plotting a lobe is shown in Figure 56. n may be divided into as many parts as desired, and the corresponding range for each obtained from equa- tion (74). Thus at » = 0.7 the angle is 0.7 X 4.92 4 X 25 d = 60 sin (90° X 0.7) = 53.46 miles. A line is drawn at this angle, and a point is marked off at a range of 53.46 miles. = (0.0344 radian , ALTITUDE IN FEET; THE CALCULATION OF VERTICAL COVERAGE a ae al AL all DEGREES > 1413 12 ll 1099 80 wm Uw Ors 50 5 32000 ————— y, 28000 a! 24000 /| ay, a te aa oe 16000 ye : fee FIRST LOBE 12000 8000 4000 (0) hy = 25 FEET f = 200 MC dwax = 60 MILES O 10 20 30 40 50 60 70 DISTANCE dq IN MILES Tiaurn 56. Low site lobes. (Example 14.) 158 68 Lobe Diagrams of Medium Height Sites In dealing with radars at medium heights, say from 100 to 1,000 ft, a more involved treatment is required, owing to earth curvature effects. The procedure followed in this section is to compute a value of dmax for each lobe from which a sinusoid is constructed at the angle of the lobe. The envelope of the lobes is considered to be of principal interest, the lobe shape being of secondary importance. The strength of a wave is measured in miles, that is, the distance at which the standard target must be to give a standard signal response such as a signal-to-noise ratio of one. The distances corres- ponding to the direct and reflected waves are added to get lobe maxima and subtracted to get minima. The direct and reflected waves will therefore be computed separately. The phase shift due to reflec- tion will be taken as 180°, and the phase shift due to other causes than path difference will be considered negligible. This assumption greatly simplifies caleu- lations and is a good approximation for small angles and horizontal polarization. For vertical polariza- tion, especially in the VHF band, it is a poor approximation. The direct wave is affected only by the modified antenna pattern. The reflected wave is affected by: 1. Shoreline diffraction. 2. The modified antenna pattern. 3. Earth curvature. 4. Coefficient of reflection. 5. Divergence. Terrain effects such as reflection areas of limited extent, the shoreline, cliff edges, and obstacles involve diffraction. A simple, flexible method for solving such problems will be developed in the next section. A, RADAR ANTENNA DIFFUSE REFLECTION SHORE LINE SITING AND COVERAGE OF GROUND RADARS TBs Shoreline Diffraction Unfortunately sites of sufficient height are frequently some distance inland, and a considerable portion of the reflection surface is on land. The poor reflecting qualities of land, especially when rough, causes the high angle lobes due to nearby reflection to be reduced as much as 50 per cent in length. This is a common cause of poor high coverage so often experienced in field installations and the inability to detect high-level bombing attacks except at perhaps 10-mile ranges. In this section will be developed a method of computing the vertical coverage pattern for the typical high site with part land and part sea reflecting surfaces. In most cases the profile of the land between the transmitter and the shore will be found to be too rough for coherent reflection, as may be determined from equation (16). If substantial regular areas or obstacles occur between the antenna and the shore line they should be treated as described in Section 15.6.12, on the modified antenna pattern. 15.6.10 Sea Reflection with Diffuse Land Reflection The problem treated in this section will be that shown in Figure 57. The land in the foreground is so rough as to cause only diffuse reflection, and no regular areas exist which will affect the vertical pattern below 15°. The diffuse reflection from the land area has a random phase relation, and the field intensity in a particular direction is relatively small. The effect of the land reflection on the interference pattern is FRESNEL ZONES FOR REGULAR REFLECTION SE, Figure 57. Fresnel zones on land and sea areas. THE CALCULATION OF VERTICAL COVERAGE 159 therefore neglected. This is equivalent to termination of the reflecting surface at the shore line. In order to describe diffraction at a shore line a system of Fresnel zones for each lobe is considered to be formed on the sea with the reflection point of the lobe as their center. The zones will be ellipses because of the inclination of the rays. The influence of the shore line will be determined by the number of zones which are not interfered with by the shore. Thus a low angle lobe which has its central Fresnel zone far out to sea would be virtually unaffected by the limited reflection area, as numerous zones are formed on the sea. This is indicated by A in Figure 57, which represents the reflected wave. At B, a higher angle lobe, there are only two zones intact, and the reflected wave is weak. Had only one zone _ been complete, the reflected wave would have been stronger than A. At C only portions of outer zones are formed on the sea, and the reflected wave is negligible. The effect of the reflecting surface may be repre- sented by an image antenna located in the earth under the radar antenna at a depth h, below the surface as in Figure 58. The nonreflecting land surface then acts precisely as a straight diffracting edge for the image antenna and indirect ray. A general formula will be developed which gives the situation of any Fresnel zone of any lobe for a given radar station. From this formula and the distance to the shoreline it may be determined for each lobe which zone is intercepted by the shore. In the graph in Figure 58 is plotted the relative intensity of the reflected ray as a function of m, the number of the zone touching the shore. In the illuminated region at large angles, as A, the relative intensity is close to unity. Approaching the shore it oscillates about unity, reaching a maximum of 1.18. In the shadow region, the intensity drops to low values. Thus, knowing m, the effect of shoreline diffraction on the reflected ray may be obtained. The derivation will be developed for a plane reflecting surface, since, as it has been shown in Section 15.6.4, for lobe angles corrected for standard earth curvature, the effect of earth curvature may be taken into account by using hy’ [equation (59)] instead of hy. In most cases a; will be small and fh; may be used with little error. IMAGE ANTENNA Figure 58. Shore line diffraction. 160 15.6.11 General Formula for the Reflection Area In Figure 59 is shown an image antenna 7” sending radiation through a plane of indefinite extent. In TO TARGET SEA SURFACE IMAGE ANTENNA Figure 59. Fresnel zones on the reflecting surface. order to simplify the calculations it will be assumed that the distance from the reflection point to the target is large, so that the rays from the Fresnel zones may be considered parallel. With regard to the transmitter distance, however, no such approxi- mation will be made. h, = depth of the image antenna below the reflecting surface, in feet. Ww = angle of the lobe considered with reference to the tangent plane at the reflection point, In radians. m = number of the Fresnel zone. m = 0 for the center of the first zone. +1 for the far edge of the first zone. —1 for the near edge of the first zone. m = m = m = and third zones. n = lobe number. For a given radar station n is related to the angle WY by the equation n = (4h,/X) sin WV. \ = wavelength in feet. d, = distance from the transmitter to the near edge for the Fresnel zone and lobe considered, in feet. d, = distance from the transmitter to the far edge for the Fresnel zone and lobe considered, in feet. d, = distance from the transmitter to the center of the first Fresnel zone for a particular lobe, in feet. +2 or —2 for the edge between the second . SITING AND COVERAGE OF GROUND RADARS In Figure 59 is shown the first Fresnel zone for an angle WY with a corresponding value of n. Ray 2 passes through the center of the first zone and rays 1 and 3 pass through the near and far edges respec- tively. Because of the great distance of the target the rays 1, 2, and 3 are parallel. For the first zone the path difference between 1 and 2 is \/2. For zone m the path difference is md/2 (where m = 1, 2, 3, etc.). Since the points d, and d, are not equidistant from the target, the distance x; cos YW must be subtracted from ray 2 to compensate for the increased path length of ray 1 above the plane. mr hy os ly (= V x1 COs v) : In the right triangle 9 9) 9G hi 2 l? = x sin?v + (= — 2x2, cosV). sin VY Eliminating i, from these equations and solving for 2 —m) cos WV + v/m2x2 + 4mxh; sin V 2 sin? V . (75) Uy, = For the far point of the zone mn hy = = 9 WV), 5 lo (= T + 2X2 COs ) ; also 5 ene hy ; lo? = Xo? sin? W + (= + 2 cos V sin VW By a similar process of elimination of l2 and solving for Xe: md cos © + V/m2r2 + 4m; sin V aa 2 sin? V (70) For the near point of the zone hy —md cos V + ~/m2d2 + 4mXhi sin V d, ~~ tanw 2 sin? Since sin VW = n\/4h, and W is small, cos YW may be taken as unity with the following error: up to 216° up to 10° up to 15° ee ( 1 i Gi) Vm? + mn Shi less than 0.1 per cent, less than 1.5 per cent, less than 4.5 per cent, 2n n? n? nN THE CALCULATION OF VERTICAL COVERAGE 16] For the far point | Vv ‘m2 —- mn\ 8hi2 l= he z : 4 (s i n° n> ) dh These equations may be combined: | ee (5 a where the plus sign gives the far point and the minus sign gives the near point. The reflection point is obtained by using m = 0 and equation (77) reduces to: m (77) cae (t) j= n- 1 Em) she 4h," dis = mr ¢ (78) Thus to obtain the range of the near edge of the first Fresnel zone for the first lobe, substitute n = 1, m = 1 and use the minus sign in equation (77): hy d, = 0.688 ae (79) The far edge of this zone is obtained by using the plus sign hy? dy = 23.3 TE (80) Equation (77) is in the form oat hy @d = 0 Te! (81) where T= ( 1 a a i Vm + mn) (82) 2n n n> or mes T= he (83) Tf d, is taken as the distance of the shoreline, 7; may be considered as a characteristic site or terrain factor at a particular azimuth and combined with the height and wavelength to obtain the range of any zone of any lobe. In order to read the relative intensity and phase lag of the reflected wave from the diffraction graphs, Figure 27 and Figure 28 respectively, it is necessary to have m expressed in terms of v. In Figure 19 the path difference is by definition of m (84) Equation (238), with A = d — b, yields dv Ae 7 8 hence m (85) wl It is also desirable to have an expression for v in terms of n and 7’. This is obtained by substituting v?/2 for m in equation (82) and solving ze. ['n? 2 ge Bar = —— (86) The width of the zones, that is, along a chord at d, parallel to the minor axis of the elliptical rings, Ficure 60. Width of Fresnel zones. may be obtained from Figure 60. Zone m is shown with a chord length b. The distance from the image antenna to the intersection of the chord and ring m is 1 + md/2. From this may be written 9 (+3) =r+(5). Neglecting m?d?/4 other terms, (87) since it is small compared to the 6). 122 + mr b = V/4mn , _ Og Us 7 @sw 9° P” from equation (78), since W is small. Where earth curvature effects are appreciable the 162 effective height, from equation (59), should be used. b = 4hy/ le. n To apply this method the distance of the shore- line, d,, is substituted in equation (81), and the equation is solved for 7;, the terrain factor. This quantity is a constant for a particular azimuth and is substituted in equation (86) along with the values of n desired and solved for v. The values of m corre- sponding to these values of v are the numbers of the zones which intersect the shoreline for each value of n. These values of v are entered in Figures 27 and 28 to obtain the intensity and phase lag relative to that which would be obtained if the rough land were replaced by the sea. Example 15. Shoreline Diffraction. A radar station is assumed to have the same height and frequency as In Example 11. The shoreline distance is 3 miles, and the intervening land is occupied by a large city. hi = 500 ft; f = 200 me; d; = 15,840 ft. At this distance the effect of earth curvature is less than 1 per cent and may be neglected. The greatest angle at which waves are reflected from the sea is given by 500 Bears 2B 15,840 K B13 = Wg In equation (16) the maximum height of roughness for regular reflection is 3,520 200 X 1.81 (88) jal = = OL7 mt - The land is evidently a diffuse reflector. From equation (83) _ a Die (hy’)? Substituting in equation (86) for n = 2 _ 15,840 x 4.92 (500 — 4.5)? = 0.317. 0.317 X 4 2, = =— 9 a 8 AS° (ig = lb vy m= i es PD That is, somewhat more than two zones are com- pletely formed on the sea. In order to determine which sign to use in reading Figure 27 it is only necessary to know whether the main reflection point d, for this lobe falls on the land or the sea corre- sponding to shadow or illuminated regions. A more general procedure is to solve equation (63) using the shoreline distance for d, : SITING AND COVERAGE OF GROUND RADARS 4 X (500 — 4.5)? ~ 15,840 X 4.92 For all values of n less than 12.6, d, will be on the sea and equation (84) applies to the near edge, and the minus sign is used in equation (82) corresponding to +v in Figure 27. For n greater than 12.6 the plus sign is used in equation (82) and —v in Figure 27. Thus, for n = 2 and v = +2.11, is read in Figure 27 the relative intensity z = 0.980 and in Figure 28 the phase lag, ¢ = —0.103 radians. Other values are listed in Table 9. The width of the second zone may be computed from equation (88). The effective height for n = 2 is obtained from Figures 50 and 51 and is 414 ft. 2 b= 4x aus)? = 1,656 ft . = 12.6. TaBLE 9. Shoreline diffraction. (Example 15.) n v Sign 2 & n v Sign z G 0 2.51 + 1.036 +0.080 |) 12 0.14 + 0.582 —0.130 1 2.31 + 1.083 —0.015 ||13 0.089 — 0.459 +0.2 2 2.11 + 0.980 —0.103 14 0.28 — 0.3877 +0.5 3 1.91 + 0.884 —0.038 15 0.49 — 0.308 +0.9 4 1.71 + 0.938 +0.100 16 0.68 — 0.261 +1.4 5 1.51 + 1.082 40.120 17 0.87 — 0.228 +1.9 6 1.32 + 1.170 +0.030 18 1.08 — 0.192 +2.6 7 112 + 1.156 —0.085 |} 19 1.27 — 0.170 +3.3 8 0.92 + 1.073 —0.181 20 1.48 — 0.150 +4.2 9 0.72 + 0.953 —0.255 |} 21 1.67 — 0.185 +5.2 10 0.52 + 0.825 —0.273 || 22 1.88 — 0.121 +6.4 11 0.32 + 0.696 —0.224 || 23 2.07 — 0.111 +7.6 15.6.12 The Modified Antenna Pattern The vertical directivity of the antenna is modified by the local terrain. Unless the ground under the antenna is an extension of the reflection plane the modification of the free space directivity character- istics should be taken into consideration in the calculation of radar coverage. The vertical pattern of the antenna in the absence of a reflecting surface is referred to as the free space pattern, f4. This is usually given in the instruction manual for the set. If this pattern is not available or if the antenna has been modified, the vertical directivity may be computed by methods given in the next section. Local terrain effects are treated in some detail as they are in many cases a controlling factor. The resultant effect of the local terrain and free space pattern is called the modified antenna pattern, f(y). It does not include the effect of the main reflecting surface. THE 15.6.13 Antenna Patterns To obtain f,, the relative amplitude of the radia- tion from the antenna, as a function of the vertical angle y it is only necessary to take into account the path differences of the elements of the array. The absolute field intensity and time phase will not be considered. In Figure 61 is shown an array of four EY ne lr | role ate ( eS Ficure 61. The four-element array. horizontal half-wave dipoles spaced a half wavelength apart. The radiation from A in the direction y may be taken as proportional to cos wt. The path differ- ence of radiation from B is \/2-sin y. The corre- sponding phase difference is 2a ; : = Se ON GS oy = —-Tsny. For C and D the phase is —2z7 sin y and —3z sin y respectively. The total field intensity pattern is fa = cos wt + cos (wt — 7 sin y) + cos (wf — 2r sin y) + cos (wt — 3m sin y) , grouping [cos wt + cos (wt — 3m sin y)] + [cos (wf — m sin 7) + cos (wt — 2m sin y)] . (89) From the identity cos A + cos B = 2cos3 (A + B) cos} (A — B) equation (89) may be written f4 = 2 cos (ot — 3 sin ) cos (F sin v) 2 Dy Om D Upto + 2 cos (wt — = sin y) cos(=sin y ) , 2 2 fa = 2.05 (wt — 3 sin y) - Ee sin v) -- COs - G sin 7) | , CALCULATION OF VERTICAL COVERAGE 163 . on. : fT, = 4 cos (0 — a sin v) cos (7 sin y) - s(x si cos {5 sin y } . Since only the rms value of this equation is signifi- cant, the terms containing wl may be dropped, and the result for the four-element array is . Tw . fa = cos (7 sin y) cos G sin v) ; (90) It is easily verified that this is a special case of the general expression for an N element array spaced at intervals of nd and excited in phase (not derived here) sin (Nn zw sin y) N sin (nz sin y) © fa (91) The effect of a reflecting screen may be computed by treating it as though it were \/4 from the dipole as in Figure 62. In practice the spacing may be DIPOLE Figure 62. The reflecting screen. more nearly \/8 but for 7 less than 30° the method given here is satisfactory and avoids a complicated analysis. The path difference QR is (A/2) cos y, and the phase difference is 7 cos y. Then fa = cos wt — cos (wt — m cos y) . From the relation cos A — cos B = —2sin34 (A + B) sin (A — B), it follows that equation (92) may be written in the form fa = — 2sin (0 — 5 008 Y) sin (§ cos v) ! (92) Dealing only with the rms value, jig = sin (J cosy ). For small angles this factor is usually unimportant. Factors are given in Table 10 for some typical arrays with horizontal radiators in a vertical column and a reflector screen. (93) 164 TABLE 10. SITING AND COVERAGE OF GROUND RADARS Antenna pattern factors. Array with screen Vertical pattern f4 c r Two radiators spaced 5 m ‘ r Four radiators spaced ) Two sets of four radiators each (Vertical spacing between centers of sets is 32.) eS) To : cos ( sin v) sin € cos 7) cos ( sin v) cos (x sin Y) sin (; cos 7) cos ( sin v) cos (7 sin Y) X N/A \ cos (37 sin Y) sin ( cos i) Example 16. Vertical Pattern of an Antenna. Using the eight element array in Table 10, the relative intensity at angle of 5° from the horizontal is com- puted as follows. fa = cos (90 sin 5°) cos (180 sin 5°) cos (540 sin 5°) sin (90 cos 5°), = cos 7°51’ X cos 15°41’ X cos 47°4’ X sin 89°39’, = 0.9906 X 0.9628 X 0.6809 x 0.9999, = 0.65. The main vertical lobe is plotted in Figure 63. The first null is at 9°36’ and the half-power beam width 1.0 a HORIZONTAL } RADIATORS 0.8 = rs = SCREEN~ Zz 06 = Ie WJ = = Ww 0.4 & a x 0.2 TT | COS(Z SIN §)COS(7SINd) COS(37SIN 4) SIN (Z COS 3) fo) 4 —_1___£1 1 2 3 4 5 6 7 8 9 VERTICAL ANGLE IN DEGREES Ficure 63. Vertical pattern of a typical antenna. (Ex- ample 16.) is 4.53°. It will be noted that the effect of the reflector screen may be neglected for small angles. The pattern from a parabola is closely dependent on the feed system which controls the uniformity of illumination. To reduce side lobes it is common practice to taper the illumination toward the edge of the dish. This is accompanied by a broadening of the beam and a loss of gain. The half-power beam width for uniform illumination is 59\/D degrees, where D is the diameter of the aperture. The first side lobe is then about 2 per cent of the maximum. A typical dish with a tapered feed would have a half-power band width of 68.8\/D degrees. This reduces the first side lobe to 0.5 per cent. Some designs are further modified by deforming the dish, off-center feeds, etc., so that the patterns may not be easily computed. Such patterns are best obtained experimentally and are usually given in the manual for the equipment. Moots Local Terrain Effects The vertical pattern of the antenna may be modi- fied by reflection from local flat areas or by diffraction over hills or other obstacles. To take these effects into account, factors are computed from the diffrac- tion equations which are used to modify the direct and reflected ray patterns. A detailed method of calculating f(y) cannot be given because of the great variety of sites encoun- tered. However, the following discussion of the effects of particular terrain features will suggest ' methods of combining them to analyze a particular site. A large, flat land area will in general produce lobes and nulls at angles given by equation (57) with an envelope twice as large as the free space pattern. If the land area is not level, the lobe pattern will be tilted by the angle of the land. However, the problem is essentially a matter of diffraction since the land is of limited extent. Equation (16) should be used to determine whether the area is sufficiently flat to act as a regular reflector. If the land is flat from the antenna out to a distance d, the relative intensity of the reflected ray is 144 when d; = hi X cot y. This assumes the land beyond d; to be nonreflecting and that the distant THE CALCULATION OF VERTICAL COVERAGE 165 boundary acts as a diffracting edge. As d; increases further, the relative intensity increases to about 1.18 and then decreases again and oscillates about unity in gradually decreasing swings. This is accompanied by a variation of phase. Several typical terrain problems will be solved in detail to illustrate the methods. Example 17. Limited Reflecting Area. A 200-me radar, Figure 64, with an antenna as described in h=SO FEET t= 200 MC LAND REFLECTING FROM 600TO 3000 FEET f 400F ANTENNA y 200 HEIGHT hy IN FEET IMAGEts REFLECTING |= ROUGH LAND SURFACE DIFFUSE REFLECTOR ) 4000 8000 12000 DISTANCE dy IN FEET Fieure 64. Lobes from a limited reflecting area. Example 16, is 50 ft above a smooth reflecting surface (a lake) which extends from 600 to 3,000 ft. From 0 to 600 ft and from 3,000 ft on is rough land. The shore line diffraction method will be used to deter- mine the effect of the reflection from the limited area upon the antenna pattern f,. The vertical pattern is plotted from Figure 63 and shown dotted. To obtain the pattern for the reflected wave the shore at 600 ft is taken as a diffracting edge, and the relative intensity computed as a function of y as though the surface from 600 ft on were a perfect reflector. This is then repeated using the shore at 3,000 ft. The difference between these two functions is then the effect of the area between 600 and 3,000 ft. From equation (83) for n = 1 600 x 4.92 ‘ Heh SiC i eee etal iJ 2 Ty a? X 1-1 + 7og = 0918 ; From equation (78) BAGO 555. % p) ~ 600 X 4.92 N3.000 = 0.678 . 600 From Figure 27, using the plus sign for doo and the minus sign for Vs 999, is obtained the relative intensity 200 = 1.073; 23.99) = 0. The reflection factor for n = 1 is given by z= 1.073 — 0.375 = 0.698. Irom equation (57) 1 X 4.92 a Al®. 4 X 5U ; y= = 0.0246 radian = Other values are given in Table 11. Tasie 11. Limited reflecting area. (Example 17.) i L(Y) 0.693 0.658 0.973 1.147 1.314 1.650 1.137 0.314 23,000 z fr 0.870 0.307 0.693 0.810 0.371 0.658 0.645 0.519 0.973 0.592 0.561 1.147 0.544 0.598 1.314 0.375 0.698 1.700 0.257 0.703 1.223 0.186 0.652 0.349 0.116 0.476 1.475 1.090 0.082 0.311 0.689 0.386 0.067 0.210 1.210 0.436 2600 1.177 1.181 1.164 1.153 1.142 1.073 0.960 0.838 0.592 0.393 0.277 V600 +1.30 +1.26 +1.15 +1.11 +1.071 +0.918 +0.727 +0.535 +0.155 —0.237 —0.619 03,000 +0.583 +0.498 +0.241 +0.155 +0.077 —0.279 —0.707 —1.136 —1.995 — 2.853 —3.710 0.14 0.56 0.70 0.85 1.41 2.11 2.82 4.23 5.64 7.05 The values of z multiplied by fs from Figure 63 are plotted in Figure 65 as the reflected pattern. The DIRECT PATTERN- f, _— ~ to) 0.2 0.4 1.0 RELATIVE 0.6 0.8 INTENSITY FicurE 65. Components of the modified antenna for a limited reflecting area. resultant of the two vectors, f, and 2/4, in terms of n is given by the cosine law: fro = V1 + 2 — 22 cos (nm) . Thus for n = 0.1 fr = V1 + (0.371)? — 2 X 0.371 cos (0.17) = 0.658 (94) 166 The product of f7 and f, is the modified antenna fac- tor f(y). This is plotted in Figure 64. With a larger reflecting surface, the length of lobes would approach twice the value of f,. Figures 64 and 65 were drawn for purposes of illustration and would not ordinarily ' be required. Example 18. Cliff Edge Diffraction. A 200-mce radar, Figure 66, with an antenna as described in Example h, =50 FEET CLIFF EDGE = 3000 FEET f= 200 MG £ (8) =zF, aS wu MODIFIED ANTENNA FE aa PATTERN FOR SEA z LOBES e _ 200 25 © z #0 fa FREE SPACE ROUGH PATTERN OF LAND b>" ANTENNA SURFACE OF SEA () 4000 DISTANCE d, 8000 IN FEET 12,000 Ficure 66. Cliff edge diffraction. (Example 18.) 16, is 50 ft above a rough land surface, the top of a cliff whose edge is 3,000 ft away. The geometrical shadow line makes an angle with the horizontal of At this angle, the relative intensity, z = 0.5. Other values of z may be read from Figure 27 after con- verting the angle of diffraction to v by means of equation (47). 64° 4.92 ny 2x 3,000 ~°"* At 0.377° in the shadow region »v = —0.377 X 0.61 = —0.23. From Figure 27, z is 0.4. This angle, referred to the horizontal at the antenna, is y = ® — 0.955 = —1.332°. Some other values are: = 0.61 62° . 7° Zz +3.5385 0.917 +1.060 1.18 —0.955 0.50 —8.335 0.05 SITING AND COVERAGE OF GROUND RADARS The modified antenna pattern f(y) is the product of z and f, and is plotted in Figure 66. This pattern gives the factors for both the direct and reflected waves for the sea lobes. Example 19. Land Reflection and Diffraction. This site is similar to that of Example 18 except that the cliff top is smooth. This is shown in Figure 67. y ANTENNA f=200 MC SMOOTH LAND 50 FT a 600 FT 3000 FT 550 FT 5000 FT Ficure 67. Land reflection and diffraction. (Example 19.) The smooth land causes land lobes to be formed as In Example 17 which furnish high angle coverage. The sea lobes are computed using the method of Example 18 for the direct and reflected rays. If the cliff top were tilted down, the land lobes would be tilted by the angle of the land. Speculation about complex sites yields many unusual patterns, but in practice the results are usually disappointing. Com- plex sites seldom have horizontal symmetry, and gaps in the coverage pattern may be expected. Attempts to reinforce the pattern in a particular direction by siting back from the cliff edge generally ~ cause poor coverage at other angles. Best all-round CHL operation results from siting on cliff edges and exclusive use of the sea as a reflector. TEO.16 Earth Curvature Effect on Lobe Lengths The effect of earth curvature on lobe angles was described in Section 15.6.4. The angles to be used with the modified antenna pattern of the image antenna are affected by earth curvature, and there- fore the strength of the reflected wave is also affected. In Figure 68 is shown a radar antenna at height hy above the earth’s surface, with the center line of the antenna pattern parallel to GH, the horizontal at THE +(B) B Cy a ae) CALCULATION OF VERTICAL COVERAGE 167 DIRECT RAY CENTER LINE OF ANTENNA PATTERN H G SS y y-20 / hy my roe REFLECTED Go TO TARGET / y-290 RAY tyv-e-) [2-— H Cc aie ——————— ct E 5 = 5 rea ee ye D x h, : a5 4 CENTER LINE OF G ANTENNA PATTERN 1 ———~ T/ IMAGE f (0) Ficure 68. Earth curvature effect on direct and image patterns. Note: GH horizontal at the antenna; CH horizontal at : : dy the reflection point 9 = ke the base of the antenna. Because of diffraction at a cliff edge the modified antenna pattern f(y) is unsym- metrical as in Example 18. The lines GH are parallel to the horizontal at the antenna. The line CH is horizontal at the reflection point and makes an angle 6 with GH. The target is at an angle y with respect to GH. The incident and reflected rays make the angle y — 6 with CEH. It will be noted that the direct ray makes the angle y ~ 6 with the centerline of the antenna pattern, and the reflected ray makes the angle y — 26. mo-6i16 Coefficient of Reflection The coefficient of reflection of the reflecting surface is in general complex. That is, both the magnitude and phase of the reflected wave are affected. The reflection coefficient varies with the conductivity and dielectric constant of the reflector and with the frequency, polarization, and angle of incidence. Careful consideration should be given to the rough- ness of the surface, and a substantial reduction in the coefficient should be made when the height of roughness is comparable to that computed from equation (16). In general the reflection obtained with microwaves is of minor importance. The magnitude and phase angle of the reflection coefficient are plotted as functions of the angle of reflection, VW in Figures 69 and 70. Curves are given for horizontal and vertical polarization and for the extreme conditions of sea water and dry soil. For dry soil the reflection coefficient is not sensitive to frequency changes, and the 100-mc curve may also be used for 3,000 me. For most purposes the reflection coefficient for horizontal polarization may be taken as unity, and the phase angle as 180°. The use of these values simplifies computations. The coefficients of reflection and phase angle for vertical polarization vary rapidly with frequency and angle of reflection for sea water and more gradually for dry land. The minimum point of the curves in Figure 69 is known as the pseudo-Brewster angle corresponding to a similar angle in optics. Cases not covered by Figures 69 and 70 may be computed from the following equations. Vertical Polarization: e, sin V — v/ ¢, — cos? V exp (=) = => OO BexDui2) e,sinW + +/e, — cos? V ) Horizontal Polarization: , .— cos? ¥ — sin’ pexp (—jd) = Ve (96) ~ 4/e, — cos? ¥ + sinv’ 168 SITING AND COVERAGE OF GROUND RADARS YW IN DEGREES (0) 2 4 6 8 10 12 8 2 — IHP- 3000 MC Fe z Ww — S ie = Ww fo) oO ia - ° VP a MG = oO Ww 2} wu i VP-3000 MG Q o=1 MHO/METER ——— DRY SOIL €-=10 o=0.002 MHO/METER (0) 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 W ANGLE OF REFLECTION IN RADIANS Fraure® 69. Reflecting coefficient curves. ae IN ee VP—3000MG VP—I00 MC SEA WATER \ ee SOIL 120 \ IN Goe G] ———!e E- =10 O = 1 MHO/METER \o @ = 0.002 MHO/METER @ DEGREES (LAG) 80 VP-100 MC 40 al Oo yo (0) 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 Vz ANGLE OF REFLECTION IN RADIANS Figure 70. Phase of reflection coefficient curves. Note: Solid curve represents seawater. Dotted curve represents dry soil. THE CALCULATION OF where YW = Ec €; r wo) Some VERTICAL COVERAGE 169 IN BS ess] Nea iss Naa a EAS Rei! SES PAG Ne (a i Ly 0.3 0.4 FiaurE 71. Divergence factor graph. the angle of reflection measured from the horizontal ; = €, — J60oA; dielectric constant of the reflector rela- - tive to air; = conductivity of the reflector, mhos per meter; wavelength, in meters; I I| phase angle, lagging. typical ground constants are given in Table 12. TasLeE 12. Terrain reflection characteristics. Type of terrain & o, mhos per meter Fresh water 81 10-3 Sea water 81 1 Rich soil 20 3 >< 10 Heavy clay 13 4 < 107° Rocky soil 14 2 S< Ore Sandy dry soil 10 2x 10° City—industrial area 5 10-3 170 ap Divergence The reflected wave is scattered somewhat by being reflected from the spherical surface of the earth instead of a plane surface, and this reduction of field strength is taken into account by the divergence factor. This is dependent on geometrical considera- tions and may be ag as follows (for y’ < 3°): nr : aa: ee CoE where nis the lobe number, is the wavelength, in feet, y’ is the reflection angle, in radians, obtained from equation 60. A convenient chart for obtaining D is given in Figure 71. The parameters are y’ in radians and nd, with \ expressed in feet. As y’ approaches zero, n also approaches zero, and the equation is indeterminate. At the point of tan- gency of the line of sight and the earth, D is 0.5773. At low angles the field is modified by diffraction around the curved earth. The lower limit of the angle y’ for which the optical treatment is valid is usually given by (97) y' > os rae 0.00382 W/r , where k is (98) 4, and 2D is in feet. For angles below this limit the theory for diffrac- tion of radio waves around the earth is required for a rigorous solution. However, in practice it is found that angles as low as the first maximum (n = 1) may be treated by the ray theory with little error. Applying equation (98) to Example 11 y' > 0.00382 /4.92 = 0.0065 radian. In Table 6 this corresponds to n = 2.25. However using n = 1 and y’ = 0.0036 the divergence factor D is found from Figure 71 to be 0.58. For angles below y’ = 0.0036 it is necessary to estimate D. Experience indicates that a fair minimum value to select for D is 0.5773. For angles much below the first maximum, the optical treatment gives values of field strength which are too low because it neglects diffraction. This may be compensated in part by using values of D between 0.5773 and 1.0. 15.6.18 Lobe Lengths The contributions of the direct and reflected waves may now be added to obtain the length of the lobes. SITING AND COVERAGE OF GROUND RADARS L = (fly) £ fly — 26) zpD]do (99) where Z is the distance to the end of the lobes or the nulls, in miles. dy is the maximum range (in miles) at which a given response (usually the mini- mum detectable signal) would be obtained if the antenna were in free space. If the lobe diagram were plotted for some signal level above the minimum detectable, d) and L would be correspondingly smaller. Example 20. Lobes for a Medium Height Radar. A 200-me radar using horizontal polarization has an antenna composed of two groups of dipoles spaced ~ three wavelengths between centers, each group having four dipoles spaced \/2, as in Example 16. The antenna is 500 ft high and 3 miles inland as in Examples 11 and 15. It is desired to compute the vertical coverage pattern. From previous tests on this type of equipment it is known that the maximum range that would be obtained in free space dy is 80 miles. Since the polarization is horizontal, p will be taken as unity. Precision is not required for most of this kind of work, and it will suffice to compute values for equa- tion (99) at each integral value of n and to consider the values for odd n’s (with the plus sign) as the average of the lobe. The lobe shape will be taken as sinusoidal and the range at the nulls obtained by using even values of n and the minus sign; f(y) and f(y — 26) are obtained from Figure 63, by using values of y and y — 2@ from Example 11 corres- ponding to integral values of n. The values of z are obtained from Example 15. The computations are shown in Table 13. Had cliff edge diffraction been involved f(y) and f(y — 26) would be read from curves as in Example 18 with marked effects on the pattern. The lobes are plotted in Figure 46 using equation (74) and the value of L for odd numbered n’s. For intermediate values of n the factors are: Fractional value of n sin (90° n) 0.33 0.500 0.50 0.707 0.70 0.891 Using these three points above and below the lobe line and the maximum and minimum values from Table 13 the lobes may be plotted quickly as explained in Example 14. THE ) Tape 13. Lobes for a medium-height radar. (xample 20. ) , Bone i= 2) ANG) ae 2) Pe aD fC — 20)peD | 0 0.999 0.999 1.036 0.577 —0.597 0.402 32.2 1 1.000 0.998 1.083 0.580 -++-0.627 1.627 130.2 2 0.999 0.997 0.980 0.735 —0.718 0.281 22.5 3 0.999 0.994 0.884 0.823 +0.723 1.722 137.8 4 0.997 0.992 0.988 0.890 —0.828 0.169 13.5 5 0.992 0.989 1.082 0.912 -++0.976 1.968 157.4 6 0.989 0.987 1.170 0.933 —1.077 0.088 7.0 7 0.985 0.981 1.156 0.942 -+1.068 2.053 164.3 8 0.980 0.978 1.073 0.959 —1.006 0.026 2.1 9 0.975 0.972 0.953 0.963 -++0.892 1.867 149.4 10 0.970 0.967 0.825 0.968 —0.772 0.198 15.8 11 0.963 0.961 0.696 0.973 -+0.651 1.614 129.1 12 0.958 0.952 0.582 0.979 —0.542 0.416 33.3 13 0.950 0.947 0.459 0.981 -+0.426 1.376 110.0 14 0.941 0.939 0.377 0.984 —0.348 0.593 47.4 15 0.932 0.929 0.308 0.987 -+0.282 1.214 97.2 16 0.923 0.920 0.261 0.989 —0.237 0.686 54.9 17 0.913 0.910 0.223 0.991 -++0.201 1.114 89.1 18 0.903 0.900 0.192 0.992 —0.171 0.732 58.6 19 0.893 0.890 0.170 0.992 --0.150 1.043 83.5 20 0.881 0.879 0.150 0.992 —0.131 0.750 60.0 21 0.871 0.869 0.135 0.992 -+0.116 0.987 79.0 22 0.857 0.853 0.121 0.992 —0.102 0.755 60.4 23 0.844 0.841 0.111 0.992 + 0.093 0.937 75.0 15.6.19 The General Lobe Formula The assumption of a sinusoidal lobe shape and the neglect of the phase of reflection and diffraction in the preceding section may in some cases lead to considerable error, especially when the direct and reflected waves are very different in strength. In general a more accurate method is required for sites over 1,000 ft in height, where vertical polarization is used or where it is desired to know the lobe shape in detail. The method given in this section provides a general solution of the coverage problem in the optical region (except along the bottom of the ' first lobe). ’ The development of the lobe formula will be reviewed, and equation (99) will be given in a some- what different form. The expression for the electric vector due to the direct wave is E, = 2 iG) exp (- j2 rt) =: (100) For the reflected wave H, = FA iy — 26) Rexp (- jaa ‘) , (101) Ez = electric field intensity at the target due to the direct wave, microvolts per meter; where CALCULATION OF VERTICAL COVERAGE 171 E, = electric field intensity at the target due to the reflected wave, microvolts per meter; FE, = electric field intensity at 1 mile in the equatorial plane of the antenna, microvolts per meter; f(y) = modified antenna factor for the direct wave (Section 15.6.12) ; f(y — 26) = modified antenna factor for the reflected wave (Section 15.6.15); R =a complex factor for the reflected wave given by R = Dpz {exp[—j@+ Ol} ; —(102) where D = divergence factor (Section 15.6.17); p exp (—7%) = complex reflection factor (Section 15.6.16); z exp (—j¢) = complex diffraction factor (Section 15.6.11). The net field at the target is Ey, — Ea a Ee ) Al Ey Bip | = ar |G) ae sae — 2G) Dpz{exp[—j@+s + d)]}|, (203) considering only the absolute value of #7 and taking ra = d except where the path difference is involved. The path difference phase shift is r= i= = (r — Ya) . (104) Equation (103) may for convenience be written | Hp | == A. (105) The target 1s assumed to have a complicated form and to be changing its aspect constantly. The reflected energy is considered to be of random phase and magnitude. The magnitude of the reradiated field (microvolts per meter at a distance of 1 mile from the target) is found by using a coefficient of reradiation, pr, which varies with the target and aspect. The received field intensity is by the reciprocity theorem: E |E|= Pel A (106) Substituting from equation (105) _ br By ye | B | bat a2 A’. 172 SITING AND COVERAGE OF GROUND RADARS For a particular coverage contour, such as the threshold of detection, usually taken as a signal-to- noise ratio of unity, a minimum received field inten- sity | Hy | may be assumed. This is related to receiver noise voltages, antenna gain, and other factors of design. Using | £,,| for | # | and solving for d d= fea = dA . N Because of the way in which £, and p,- are defined, do, the maximum free space range, has the dimen- sions of length (in miles). It depends on the design of the transmitter and receiver and on the target. A may be considered a coverage factor which depends on y and terrain effects. Because of the implicit character of the parameters of A in equation (103), a general solution of A as a function of y is not feasible. However, examination of typical problems discloses that the range of varia- tion of some of the factors is limited, and a method of successive approximations may be = applied. (107) 200 160 In most cases ¢ and ¢ will vary slowly (about % as fast) compared to 6 below 2° or 3°. At higher angles the rate of change may be faster, but contribution of the reflected wave at these angles is likely to be unimportant. The method described here consists in computing the lobe angles, diffraction, and divergence as though the only phase shift involved was that due to path difference as in Sections 15.6.4, 15.6.11 and 15.6.17. The phase shifts from the apparent lobe angles thus computed are then determined. The diffraction phase shift is ¢, and the reflection phase shift is ¢’ = ¢ — 180°, (108) where ¢ is obtained from Figure 70. If horizontal polarization is used ¢ may be taken as 180°, and ¢’ is then zero. With curves of the phase shift ¢’ + ¢ and the product f(y — 26)Dpz plotted against y the apparent lobe angles and lengths computed above may be corrected to obtain the actual values. The details of this method will be aa in the rT below. 40 PHASE LAG IN DEGREES RELATIVE STRENGTH OF REFLECTED RAY ZIN RADIANS Ficure 72. Relative magnitude and phase of the reflected ray. THE CALCULATION OF VERTICAL COVERAGE is Example 21. The General Lobe Formula, An inter- rogator equipment is used with the radar of Example 20. It operates on 160 me; the height of the antenna above the sea is 500 ft; and the distance to the shore is 15,840 ft. The intervening land is too rough for coherent reflection. The antenna consists of two vertical radiating elements and parasitic reflectors. The radiators are approximately a half wavelength long and spaced a half wavelength apart. The maxi- mum distance at which reliable interrogation may be obtained in the absence of a reflecting surface has been found to be 110 miles for this particular equipment. It is desired to construct for this site the vertical coverage diagram of the interrogator system. The vertical pattern of a vertical half-wave dipole is given by 2 cos { = sin iE 7) cos y WA = Since this factor is over 0.98 for angles up to 10 degrees, f(y) and f(y — 26) will be taken as unity. The lobe angles are then computed neglecting ¢ and ¢, as in Example 11. Diffraction and divergence are computed as in Example 15 and Section 15.6.17. The results of these calculations are listed in Table 14. The values of p and ¢ depend on 7’ and are read from Figures 69 and 70. Using equation (108), %’ is obtained and added to ¢. The sum ¢’ + ¢ is the net phase shift of the reflected wave from the values used in computing the lobe angles and is plotted against y in Figure 72. For purposes of comparison 6 has also been plotted, but this curve is not required otherwise. The product Dpz is the relative strength of the reflected ray and is plotted in Figure 72. The points on the coverage diagram are obtained in polar form from equation (107). d = 1101/0 => (pz)? = 2Dp2 cos (¢’ == F + 8). The vector representing the reflected wave is shifted in the lagging direction by ¢’ + ¢ degrees when this ‘sum is positive, and in the leading direction when the sum is negative. The effect of this phase shift on the point on the lobe being considered may be determined by inspection of Figure 72. Thus, to determine the first maximum point the following procedure may be used. At n = 1 the angle y is 0.0011 radian and ¢’ + ¢ is —14.8 degrees. This means that for the cosine term to be —1 the path difference must be increased until 6 is 194.8 degrees. The angle ya at which this value of 6 occurs is found by interpolating between 0.00110 and 0.00492 since 6 changes from 180° to 360° in this interval. This angle is then 0.00141 radian. Had the angle ¢’ + ¢ changed appreciably from 0.00110 to 0.00141 the interpolation would be repeated using the new value of ¢’ + ¢. In most cases the new value of ¢’ + ¢ may be estimated from the curve, and the first approximation will be close enough. TasieE 14. The general lobe formula. (Example 21.) ve Y 5 ~ Ya radians radians - ; radians 0 0 —.00600 1.061 — 2.86 1.000 —.00589 0 1 .00421 +.00110 0.920 — 5.27 0.640 +.00141 165.0 2 .00712 .00492 0.897 + 3.04 0.792 .00527. 48.5 3 .01000 .008385 1.0389 + 7.56 0.862 .00858 180.5 4 .01295 .01163 1.158 + 2.75 0.908 .01206 36.3 5 .01595 .01485 1.158 — 5.04 0.9388 .01557 178.5 6 .01897 .01802 1.067 — 10.88 0.955 .01894 52.7 7 .02200 .02119 0.930 — 15.00 0.963 .02225 155.6 8 .02500 .02428 0.779 — 15.00 0.969 .02544 66.5 9 .02810 .02744 0.648 — 11.00 0.973 .02860 137.0 10 .03110 .03051 0.500 0.00 0.982 .03161 89.1 11 .03420 .03365 0.408 + 17.18 0.984 .03453 126.4 12 .03720 .08669 0.332 + 43.0 0.987 .03731 96.6 13 .04050 .04005 0.267 + 74.4 0.991 .04024 120.6 14 .04330 .04288 0.222 +108.9 0.991 .04253 100.7 15 .04640 .04600 0.190 +154.6 0.992 .04493 117.7 16 .04950 .04912 0.165 +206.2 0.9938 .04894 103.0 17 .05250 .05216 0.143 +263.3 0.993 .05010 116.5 18 .05560 .05528 0.129 +326.2 0.994 .05264 104.0 19 .05870 .05840 0.114 +412.3 0.995 .05479 115.6 20 .06170 .06142 0.104 +492.6 0.997 .05694 104.5 21 .06480 .06454 0.094 +590.0 0.998 .05909 114.6 22 .06780 .06755 0.089 +687.0 0.998 .06127 105.6 23 .07090 .07067 0.081 +813.0 0.998 .06436 114.2 At 0.00141 radian Dpz is 0.501. Substituting this value: d 1100/1 + (0.501)? = 2 X 0.501 X (—1) 165.0 miles , which is laid off on the coverage diagram at an angle of 0.00141 radian. As many other points as required to sketch the diagram may be computed in a similar fashion. For an intermediate point it is convenient to use the net angle equal to 90° since the equation then reduces to d = 110V/1 + (Dpz)? . The angles of the lobes have been listed in Table 14 under ya and the lobe lengths under d. The vertical coverage diagram is shown in Figure 73. The lobe maxima and minima and the 90-degree points have been sufficient for sketching the lobes except on the first lobe where a few additional points have been computed. When the net angle is 60 degrees, the field strength at the bottom of the first RADIANS-—> ALTITUDE IN FEET £=160 MC h,= 500 FEET SHORE LINE = 15840 FEET d=l10 MILES ANTENNA-VERTICAL HALF WAVE DIPOLE VERTICAL POLARIZATION SITING AND COVERAGE OF GROUND RADARS 0.08 0,07 0,04 PPPOE TP OD LT LEI IL a ZA ae eee Beso. Dis Se ae 22) FSS... ba tee TS Baa Sere. See esos Sesee see, eis ie L — EE 70,01 Ficuren 73. Coverage diagram for Example 21. lobe is equal to the free space field. At ranges shorter than this the reflected wave opposes the direct wave. Directly under the antenna the contour passes near the surface so that the waves are very nearly in opposition. Because of the variation in Dpz with y the maxima will not occur exactly when the cosine is unity, but this effect is generally negligible. 15.7 CALIBRATION AND TESTING tere Introduction It should not be inferred from Section 15.6 that a reliable coverage diagram can be obtained by calcu- lation alone. Under field conditions it is necessary to make test flights and other checks before equip- ment can be depended upon to meet a calculated performance. On the other hand it is seldom possible or desirable to obtain a satisfactory coverage diagram from tests alone. Best results are attained when tests and analysis supplement each other. Test flights are arduous, expensive in personnel and materials, and time consuming. In most theaters a number of agencies become involved, and careful planning and organization are required to achieve a useful result. For these reasons the amount of test flying should be held to a minimum by intensive analysis and equipment tests before and after the test flights. “Calibration and testing” might well be a book in itself, but only a very brief discussion will be given here for the sake of completeness. ie Equipment Tests It is difficult to overemphasize the importance of. proper equipment maintenance. An unfortunate ten- dency of inexperienced personnel is to maintain on an emergency basis, rather than as a matter of system- atic routine. In most cases the need is for a careful check of all elements and restoration to as-good-as-new condition, rather than a brilliant intuitive process known as “trouble shooting.’”’ One survey of a large -number of systems disclosed an average reduction from optimum performance of 13.5 db. This corre- sponds to a maximum range of 50 per cent of normal. Careful tests have shown the use of “standard tar- gets” to be very misleading in many cases. Large changes in the maximum ranges of small targets were found without appreciable changes in the strength of the permanent echoes used for checking purposes. Full use of test instruments available should be made in checking the equipment. Orientation should be completed and the accuracy of range and azimuth indicators checked. Tuning and modifications should be done before the test flights are made, unless the tests indicate poor performance. A great handicap CALIBRATION AND TESTING l ~I a A SCOPE SENSITIVITY —LOW SCOPE DEFLECTION IN INCHES RECEIVER INPUT IN LV Fieure 74. Typical receiver characteristics. in this work is the lack of absolute measures of power output, but much may be done with echo boxes and field intensity meters. Reference is made to service publications and instruction manuals for further details. 15.7.3 Signal Measurements Several methods are used for recording signal strengths, and these determine the type of receiver calibration required. Estimation of signal-to-noise ratios by means of scales on the face of the scope requires some means of specifying the gain setting. The means used, such as height of noise, position of gain dial, and so forth, should be calibrated with a signal generator so that there is an assurance of adequate sensitivity and a way of checking the measurements. The saturation line on the scope is assigned a height of 10, and the signal and noise heights are read in proportion. Ratios in excess of 10 are usually read as 10+. This method requires considerable skill on the operator’s part and is limited in scope. In Figure 74 is shown a calibration curve on a typical “square law” receiver. In the circle is represented a signal on an A scope which would commonly be read as a signal-to-noise [S/N] ratio of 8. Actually the ratio of receiver inputs correspond- ing to the signal and noise heights is 8.5/3.25 or 2.6. A considerable improvement over the above method may be obtained as follows. An index line is drawn on the face of the A scope about an inch from the baseline. To measure a signal it is brought to the index line by adjustment of the gain control, and the gain control voltage is recorded. The gain voltage required to bring the noise to the index line is also noted occasionally during the test. A calibra- tion curve is made using a pip signal generator or a modulated signal generator connected to the receiver input. The gain voltage required to bring the signal to the index line is measured for various inputs. Gain voltage readings on the test target and noise are converted by means of the curve to equivalent input voltages. Test data may be conveniently plotted as decibels above noise after this conversion. It should be noted that the calibration depends upon the type and percentage of modulation. A third method involves calibration of the gain control dial by comparison of permanent echoes. Three lines are drawn on the scope face such as 44, 1, and 11% in. from the baseline. The position of the gain dial with the noise at 1% in. is marked 0 db. A permanent echo is selected which comes to the 1-in. line at this setting. The gain dial is then turned to bring this echo to the 144-in. mark, and this position of the dial is marked 6 db. Another echo is then selected which is 1 in. high, and it is brought down to 44 in. by further adjustment of the gain dial. This position is marked 12 db. In this manner the gain dial may be calibrated over the full range of adjust- ment. It may be necessary to change the series resistor on the gain potentiometer to spread the 176 working part of the scale over a sufficiently wide angle. A common difficulty with this method is lack of suitable permanent echoes (Section 15.5.3). A fourth method is suitable for microwave gear where search is conducted with a PPI scope. As the beam sweeps past the target a hit or miss is recorded. If desired, additional note may be made such as miss, very weak, weak, or hit. In analyzing the data the percentage of hits in an arbitrary period of 30 sec is plotted against range, counting very weak signals or stronger as a hit, asin Figure 75. The data may be 109) 5000 FEET INCOMING o ANTENNA E 15 RPM x bE 550 ) | & MAXIMUM | a RANGE | ' fo) | ° 15 25 30 20 RANGE~ MILES Ficure 75. Test flight data for PPI scope. scattered, but it is not difficult to decide the range at which the percentage of hits is 50 per cent. This is taken as the maximum range. At lower altitudes a lobe structure may be detected, indicating ground reflection. 15.7.4 Conduct of Test Flights The test planes should have two or more engines. Slow-speed, high-ceiling, long-range planes are most desirable. They should be equipped with navigational aids such as radio compass, DF system, and loran, and full complement of communication sets, trans- ponders, and altimeters. For positive identification in regions of high traffic density, a distinctive [FF (identification friend or foe) response is essential. Mark II transponders may be readily modified in the VHF band to give a double pulse by shifting the condenser rotors. Tests are conducted by flying out from the station and returning at a specified altitude to a range estimated to be about 10 per cent beyond the maxi- mum of the lobes. Suitable altitudes are from 5,000 to 20,000 ft. Little is learned from tests below 1,000 ft since nonstandard propagation effects are most pronounced in this region. Data should be taken by specially trained opera- tors as considerable judgment is required. Flights should be carefully planned and full provision made SITING AND COVERAGE OF GROUND RADARS for various contingencies. Changes from prearranged plans should be held to a minimum. Close liaison should be maintained with the flight section and every effort made to avoid hazardous flying. Where feasible, flights over sea should pass near landmarks, etc., to check navigation. Other radars and agencies should be employed to assist the test plane in holding its course. The permanent echoes should be noted during the test and compared with average condi- tions so that an estimate of nonstandard propagation may be made. Similar checks should be made at other nearby radars. 15.7.5 Analysis of Test Data Test data should be accompanied by a complete description of the conditions of the test. Data should be analyzed promptly, and every effort should be made to extract the full amount of useful information. In Figure 76 is shown a signal-to-noise graph for INCOMING MEDIUM BOMBER~ 12000 FEET \ FIXEO \ SIGNAL /NOISE RATIO wy () 20 40 60 80 100 DISTANCE~ MILES Ficure 76. Typical signal-to-noise test data. a station similar to Example 20. The noise is set at a relative height of 1, and the signals are read in proportion as the plane comes in. The weak signals at medium ranges are due to shore line diffraction. The peaks correspond to lobe maxima and ranges at. S/N = 1 to the locations of the lobe contour at 12,000 ft. The receiver in this case is of the “linear” type, and the lobe maxima may be obtained by extrapolation. Along a line of constant path difference such as the maxima of the lobes the signal-to-noise ratio varies as the inverse square of distance. Thus the fourth lobe has a peak S/N ratio of 6 at 68.5 miles, and the lobe length is L = 68.5+/6 = 167.5 miles. In practice the length computed in this manner would be compared to those obtained from tests at other altitudes. Notes made during the test and other factors would be considered and the data weighted accordingly. For example, at 90 miles the S/N ratio CALIBRATION AND TESTING Q < <- oO WwW 2) fe) z N = 3 9 w 40 Wen AL 100 120 140 wes TARGET~ INCOMING MEOIUM BOMBER 5000 FEET — 100 MILES Figure 77. Test flight data from a calibrated receiver. is 2 and the percentage error is probably greater than on the reading at 68.5 miles. The location of points on the lobe cannot be read with accuracy from Figure 76 at S/N = 1 since this is threshold data which may be in considerable error. To determine the maximum free space range F, the lengths of the lobes obtained from the test data may be listed along with the site factors from equa- tion (99) or equation (107). A value of F is then selected which will most nearly fit the test data. Variations in performance of the equipment affects the lobe lengths in proportion. Variations from the standard atmosphere assumed will shift the position of the lobes, particularly at low altitudes. Where better accuracy is desired or the receiver is nonlinear, the calibrated receiver method is required. Such data are recorded as gain voltage, range, and time. For each gain voltage, the equivalent receiver input voltage is read from a calibration curve such as Figure 74. The equivalent value of the noise voltage of this set is 30 wv. Dividing the equivalent receiver signal voltages by 30 gives the S/N ratio which is plotted against range in Figure 77. The lobes are identified by reference to a lobe angle diagram. The extrapolated lobe lengths may be listed as follows: Height, feet Length of lobes, miles 1 2 3 4 20,000 ... 243 196 235 10,000 159 212 169 162 5,000 156 216 163 158 The 20,000-ft data were taken last and indicate the effect of certain equipment adjustments. The ability to maintain this performance is one of the questions to be considered in arriving at a weighted average value of lobe lengths. Comparison of these lobe lengths with the computed lobe factors will indicate a fair value to be used for the free space maximum range. Until suitable instruments are provided for measuring set performance the conduct of successful tests will continue to be a challenge to the ingenuity and diligence of field personnel. However, with a careful analysis of the propagation characteristics of a given site and radar equipment and a well-conducted test with inadequate instrumentation minimized by determined improvisation, it is still practical to obtain a reliable solution to the coverage problem. Chapter 16 VARIATIONS IN RADAR COVERAGE* Vo IN COVERAGE of radio and radar equipment are caused by atmospheric factors which influence propagation of very short radio waves. The rapid and accurate evaluation of radar signals is dependent to a great extent upon our knowledge and understanding of the effects produced by the variable conditions of the lower atmosphere. Evaluation of radar signals influenced by weather introduces problems of identification, actual range determination with second or third sweeps, and radar coverage characteristics, each having a direct bearing on the tactical situation. Enemy ships far beyond the horizon have been located by radar and sunk by radar-controlled gun- fire. United States warships in the Pacific, in several instances, have picked up targets by radar at ranges four to five times those obtained under standard conditions. Army coastal radars have tracked convoys on some occasions to 20 or 30 miles beyond normal radar ranges. The same radars, a few hours later, may have failed entirely to pick up targets clearly visible to the eye. Allied forces are employing radar and VHF (very high frequency) equipment with steadily increasing effectiveness. But we are forced to revise and improve our early conceptions of the capabilities and hmita- tions of these useful instruments of World War II. Serious errors and false evaluation of radar presenta- tion may result if we do not take into consideration the effects of weather and atmosphere on radar ranges and VHF coverage. Complete reports of the variability of radar cover- age show that certain weather and atmospheric conditions prevailing along the transmission path may greatly modify the normal range characteristics of radar and VHF radio. The operator, at certain times, can ‘‘see”’ targets or hear messages far beyond the horizon, sometimes at unbelievable distances. At ®This document was published June 1, 1944 and distributed widely to Service personnel under the above title, and under short title JANP 101, by authority of the Joint Conimunica- tions Board. Originally prepared by the Columbia University Wave Propagation Group, it was amended and improved by representatives of both Services in an effort to prepare a brief, qualitative but authoritative statement of the then known facts concerning the factors contributing to nonstandard propagation. 178 other times he is unable to contact, by radar or VHF, aircraft or surface craft well within the normal range limit. These effects of a nonstandard atmosphere might leave doubt in our minds as to the effectiveness of radar and the usefulness of VHF radio. But we should adopt the reverse view. We can, by understanding and allowing for these phenomena, make a useful instrument more effective—the weather will work for, instead of against, radar and microwave equipment. Unusual ranges are caused by bending or refraction of the radio waves by the atmosphere. A most import- ant special case of refraction is the concentration of the wave energy in ducts within the atmosphere. This bending and duct formation is a direct result of the meteorological factors involved—factors of weather and atmosphere—peculiar, in many cases, to the locality and the season. Such factors are dis- cussed later. ree BENDING The VHF or radar operator usually assumes that short waves and microwaves, at frequencies above about 30 me, travel along the line of sight from the transmitter to the receiver and, in the case of radar, to and from the target. Experience has shown that this assumption, nearly true in many instances, may lead to serious errors or false evaluation if applied to radar operation and microwave communication. Radio waves are bent from a straight line path as a result of refraction by the lower atmosphere. This bending, or refraction, is generally recognized as a property of light. It is equally a property of radio waves. The underlying principles are exactly the same in both cases. The quantity that determines refraction is called the index of refraction. Refraction occurs whenever there is a change of index of refraction, as at the boundary of two substances. In the interior of a material of constant refractive index, the rays travel in a straight line. The change in angle at the bound- ary is the larger, the greater the difference in refrac- tive index from one material to the next. Radio waves are refracted or bent in the atmosphere because the index of refraction of the atmosphere changes with height. The properties of the atmos- phere which determine the refractive index and which BENDING 179 Ficure 1. Actual pattern showing radar coverage for standard propagation. FieurE 2. Modified presentation of the information shown in Figure 1. change with height are temperature, pressure, and moisture content. These changes from one level to another are very small compared with that from water to air, and the resulting refraction itself is small. Nevertheless this refraction is of great import- ance in radar operations and radio communications above 30 me. If the atmosphere were composed of a number of successive layers each having a different index of refraction, a wave passing across the successive boun- daries of the layers would be abruptly deflected at each surface. The atmosphere does not consist of such distinct layers. Instead, the change in its physical properties and its index of refraction is gradual, continuous. There is, then, no sudden change in direction of the waves; the change in direction becomes gradual and continuous. In other words, a bending of the waves occurs as they pass through the atmosphere. Radio waves passing through the lower atmosphere are usually bent downwards. As can be seen from the illustration of the actual pattern (Figure 1), the bending of the waves, or rays, by the atmosphere permits one to see farther than he would otherwise. In the figure the vertical dimen- sions have been strongly exaggerated so that the earth’s curvature becomes clearly visible. Under average weather conditions the horizon distance is increased by about 15 per cent, but at an elevation near the first lobe the increase in range is much less than this amount. This is the case of standard refraction, or standard propagation. It, is rather inconvenient to draw curved rays in radar coverage and calibration diagrams. This can be avoided by assuming that the earth’s radius is 4 the actual radius. Then in the diagrams the rays appear as straight lines when the propagation is of the standard type. This method often is adopted in radar calibration practice, with coverage diagrams drawn or printed to the % value of the earth’s radius (see Figure 2). This corrects for the effect of normal bending in the atmosphere. The radar operator merely plots the position of his target on such a diagram and assumes that the radiation travels along a straight line between the radar and the target. In this way he takes into account the effects of standard refraction while doing his work. VARIATIONS ep Fiaure 3. Radar lobe pattern in nonstandard atmos- phere. A duct has been formed on the surface of the ocean and a ship is detected. Lobe No. 1 is bent down- ward more than normal, but the other lobes remain sub- stantially unchanged by the duct. Wave propagation deviating from standard occurs under special weather conditions. The most import- ant type is called “guided propagation,” “trapping,” or ‘‘superrefraction”—formerly referred to as anomalous propagation. The main feature of this type of propagation is an excessive bending of the rays due to refraction. This bending occurs prin- cipally in the lower layers of the atmosphere and mainly in the lowest few hundred feet. In certain regions, notably in warmer climates, excessive bend- ing is observed as high as 5,000 ft. The amount of bending in regions above this height is almost always that of the standard atmosphere. As a consequence of the excessive bending in the lower layers the coverage pattern of a radar set is deformed, as illustrated in Figure 3. The fact that atmospheric influences are effective only in the lower layers does not imply that the echo strength from a target will be affected only as it lies in these layers, though the effects will be strongest there. It merely means that excessive bending is suffered by the rays. only while passing through the lower layers. How- ever, the deformation of the coverage pattern itself will in general extend to a greater height. Two factors are operative in producing a rapid change of refractive index with height: variation of moisture with height and variation of temperature with height. Excessive refraction occurs when there is a rapid decrease of moisture with height (‘moisture lapse’’) and, to a lesser degree, when there is a rapid increase of temperature with height (“temperature inversion”). The most pronounced cases of excessive refraction occur when both these conditions prevail at the same time. These conditions will be discussed later from the meteorological viewpoint. IN RADAR COVERAGE Since the atmosphere is a very tenuous substance, the amount of refraction, that is, the amount of angular deflection of the rays, is very small and in no case exceeds a fraction of a degree. How then can these small effects influence radar operations? The answer is that they do not influence operations unless the angle between the ray itself and the horizontal is very small. If radar is used for fire control, search- light control, or fighter intercept control, the targets are usually at medium or short ranges, and the angle between the line of sight and the horizontal is usually larger than one to two degrees. Refraction has practically no effect on such an application of radar. However, the same equipment may be used for long-range search and then the story is different. With early warning radar the target may be an airplane 50 or 100 miles away, and it may fly at an elevation of only a few thousand feet. In this case the angle of elevation of the target above the hori- zontal, as seen from the radar, is only a fraction of a degree. This applies still more to seaborne targets. The atmospheric effects then become operationally important. It should always be kept in mind that only low-angle search is affected by meteorological conditions. Asa rule, the operational characteristics of a radar for angles of elevation of the target exceeding 1 degree may be calculated on the assumption of a standard atmosphere, with confidence that all non- standard meteorological effects are negligible. RADAR STATION THE GRITICAL ANGLE IS ALWAYS LESS THAN te Ficure 4. Wave paths illustrated as rays in ground- based duct. 16.2 GUIDED PROPAGATION It is obvious that excessive bending of the rays in the lower layers of the atmosphere must distort radar coverage patterns. One case of special import- ance is illustrated in Figure 4. Four rays, out of GUIDED PROPAGATION 18L many, are shown which leave the transmitter at different angles with the horizontal. Ray 1 is bent so much that after some distance it returns to the ground; there it is reflected and then the same course is repeated again. In this way the ray may be reflected a number of times in succession, remaining always in the lowest layer. This super- refraction “traps” the rays in a “duct” and results in guided propagation of the radar waves. Trapping does not occur under standard atmospheric condi- tions. A ray, under standard conditions, may be re- flected by the earth’s surface only once before it escapes into space. Ray 2 is also bent in the lowest layer but not enough to keep it from escaping into the upper atmosphere whence it does not return to earth. Ray 3 is similar to 2 except that it undergoes one reflection by the ground before it escapes into the upper atmosphere. Ray 4 separates the two types of rays illustrated by rays 1 and 2. This ray becomes horizontal when it reaches the top of the trapping layer or duct and from there on travels along at the same height. All rays are divided into two groups: those that leave the transmitter at an angle with the horizontal less than the eritical angle and are trapped, and those that leave the transmitter at a larger angle and proceed into the upper atmosphere. WILL BE DETECTED Figure 5. Rays in an elevated duct. In this, another common form of duct, the amount of bending may be approximately normal both below and above the duct. The rays oscillate between the upper and lower bound- aries; maximum ranges in or near the duct may be even greater than with a ground-based duct. The critical angle 1s aways small, practically never larger than 1% degree. Its magnitude may be taken as a measure of the intensity of guided propagation, that is, of the amount of radiant energy trapped within the duct. Rays that leave the transmitter at a somewhat larger angle up to about twice the critical angle are sufficiently deflected while passing through the lowest layers to distort that part of the radar coverage pattern lying just above the duct. Rays leaving the transmitter at a still larger angle are not appreciably affected. The ground-based duct or trapping layer guides the wave along the earth’s surface in much the same way that hollow metal tubes guide microwaves. Within the duct there is less decrease of signal strength with distance than there is above the duct. Radar ranges on surface craft and low-flying aircraft located within a duct, similar to the one illustrated in Figure 5, are increased—sometimes to two, three, or four times the normal ranges. Ground echoes would be increased at the same time and might, in some cases, obscure partly, or even entirely, the echoes from incoming aircraft. When the radar is located within the duct, ranges on aireraft flying above the duct will be decreased only slightly, if at all. Often there may be a shght increase in effective ranges. If the angle of elevation of the aircraft is greater than 1 degree, the effects become inappreciable and failure to detect the target cannot be attributed to excessive refraction. If the duct does not include the radar within its boundaries, as, for example, when a duct forms below a high-sited radar, the effective ranges on surface craft may be either increased or decreased. Similar reasoning may be applied in the case of airborne VHF radio communication. Usually there is no very pronounced effect upon the signal strength when VHF communication is carried on between two aircraft, both flying above the duct. Interference between the direct rays and the rays reflected from the ground—resulting in the well- known lobe pattern of the coverage diagram—has not been mentioned. Under standard conditions the position of the lobes depends only on the wavelength used and the height of the radar above the ground. When a duct is present the lowest part of the coverage diagram may be strongly distorted. Coverage depends upon a variety of factors of which the most important are these: height of the top and base of the duct, amount of refraction in the duct, position of the transmitter relative to the duct, frequency (or wavelength) of the radar equip- ment, and height of the transmitter above ground. A coverage diagram for standard conditions is shown in Figure 6, diagram 1, with height strongly exaggerated. Only the lowest three lobes are shown, and the higher lobes appear compressed as compared 182 VARIATIONS ALTITUDE IN FEET 7000 a GROUND BASED DUCT 5 — GROUND BASED DUCT) _ 2000 ELEVATED puct) 1000 TRANSMITTER HEIGHT-100 FEET FREQUENCY- 200 MC NORMAL LIMITING COVERAGE 0) RANGE IN NAUTICAL MILES 50 Ficurn 6. Standard and nonstandard coverage diagrams to the lowest lobe. In diagrams 2, 3, 4, 5 the lower part of the same diagram is drawn as it appears under various conditions of guided propagation. The bottom part of the “standard” main lobe is shown by a broken line. The lines which separate the ‘blind zones” from the ‘detection zones’? represent the range at which a medium bomber would just become visible to this particular radar set. IN RADAR COVERAGE The diagrams clearly indicate the great extension of ranges in the duct and also the moderate change in ranges—sometimes an extension, sometimes a reduction—above the duct. Another feature of some of these diagrams is the appearance of “skip-ranges.”’ A plane flying at an altitude of 500 ft, for instance, would be detected early under the conditions shown in diagrams 4 and 5. As the plane approaches, the echo will disappear from the scope and reappear only at a range less than 20 miles. Similar conditions will prevail for ground clutter. In diagram 3 there would be ground clutter close in and also from beyond 33 miles but not from the space between. For conditions shown in diagram 5, there would be echoes from very remote ground targets but not from targets at inter- mediate ranges. A change in echo strength from day to day is not necessarily caused by the weather but might simply be caused by a variation in performance of the set. Cases have occurred where there was extensive trap- ping, but because of lowered set performance there was no corresponding increase in fixed echo strength. The set then will appear to be in good operating con- dition, and the operator will be deceived about ranges of detection for craft flymg above the duct. Equip- ment for checking set performance is not usually available in the field. The change in intensity of nearby fixed echoes may be, in some cases, a measure of set performance, but in the absence of more elaborate checks this method can be misleading and should not be relied upon entirely. Failure of detection of targets is not necessarily due to weather influences. Electrical failure of the set or inadequate adjustment may be the difficulty and may be far more troublesome to identify than meteorological effects which should not be used as a “scapegoat” to be indiscriminately blamed for poor coverage. 16.3 METEOROLOGICAL FACTORS The atmosphere is responsible for bending and duct formation. To understand the ‘‘why”’ of non- standard ranges of radar and radio with respect to the weather, it is necessary to consider the meteoro- logical factors involved. The strong refraction which results in guided propagation is caused by a rapid decrease of index of refraction with height within certain layers. The decrease depends upon distribution of moisture and temperature in the atmosphere, particularly in the METEOROLOGICAL FACTORS 183 lowest few hundred or thousand feet. Normally the temperature decreases with height in the atmosphere (at a rate of about 2°C per 1,000 ft), and the mois- ture decreases gradually with height. Under these conditions the propagation is of the standard type. Temperature may sometimes increase with height for a few hundred or thousand feet above ground and then, at greater heights, begin to decrease again. The vertical increase of temperature is called a tem- perature inversion. Sometimes a layer of moist air is found near the ground, and the air overlying it is very dry. There is then a rapid decrease of moisture over a short vertical distance; in other words there is a pronounced moisture lapse (see Figure 7). A 1500 IN FEET 1000 500 ALTITUDE MIXING RATIO INCREASE > Freure 7. Moisture variation aloft. 1. Moisture distri- bution with height in standard moist atmosphere. 2. Example of sharp moisture lapse (dry air overlying moist air) conducive to guided propagation. Mixing ratio is amount of moisture in a unit weight of dry air expressed as grams of water per kilogram of dry air. moderate or strong moisture lapse almost always will produce trapping, but a temperature inversion (except at low temperatures) will lead to trapping only if the moisture distribution is favorable. A combination of both effects within the same layer usually will produce trapping. The meteorological conditions to be found over sea and over land are quite different and must be con- sidered separately. OviR SEA When warm, dry air flows over colder water, a temperature inversion will be established, and there will be evaporation into the lowest layers of the air, thus creating conditions of pronounced trapping. This weather condition is one of the most common causes of guided propagation. An example in point is the Mediterranean, which to the south, east, and west is surrounded by dry land masses producing a flow of dry, warm air over the water when the winds AIR OVER AFRICA \ TEMPERATURE S DISTRIBUTION \ AIR FROM SAHARA]. VERY DRY HEIGHT IN FEET TEMPERATURE DISTRIBUTION MOISTURE DISTRIBUTION HEIGHT IN FEET TEMPERATURE —=UP MIXING RATIO —=INCREASE Ficure 8. Modification of air from Sahara Desert in passing over the Mediterranean. blow from these directions (see Figure 8). Similar conditions are often caused by westerly winds blow- ing from land to sea across the eastern boundary of a continent. Land and sea breezes may influence radar operation along a coast line. The wind direc- tion at a coast is often an important factor in deter- mining propagation conditions and should be closely watched. Whenever unusual propagation is observed by coastal radar stations, a record of prevailing winds at the time is very helpful in determination of future expected performance. HEIGHT IN FEET — UP TEMPERATURE Ficure 9. Formation of temperature inversion over land due to nocturnal cooling. Over Lanp Temperature inversions are produced mainly by nocturnal or night cooling of the ground (see Figure 9). Trapping may occur when the moisture distribu- 184. VARIATIONS IN tion in the lowest layers is such as to reinforce or at least not to counteract the effect of the temperature distribution, that is, when the moisture decreases not too slowly with height. Nocturnal cooling is greatest with clear skies and is quite small under an overcast. Hence guided propagation over land occurs at night almost exclusively with clear skies. This type of temperature inversion Is strictly confined to land areas. It does not occur over the ocean because the sea temperature does not show appreciable daily variations. Temperature inversions caused by noc- turnal cooling are most pronounced over dry land (desert) but will occur almost anywhere over land with a clear sky and a not too humid atmosphere. SUBSIDENCE Another weather phenomenon favorable to trap- ping is subsidence. By subsidence is meant the slow downward motion, combined with horizontal spread- ing, of air above the lowest layers of the atmosphere. This process, which most frequently occurs in the area of barometric high, will produce temperature inversions; the subsiding air moreover becomes rel- atively much drier than the unaffected air below. In general the subsidence inversion is quite high (e.g., above 4,000 to 5,000 ft). In the light of present knowledge it appears that high subsidence inversions do not generally affect guided propagation when the sets are situated at low altitudes. It appears, how- ever, that such subsidence inversions might materi- ally affect communications or airborne radar search aloft. Lower subsidence inversions (1,000 to 2,500 ft) along the southwestern coast of the United States are known to produce stable duct layers affecting radar coverage at low angles. TURBULENCE OF THE AIR This has a distinct normalizing effect in that it tends to smooth out the temperature and moisture variations which are conducive to guided propaga- tion. Moderate to strong winds produce a turbulent layer extending normally to a height of about 4,000 ft. The air is well mixed within this layer, and consequently the standard type of refraction prevails. Regions of a barometric low are characterized by strong to moderate winds and pronounced turbu- lence in the lower layers. In addition low pressure areas usually have overcast skies. Hence a barometric low will as a rule lead to propagation of the standard type. RADAR COVERAGE FREQUENCY OF OCCURRENCE It is extremely difficult to estimate in general terms the frequency of occurrence of guided propa- gation, since statistical data are almost nonexistent at present except for very limited regions in Europe such as the North Sea. In the central Mediterranean during the summer months of 1943, ducts have been observed on 9 days out of 10. Frequent trapping has also been observed in some parts of the Pacific. At other times and places guided propagation might be an unusual occurrence, especially if the barometric pressure is generally low and the winds strong. It seems advisable to consult a weather officer with regard to any given locality. MEASUREMENTS In order to determine weather’s influence upon radar in a quantitative way, the variation of refrac- tive index with height must be determined. This requires accurate knowledge of the temperature and moisture distribution in the lowest few hundred or thousand feet of the atmosphere. The ordinary radiosonde is not well adapted to measurements of this type because the measured points on an ascent are usually spaced several hundred feet apart. Among the methods which have been developed for this purpose during the past two years, the one most generally adopted uses a captive balloon (or kite) which carries aloft electrical temperature and moist- ure—measuring elements. These are connected to a meter on the ground by means of thin wires attached to the cable holding the balloon. This device permits measurements at intervals as closely spaced as desired. A psychrometer held out of the window of a slowly flying plane has been used with good success in the absence of more elaborate equipment. 16.4 CLOUD ECHOES IN RADAR Cloud echoes (more precisely, precipitation echoes) are observed frequently on radar scopes. At times they have caused confusion by blotting out other targets. Their similarity, upon certain occasions, to actual targets have caused some difficulty in the interpretation of the signals. These echoes are caused by a reflection of the radar pulse from the raindrops in the clouds (or in rain storms). The amount of reflection increases very rapidly with frequency. Cloud echoes are quite exceptional below about 1,000 me. In microwave SUMMARY OF BASIC FACTS CONCERNING PROPAGATION AT RADAR FREQUENCIES radar they first appeared as a nuisance, but more recently they have been put to practical use. In tropical climates they are very helpful for aerial navigation. Cloud echoes may be distinguished from other echoes by their fuzzy and diffuse appearance. Not all clouds show up on a scope with equal strength. The strength of the echo seems to depend primarily on the size of the water drops within the cloud or rain storm. Ordinary clouds such as form an even overcast (stratus clouds) are not usually visible on the scopes; the droplets that compose these clouds are so small that they reflect very little energy. Violent showers give intense echoes on the scopes. Storm echoes can be seen much farther than normal land targets, even under standard conditions, because of their great spread in the vertical direction. In discussing cloud reflections it must be clearly understood that there is no physical relation between cloud echoes and refraction; the mechanics of duct formation is not related to clouds, and with respect to the bending of radio waves a cloud is merely another airborne target. Hoe SUMMARY OF BASIC FACTS CONCERNING PROPAGATION AT RADAR FREQUENCIES 1. Standard propagation results in a slight down- ward bending of the rays throughout the atmosphere, leading to an increase of the horizon distance com- pared to the geometrical value. It is taken into account operationally by using coverage diagrams with a % earth’s radius; on a diagram modified in this way the rays appear as straight lines. 2. Guided propagation occurs almost exclusively in the lowest 2,000 ft above the ground and usually is confined to the lowest few hundred feet (except in warm climates). 185 3. Superrefraction resulting in guided propagation or trapping is produced: a. By a pronounced decrease of moisture with height (moisture lapse), or b. By a pronounced increase in temperature with height (temperature inversion), and c. Particularly, by a combination of both of the above conditions. 4. Of the meteorological conditions conducive to guided propagation or trapping, the most outstand- ing are: a. Over sea: flow of warm, dry air over colder water producing temperature inversions and evaporation into the lowest layers. b. Over land: nocturnal cooling of the ground with clear skies and calm air or light winds (if moisture distribution is favorable). c. Over both sea and land: low-level subsidence. 5. Conditions in a barometric high, including calm and clear skies and especially low-level subsidence, favor trapping especially during the night (but do not necessarily produce it). Conditions in a baro- metric low, including strong winds, intense turbu- lence in the lowest layers, and overcast skies are conducive to standard propagation. 6. When the transmitter is within the duct, radar range is increased for surface targets (ships) and air- craft flying in the duct. At the same time there is an increase in fixed echo strength and consequently in ground clutter on the scopes. This may be accom- panied by a change in the range of detection for craft flying above the duct. 7. When the transmitter is outside the duct, the range may be either increased or decreased from its standard value. 8. Effects of nonstandard propagation are negli- gible when the angle of elevation of the target is over 1 degree. Failure of detection at such angles must be attributed to other causes. i a *s toa + Oh ay cy @ ‘< 5 r . ve S . i LD Vy y ar ry A - is —_ i re wo! (ir aa e. o a 7 i, ¥ i] 7 2 - - % 4 at (s r i a i iy i os a Be: PART IV CONFERENCE REPORTS ON NONSTANDARD PROPAGATION fc : r : v iy ra 7 De n be ae _ i oad nT 1 in 7 : oA it Chapter 17 TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY* M1 PUNDAMENTALS OF PROPAGATION -LT Significance of Propagation Problems | Raa CENTRAL PROBLEM of short and microwave propagation (at frequencies greater than 40 to 60 me) is the determination of accurate coverage patterns for a given transmitter. These patterns are usually calculated from electromagnetic theory and then may be checked by experiment. For communi- cation work the check is simple, namely, the estab- lishment of satisfactory communication. In the case of radar it is necessary to calibrate by time-consum- ing airplane flights. Experience has shown that actual coverage is not constant in time but suffers large variations which are caused by the changeable refraction of the at- mosphere. The variations in weather conditions that influence the refraction often are irregular and very rapid, and it is technically impossible to test all these conditions. Coverage diagrams, therefore, must be based on the physical principles of wave propaga- tion, assuming that the characteristics of the atmos- phere remain constant for reasonable periods. These principles are outlined here. At the present stage of technical development it is not always permissible to ascribe an observed varia- tion in coverage to changing atmospheric conditions. Variations in transmitter output or receiver sensi- tivity are always likely to be present to a degree sufficient to influence results considerably. In prac- tice it is often extremely difficult to tell these causes apart. In fact, investigations carried out with opera- tional radar equipment make it probable that an in- crease in surface coverage due to favorable conditions of refraction frequently passes unnoticed because of poor set performance. The coverage appears normal, while the set in reality is operating considerably be- low peak efficiency. A knowledge and understanding of the effects of weather upon propagation therefore will also be of help in checking set performance in the absence of suitable electrical equipment for measuring output and sensitivity. In dealing with coverage problems this double aspect of propagation phenomena should always be kept in mind. By a suitable analysis of the ®By Columbia University Wave Propagation Group. various factors determining coverage, and by an in- telligent understanding of their interplay, the re- sponsible officer may achieve a better control of the operational performance of his equipment. In tactical operations and in planning, a knowl- edge of the nonvariable factors affecting propaga- tion, such as dielectric constant and conductivity of the ground or sea, contours of the terrain, vegetation, etc., is equally important. Many problems concern- ing these factors cannot be considered in this manual “12 Factors Influencing Propagation This volume is confined to the propagation of waves within the troposphere and hence is not con- cerned with ionospheric propagation, which is re- sponsible for the long distance transmission of short waves (high frequency band). The higher the fre- quency above 30 me, the less frequently radio waves are returned to the earth by the ionosphere. Conse- quently very short radio waves are confined to the troposphere, and the treatment given here does not need to be supplemented by a study of the ionos- phere. Propagation in the lower atmosphere is called ‘tropospheric propagation” (see Figure 1). = a pe SS oe ee — — —ONOSPHERE — oe — — Be SS GS iN ee = —— >> ~ TRANSMITTER> FART, Figure 1. Tropospheric versus ionospheric propagation. The main factors influencing the shape of a cover- age diagram under these circumstances are: (1) re- flection by the ground, (2) diffraction by the ground contour, (3) refraction by the atmosphere, and (4) guided propagation by superrefraction in the lower atmosphere. The present chapter deals mainly with refraction phenomena, but reflection and diffraction will be briefly considered. Refraction is influenced by the physical state of the 189 190 TROPOSPHERIC PROPAGATION atmosphere, in which the distributions of the temper- ature, pressure, and humidity are the most important elements. With refraction, rays are bent, and the electromagnetic energy flows along the curved ray paths. A situation frequently realized in practice is that in which the curvature of the rays is independent of height above ground. This is known as standard refraction. The term standard propagation is used to designate propagation under conditions where the refraction is of the standard type. During the war years the increased number of ob- servations, which resulted from the world-wide use of radar, showed that, under certain weather conditions, radio field strengths may depart markedly from the values expected with standard refraction. These deviations are now known to be attributable to a stratification of the atmosphere which is predomi- nantly horizontal and is produced by vertical varia- tions in water-vapor content and temperature. Since these quantities control the index of refraction, and therefore the curvature of the rays, it follows that this curvature varies with the elevation above ground. Any stratification of the atmosphere tends to pro- duce a distribution of the radiated energy different from that which occurs in the standard atmosphere. Of particular importance is a type of stratification which results in a duct being formed in the atmos- phere. In this event, a portion of the wave energy may be guided horizontally along the duct and may be effectively “trapped” within the duct’s upper and lower boundaries. This is known as “‘guided”’ propa- gation. The radiation energy may then travel to dis- tances far beyond the geometrical horizon, producing unusually long ranges for short wave receivers or radar targets. The phenomenon which tends to con- strain the wave energy to follow the duct is called “superrefraction.’’ When this occurs, the rays in pass- - ing through the inversion layer in the upper part of the duct are bent downward with a curvature which exceeds that of the curvature of the earth. The regions covered by the inversion layer and the duct are illustrated in Figures 15, 20, 22, and 23. The dis- tribution of moisture and temperature in the atmos- phere, responsible for the formation of ducts, is dis- cussed in Section 17.3.1. As the stratification of the lower atmosphere that produces superrefraction is part of the weather, the prevailing meteorological conditions become of im- portance for problems of propagation and coverage. Meteorology as related to wave propagation is treated in Section 17.3. AND RADIO METEOROLOGY Ti Reflection from the Ground A coverage diagram is a curve, or a set of curves, of constant field strength in a vertical or horizontal plane. The horizontal coverage diagram is deter- mined chiefly by the antenna pattern itself. In the vertical plane, however, the diagram depends pri- marily upon the interference between the radiation coming directly from the transmitter and that which is reflected from the ground or sea surface. This effect produces the lobe structure of the vertical coverage diagram. At the lobe maxima the two rays reinforce each other, while they cancel each other out, more or less, at the lobe minima. The propagation problem in its full generality leads to mathematical formulas of forbidding com- plexity. In order to understand the processes at work it is necessary to proceed in steps and gradually add refinements to the basic features of the problem. Consider first the field radiated from an antenna which is remote from the earth. This free space field decreases in strength in inverse proportion to the dis- tance, R;, from the transmitter and varies with the angular position in accordance with the shape of the radiation pattern of the transmitting antenna. Let this free space field strength at any point at distance R, be designated by Eb. GROUND Figure 2. Interference of direct and reflected rays. If, instead, the transmitter is placed near the ground, as at 7 in Figure 2, the field at any point in space is produced partly by the direct wave (giving the free space field Hy) and partly by the wave which is reflected from the ground. The resultant field is given by the vector sum of the two component fields. The magnitude of the field strength of the reflected beam depends upon: FUNDAMENTALS OF PROPAGATION 191 1. The antenna radiation pattern, which gives the relative streneth of the radiation field for different directions. 2. The attenuation, proportional to 1//2, resulting from the length of path Rs» of the reflected wave. 3. The attenuation due to increased divergence of nearly parallel rays reflected from the curved earth. This is taken into account by the use of a divergence factor, D, which depends on range and heights of transmitter and receiver. 4. The magnitude, p, that the coefficient of reflec- tion of the ground would have if the ground were plane. The reflection surface for a spherical surface, F, is then equal to pD. 5. Irregularities of the earth’s surface which affect the reflection coefficient. If HZ, is the magnitude of the direct wave and F is the magnitude of the reflection coefficient, then the field strength of the reflected ray is FE. The phase difference between the direct and re- flected fields is given by an angle 6 which is the sum of: 1. The phase difference, V, resulting from the difference in path length, Re—R,; 2. The phase difference, ¢, suffered by the reflected wave upon reflection from the ground. The amplitude of the resultant field for a non- directive antenna is then given by GH, where G = V1 + F? + 2F cos 5 (1) is the earth gain factor which is illustrated in Figure 3. Ficure 3. Phase addition of direct and reflected rays. A curve drawn to represent the contour of constant field strength H=GE) as a function of the range hy and the angle of elevation 6 gives the vertical cov- erage diagram for that particular field strength. Cal- culation of these diagrams usually requires a con- siderable amount of detailed and laborious work. Consider the simple case of the vertical coverage diagram of a horizontal dipole antenna located above a plane earth in a homogeneous atmosphere. If the plane of Figure 2 is perpendicular to the dipole axis, the radiation pattern of the antenna is a cirele of unit radius. The ratio, /s, of the magnitude of the re- flected wave to that of the incident wave is given by the magnitude, p, of the reflection coefficient. For propagation to distances that are great compared with the antenna elevation, the path lengths R. and R, are not greatly different, and the attenuation due to path length is approximately the same for both direct and reflected waves. For this set of conditions the resultant field is H=GH,, and equation (1) reduces to G = V1 + p? + 2p cos 6 (2) In this form G is the plane earth gain factor and a plot of the curves H=G#,)=constant as a function of range and angle of elevation gives the coverage dia- gram. It depends only upon the magnitude of the re- flection coefficient, the phase changes related to re- flection and to the difference in path length Ro—R,. Since radar requires two-way transmission the re- ceived field strength is proportional to G?/R%;. Other modifying factors must, however, be introduced if the antenna and the target have directional radiative properties Both the magnitude of the reflection coefficient +fF and the phase angle ¢ by which the reflected wave lags behind the incident wave are functions of the frequency, the polarization of the radiation, the angle of grazing with the surface, the conductivity, dielectric constant, and roughness of the ground or sea surface. Figure 4 illustrates the variation of F(=p) and ¢ for reflection from a smooth plane sea surface for frequencies of 100 to 3,000 me, for both types of polarization, at different grazing angles. It may be noted that for horizontal polarization p is approximately unity and ¢ nearly 180°, irrespective of the frequency and the magnitude of the grazing angle. This is the simplest situation to be encountered and most nearly approximates the idealized case of a perfect reflector with horizontal polarization. For this case p is exactly unity, and ¢ is exactly 180°. For vertical polarization over the sea or either type of polarization over ground, both p and, ¢ depart widely from unity and 180°, respectively. Variations in these quantities greatly complicate the calculation of coverage diagrams. The reflection coefficient of microwaves is usually found to be small over land. This is essentially due to TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY in HORIZONTAL POLARIZATION 100 MG | VERTICAL POLARIZATION ~ Fale] ee ae KGSh eee Sei oO [o} 10 20 ie 09 _ é Wie TERTICAT A ” 420 > IN DEGREE 30 40 50 60 70 IN DEGREES 80 90 e ae) Oo 60 OMNI ONNCONNSONNAONNES 70 80 90 yy IN DEGREES IN DEGREES (LAG) \) 200 eee ee NSS NN 0 O05 1.0 15 20 25 3.00 3.5 4.0 4.5 5.0 55 y IN DEGREES VERTICAL POLARIZATION (0) 0 O56 10 15 20 25 30 35 40 4.5 5.0 55 y IN DEGREES FicurE 4. Phase and magnitude of reflection coefficient for sea water. irregularities of the land surface. When these irregu- larities are sufficiently small, reflection from land is found to be considerable. Since the receiver, or target, is usually located at a distance from the transmitter which is large in com- parison to the height above the ground, the direct and reflected rays are very nearly parallel, making an angel 8 with the horizontal (Figure 2). The reflected ray may be supposed to issue from an image trans- mitter 7’, which is as far below the ground as the true transmitter is above it. The path difference be- tween the direct and reflected rays is equal to the distance 7’ A. By the figure this is equal to 2h: sin 8, where h; is transmitter height. For small values of B this is practically equal to 2h,6 if 8 is measured in radians. The corresponding phase shift due to path difference is equal to 2 Y= 2haB > - At the point of reflection the phase of a ray changes FUNDAMENTALS OF discontinuously by the amount ¢, which is the phase angle of the reflection coefficient. For horizontal polarization, to again take the simplest case, the phase shift @ at reflection is practically 180°, or m7 radians. (For vertical polarization, see Figure 4, ¢ is more complicated.) Adding the phase change W, corresponding to difference in path length, gives the complete phase change 6 in the form ») 6=V+¢=2h By + 7 (for horizontal polarization).(3) Maximum values of the earth gain factor G occur when 6 is an integral multiple of 27; minimum values, for odd integral values of 7. The corresponding values of the angle of elevation 8 are given by m= i1,3,5,°: : 0,2,4,° °° (maxima) (minima) RD | i > 5 ES = OTS = ll (for horizontal polarization.) If the reflection coefficient F of the surface is assumed to be unity (see Figure 4) the plane earth gain factor G, from equation (2), reduces to G = 2005 (5), which fluctuates between the limits of 2 and zero. The coverage diagram drawn for propagation over a perfectly conducting plane on horizontal polariza- tion is illustrated in Figure 5. As an example, consider FREE SPACE FIELD tT’ FLAT EARTH Figure 5. Simplified coverage diagram. f=200 me, \=1.5 m, 4=30.5 m. The values of 6 for the first three lobe maxima are 0.68°, 1.37°, and 2.05°, and the maximum ranges are twice the free space values. The angles at which the minima occur lie half way between. The scale of vertical distances is greatly exaggerated compared with the horizontal scale. Coverage diagrams for the same frequency and transmitter height, but taking account of the earth’s curvature, are shown in Figure 24. Coverage diagrams for more complicated situa- tions must take into account, in addition to the factors already mentioned, the curvature of the PROPAGATION 193 earth, the refraction of the atmosphere, and diffrac- tion into the region below the line of sight. _ Horizontal 1 _ SUivaten= => ala eS GRoun pS aot ae a UND PLANE Figure 6. Use of equivalent ground plane. When the ground is sloping, the above construction may be modified as indicated in Figure 6. For any specified lobe, determine approximately the part of the ground where reflection takes place. Draw a tangent to the ground in this region and determine the perpendicular projection of the antenna site on this plane (“equivalent ground”’). Use the equivalent height thus determined in equation (3), and let the angle 6 refer to the plane of the equivalent ground. This procedure is also required when the transmitter and receiver or target are of comparable height so that the reflection point is not near the transmitter. When the transmitter is set up near a coast, the lobe pattern over the ocean will undergo periodic variations caused by the tides. Since, in equation (3), Bis multiplied by fu, it follows that the lobes will be low at high tide and high at low tide. This phenom- enon may become very important for heightfinding sets. A more complicated case occurs if ground reflec- tion is not complete. Then p is less than| unity, and ¢ differs from 180°. In this event the lobes have max- FREE SPACE FIELD 6 FLAT EARTH Ficure 7. Coverage diagram for incomplete reflection. ima which are less than twice the free space field and minima which never reach zero. The angular posi- tions of the lobes are changed somewhat, but the most noticeable change is found on the lower side of the first lobe. It is likely to lie at a lower elevation and reaches the ground at some distance from the transmitter (compare Figures 5 and 7). 194 TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 1714 Refraction—Snell’s Law The bending of rays in the atmosphere depends upon the refractive index n which is a function of the temperature, pressure, and moisture content of the air. The manner in which these quantities control the index of refraction is explained in Section 17.2.1. Toa first approximation, assuming horizontal stratifica- tion of the atmosphere, the index may be considered to be a function only of height above the ground. The corresponding case; familiar in optics, is that of two media, such as water and air, with different refrac- tive indices ni and nz (Figure 8A). If a: and az are the angles between the rays and the plane of the bound- ary, Snell’s law of refraction states that nN, COS @1 = Ne COS Ao. In the atmosphere the refractive index changes continuously with height. The simplest case, often CF BOUNDARY REFERENCE oF] n=n(h) A B Figure 8. A. Refraction at a sharp boundary. B. Re- fraction through a layer with variable n. encountered in practice, is that of a refractive index which decreases linearly with height. This is known as standard refraction. Snell’s law applies here also, since the atmosphere may be divided up into an in-. finity of parallel boundaries, the change of refractive index from one boundary to the next being infinites- imally small. Instead of a sudden change of direction there is then a gradual change or bending of the rays (Figure 8B). Snell’s law may then be stated gen- erally as nN COS a=Np COS ao , where now n and @ are continuous functions of height and the zero subscript on the right-hand side refers to any fixed reference level. The curvature of the re- fracted rays is downwards or upwards according to whether the refractive index decreases or increases with height. “15 Refraction over a Curved Earth In reality the surfaces of constant refractive index are not planes but are concentric spheres about the earth’s center. In this case Snell’s law assumes a slightly different form. Instead of using angles re- ferred to the plane surfaces it is now necessary to refer the angles to horizontal planes tangent to spheres about the center of the earth (see Figure 9). The new form, as given in Section 17.4, is mr COS @=ANo COS ao , (4) where r and a are values of the radius vector from the center of the earth to a point in the atmosphere and a oo Ficure 9. Refraction through a curved layer. to the earth’s surface, respectively. a now stands for the angle formed by the ray with a plane normal to the radius vector. ao and 7m are the values of a and n at the ground surface. If h is the height above the ground surface, so that r =h-+a, the above equation may also be written in the form n (1 +2) cos a = ny c0s ay (5) h/ais a very small quantity, and n differs from unity by only a few parts in 10,000. Under these conditions n(1 + h/a) may be replaced by n + h/a with neg- ligible error. The quantity n + h/a is called the modified refractive index, or the modified index for short. Equation (5) then assumes the form (n + *) COS @ = Np COS a. (6) As a result of general agreement it is customary to use, instead of n + h/a, the symbol M defined as follows: M=(n+2-1) 10°. (7) At the surface of the ground M reduces to M,y=(nm—1) 10°. (8) FUNDAMENTALS OF PROPAGATION Hence M is the excess of the modified refractive in- dex above unity, measured in units of one millionth. This unit is called an M unit [MU]. Values of 1 for the atmosphere lie in the range of 200 to 500. Cus- tomarily M is referred to simply as the modified index of refraction. Using the numerical value for the radius of the earth, 6.37 X 10°m (21 X 10° ft), the rate of increase of M with height, owing to the term h/a, is (1/a) 108, which is equal to 0.157 MU per meter (0.048 MU per foot). As the result of a large number of experiments, carried out chiefly in the northern temperate lati- tudes, the rate of decrease with height of the re- fractive index has been found, on the average, to be dn ——— 11 6 ah Qe = 4 10 = —0.039 MU per meter . (9) This is the rate of decrease assumed for the standard atmosphere. It will be noticed that the average rate of decrease of n with height is one quarter of the rate of increase of the term h/a which results from the curvature of the earth. The fact that these quantities are of com- parable magnitude is of great importance, as will be seen later. Consequently the vertical gradient of M for the standard atmosphere is dM _f[dn , 1 5 a = (Geta) 22 = (34) 108 = == 1108 oo which has the value 0.118 MU per meter (0.036 MU per ft). The value of M at any height, relative to the surface value Mo, for the standard atmosphere, is equal to M—M,=0.118 h; h in meters, M—M,=0.036 h;_h in feet. (10) (11) 17.1.6 Equivalent Earth Radius— Flat Earth Diagram An important conclusion may be drawn from equation (11). As will be shown in Section 17.2.4, dn/dh is the negative of the curvature of a ray in the atmosphere, and 1/a is the curvature of the earth. The algebraic sum of these two quantities (their numerical difference) is the curvature of the ray relative to that of the earth. The net result is this: if 195 the earth is replaced by an equivalent earth with an enlarged radius equal to 4a/3 the rays may be drawn as straight lines. To state the result in another way: using the equivalent earth with radius equal to 4a/3 corresponds to replacing the actual atmosphere, in which the index n decreases with height, by a homo- geneous atmosphere with an equivalent index n’ which is independent of height (see Figures 10, 11, 13, 14, and 15). This transformation of coordinates great- ly facilitates the calculation and interpretation of cov- erage diagrams for the standard atmosphere. More generally, if the rate of change of n with height ditfers from the value—(1/4) (1/a) 10° MU per meter given above, which may be true in certain parts of the world, the equivalent earth radius de- parts from the value 4a/3. In general the equivalent earth radius is designated by ka. For a steeper drop of refractive index with height, & increases and be- comes infinite when the curvature of the ray is just equal to the curvature of the earth. In the general case, when k& is not equal to %, equation (11) must be modified to the form: h M — M) = ina 10° , h : = 0.157 ih? h in meters , h : = 0.048 Bo h in feet , (12) to account for a linear moisture gradient correspond- ing to a different value of k. Since the change of the earth’s radius takes care of the variation of refractive index and substitutes a homogeneous atmosphere for the actual atmosphere, it follows that in a diagram in which the earth is given a radius ka, the radiation propagates along TRANSMITTER Ficure 10. Ray curvature over earth of radius a in an actual atmosphere. straight lines. The difference is illustrated in Figures 10 and 11. In Figure 10, which shows the true geo- 196 TROPOSPHERIC PROPAGATION metrical conditions, the radio horizon appears ex- tended as compared to the geometrical horizon, be- cause of the curvature of the rays. In Figure 11 the rays have been straightened out, but a line that was straight in Figure 10 appears curved in Figure 11. The value of % for k is a good average for the at- mosphere in the middle latitudes. For particular Figure 11. Rays in a homogeneous atmosphere. Equiv- alent radius ka. atmospheric conditions the value of k may be con- siderably different. The moisture content of the at- mosphere is small at the low temperatures of the arctic regions and increases considerably with the higher temperatures of the tropics. However, the AND RADIO METEOROLOGY value of k depends more particularly on the manner in which the moisture content varies with height above the surface of the earth, and to a lesser extent on the distribution of temperature with height. Figure 12 has therefore been constructed to show the dependence of & on the gradient of relative humidity, measured in per cent per 100 m, for a series of surface temperatures varying between 7,>=—30C and T,) = +40 Cj It has been found convenient to plot 1/k rather than k itself. The lines drawn correspond to the assumption of saturation humidity at the ground; if the humidity at the ground is less than 100 per cent the correction read from the auxiliary table is added to the value of 1/k obtained from the graph. The standard temperature gradient of —0.65 C per 100 m is assumed for all the curves. The curves of Figure 12 indicate that as the tem- perature increases, smaller and smaller values of rela- tive humidity gradients are required to produce changes in k of considerable magnitude. This should be of greater importance in the tropics where the moisture content is relatively high. Changing k from its standard value of 4% has an important influence on the strength of the field at any 1,2 (RH)g-30C ~25C -20C -15C -10C_ -5C_ OC _+45C +10C +15C +200 +25C 4+30C +35C +40C 1 10% e151 .194 .240 .301 1.371 .455 1 EAE 20% ~134 .172 .214 .267 .329 .405 30%}.007 .009 .014 .021 .030 .043 .060 .070 .092 .118 .151 .187 .234 .288 .354 10 40% 1.006 .008 .012 .018 .026 .037 .052 .060 .079 .101 .129 .161 .200 .247 .304 OK 35 50%].005 .007 .010 .015 .021 .031 .043 .050 .066 .084 .108 .134 .167 .206 .253 0 60%].004 .005 .008 .012 .017 .024 .034 .040 .052 .067 .080 .107 .134 .165 .202 70%|.003 .004 .006 .009 .013 .018 .026 .030 -039 .050 .065 .080 .100 .123 .152 9825 80%}.002 .003 .004 .006 .009 .012 .017 .020 .026 .034 .043 .065 .067 .082 .101 (5 90%].001 .001 .002 .003 .004 .006 .009 .010 .013 .017 .021 .027 .033 .041 .051 8 Tr lama] =p 7‘ =30 =3 7 -—— = =| ‘-) is | 4 gu & -5 E pt C 5) a > i 4 | S| 4-0 ae 3 3 = 3+ 9 10 | x | °o | 2 © ] ! a [ © | ; Sy REL HUMIDITY GRADIENT 40° 5° 30) 25° 20° jaeetetal % PER 100 METERS ———> r | | | ary war eT a ea my TS es SO. Sy SO a le Ficure 12. Graph: 1/k versus RH gradient and temperature for 100 per cent RH at ground. FUNDAMENTALS OF PROPAGATION 197 point in space. Though it is not easy to state the re- sult in general terms for any position, it is possible to evaluate the change in field strength near the surface (below 60 m altitude for 600 me and somewhat higher for lower frequencies) and well within the diffraction region, for moderate changes in k. Here the decibel attenuation below that for the free space field is de- creased approximately in the ratio £3. If, for in- stance, k changes from 4 to 8, the original decibel attenuation is to be divided by 3.3. To state the mat- ter another way, the range at which a given field strength is found will be increased approximately in the ratio k3. This has an important bearing on the problem of propagation for communication purposes in this region. It has been shown above that a linear variation of refractive index can be converted into a change of earth’s curvature. The reverse process is equally feasible: to eliminate the earth’s curvature by using a modified refractive index curve. This is a general procedure which involves no assumption about the variation of refractive index with height. From the equations in Section 17.1.6 it is seen that the effects of the earth’s curvature are equivalent to those of a refractive index increasing linearly with height at the rate of 1/a. Hence one effectively flattens the earth, thus eliminating the curvature effect, by adding to the refractive index the term h/a. In other words, the angles between a ray and the horizontal over a curved earth are the same as the angles between a ray and the horizontal over a flat earth when the re- fractive index n has been replaced by n + h/a. In practice, the quantity M defined by equation (7) is used. If MW increases steadily with height, which is the case for the standard atmosphere, the rays appear curved upwards on a flat earth diagram, which is illustrated in Figure 13. TRAN SMITTER, INTERFERENCE REGION DIFFRACTION REGION HORIZON RAY Se Sie NY GEOMETRIC YY pps EARTH MMMM MMMM Figure 13. Rays in a plane earth diagram. Summarizing, it is seen that three types of graphi- cal representations of a coverage diagram may be used. (These are illustrated in Figure 14 for the lowest lobe.) 1. The true geometrical representation. With ee TRUE EARTH RADIUS a EQUIVALENT EARTH RADIUS ka od FLAT EARTH k=©oo Ficure 14. Shape of lobes as affected by method of representation. standard refractive conditions the lobes appear bent downwards. Refractive index n decreases with height. 2. The equivalent earth radius representation. Earth’s radius changed to ka (normally k=%). For standard refractive conditions the lobes appear straight. Equivalent refractive index n’ is inde- pendent of height since the equivalent atmosphere is homogeneous. 3. The flat earth representation. The earth’s sur- face and other surfaces of constant height have been flattened out. For standard refractive conditions the lobes appear bent upwards. Excess modified index M increases with height. The quantities n, n’, and M for these three cases are illustrated in the left-hand series of diagrams in Figure 15. Wil The Horizon— Diffraction Krom simple geometrical considerations it can be 198 TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY shown that two points at elevations h; and hz are within sight of each other when their distance 1s less STANDARD ATMOSPHERE NONSTANDARD ATMOSPHERE Zs CURVED EARTH h RADIUS a HEIGHT h CURVED EARTH h RADIUS ka (HOMOGENEOUS ATMOSPHERE) INVERSION PLANE EARTH (MODIFIED INDEX CURVES) M M Ficure 15. Types of index curves. than the horizon distance d, (Figure 16) given by d, = V/2kahy + ~/2kahe , (13) where d,, a, and h are all expressed in the same units. For the particular value of k=%, dy = V1ihy + V1Th , (14) where d, is measured in kilometers and hf is in meters; and dy = V/2hi + V/2hz , where d;, is given in statute miles and h in feet. The field strength at different elevations he (Figure 16) for a given range varies in the manner illustrated in Figure 17. The field is given in decibels, relative to the intensity at 1 m from the transmitter, for a range of 50 miles over sea water for frequencies of 100, 200, 500, and 3,000 me. The horizon elevation for this point is 888 ft. Above point P in Figure 16, is the interference region where, with increasing height, the (15) INTERFERENCE Figure 16. Horizon distance. field strength first increases rapidly and then oscil- lates between maxima and minima determined by the lobe patterns of the coverage diagrams. Below point P, the field strength declines rapidly 10,000 5000) i uu i 4000 = pa fete on |e zee i 50; — == [] Ty] “160 -200 -180 “140 -100 -80 0B -120 Ficure 17. Diffraction and interference fields at height h,. Field strength at 50 statute miles over sea water in db relative to field at 1 m from transmitter. Horizontal polarization. Transmitter height 30 feet. with decreasing height to a minimum at ground level; the rate of decrease is larger for the higher fre- quencies. Neither the direct nor the reflected rays can penetrate into this region, which therefore, re- ceives radiation entirely by diffraction of the energy around the earth’s curvature. Radar targets are rarely visible when they are in the diffraction region. This is certainly true for air- plane targets. Very large targets, such as warships or islands, are occasionally visible in this region; but, more often the detection of targets is caused by superrefraction. For communication work, on the other hand, the diffraction region is of importance, especially at the longer wavelengths. 72 ATMOSPHERIC STRATIFICATION AND REFRACTION 21 Origin of Refractive Index Variations The variation with height of the index of refraction n controls the curvature of rays in the atmosphere. The value of n exceeds unity by only a few hundred ATMOSPHERIC STRATIFICATION AND REFRACTION 199 parts in a million and may be computed from the following formula: D 3.8 O5e = He 8 x 10% (16) = Gr (n 1) 10 p iE 79p Ip in which n = index of refraction at height h above ground; p = barometric pressure of the atmosphere in millibars at height h. (1 mm Hg pressure = 1.334 mb); e = partial pressure of the water vapor in millibars (order of 1 per cent of p); T = absolute temperature ((C + 273) at height h. In equation (16) the term 1le/T is very small in comparison with the other terms and may, without serious error, be neglected. This simplification has been used in obtaining the values in the last two columns of Table 1 and in designing the nomogram, Figure 19. Workers in the field may prefer to use mixing ratio (practically equal to specific humidity) in place of the water vapor pressure. The relation is given by 621e or s = —, Dp e = 0.00161 ps (17) where s is in grams of water per kilogram of air. The variation of n with temperature and relative humidity for an air pressure of 1,000 mb is illustrated in Figure 18. It is seen that the refractive index de- pends on humidity more critically than on tempera- ture. The dependence on humidity is greater at the higher temperatures where a given relative humidity represents a larger amount of water vapor. In practice it is customary to use the modified refractive index given by 79p M = (n+ 2-1) 1012 De 4 38 A a T T? + 0.157h (h in meters). TABLE 1. 460 440 420 380 — —— 8 e— 7 TEMPERATURE IN DEGREES C Figure 18. Relation of n to temperature and relative humidity. In order to compute M directly from temperature, relative humidity, and height data, the nomogram (Figure 19) has been constructed. Detailed instruc- tions for its use are given. The National Advisory Committee on Aeronautics [NACA] standard atmosphere commonly used in aeronautics assumes a sea level pressure of 1,013 mb ( = 760 mm Hg) and asea level temperature of 15 C, decreasing at a rate of 6.5 C per kilometer in the lower atmosphere. The NACA standard atmosphere is not concerned with the moisture content. In the actual atmosphere the moisture may vary between extremely wide limits, but as a typical value a rela- tive humidity of 60 per cent may be assumed as the Standard atmosphere with 60 per cent relative humidity. NACA standard atmosphere Moist standard atmosphere Dry air Dry air e(mb) Moist Altitude, Temp, pressure, index, for air index, M = meters Cc mb (n — 1)10° 60% RH (nm — 1)105 (n + h/a — 1)10° 0 15.0 1013 278 10.2 325 325 150 14.0 995 274 9.6 318 342 300 13.0 977 270 9.0 312 359 500 11.7 955 265 8.3 304 382 1000 8.5 894 251 6.7 283 440 1500 5.2 845 240 5.3 266 501 200 standard condition. This corresponds to a water vapor pressure of approximately 10 mb at sea level and a rate of decrease of water vapor pressure in the lower levels of about 1 mb per 1,000 ft. At higher levels the rate of decrease of the water vapor pres- sure is less rapid. These conditions are represented in Table 1 for the atmosphere up to 1,500 m. Both the dry and the moist standard atmosphere exhibit a very nearly linear increase of M with height. According to equation (12), Fal 10° = 0.157" ; hin meters . By using this formula in conjunction with Table 1 it is easily shown that k = % for the dry standard atmosphere, and k = % for the standard atmos- phere with a 60 per cent relative humidity. This value of k is the one commonly adopted in coverage diagrams corrected for standard refraction. Because of the great variability of the moisture content of the atmosphere with season, geographical location, etc., a moist standard atmosphere has a limited physical significance. The standard should rather be defined in terms of a fixed linear slope of the refractive index, and for this purpose the value k =% has been chosen. "22 The Measurement of Refractive Index The lower atmosphere frequently is stratified by nonstandard distributions of temperature and hu- midity which vary rapidly and irregularly as func- tions of the height. The refractive index is then no longer linear but has a more complicated dependence on height, determined from equation (16). The strati- fication which is of particular importance in tropo- spheric propagation is found in the lower part of the atmosphere, that is, below about 4,000 to 5,000 ft and frequently in the lowest few hundred feet above ground. Since the variation in the atmospheric pressure gradient is small, interest is mainly centered in the dependence of the modified refractive index M on the temperature and humidity distributions. Methods, useful in the field, have been developed for obtaining rapid determinations of temperature and humidity in the lowest levels of the atmosphere. The ordinary radiosonde (radiometeorograph) is not well adapted for this purpose since it is usually designed to give data at levels about 100 m apart, which often is not TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY close enough to reveal the significant details of the M curve. Consequently it has proved to be necessary to develop new instruments for this purpose. Several types of instruments have been designed which can be placed on towers, or carried by slow- flying airplanes or dirigibles or carried aloft by captive balloons or kites with wires connecting the tempera- ture and humidity elements to measuring or record- ing equipment located on ground or aboard ship. Some such measurements have been made with instruments using electrical methods in which dry and wet electrical resistance elements are connected into a circuit to give “dry bulb” and ‘wet bulb” temperatures. Another electrical method uses the same ‘‘dry’”’ temperature element but, in place of the wet bulb, obtains a relative humidity measure- ment by using an electrolytic humidity element of the type employed in the U. S. Weather Bureau radiosonde. Hair hygrometers are definitely not suitable for this type of work on account of their lag in adjusting themselves to changes in relative humidity (of the order of 3 to 5 min for appreciable changes in humidity). Measurements made from airplanes have the advantage that it is possible to survey a compara- tively large area within a short time. This can be of great importance along coasts where conditions in the lowest levels of the atmosphere sometimes change rather rapidly with increasing distance from the shore. In the absence of suitable special equipment an ordinary psychrometer held out of the window of a plane will give quite satisfactory results in slow- flying planes, providing care is taken to keep the wet bulb sufficiently moist. When measurements are made from an airplane the height above the ground is determined for each measurement by means of the plane’s altimeter. Unless carefully done this introduces the possibility of considerable error. In another method captive balloons, kites, ordi- nary radiosonde balloons, and, occasionally, barrage balloons have been used to carry the measuring elements aloft. Ordinary captive balloons will work in wind speeds up to about 8 miles per hour; in higher winds kites or, occasionally, barrage balloons are used. Kites can be flown from boats even at low wind speeds or in calm weather. With this type of equipment the electrical measuring elements aloft are connected to an indicating or recording instru- ment at the ground or aboard ship by means of fine insulated wires that are wound around the cable holding the balloon. 201 FRACTION 4 STRATIFICATION AND RE RIC 7 ATMOSPHI “A Suynduos tof wre«sourou Ayrprumny satyepei-emyersduray, “G] AAAS NI LH9O)3H 009 Oss 00s Ose 60% Ost Sean 2 ose 002 os! oo! Os 0002 006) o0o8! OL! 0091 00s! Or! OOK! foley 4) oon 0001 006 008 002 0098 00S 0Ov 00f 008 001 ° 4334 NI 1HOI3H W OSs =O8sS ozs O1IS OOS Of O08 Oty OS Ory 8Ofe OOp 8 O& Ost Os 8 Ove OfE OzE og (ole. 00s O6e Coy ale 09 Ose Ove Ofte Oeb Ow 00v Oe Ost OLE og¢ Ose Ove cee Oe og O00F qwOOd!l 3O 3YNSS3Yd Yds ,O! X(I-U) dl nr Non gs Ors as oF. s & Ol ot 2 rx 8 “BIDDS yNo) By) SESOID 494N4 & 8y} BBM W POBY “jYbrey pesrsep 94) 40 2/09S 8 a W0}j0Q BY} SBSSO1D 41 [YUN yuIod Smy UO 4B Buy JOAig “quOOO! 40 eunsseud D 2} gOIx(I-u) SBAIB Siu] ‘9}D9S Plus a4) O4 ‘(9]095 parund)sj0oS puodas ayj uO aunjosedwa, ayy YOnoAy DOS do} ayy uo Ajipiuiny aAijoj8s 84) WOsy JOINA OD BdDid ‘yybiay yo suoyouny so uaaib aso aunjowdwa; puo Ajipiwny eaiyojes usym pasn si W Buyndwoo 40) wosbowonN Ajiprwny eAyojay- aunjosedwa) ay) W BuiuiojgO 40} SudlydN4ySu} %0 i) %01 SI %0z sz “Of se %0v- Se %0S ss %09 $9 %OL SL %08 7) %06 sé % 00! ALIGINNH SALW 138 202 17.2.3 Types of Modified Index Curves A large number of meteorological soundings of the lower atmosphere have been carried out by several laboratories and Service units. From these measurements the modified index curves have been calculated as a function of height, and it has been shown that practically all these curves fall into one of the six types illustrated in Figure 20. STANDARD TRANSITIONAL SUBSTANDARD I Iq Ip h b h M M M SIMPLE SURFACE TRAPPING ELEVATED S SHAPE GROUND-BASED S SHAPE I I, Wp a) INVERSION ei: h INVERSION LAYER | ! za ~ J ouct —Y) buct DUCT | ne | - |\ INVERSION LAYER = I M M M Figure 20. Types of M curves. For the standard atmosphere the MW curve increases with height as shown in curve I. For nonstandard atmospheres, the M curves will take one or another of the forms illustrated in curves Ia, Ib, II, Illa, and IIIb. Of particular interest are those curves in which M decreases with height for a range of alti- tudes. (This decrease is the result of a sufficiently sharp decrease in n with height as illustrated in Figure 15.) In this event an inversion layer is formed in the atmosphere. Throughout the range of altitudes of decreasing © M the curvature of the rays exceeds the curvature of the earth. Nearly horizontal rays which either originate in, or penetrate into, this layer are trapped, and, if the layer extends far enough, energy may be carried to distances far beyond the geometrical horizon. However, the region in which the waves or rays are trapped may have a thickness or depth exceeding that of the inversion layer. This region is known as a duct. Its precise definition may be taken from Figure 20. It is the strip between an upper minimum of the M curve and either the ground or the point where the vertical projection from the upper minimum intersects the M curve. There are two main types of ducts, the ground-based duct, TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY illustrated by curves II and IIIb, and the elevated duct, illustrated by curve IIIa. The height in the atmosphere at which the varia- tions in refractive index occur may vary from a few feet to several hundred or even a few thousand feet. These variations are likely to be found at fairly low elevations in cold climates and at the higher elevations in warm climates. The meteorological con- ditions which yield these various M curves are described in Section 17.3. The opposite effect occurs when the M curve takes the substandard form (curve Ib in Figure 20). Here the lower portion of the M curve has a slope which is less than standard. In this event the rays in the lower atmosphere are bent downward to a lesser degree than in the standard atmosphere or may even be bent upward. Depending to some extent upon the elevation of the transmitter, the field strength in the substandard region may be reduced considerably below normal, even to the point of producing a radar and communication “blackout.” If the M curve is steeper than average in the lowest layers, the transitional case arises (curve Ia). Here a slight change in the temperature and moisture distribution might lead to a curve of type II and a duct. 2" Rays in a Stratified Atmosphere Nonstandard vertical variations of refractive index occur frequently in the lower atmosphere. In addi- tion there may be gradual variations in the horizontal direction. So far, the theory of propagation has not reached a stage where such horizontal variations can be taken into account. Unless otherwise stated it is always assumed that the stratification extends hori- zontally as far as the coverage of the transmitter and that the variation in the M curve is entirely vertical. Weather conditions often are sufficiently homogeneous horizontally to warrant this assump- tion, but there are exceptions, mainly near coasts (see Section 17.3). Only those rays are affected by the vertical varia- tions of refractive index in the lower atmosphere which leave the transmitter at a very small angle. Both theoretically and practically it has been found that the effects of nonstandard refraction are negli- gible for rays that leave the transmitter at an angle with the horizontal of more than about 1.5°. Rays that leave at an angle with the horizontal of less than 1.5°, and especially those emerging at angles ATMOSPHERIC 203 STRATIFICATION AND REFRACTION with the horizontal of 0.5° or less, are strongly affected by nonstandard refraction. This part of the transmitter radiation is of paramount importance in early warning radar and in communications. For such applications of radar as gun-laying or search- light control the effects of nonstandard propagation are usually negligible because the rays which reach the target have emerged from the transmitter at a fairly large angle with the horizontal. The progress of a ray through the stratified atmos- phere is described by Snell’s law, discussed in Section 17.1.4. When the angle a between the ray and the horizontal is small 2 a cosa=1-— >, provided @ is expressed in radians. Introducing this into Snell’s law for a curved earth, equation (6), noting that n + h/a=1-+ M- 10-° and neglecting second order quantities, it is seen that 2 (Ge = cap) = GW = ils (als) Since a is the angle which the ray makes with the horizontal it is equal to dh/da, the slope of the ray. Solving equation (18) for a, dh a = = Yan? + 20 — M10 (19) These relations apply to any two levels provided a and ap are the angles at the levels to which M and My refer. GROUND OR SEA LEVEL ~ My M variations of the modified index. Although this ray tracing method is only an approximation of the true solution of the wave equation, it can be used, subject to certain limitations, for computing quantitatively the strength of the field. The approximation breaks down when neighboring rays cross each other and form caustics. The method may be illustrated by the case of standard refraction with k = 4. As shown in Figure 21, draw the M curve with a slope ka = 4a/3. Let the subscript 1 stand for the transmitter level (of height h;). Pass a vertical line through the corre- sponding point M, of the M curve. Lay off the distance a,2/2 to the left of M, for a particular ray, 1, which emerges from the transmitter at angle a1 with the horizontal. In order to make a and M comparable numerically, the factor 10~® should be eliminated from equation (18) above. For this pur- pose a? should be measured in the same unit as M, that is, in 10-® radian. The distance between M and lat any height h then is equal to (M — My) + a?/2, and by equation (19) the square root of twice this quantity is equal to the slope of the ray at height h. Hence, ray 1 starting downward from the transmitter is bent more and more toward the horizontal as h decreases. At point P this ray becomes horizontal and from there on increases in slope with increasing height. Ray 1’ starting upward from the transmitter at the same angle a continues to curve upward more and more rapidly as the height increases. Ray 2 is the TRANSMITTER DIFFRACTION REGION ———— DISTANCE x Frcure 21. Rays in the standard atmosphere. Equation (19) provides a technique for tracing the paths of rays emitted by a transmitter at various angles with the horizontal, and it indicates how their passage through the atmosphere is controlled by the horizon ray which represents the limit to which rays can be directed by refraction. Beyond this lies the diffraction region where ray tracing cannot be used. To study the field in the diffraction region the original 204. wave equation must be used. Ray 3 is reflected from the ground and in crossing some of the other rays produces the phenomenon of interference. In connec- tion with Figure 21 it must be emphasized that the height scale is tremendously exaggerated and that all the rays shown come from a small group which are propagated in a nearly horizontal direction. Sometimes it is convenient to express the path of the ray in terms of ray curvature. The true curvature of a ray as it appears on an undistorted (curved earth) diagram is different from the curvature exhi- bited by a ray on a plane earth diagram. The true curvature of a ray is given by 1/p, where p is the radius of curvature, and it can be shown that, for nearly horizontal rays, this is related to the gradient of n by 1 dn : oT (20) However, the relative curvature of the earth with respect to that of a ray is (1/a) — (1/p). Now let us set this equal to the curvature 1/ka of an equiv- alent earth. Then 1 1 ep a ey a 2 a2 (21) and, introducing equation (20), 7p 1 1 ain ° (22) dh This amounts to a definition of k which is more general than the one introduced in Section 17.1.6 but reduces to the latter when the index curve varies linearly with height. For a plane-earth diagram, M is used in place of n. Since a 1-—- 1 = @ p M= (n+4 — 1)10°, dM _1f dn de @ et 6 an ar 1)10 ; Substituting the last equation into equation (22) gives ie adhe. serail (23) and shows that k, in its most general form, is propor- tional to the slope of the M curve. Reference to Figure 20 shows that k assumes negative values for a range of altitudes whenever a duct is formed in the atmosphere. TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY These relations may also be expressed in terms of m, where m= a (24) is the ratio of the radius of curvature of a ray to the radius of the earth. From equation (22) it follows that Boh ae (25) Both k and m vary with height except in the special circumstance that the M curve is linear. Table 2 gives a number of corresponding values of k and m and indicates their significance. TABLE 2. Relation of k and m. 6 5 4 k 1 = ~ = 2 o —2 — 5 4 3 } m cS 6 5 4 2} 1 2h Yili 3D U.S. Brit. Moist Zero ——~— —~—~ _ stand- rela- Duct Standard ard tive formation curva- ture U2 The Duct—Superrefraction When the M curve has a negative slope, k is negative; the curvature of the rays is concave down- ward on a plane earth diagram, and the true curva- ture of the rays is greater than the curvature of the earth. Hence rays which enter the duct under suffhi- ciently small angles are bent until they become horizontal and then are turned downwards. This particular form of refraction is called superrefrac- tion. Such rays will be trapped in the duct, oscillating either between the ground and an upper level, or between two levels in the atmosphere. These condi- tions are illustrated by Figure 22 for the case of a ground-based duct and by Figure 23 for an elevated duct. The detailed construction of a ray diagram in the case of an elevated duct is shown in Figure 23. It is assumed, for illustration, that the transmitter is placed at the point which produces the maximum amount of trapping, and this point turns out to be located at the maximum of the bend in the M curve. The vertical line for My corresponding to hi is drawn as shown, and again the line 1 is drawn to the left of M; at the distance a,?/2, to represent ray 1 which ATMOSPHERIC STRATIFICATION AND REFRACTION 205 Ficure 22. Rays with a ground-based duct. 2 ©Q@oOo2# , M- My ae =P ov oe 3 DIFFRACTION REGION: DISTANCE x FiGurE 23. Rays with an elevated duct. departs from the transmitter at angle a1 measured from the horizontal. As the ray proceeds outward and downward it is bent less and less, corresponding to the decreasing distance between the M and 1 lines. Finally it reverses and rises to the height indicated. Ray 1 must therefore oscillate between the heights determined by the crossing of the M and 1 lines. Ray 1’ starting upward at the same angle a oscillates between the same height limits as ray 1. Rays 2 and 2’ emerging at angle a, are the limiting rays which are trapped in the duct between the heights h, and h,. Beyond the horizon ray 3 and below the duct lies the diffraction region for this case. Ray 4 emerging at an angle greater than a, is not trapped but after reflection passes entirely through the duct. Ground-based ducts are likely to be found along coasts where warm, dry air from over land flows out over a colder sea. This situation, for instance, prevails in the summer months along the northeastern coast of the United States. Elevated ducts occur frequently along the southern California coast. An illustrative series of theoretical coverage diagrams as obtained by the ray tracing method described are collected in reference 448. A few of these diagrams are reproduced in Figure 24, for a frequency of 200 me and a transmitter elevation of hy = 100 ft, corresponding to an h;/) ratio of approxi- TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY ALTITUDE FEET 7000 NAUTICAL MILES 30 ~ BLIND ZONE [===] [[_]ZONE OF DETECTION 40~ 200 MC TRANSMITTER ELEVATION 100 FEET 50 Ficure 24. Calculated coverage diagram. mately 20. The height scale is exaggerated in the ratio 40/1. Transmission over sea water is assumed. The coverage range is adjusted to “define the probable low-level zone of detection of a medium bomber with fair aspect by an SC-1 or SC-2 radar at 100-ft elevation. For SK radars and higher alti- tude installations, the diagrams are conservative. For SC and SA radars or for lower altitude installa- tions, they are optimistic.”’ Figure 24A shows the lobe structure for the standard atmosphere in which J increases 36 MU per 1,000 ft. It also shows the value of M — Myo; that is, the MW curve is drawn so as to pass through zero at the transmitter elevation of 100 ft. On diagrams B through E the lower portion of the standard lower lobe is indicated by a dash-dot line. The blind zones are cross-hatched, and their boun- daries represent the calculated limits of detection. An interesting feature of these diagrams is the appearance, In some cases, of blind zones of consider- able range and altitude along the surface. These cause “skip ranges” for ground targets that are significant in operational problems. Ray diagrams were used in calculating the field strengths in Figure 24. The relative heights of the transmitter and the duct have an important bearing on the mechanism of transmission. The duct may develop entirely below the transmitter site or entirely above, or the duct may include the transmitter. With these alter- natives a variety of propagation conditions is possible. One of the important concepts of radiation theory is contained in the principle of reciprocity. This principle states that when a transmitter is at a point in space A, and the receiver at a point B, the received intensity is the same when they are inter- changed, the transmitter being at B and the receiver at A. (It is assumed in making this statement that the transmitter and receiver may be regarded as point sources.) Similarly, for radar the signal inten- sity remains unaltered if the positions of radar and target are interchanged. It is known that there are serious limitations to the reciprocity principle where ionospheric reflections are involved, but for shorter waves and tropospheric propagation the principle may be applied without restriction. By means of the reciprocity principle any coverage diagram may be used to obtain the field strength when the heights of the target and the radar are interchanged. From a study of such evidence on coverage diagrams as is available, it appears that (a) the effects of superrefraction are most marked when the transmitter lies in the duct; (b) they exist to a lesser degree if the transmitter lies below the duct: in particular no excessively long ranges for targets are then found above the duct—sometimes the ranges ATMOSPHERIC are extended slightly, other times slightly decreased; (c) for a transmitter above the duct no excessive changes in field strength occur below the duct—this ean be deduced from (b) by using the reciprocity principle; (d) there is no appreciable superrefraction when the transmitter lies appreciably above the duct. For some time after the discovery of superrefraction it was thought that the concentration of radiative energy in the duct might result in a decrease of the amount of radiation above the duct and hence in a reduction of coverage there. The cases illustrated in Figure 24, at least, are not in accord with this presumption. In spite of the great increase in ranges in the duct the amount of energy trapped is small compared to the total energy of the radiation field. “2° Wave Picture of Guided Propagation It must be realized that while ray treatments give accurate results under certain conditions, there are features of the propagation problem which can be satisfactorily discussed only on the basis of the electromagnetic wave equations. As an aid to under- standing the wave treatment the close analogy between the functioning of a duct and a hollow metal waveguide (or dielectric wire) may be used. In both cases the field which is being propagated may be represented as the sum of an infinite number of terms (modes). Each waveguide mode is propagated with a separate phase velocity and an exponential attenuation factor and has a field distribution over the wavefront that is independent of distance in the direction of propagation. In a metallic waveguide a finite number of modes are propagated with very small attenuation, while the remaining modes, infinite in number, have attenuations so high that they are, practically speak- ing, not propagated at all. The same division of modes into those that are freely propagated and those that are highly attenuated is found for duct propagation. In the duct, however, the difference between the two types of modes is less pronounced than in a hollow metal tube. As the frequency is decreased, the number of transmission modes decreases both for the hollow metal tube and the duct until the cutoff frequency is reached, below which neither serves as a wave- guide. For the case of simple surface trapping (Section 17.2.3) the following formula gives the approximate maximum value of the wavelength for which guided propagation inside the duct can still take place: STRATIFICATION AND REFRACTION Nmax = By! \/AM - 107°. Here d is the height of the top of the duct above the ground in the same units as A,,x, and AM is the decrease in M inside the duct. This relationship is represented in Figure 25 where, it should be noted, 100 50 4M 10 100 d IN FEET Figure 25. Maximum wavelength trapped in simple surface trapping. Duct width d in feet. AM is total decrease of M in duct. the duct width is given in feet and the wavelength in centimeters. When the wavelength exceeds the critical value obtained from this graph, guided propagation is no longer to be expected. M curves of different shapes will require slightly different numerical factors in the formula. The main difference between the modes is found in the vertical distribution of field strength. The first three modes for a simple ground-based duct are illustrated in Figure 26. The lowest mode has h HEIGHT —e M GURVE 1ST MODE 2ND MODE 3RD MODE FIELD STRENGTH —= Ficure 26. Vertical distribution of field strength for first three modes in a duct. 208 approximately %@ of a cycle of an approximate sine wave, followed by an exponential decrease. Higher modes have multiples of half cycles added to the sinusoidal part. How these modes must be combined to give the total field strength and its vertical distribution is a question which depends on the height of transmitter, the distance out to the point where the total field strength is to be obtained, the rate of attenuation of each mode as a function of the distance, and its phase velocity. Since the attenuation and the phase velocity are different for the various modes, the vertical distribution of the total field changes with the distance from the transmitter, and the number of modes composing the total field decreases with increasing distance. 172.7 Reflection from an Elevated Layer This phenomenon has been studied extensively at San Diego. The meteorological situation there is rather unique in that the warm and extremely dry upper air overlies a cooler and very moist lower stratum. The transition between the two layers is very sharp. This gives rise to an elevated duct of the type exhibited by the M curves of Figures 24D and 24K. Often the reversal of the M curve takes place over an even narrower interval of height than shown in these graphs. In such cases there is a reflection analogous to the reflection of waves at a true discontinuity between two media and which cannot be accounted for by the bending of rays. At an interface between two media of different refractive indices there is partial reflection of radia- tion for any angle of incidence, but when the phenomenon (partial reflection and partial trans- mission) takes place in a layer of finite thickness, the reflected radiation is appreciable only at angles near grazing (less than 1° under the conditions found at San Diego). Furthermore, other things being equal, the reflection coefficient increases with increas- ing wavelength. This feature distinguishes the reflec- tion by a layer from the duct effects produced by this layer, as the latter generally tend to become less pronounced for longer waves. The reflection gives rise to an additional field strength near the ground, often well beyond the optical horizon. Transmission experiments carried out at San Diego at frequencies between 50 and 500 me gave results that are explained satisfactorily on the basis of reflections of the type just described but not on the TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY duct theory. Thus most of the ducts caused by reversals of the M curve of the type shown in Figure 24D will be beyond cutoff for a frequency of 50 me, according to Section 17.2.6. No guided propagation should therefore be expected, whereas the observed field at the receiver, located well beyond the optical horizon, was consistently very high. At a frequency of 500 me the reflection is found to be highly critical with respect to the angle of incidence at the reflecting layer. When meteorological conditions are such that the layer is high (8,000 to 4,000 ft), and therefore the angle of incidence large, the intensity of the reflected radiation is found to be very low; when the layer forms at a low level (a few hundred feet only) the reflected radiation becomes very strong. This behavior agrees with the predictions of electromagnetic theory. So far, the experiment at San Diego is the only instance where a clear-cut case of reflection by an elevated layer has been found, although indications of similar effects have been observed elsewhere. Whether or not this phenomenon will occur at other places in or near the subtropical belt is not conclu- sively known since our knowledge of meteorological conditions in these climates is far from complete. If it does occur, it will obviously be of great opera- tional significance. 17,.2:8 Operational Applications RaDAR Ground radars have experienced most of the effects of propagation in nonstandard atmospheres so far observed operationally. Phenomenal ranges on ship and low-flying airplane targets have been observed, especially in the Mediterranean area, the Arabia- India area, in Australia, and the Southwest Pacific theaters. In the United States and Europe ground- based ducts over land have occasionally produced fixed echo clutter seriously interfering with the plotting of aircraft targets over land. This ground clutter interference is especially troublesome with microwave early warning sets plotting targets over land. On ground radars with high pulse repetition rates, echoes from large distances frequently return on the second or later traces. Such echoes interfere with first sweep echoes and sometimes are misinter- preted as having ranges appropriate to the first sweep, with serious tactical consequences. One of the most serious operational consequences of superrefraction is a secondary effect, that of ATMOSPHERIC misleading operators as to the overall performance of the equipment. Long-range’ echoes caused by superrefraction have frequently been assumed to indicate good condition of the equipment, when precisely the opposite is actually the case. The phenomenon of superrefraction does not, however, in the same degree invalidate the measurement of signal-to-noise ratio of nearby echoes, as a criterion of relative overall set performance. Field strengths from nearby objects well within the optical horizon are far less subject to propagation variations. Echo strengths (signal-to-noise ratio) from nearby objects are still considered a good relative index of overall performance, provided that easily recognized echoes can be measured which are not sensitive to very small changes in the radar frequency. There are other sources of echo fluctuations such as the motion of objects (trees, towers) caused by the wind (import- ant at wind speeds above 15 miles per hour). Great care is needed in the choice of fixed echo “standards” so that they are kept free of the effects enumerated. Sometimes artificial echoing objects are constructed of flat mesh screens perpendicular to the beam in order to secure suitable echoes which are not frequency sensitive. The extreme variability of long- range fixed echoes emphasizes the operational need for reliable test equipment for making quantitative tests on the components as well as on the overall performance of the equipment aspects of radars, as distinct from propagation effects. In addition to the direct electrical checks on set performance there are a number of ways of making sure indirectly whether any failures of detection by radar may be due to a deformation of the coverage pattern by superrefraction. In the first place, super- refraction rarely affects detection at angles of eleva- tion above about 1.5°. Any irregularity at higher angles must be attributed to other causes. Even between 0.5° and 1.5° failures of detection are excep- tional and occur only where there are very strong ducts. A clue to the probability of occurrence of such conditions can be ascertained from a study of the primary meteorological effects which cause them; and even with only a moderate amount of meteoro- logical information it is usually possible to make an estimate of this probability. Such superrefractive conditions almost invariably show up in intensified and extended ground echoes (ground clutter on the scopes) and, in case of an overwater path, in extended ranges of ship detection. A record of meteorological data will be very helpful in deciding, after the fact, STRATIFICATION AND REFRACTION 209 whether any specific failure of aircraft detection might have been ascribed to weather. Even if this is probable, there are, of course, a number of other operational causes that might be responsible rather than the weather. Experience gained in England indicates that the technique of forecasting whether or not superrefrac- tion occurs is, on the whole, fairly successful, but there are still many occasions when the predictions are not fulfilled. It has been intimated that in England this was due, at least partly, to variations in the sensitivity of the 10-em set used; when the set is not at peak efficiency, maximum ranges of surface targets appear shortened, and the coverage in the duct may be reduced to a value corresponding to standard conditions. A major problem in any early warning radar system is that of heightfinding by means of maximum ranges. On this it is difficult to make general state- ments. The method of heightfinding usually employed in long-range radar work consists in using the boun- dary of the lowest lobe as a height indicator, assum- ing that when the target is first sighted it has just entered the lowest lobe. When superrefraction is present, the height estimated in this way can be seriously in error. It may be too high if the enemy is flying in the duct, so that he is discovered earlier than he would be normally; or it may be too low if the enemy is flying in the region above the duct and so he is discovered later than he would be under standard atmospheric conditions. Here, again, it should be possible to find out whether repeated errors in height determination are the result of superrefraction or whether they are due to faulty calibration or to other features not related to the weather. Other methods of heightfinding, such as are used in fighter control and control of antiaircraft fire, are usually carried out at angles of elevation too large to be affected by nonstandard types of atmos- phere. VHF ComMunicaTIons AND NaviGaTIoNnAL AIDS The extension of the maximum range of very high frequency [VHF] navigational aids has already been mentioned as an important consequence of super- refraction. Similar extensions of communication ranges of VHF radio sets also occur. Because VHF air-to-ground communications are relied upon only for comparatively short-range communications, this 210 extension of the normal range by atmospheric conditions is important primarily from a security standpoint. It must always be borne in mind that transmissions on VHF may frequently be propagated hundreds of miles beyond the normal limiting range and are subject to enemy interception. Superrefrac- tion has also been observed to cause very objection- able mutual interference between two control towers attempting to use a common VHF channel, although the distance between the airports was great enough to prevent serious mutual interference under normal conditions. Point-to-point VHF radio links are also affected by refraction, over longer paths than optical. Rapio COUNTERMEASURES The laws of radio propagation enter into the problem of jamming the enemy communication and radar equipment. Since it is rarely possible to locate the jamming transmitter coincident with the enemy transmitter whose signals it is desired to mask, the efficiency of propagation of the signals from the enemy transmitter relative to those of the friendly transmitter enters into the problem. This has been worked out in detail for the standard atmosphere. When conditions are not standard, however, the effectiveness of the enemy transmitter, as determined for standard conditions, no longer applies. A case of special interest occurs when an airborne jamming transmitter is used as a countermeasure against an enemy radio communication link operating between two points on the ground. If the meteorological situation is such as to be favorable to formation of a ground-based duct the enemy signals may be propagated with small attenuation, whereas the signals from the jamming transmitter may be unaf- fected or even weaker than would normally be expected. Plans for the employment of ground-based jammers against enemy radio and radar systems should take into consideration the ability of atmospheric refrac- tion to increase, or occasionally to decrease, the signal propagated to the enemy’s installation for jamming purposes. However, there has been only limited use of ground-based jamming so far. Unin- tentional mutual jamming has occurred between the spaced radar sets of a coastal system on the same frequency, where nonstandard propagation condi- tions caused strong signals to be propagated between normally noninterfering radars. TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 17.3 RADIO METEOROLOGY 31 Temperature and Moisture Gradients Section 17.3 is devoted to a survey of the meteoro- logical conditions which produce the various types of propagation described in the preceding sections. This brief outline is not intended to replace the assistance of a professional meteorologist in analyzing short and microwave propagation problems; but by familiarizing radar or communications personnel with the fundamental physical processes of low-level weather it may open the way toward a more fruitful consultation with the meteorologist. Duct formation is the most important phenomenon for which a detailed knowledge of the physical state of the lower atmosphere is required. Whenever a duct is formed, M decreases with height within a certain height interval. Since, according to Sections 17.1.5 and 17.2.1, M = (nm — 1) - 108 + 0.157h, the existence of a duct presupposes that the refractive index n decreases with height over at least a limited range of altitudes at a rate more rapid than 0.157 MU per meter. Such a decrease can be produced by two different meteorological conditions. 1. A rapid increase of temperature with height. This temperature inversion must be very pronounced in order, by itself, to produce a duct. In practice, a temperature inversion contributes to duct formation when accompanied by a sufficiently strong moisture lapse. 2. A rapid decrease of humidity with height desig- nated as a “steep moisture lapse.” When ducts are produced by only one of these causes, they may be designated as ‘dry ducts” and “wet ducts,” respectively. In the general case a temperature inversion and a moisture lapse cooperate in producing a duct, but one of the two factors will be preponderant, thus facilitating the analysis of the meteorological problem. Whether or not a duct occurs under given meteoro- logical conditions and what the rate of change of is inside the duct may be determined by means of the diagram, Figure 27. (This discussion is presented for the purpose of illustrating the importance of temperature and moisture gradients. The technique more readily usable in practice is to compute the values of M at various altitudes directly from tem- perature and relative humidity data with the aid of Figure 19.) The abscissa in Figure 27 is the rate of decrease of humidity with height (—de/dh), where e is the water vapor pressure in millibars. (e can be RADIO METEOROLOGY 211 WZ Wy IN DEGREES C PER 100 METERS aT dh 2 de iusel (iein Eeeo8) S pb +5 +10 | 4.706 100% RH 50 % RH 4,389 — —— IN MB PER 100 METERS dh Ficure 27. Temperature and humidity gradients. found from meteorological tables when relative humidity and temperature are known.) The ordinate is the rate of increase of temperature with height (dT /dh).The slanting lines represent various values of temperature and relative humidity at some particular height h. The lines passing through the same point at the upper right of the diagram correspond to the same mean temperature; lines of different slopes represent different mean relative humidities. In order to determine the rate of change of M at a given level, find the point in the diagram corre- sponding to the actual rates of change of moisture and temperature. Also pick out the straight line representing the actual mean values of temperature 212 TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY and humidity in the layer considered. If the point is at the lower right relative to this straight line, M decreases with height in the layer chosen; that is, a duct exists. If the point is at the upper left of the straight line, M increases with height and there is no duct. The rate of change of M, (dM/dh), may be obtained from the diagram by measuring the hori- zontal distance from the point to the line and multiplying by the function of the temperature f (7) given in the table on Figure 27. The result is the value of dM/dh, the rate of change of M/, in M units per 100 m. This quantity is negative when the point is to the right of the line and positive when the point is to the left of the line. It is seen at once from the diagram that for small values of the moisture lapse an extremely steep temperature gradient is required in order to produce a duct (lower left part of the diagram). In cold air such as is found in the arctic the total moisture is small, and hence the moisture gradient will in general be quite small. Ducts will then only occur when a very strong temperature inversion exists. Strong temperature inversions occur only under special meteorological conditions which will be discussed below. Ordinarily the temperature of the air decreases with height; and this will put our representative point into the upper part of Figure 27. A duct can then exist only when the moisture lapse is large enough, so that the representative point falls to the right of the appropriate slanting line. Such conditions are common in the lower atmosphere. This leads to a wet duct, which is determined almost completely by the moisture lapse. 17.3.2 Physical Causes of Stratification— Turbulence There are three basic meteorological factors which tend to modify the temperature and moisture distri- butions in the lowest layers of the atmosphere. These are: (1) advection, (2) nocturnal cooling (over land), and (8) subsidence. Advection is a meteorological term used to desig- nate the horizontal displacement of air having particular properties. Advection is of great interest in propagation problems particularly because it leads to an exchange of heat and moisture between the air and the underlying ground or sea surface and thus affects the physical structure of the lowest layers. Nocturnal cooling over land is caused by a loss of heat from the ground by infrared (heat) radiation. The cooling of the ground is communicated to the lower layers of air and leads to the establishment of a low-level temperature inversion. Subsidence means a slow vertical sinking of air over a very large area. It is most likely to be found in regions where barometric Highs are located. Subsidence tends to produce a temperature inversion and also produces very dry air which, spreading out over a humid surface, creates a situation which is favorable for the formation of a duct. The processes (1) and (2) change the physical characteristics of the air through transfer of heat; or moisture between the air and the underlying surface of the ground or sea. The operating factor in this exchange is turbulence. The main features of turbulence in the lower atmosphere are outlined briefly below. Convection occurs spontaneously whenever the decrease of temperature with height exceeds a value of about 1 C per 100 m. This convective condition is usually produced as a result of the heating of the ground by the sun’s rays. Even with a cloudy sky the diffuse daylight often is strong enough to produce moderate convection. On a hot summer day convec- tion over land extends to great heights. Convection mixes the air thoroughly and thus causes a uniform distribution of moisture and a uniform decrease of temperature with height of about 1 C per 100 m. Hence even moderate convection tends to produce a smooth M curve which varies linearly with height. Standard conditions may therefore be assumed to prevail on clear summer days (and not infrequently on clear days in the cooler seasons) from the hours of late morning until late afternoon, during which time convection is most active. Frictional turbulence occurs frequently in the lower atmosphere even in the absence of convective condi- tions. It is caused by the wind and requires the presence of at least light winds, but with moderate or strong winds the effect is more pronounced. In conditions of calm or with a gentle breeze, frictional turbulence is confined to the lowest strata. Moderate or strong winds develop a layer of intense turbu- lence, caused by friction of the air at the irregularities of the ground. This layer is usually quite well defined in height and extends to an average elevation of about 1,000 m over land. Over a relatively smooth sea where friction is small the height of the layer is much reduced. In this frictional layer the air becomes thoroughly mixed; the vertical temperature gradient RADIO METEOROLOGY 213 caused by convection is about —1 C per 100 m, and the moisture lapse is steady and rather small. Standard refraction will therefore prevail when winds are moderate to strong over land, and over the ocean also when the winds are sufficiently strong. Temperature inversions occur when the temperature of the surface (sea or land) is appreciably lower than the temperature of the air. The transition from the ground temperature to the free air temperature takes the form shown in Figure 28. The heat and moisture T GROUND T Figure 28. Air temperature versus height for an inversion. transfer caused by turbulence in a temperature inver- sion is less simple than that in a frictional layer. The turbulent processes active in inversion regions are highly complex and are not yet very well explored. It is known, however, that the intensity of the vertical transfer of heat and moisture is greatly reduced as compared to the rate of transfer with frictional turbulence. The reduction is the more pronounced, the steeper the vertical increase of tem- perature; in a steep inversion the rate of transfer may be many times less than in a frictional layer. This tends: to produce a vertical stabilization of the air layers in the inversion region. ‘As soon, therefore, as a temperature inversion has begun to form, the rapid mixing in the lowest layers, usually effected by frictional turbulence, stops and is replaced by a much more gradual diffusion. Assume now, for instance, that the rate of diffusion has become so slow that the transfer of moisture over a height of a few hundred feet takes many hours or, perhaps, a day or two. When the air in the inversion is dry to begin with and flows over ground capable of evaporation (the sea or moist land) there will be established, in such an air mass, a steep moisture lapse, since the water vapor that has been taken up by the air near the ground will only gradually diffuse into the dry air aloft. Conditions are then favorable for the formation of an evaporation duct, in addition to whatever tendency toward duct formation may be caused by the temperature inversion itself. 1733 A dyvective Ducts—Coastal Conditions Advective formation of ducts may occur both over land and over sea, but this process is most important over the ocean near coasts. The most common illus- tration is that of air above a warm land surface flowing out over a cooler sea. Over the land the air will usually have acquired a convective or nearly convective temperature gradient of —1 C per 100 m. When this air flows out over the cool water surface, a temperature inversion is rapidly formed which grows in height as the process of turbulent transfer progresses. The temperature inversion does not, in itself, give rise to a pronounced duct because the effect of a temperature gradient upon the M curve is relatively small; but when the air is dry, evapora- tion from the sea surface takes place simultaneously with the heat transfer, and a moisture lapse rate is established in the lowest layers. The combination of temperature inversion and moisture lapse rate is most favorable for the formation of a duct off shore. The gradual formation of this type of duct is illustrated in Figure 29. This shows MW curves, corres- a a eae — ie ra e Jl |_| Ec i | t 300 = iw 200 fo} 10 20 30. 40 50 Si 70 #680 30 100 M-Mo Ficure 29. Development of duct off coast. Initial state corresponds to air at coast line. 14 hr, 4% hr, etc., refer to time air has been over water. Initial conditions for this set of curves: unmodified air Tp = 32 C, e = 12.3 mb; water 7» = 22 C, e» = 26.5 mb saturation. ponding to the simple surface type of trapping (see Figure 20, curve II) for a series of time intervals 214 (and distances) as the air moves out over the water. The top of the duct is given by the elevation of the minimum value of the M curve. It will be noticed that the duct acquires a maximum depth some time after the air has touched the cold water surface; thereafter the depth decreases. The cause of this behavior is found in the progressive decrease in moisture and temperature differences which is the final result of the diffusion process. Thus the final stage of this transformation is an air mass whose temperature and moisture distributions are in equi- librium with the underlying water surface and no longer show a rapid variation with height. Duct formation in such a case depends on two quantities: (1) the excess of the unmodified air temperature above that of the water and (2) the humidity deficit, that is, the difference of the satura- tion vapor pressure corresponding to the water tem- perature minus the actual water vapor pressure in the unmodified air. If these quantities are large, especially the humidity deficit, a duct will develop. A great variety of local conditions may, however, be encountered in problems of this type, and empiri- cal rules developed for one locality may not at all apply to others. Advective processes may also occur over land, but the conditions required for duct formation are likely to be found much less frequently. Evaporation over land need by no means be small unless the land surface is very arid (desert) ; in fact, evaporation over a moist soil or a ground covered with vegetation may be comparable to, or even larger than, evaporation from a sea surface. A duct may therefore be formed when dry, warm air flows over a colder ground surface capable of evaporation. The temperature excess and humidity deficit may again be defined as above. Land and sea breezes often produce ducts near coastal regions. These winds are of thermal origin and are produced by temperature differences between land and sea. The mechanism is illustrated in Figure 30. During the day, when the land gets warmer than WARM COLD COLD WARM LAND SEA LAND SEA SEA BREEZE LAND BREEZE Figure 30. Land and sea breezes. the sea, the air rises over the land and descends over the sea and causes an air circulation in which the wind blows from sea to land (sea breeze) in the lowest TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY levels. Vice versa, if during the night the land becomes colder than the sea, a circulation in the opposite direction arises. This is the land breeze. As a rule, this type of phenomenon is extremely shallow, and the winds do not extend above a few hundred feet at the most. Often there is a reverse wind in the layer above the land or sea breeze layer. A sea breeze may modify the advective conditions described above In various ways, and extremely strong ducts have been observed repeatedly under sea breeze condi- tions. The land and sea breezes are of a strictly local nature and in some cases will extend only a few kilometers to both sides of the shore. Nevertheless this region may be an important part of the trajec- tory of radiation. These breezes develop only under fairly calm conditions; under conditions of moder- ately strong wind, the sea and land breeze will be perceptible only as a slight modification of the existing wind. Because of their limited extent, fore- casting of these breezes requires a study of the local wind and temperature conditions. Advective ducts caused in the manner described here are often quite limited horizontally. This is especially true if a sea breeze is involved. The assumption made throughout this report, namely that the stratification of the air is of infinite extent horizontally, will no longer be valid, and superrefrac- tion may be restricted to a stretch along the coast. es Ducts over the Open Ocean A type of duct that is somewhat similar to the advective duct described above is found over the open ocean where the air has had an extensive over- water trajectory. It has been studied in experiments carried out at the island of Antigua in the West Indies. The subsequent description refers to this particular location, but on the basis of experience gained operationally and in other experiments it may be presumed that similar conditions prevail in numerous other regions of the world, particularly in the trade wind regions. At Antigua, in winter and early spring when these tests were made, the wind is usually from the north- east since the island is situated at the southeastern fringe of the so-called Bermuda High, a large semi- permanent circulation system over the North Atlantic, extending from about 10° to 30° North latitude. The air at Antigua has thus had an ocean trajectory of thousands of miles. The relative hum- idity is of the order of 60 to 80 per cent, indicating RADIO METEOROLOGY that in spite of the long passage over the sea no diffusion equilibrium has been established between the sea surface and the moisture in the lower atmos- phere. On the other hand, there is little difference between the air and sea temperature, the latter being rather constant at 25 C and the former varying between 23 and 26 C. The air is, therefore, nearly in convective thermal equilibrium with the sea sur- face, and no appreciably “dry” duct can develop. The duct is caused by the moisture variation in the lowest layers. 200 160 120 oO fo) HEIGHT IN FEET ——e 40 ee WATER SURFACE Q ee O te) 360 370 380 380 10) 340 35 M MODIFIED INDEX ———————e Figure 31. M curve over West Indian Ocean. A typical M curve is shown in Figure 31. It may be seen that at as small a height as 0.5 m above the sea M has a value much lower than at the surface itself. As the surface value of M is obtained by the assumption that the air in immediate contact with the water is saturated with moisture, this indicates that 0.5 m above the water the moisture content of the air is still appreciably below saturation. The moisture in the lowest levels is subject to consider- able variations caused partly by turbulence, partly by the waviness of the sea surface. M curves, such as Figure 31, are obtained by averaging over several measurements. These ducts are much lower than the advective ducts discussed in the previous section; their height is about 12 to 15 m (around 40 ft). The effective decrease of M in the duct (apart from the sharp decrease in the lowest half meter) is of the order’ of 4 to 8 MU. 215 The latter figure depends somewhat on the wind speed. There is a maximum decrease of 8 MU at a wind speed of about 8 m per see (13 miles per hour) and lower values for both lower and higher wind speed. The duct height in turn shows a very slight dependence on wind speed, increasing somewhat with increasing speed. These ducts are so low that they are not very effective for trapping of waves even as short as S band, presumably on account of strong leakage (see Section 17.2.6), and signal strength is not increased when an S-band transmitter or receiver is placed inside the duct. For K band, on the other hand, the trapping effect is marked; on raising the transmitter or receiver from the ground a maximum of signal strength is observed at about 9 m, but from there on the signal begins to decrease up to about 20 m (overall decrease 5 db); at greater heights the signal gradually rises again. These ducts appear to be a permanent feature at Antigua, at least during the season these observa- tions were carried on. This is probably true also for many locations in the trade wind belt. The daily variation of weather phenomena and of duct charac- teristics at such purely maritime locations seems to be insignificant. “35 Nocturnal Cooling— Daily Variations A daily variation of surface temperature occurs only over land. During the day the heating is caused by the sun’s rays, and the cooling of the ground surface during the night is produced by radiation from the ground. The diurnal temperature variation of the sea is extremely small. However, shallow bodies of water sometimes have an appreciable diurnal variation. The radiation which causes nocturnal cooling of the ground is temperature or heat radiation which is composed of waves in the infrared portion of the spectrum. It is the same kind of radiation that is given off by a hot stove or electric heater, but since the temperature of the earth is less than that of a stove the earth emits comparatively less heat radia- tion. Nevertheless, radiation is a very powerful agent in cooling the ground. From about sunrise until the late afternoon, the surface of the earth gains more heat from the sun and atmosphere than it loses by radiation to space; in the late afternoon and during the night, the surface loses more heat than it gains. The amount of heat radiated is very nearly inde- 216 pendent of the physical constitution of the ground but is dependent upon its temperature and increases very rapidly with a rise in ground temperature. The atmosphere has a “blanketing”’ effect upon the infrared radiation emitted by the ground. The atmosphere itself absorbs and emits infrared radia- tion, and the cooling of the ground may be greatly reduced by the action of the atmosphere. The blanketing effect is least with a clear sky and dry, cool air; it is somewhat stronger when, with a clear sky, the atmosphere is very warm and humid, as in the tropics. A cloud will produce a distinct blanket- ing effect, and with a complete overcast of low cloud the blanketing is so pronounced that the nocturnal cooling of the ground is reduced to only a small fraction of its value with clear skies. The loss of heat from the ground is distributed by turbulence over the lowest layers of the atmosphere, thus giving rise to a temperature inversion. Inver- sions of this type are strongest in temperate and cold climates with a clear sky and cold, dry air overhead; they are less pronounced in the tropics with humid air and a clear sky and are practically absent with an overcast sky. A meteorologist, after some experience, can estimate the magnitude of an inversion to be expected with given local weather conditions. Temperature inversions, by themselves, can at best produce only weak ducts, but strong ducts may result when the inversion is accompanied by a suffi- cient moisture lapse. This requires that the air be dry enough to allow evaporation into it from the ground. In warmer climates where the transition between night and day is rapid, evaporation may set in in the early hours of the morning before the nocturnal inversion has been completely destroyed by the action of the sun. A strong duct will then be. formed for a short period. This condition seems to be frequent during certain seasons in Florida. It is obvious that the shape of the M curve, when it deviates from the normal, may undergo rapid variations with the period of a day. One example has just been quoted; another is illustrated by the advective ducts over the North Sea produced by the mechanism described in Section 17.3.3. These ducts usually form in the hours before midnight and last until the early hours of the morning. 17.3.6 Fog Contrary to what might perhaps be expected, the formation of fog results, in general, in a decrease of TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY refractive index. When fog forms, e.g., by nocturnal cooling of the ground, the total amount of water in the air remains substantially unchanged, but part of the water changes from the gaseous to the liquid state. The contribution of a given quantity of water to the refractive index is found to be far less when the water is contained in liquid drops than when it exists In the form of vapor. The formation of fog, therefore, results in a reduction of the amount of water vapor contributing to the value of M. If there is a temperature inversion in the fog layer, the saturation vapor pressure increases with height, and a substandard M curve frequently results (see Figure 20, curve Ib). This occurs with radiative fog (caused by nocturnal cooling of the ground) and also with advective fog (caused by the advection of warmer air over a cooler surface). Advective fog is very common in the Aleutian Islands and off Newfound- land. If fog causes a substandard M curve, it is to be inferred that the rays will be bent upward, instead of downward as with superrefraction, and lead to a weakening of the field in the lowest layers, even to the point of producing a complete fade-out of radio reception. Appreciable reduction of radar ranges and interruption of microwave transmission have frequently been observed in such cases. Fog, however, does not always produce a sub- standard M curve, though this is the most common case. In certain other less frequent types of fog, the temperature (and thereby the vapor pressure) may be constant or increase with height through the fog layer. In this event near-standard propagation will prevail, or a duct may develop when the temperature inversion is strong enough. An example is steam fog, formed when cold air passes over a warm sea (see also Section 17.3.9). "37 Subsidence— Dynamic Effects The temperature inversions discussed so far owe their existence to the modification of air by contact with the ground, but subsidence inversions are produced by a mechanism of an entirely different nature. By subsidence is meant the sinking of air, that is, a vertical displacement, which must of course be accompanied by a lateral spreading (divergence) in the lower part of the subsiding column of air; otherwise there would be an accumulation of air in the lower levels. The thermodynamic analysis of this complex process shows that if the effect of subsidence RADIO METEOROLOGY is strong enough a temperature inversion will be created. Since this process does not require the presence of a ground surface, it may occur, and in fact often does occur, aloft in the atmosphere. The effects of subsidence frequently are the most pro- nounced at an elevation of the order of a kilometer or more. As a general rule, subsidence occurs in regions of high barometric pressure. In fact, subsidence always does occur in such regions, but it may not always be intense enough to give rise to a strong temperature inversion. The flow of air in a barometric High is shown in Figure 32 as it appears on a weather map ILLUSTRATING SUBSIDENCE (SINKING) IN HIGH PRESSURE AREA AS IT APPEARS f ON THE WEATH- ER MAP HIGH PRES- SURE AREA Tl R_AS IT SINKS GETS WARMER—MORE SO IN THE HIGHER LEV ne ELS—AND A TEMPERATURE INVERSION IS CREATED + Y ee Beis a Co Ss UNAFFECTED AIR SURFACE Figure 32. Characteristics of subsidence. in horizontal projection, and also in a vertical cross section. With subsidence, the air as a rule is very dry, and there is nothing in the process which can change the moisture content or produce moisture gradients. If, however, the dry air finds itself over a surface capable of evaporation, such as the sea surface, a steep moisture gradient may be established and a duct will be created. It is thus seen that subsidence in itself does not produce a duct, except in extreme cases, but it can act as an auxiliary factor and greatly enhance the formation of a duct whenever other conditions are favorable. Thus, forecasts of super- refraction based on a purely advective mechanism, or purely on radiative cooling or evaporation, may have to be modified in the presence of subsidence; an otherwise very weak duct may be converted into a strong duct by the effect of subsidence upon the lower strata. Strong subsidence effects are of frequent occur- rence on the southern California coast where they may continue with little change for days at a time. 217 At times the duct is elevated, giving an elevated S-shaped M curve like I[la in Figure 20. Again the duct may extend practically from the ground up with M curves similar to curves II or IIIb in Figure 20. The elevation of the top of the duct may vary from 300 to 5,000 ft, and the thickness may lie between a few feet and 1,000 ft. Coverage diagrams and the corresponding M curves for several typical situations are illustrated in Figure 24. For a number of reasons the meteorological condi- tions in a barometric High are favorable for the formation of ducts. Among the favorable factors are: subsidence, creating very dry air into which evaporation from the surface can take place; again subsidence, creating temperature inversions; calm conditions preventing mixing of the lowest layers by frictional turbulence and maintaining the thermal stratification caused by radiative cooling or local breezes; clear skies producing nocturnal cooling over land. The conditions in a barometric Low, on the other hand, generally favor standard propagation. A lifting of the air, the opposite of subsidence, usually occurs in such regions and is accompanied by strong winds. The combined effect is to destroy any local thermal stratification and to create a deep layer of frictional turbulence. The air is therefore well mixed, and nonstandard vertical temperature and moisture gradients are wiped out in the early stages of their creation. Moreover, the sky is usually overcast in a low-pressure area and nocturnal cooling, therefore, is negligible. To summarize, high-pressure regions, clear skies, and calm air are conducive to duct formation, while low-pressure areas, cloudy skies, and winds favor standard refraction. Fronts in the atmosphere are possible sources of refractive effects. A front is a surface of discontinuity which separates two air masses of different tempera- tures. The surface slants at an angle of 1° to 2° with the horizontal, with the colder air forming a wedge under the warmer air. Fronts are a common occur- rence in the atmosphere, and it might be thought that they should have a considerable influence on wave propagation. This is, however, not borne out by English radar experience, which shows very little superrefraction connected with fronts. The explana- tion is probably that fronts are invariably accom- panied by low-pressure areas, and turbulence along a front is usually so strong that the transition from the cold air to the overlying warm air takes place 218 continuously over a vertical distance of about a kilometer. Propagation conditions might, however, be somewhat different with fronts in sub-tropical climates, although our knowledge is still inadequate on this point. In one-way transmission frontal effects have been studied to a limited extent (see Section 17.3.9). 17.3.8 Seasonal and Global Aspects of Superrefraction Although the general picture is still incomplete, enough is now known about the geographical and seasonal aspects of superrefraction to warrant a general summary. ATLANTIC COAST OF THE UNITED STATES Along the northern part of this coast superrefrac- tion is common in summer, while in the Florida region the seasonal trend is the reverse, with a maximum in the winter season. WESTERN EUROPE On the eastern side of the Atlantic, around the British Isles and in the North Sea, there is a pro- nounced maximum in the summer months. Conditions in the Irish Sea, the Channel, and East Anglia have been studied by observing the appearance or non- appearance of fixed echoes (see Figure 33). Additional SEPTEMBER OCTOBER 12 18 te) 6 1212 18 O 6 1212 18 fo) 6 12 TIME GMT. Ficure 33. Diurnal frequency of long-range fixed echoes at North Foreland, Kent. Wavelength 10 cm. data based on one-way communication confirmed the radar Investigations. MEDITERRANEAN REGION The campaign in this region provided good oppor- tunities for the study of local propagation conditions. The seasonal variation is very marked, with super- refraction more or less the rule in summer, while TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY conditions are approximately standard in the winter. An illuminating example is provided by observations from Malta, where the island of Pantelleria was visible 90 per cent of the time during the summer months, although it lies beyond the normal radio range. Superrefraction in the central Mediterranean area is caused by flow of warm, dry air from the south (siroceo) which moves across the ocean and thus provides an excellent opportunity for the formation of ducts. In the winter time, however, the climate in the central Mediterranean is more or less a reflection of Atlantic conditions and hence is not favorable for duct formation. Tur ARABIAN SEA Observations covering a considerable period are available from stations in India, the inlet to the Persian Gulf, and the Gulf of Aden. The dominating meteorological factor in this region is the southwest monsoon that blows from early June to mid-September and covers the whole Arabian Sea with moist equa- torial air up to considerable heights. Where this meteorological situation is fully developed, no occur- rence of superrefraction is to be expected. In accord- ance with this expectation the stations along the west side of the Deccan all report normal conditions during the wet season (middle of June to middle of September). During the dry season, on the other hand, conditions are very different. Superrefraction then is the rule rather than the exception, and on some occasions very long ranges, up to 1,500 miles (Oman, Somaliland), have been observed on 200-me radar on fixed echoes. When the southwest monsoon sets in early in June, superrefraction disappears on the Indian side of the Arabian Sea. However, along the western coasts conditions favoring superrefraction may still linger. This has been reported from the Gulf of Aden and the Strait of Hormuz, both of which lie on the outskirts of the main region dominated by the monsoon. The Strait of Hormuz is particularly inter- esting as the monsoon there has to contest against the shamal from the north. The Strait itself falls at the boundary between the two wind systems, forming a front, with the dry and warm shamal on top, and the colder, humid monsoon underneath. As a conse- quence, conditions are favorable for the formation of an extensive radio duct, which is of great importance for radar operation in the Strait. RADIO METEOROLOGY Tur Bay or BENGAL Such reports as are available from this region indicate that the seasonal trend is the same as in the Arabian Sea, with normal conditions occurring during the season of the southwest monsoon, while superrefraction is found during the dry season. It appears, however, that superrefraction is much less pronounced than on the northwest side of the peninsula. Tue Pactric OCEAN This region appears to be the one where, up to the present, least precise knowledge is available. There seems, however, to be definite evidence for the frequent occurrence of superrefraction at some loca- tions; e.g., Guadalcanal, the east coast of Australia, around New Guinea, and on Saipan. Along the Pacifie coast of the United States observations indi- cate frequent occurrence of superrefraction, but no statement as to its seasonal trend seems to be available. The same holds good for the region near Australia. In the tropics there is found a very strong and persistent seasonal temperature inversion, the so- called trade wind inversion. It has no doubt a very profound influence on the operation of radar and short-wave communication equipment in the Pacific theater. 739 Fluctuations in Signal Strength with Time A number of different causes tend to produce variations of signal strength with time. These are discussed briefly in the following paragraphs. TarGeT MopuLaTion Very rapid fluctuations having periods of only a small fraction of a second frequently are encountered im radar observations, especially with centimeter waves. These fluctuations arise as a consequence of the internal motions of the target and are especially noticeable for aircraft. Similar effects have been observed with reflection of microwaves from wooded hills, the fluctuations in signal probably being caused by foliage moving in the wind. Errect oF WAVES ON THE SEA A similar phenomenon is observed when the trans- mitter and receiver are so situated that reflection 219 from a water surface contributes to the received signal strength. Owing to irregularities of the water surface and their rapid change with time, variations in signal strength will appear. The fluctuations arising in this way have a time scale of the order of a second, in the case of a lightly ruffled sea (see Figure 34). Evidently rays reflected from different 3 4 S 6 7 8 9 SECONDS Ficure 34. Variation in signal strength with time in radiation reflected from the sea (direct radiation cut off). AX = 9cm. parts of the water surface interfere, and with the changing form of the surface the interference pattern at the place of the receiver changes accordingly. The time scale of these changes must be connected with the speed, wavelength, and amplitude of the waves. but the exact relation is not known thus far. TipaL HFrects The rise and fall of the tide produces a gradual variation in signal strength by changing the inter- ference between the direct and the reflected rays. The path difference between these rays is 2hih2/R, where fi, ho are the heights of the transmitter and receiver relative to the instantaneous water level and R is the range. The corresponding difference in phase between the two rays is equal to Qhihe Qa ts REL oer (26) measured in radians. The variation in the signal strength depends upon the variation in ¢. It is small when the change in ¢ is small and increases to a maximum for a change in ¢ of z radians. It follows from equation (26) that the tidal effect increases with the variation in the water level of the tide and with the heights f; and hz and decreases with the range and the wavelength. ScINTILLATIONS The really conspicuous fluctuations in propagation conditions, however, are due to changing meteoro- logical conditions. A characteristic type is an irregular fluctuation in signal strength on a time scale of the order of a minute and with an amplitude rarely 220 exceeding 2 db. It varies in intensity according to the state of turbulence in the air along the propaga- tion path. In perfectly calm air the fluctuation is practically nonexistent but becomes quite noticeable in turbulent air. This sort of fading is analogous to the scintillation of the fixed stars or the unsteadiness of the telescopic picture of distant objects occurring especially on warm summer days. The physical explanation for the scintillations 1s found in the fact that the turbulent motion of the air produces irregular variations in refractive index. The conse- quent irregular bending of rays passing through such - a medium produces a patchy distribution of intensity over the wave front. In the case of stellar scintilla- tions the main change in refractive index is caused by fluctuations in air density, and the significant level of turbulence is at an elevation of several thousand feet. For radio waves fluctuations of water vapor density are the chief cause of the scintillations, and the active region is consequently close to the ground. For typical radio scintillations see Figure 35A. OB BELOW 1 WATT A STEADY SIGNAL AVERAGE LEVEL = F SIMPLE SURFACE TRAPPING DUCT HEIGHT 250 FT OB BELOW 1 WATT B HIGH AVERAGE SIGNAL WITH DEEP FADING h, = 125 FT ho= 25 FT Fe = a = = fo) 4 Ww a o {=} Cc LOW SIGNAL h, = 125 FT ho= 50 FT Ficure 35. Signal strengths for \ = 10 cm over sea. TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY Ducr Faprs A duct is normally accompanied by fades in the signal strength of large amplitude (up to 30 db) and of moderate periods (of the order of 15 min). A detailed theory of this type of fluctuation in signal strength is not available. When the duct is fully developed, there is a large-scale deviation from standard conditions with regard to mean field strength. If, in particular, both transmitter and receiver are situated inside the duct, there is a great, increase in received field strength. Suppose, however, that for some reason the duct does not function according to the simple theory. The field strength at the receiver may then drop to the value correspond- ing to standard conditions. The observed fades exhibit just this characteristic in that they consist in sharp drops of signal strength down from a mean upper level. The conditions are illustrated in Figure 35, which shows three records obtained for a 22-mile path over sea. Figure 35A shows the normal record on a calm day when the only disturbances are due to scintillations. The record shown in Figure 35B, on the other hand, was obtained for a condition of simple surface trapping, with transmitter and receiver inside the duct. It will be noted that the signal strength is considerably above the 95-db average as given in Figure 35A. Duct-type fades have been observed over land as well as over sea and appear to form a characteristic feature from which the presence of superrefraction may be inferred. BuackouT Figure 35C shows a fade in which the signal level is far below average and which for this reason is called “blackout.” This type is liable to occur when warm, moist air is cooled from below (see the sub- standard M curve Ib in Figure 20) and is often correlated with fog. The main irregularities in signal strength are again on a time scale of the order of 14 hour; the amplitude of variation is smaller than in the preceding case and rarely exceeds 10 db. FRONTS AND THUNDERSTORMS On several occasions marked variations in signal strength have been observed when fronts pass between the transmitter and receiver. The passage of the front itself is marked by very rapid and deep fluctuations, followed by less violent changes on a RADIO METEOROLOGY longer time scale (see Figure 36). It appears that similar effects are likely to occur during thunder- storms. INPUT DB ABOVE ipV RECEIVER TIME GMT Fieure 36. Effect of a front on signal strength (Hasle- mere-Wembley Link, England). Foe Some peculiar effects were observed by transmission through fog over an experimental overland radio link in England. The effect of a shallow layer of radiation fog in the early autumn (September-October) was to produce a nearly complete fade-out of signal strength which lasted for hours and rose to normal as the fog cleared. The explanation of this effect is probably the same as in the case of the “blackout”’ type fades discussed above, indicating that radiation AL aa Bi | Ah bo fog produces a substandard M curve. Later in the autumn (November-December) or winter (January) it was found that the effect of fog was quite different. In this season the signal strength was increased and deep fades appeared which are reminiscent of the duct-type fades described earlier. FADING ON DiIrrERENT WAVELENGTHS Several experiments have been performed in which transmitters working on different wavelengths oper- ate simultaneously over the same path and the received field intensities are recorded on the same chart. Figure 37 shows one such record for the 42.5- mile (optical) path from the Empire State Building, New York City, to Hauppauge, Long Island, for May 14 and 15, 1943, at frequencies of 474 me and 2,800 me. It will be noticed that on May 14 up to about 5:45 p.m. the two records show a close agreement. At 6:00 p.m. violent fading sets in on both frequencies, but with great diversity in detail. Not infrequently the signal on one frequency increases while on the other frequency it decreases. About 1:00 a.m. on May 16 the disturbance dies down, and the initial harmony in the two records is restored. 600 pv Across Receiver Input 250 pv Across Receiver Input| Ficure 37. Simultaneous variations of signal strength with frequency. (Empire State Bldg. to Hauppauge, L. I., N. Y.) iw) ie) bo Experiments over the longer (nonoptical) path from the Empire State Building, New York City, to Riverhead, Long Island (range 70.1 miles), showed much greater diversity in the fading patterns for the different frequencies. On the other hand, observa- tions over the British radio link from Guernsey to Chaldon on 60 me and 37.5 me (range 85 miles) showed that if there were marked variations on one frequency similar results were likely to be found on the other frequency. RELIABILITY OF CrRcUITS The reader must be warned that the amount of the fading in the signal strength is not a measure of the performance of radar and communication circuits. These will operate successfully so long as the periods of low signal are relatively short. Neither the scin- tillations of Figure 35A nor the larger dips of Figure 35B would seriously affect operation, but a prolonged signal such as in Figure 35C would certainly interfere seriously with communication and radar performance. Some quantitative data are available from the transmission path referred to in the previous para- graph. On the optical path, New York to Hauppauge, the range of signal fluctuations increased rapidly with increasing frequency. On 45 me the “undisturbed” level (the observational equivalent of standard) was 21 db below free space with an amplitude of fluctua- tions that very rarely exceeded +4 db. On the 474- me circuit the undisturbed level was 3.5 db below free space while the fluctuations varied between 10.5 db above to more than 30 db below free space. The level was 5 db or more below the undisturbed value during 0.01 per cent of the time in January and during 0.4 per cent of the time in July. On the 2,800- me circuit the undisturbed level was —2 db below free space; the maximum was 12 db above and the minimum more than 25 db below free space. During 0.15 per cent of the time the signal was 5 db or more below the undisturbed level in January; the corre- sponding figure for July was 3.6 per cent. The conclu- sion may be drawn from this and similar experiments that over optical paths transmission becomes gradu- ally less reliable as the frequency is raised. Over the nonoptical path, New York to Riverhead, the margin of fluctuations was much larger. On the 45-me circuit the undisturbed value was 35 db below free space, the maximum 18 db below, and the minimum more than 50 db below free space. During 1.6 per cent of the time the signal was 5 db or more TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY below the undisturbed level. On the 474-me circuit the undisturbed signal was 30 to 35 db below free space, the maximum 10 db above, and the minimum 44 db below free space. During 0.47 per cent of the time the signal was 5 db or more below the undis- turbed value. At 2,800 mc the undisturbed signal was 50 to 60 db below free space near the limit of sensitivity; the observed maximum was 13 db above free space, and the minimum could not be observed. In this case the effects of superrefraction were quite pronounced. In January the signal was less than 40 db below free space during 6.5 per cent of the time; the corresponding figure for July is as high as 33 per cent. The reliability of these transmission circuits is shown in Figure 38. Here, both for the optical and nonoptical paths, the percentage of time during which the signal strength was below specified values is plotted for the various frequencies used. The specified values of signal strength, for each frequency and path, are measured relative to the corresponding undisturbed value. The results, which give averages of the performance during July 1943 and January 1944, indicate that the reliability increases appreci- ably with decreasing frequency. It must be said that the New York area where these experiments were made is not particularly affected by blackout situations, and the results are probably not typical for locations where blackouts are a frequent occurrence. The general nature of these data is confirmed by results of extensive experiments in England and in Massachusetts Bay. MBO Scattering and Absorption by Water Drops As microwave sets have come into general use in recent years the “rain echoes” frequently seen on the scope have attracted attention. The possibility of using microwave radar as an aid to meteorological forecasting and for aerial navigation was early recog- nized and is now being put to operational use. At first sight, ground clutter resulting from trap- ping of radiation in a ground-based duct and rain reflections look somewhat alike on the scope of a radar set. At closer inspection differences appear; the cloud pictures are usually more fuzzy and less sharply defined than the echoes received from ground targets. An experienced operator usually has little difficulty in distinguishing rain echoes from echoes of targets or objects at the ground, but occasional RADIO METEOROLOGY 223 100 =, C | ; : il OPTICAL PATH 10 474 MC HAUPPAUGE 2800 MC HAUPPAUGE NON— 45.1 MC RIVERHEAD OPTICAL 474 MC RIVERHEAD SIGNAL WAS BELOW ABSCISSA PER CENT OF TIME 0.1 Ol RELATIVE SIGNAL STRENGTH IN DB Ficure 38. Reliability of circuit. Average of July 1943 and January 1944. (Empire State Building to Hauppauge and Riverhead, L. I., N. Y.) mistakes have been reported, especially from the shows that the amount of scattering increases very tropics. rapidly as the wavelength is decreased. It also Rain echoes are a result of the scattering of micro- increases rapidly with increasing drop diameter. On waves by the raindrops. Electromagnetic theory account of this sharp variation the scattering effects 224 become appreciable only when the wavelength is below a certain maximum value and when the drops exceed a certain critical size. Rain echoes are rarely observed at longer waves than S band, but they are common at S band and become very important at the shorter microwaves. For a time it was thought that clouds could produce microwave echoes, but more thorough inves- tigations have now established the fact that the droplets in clouds are too small to produce appreci- _ able scattering. Only drops that are large enough to constitute genuine rain are seen by a radar, and, especially at S band, light rains will often escape detection. The term “storm echo,” invented at a time when the origin of these echoes was not yet clearly understood, should be avoided, and the terms “vain echo” or “precipitation echo”’ should be used instead. A rain seen by the radar is not necessarily recorded by an observer at the ground, as the rain may be confined to the free atmosphere and never reach the earth. This occurs either when the rain falls in an ascending stratum of air where the air rises more rapidly than the drops fall or when the raindrops evaporate again before reaching the ground. Both cases occur quite commonly in the atmosphere, especially under convective conditions such as are indicated by cumulus clouds and thunder- storms. Snow may also be seen on microwave scopes provided the snowfall is sufficiently heavy. While clouds themselves do not produce microwave echoes, they may contain falling rain of one of the forms just indicated. Visual appearances are deceiv- ing, and an imposing looking cumulus cloud might be entirely invisible on the scope, whereas a cloud that is inconspicuous to the eye but contains falling raindrops might give a pronounced echo. The question of “shadow” cast by a storm echo is of some operational interest. A shadow is formed when the absorption that accompanies scattering by the raindrops becomes so strong that the remaining radiation no longer suffices to produce visible echoes from targets behind the rain area. This effect is pronounced on X band, and even more on K band, and is often quite conspicuous with airborne equip- ment where it may happen that a rain storm blanks out a sector of the sweep. On 8 band the absorption is usually much weaker and targets can often be seen behind a rain echo. The usefulness of rain echoes for aerial navigation, particularly in the tropics, is now so generally known that the subject need not be discussed further. TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY Lie SNELL’S LAW The ordinary law of refraction known as Snell’s law may be expressed as No sin Bo = mh sin By ) where 8 and f; are the angles which the ray makes with the perpendicular to the boundary. Here it is more convenient to take the angle a between the ray and the boundary surface. Snell’s law then reads No COS ao = M1 COS a1. The refraction at a sharp boundary is shown in Figure 39A. If there are several boundaries it is 9 CENTER OF EARTH Figure 39. Application of Snell’s law of refraction. readily seen that Snell’s law generalizes (Figure 39B) to No COS ao = % COS a1 = iy OOS) Gey = 8 9 Oo 5 and for a continuously variable layer it becomes nN COS a = No COS ao, where n and @ are continuous variables which are functions of the height and the index 0 designates an arbitrary reference level. Snell’s law for a curved earth may be derived from Figure 39C. For successive boundaries it is found: SNELL’S LAW 225 No Sin Bo = nN; sin B’o Noro SIN Bo = Ny Sin By = Nore sin Bp = ’ m sin B;} = ne sin B’,, ete. ey ; ; : Again introducing the angle a with the horizontal Multiply the first equation by 7, the second by m, and making the transition to a continuously variable rly . . . ete. Then refractive index gives Moo SiN Bo = Niro sin B’o , Myr, Sin By = Nor, sin B's, ete. mr COS a = NoFo COS ao , But from the triangle OAB which is the generalization of Snell’s law for a curved ; ; earth. ro may be chosen as any convenient height, sin B’y _ sin Bi ete. , say a for the surface of the earth or a + fy for the Us! no height of the transmitter, and ny is the corresponding so that: value of 7. Chapter 18 THEORETICAL TREATMENT OF NONSTANDARD PROPAGATION IN THE DIFFRACTION ZONE* HE ASSUMPTIONS and restrictions underlying this presentation are: 1. We concern ourselves with problems of the diffraction region only: the field is calculated at considerable distance from the transmitter and not too great height above the ground. 2. The plane-earth model is used, in which the effect of curvature is simulated by using the modified index M instead of the index of refraction n. 3. The earth’s surface is assumed smooth, and M depends on height only (horizontal stratification). 4. Simplified boundary conditions at the earth’s surface are used, appropriate to the treatment of the diffraction zone at microwave frequencies. This results in a formula which refers only to a discrete spectrum of modes and makes the calculations independent of polarization. 5. The directional pattern of the transmitter need not be considered, since only the intensity at the azimuth in question and within 1 degree of the hori- zontal plane is of importance. The problem solved is that of a vertical dipole, electric or magnetic. 6. The field is described in terms of a single quantity WV, the Hertzian vector being (0,0,V). Then, at a point in the diffraction region, actual field strength = |W |? - d?- Ey), (1) with d = horizontal distance from source, E, = free space field at distance d. An expression for VY can then be found in the form ; 2m r(d.2) = eivt — iml4 W(d,z) =e ae where h,; = transmitter height; en tn Un(hi) Un(2) ) (2) z = height at which W is calculated; Qn =a, kse=., w mf y Ym and U,» are characteristic values and functions of the boundary value problem CU 6 PNRG) 40 = 0, (3) dz? @By W. H. Furry, Radiation Laboratory, MIT. 226 Ue wave moving upward, z—> o, (4) where ee Le (5) The modified index of refraction M is supposed to be defined without the factor 10° usually included. The functions U must be normalized in a suitable way. If we had not agreed to use simplified boundary conditions, the last equation (5) would be more complicated and would depend on the type of polari- zation. Also an integral would appear in addition to the discrete sum in the expression for WY. The actual value for WV, for the diffraction zone and microwave frequencies, would not be affected sig- nificantly. The quantities y, are complex: Am and Bm are positive real quantities. It is convenient to think of the terms of the series as arranged in order of increasing a: a1 < az < a3 < age *: These quantities determine the horizontal attenuations of the various modes. For large d only one or at most a few terms of the series are required to give the value of YW. The quantities 8,, are all very nearly equal to k. The slight differences between the £,,’s determine the phase relations and hence the inter- ferences between the various modes. It is convenient to classify the modes into two types: (1) ‘““Gamow’”’ modes which are strongly trapped, so that a is very small; (2) “Eckersley” modes which are incompletely trapped or untrapped. The names ‘“Gamow” and “Eckersley” refer to the men who devised the approximate phase integral methods which apply in the two sorts of cases. For practical purposes, when working within the diffrac- tion region, we need consider only the Gamow modes, or at most the Gamow modes and the first Eckersley mode. In order to be able to use the formula to calculate W for a given index curve M(z), we must obtain the following information about the modes which are to be used: 1. The characteristic values. 2. “Raw’”’ or unnormalized characteristic func- NONSTANDARD PROPAGATION IN THE DIFFRACTION ZONE 227 tions, which satisfy the differential equation and the boundary conditions but still require multiplication by suitable normalization factors. 3. The normalization factors. There are three methods of attack on the problem: 1. Numerical integration of the differential equa- tion, accomplished in practice by the use of a differential analyser. 2. Phase integral methods. 3. Use of known functions and tables, for suitably chosen M curves. The method of numerical integration is being used intensively in England by Booker, Hartree, and others. It encounters considerable difficulties in con- nection with the fitting of the boundary condition at 2— o and also in the determination of normali- zation factors. These difficulties have been overcome by special and fairly elaborate procedures. In this country the feeling has been that we should direct our efforts toward the use of the other methods. If either method (2) or method (8) is to be readily applied to a variety of cases without a prohibitive amount of labor, the MW curves must have a suitable form. The form indicated turns out to be the same in both eases. It consists of portions, each of which is a straight line. If enough such portions are used, any actual M curve can be accurately represented, but it is impractical to use more than a very few. Present efforts are directed toward dealing with cases where there are just two straight-line portions and there is no prospect of going beyond the cases with three (Figure 1). f: M ——> Figure 1. Schematic straight-line M curves. At first sight these curves look overly artificial, but there are considerations which indicate that they are really an altogether reasonable choice. First, some actually occurring curves have very much this sort of appearance. Second, the sharp breaks in the curves have no really strong effect on the results. Third, practical considerations severely limit the number of parameters which can be used in specify- ing the curve, so that a meticulous reproduction of every actual curve is out of the question. Fourth, the assumption of horizontal stratification is usually not well enough justified to make highly precise results really significant. The use of the jointed-line model for phase integral work was decided on last winter in the Radiation Laboratory.” The phase integral methods were pushed first, because the calculations are quite easy and do not require special tables of functions. Unfortunately the gaps between the regions of validity of the different phase integral approximations turn out to be extremely wide and to cover just the more inter- esting ranges of slope and duct height. This makes it necessary to resort to the exact solutions to deter- mine characteristic values and normalization factors. The phase integral methods provide limiting cases which can help in guiding the exact computations. Also the phase integral formulas are usually quite adequate for the computation of the “raw” charac- teristic functions, once the characteristic values are known. In order to make the exact calculation, we need tables for complex arguments of the solutions of the equation a dz? These solutions can be expressed in terms of the Airy integrals, but for greater convenience the solu- tions have been standardized in the form ING 2 )//D. : 2) = () es #3 (32) (j = 1,2). The tabulation of these functions for | z| < 6, on a square mesh 0.1 unit on a side is being done on the automatic sequence-controlled calculating machine at Harvard University. Work was begun in the latter part of August 1944, under authorization from the Bureau of Ships. Photostats of about one-fourth of the tables were obtained by November 1944. The present objective is to produce charts from which a; and 6; and the normalization factor for the first mode can be obtained for any M curve made up of two straight portions, the upper one being of standard slope. After this, similar charts for the second mode, and perhaps the third and fourth, will be undertaken. When this has been done, the approximate determination of field strengths and coverage will be possible by a definite routine procedure. bThe use of the solutions for this case in terms of Hankel functions was suggested by Lt. Comdr. Menzel. Chapter 19 CHARACTERISTIC VALUES FOR THE FIRST MODE FOR THE BILINEAR M CURVE* ae MODEL of an M curve composed of straight- line segments suggested itself to workers at the Radiation Laboratory early in 1944 as one in which phase integral calculations could be carried out very rapidly. At about the same time Lt. Comdr. Menzel suggested the use of this model together with tables of Hankel functions to obtain exact solutions. In the fall of 1944 it became evident that phase integral methods were not of much use with this model. Tables of the required Hankel functions, essentially standard height-gain functions, for complex argu- ment were prepared at the Harvard Computation Laboratory, and considerable effort was directed to the obtaining of exact solutions. Work at the Radiation Laboratory has been largely confined to the first mode for a curve composed of two segments. This work has progressed largely through the efforts of Miss Dodson and Miss Gill and Howard and Parker. Dr. Pekeris of the Columbia University Wave Propagation Group has been di- recting work on the second mode. The units, notation, and model are given by the following formulas and illustrated in Figure 1. Y=h)"8x2mxio ° Fiaure 1. Models and units. LRA i d \3 4q\3 w= wer = (5) (3) H (feet) = 7.24 [d(em)]} , X \3 4q\i = Wo\-3 == | — |) of S= 1 = 2(hy!)-+ = 2( +) -($) with L(thousand yds) = 6.69 [\(cm)]* , bt CU on e S97 8 SP hae ar Us + D)U=0. with z @8By W. H. Furry, Radiation Laboratory, MIT. 228 The natural units of height and distance represent two different compromises between wavelength \ and earth radius a, so that \ + H + L + a form, very roughly, a geometric progression. It is seen that for microwaves, heights and distances occurring in practice are fairly small numbers of natural units. The M curves are plotted in terms of the height z in natural units and of a quantity Y which is simply M multiplied by a suitable wavelength dependent factor. The standard part of the curve then has slope unity. In the bilinear model the anomaly consists of a segment with slope s* times standard, or, in these diagrams, simply slope s*. For negative s there is a duct; s positive but less than 1 gives transi- tional cases; and s greater than 1 gives substandard cases. The essential quantity WY used in calculating the field is given by: WV = (cist-2ni dih—anit ) 2a at xX Veta te" Ul2s) Un(2s) . The power density is equal to the free space power density multiplied by W?d?. The characteristic values are complex: D = B + 7A. For the standard case: D, = —1.17 + 2.027. (For )} = 10 cm this corre- sponds to an attenuation of 1.22 db per thousand yards.) W consists of three factors: one, that for a plane wave, which can ordinarily be omitted; the second, a constant factor which depends on wave- length through L, the natural unit of distance [this factor can be replaced by just 2+/x if a?2(= d?/L?) instead of d? is written in the first line]; and finally the critical factor written in terms of natural units only and involving characteristic values and charac- teristic functions. The imaginary parts of the charac- teristic values are the coefficients of horizontal attenuation, and the characteristic functions are the height-gain functions. It is seen that for a typical microwave frequency the horizontal attenuation of the first standard mode (g = 0) is rather sizable. The plot of the height-gain curve shows that if both transmitter and receiver are at about 200 ft there is a gain of 50 to 60 db. CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE 2 an 6 FIRST STANDARD MODE FIRST MODE TRAPPED (QUALITATIVE) ~~ = =—1.52 9=1.9 Zam2o wis Os) 0-5 — 20 L06,9lul Figure 2. First standard and first trapped mode. In discussing the behavior of U in relation to the Y curve, it is best to plot U or | U| rather than decibels. It is also helpful to draw a vertical line at the abscissa —B, and this is then usually used as the axis in plotting U or | U|. The diagram for a trapped mode shows that | U | shows exponential decay in the “barrier” region where the Y curve lies to the left of the line at —B. Below the barrier U shows oscillatory behavior, but with no nodes for the first mode; above the barrier U is a spiral, which shows only as a slow increase in the plot of | U|. This same difference in the behavior of U for Y > 2.5 229 or < —B is a useful thing to remember in more general cases. Sometimes it is not quite so clear-cut as in this case of trapping. If A is not small, the situation cannot be so completely defined in terms of B alone. It is certain, however, that | U | will show essentially exponential behavior in any region where the “height of the barrier,” 1.e., the amount by which the Y curve lies to the left of the line at —B, is greater than A. This sort of general physical consideration about the U curve leads, on being put in more precise mathematical form, to the phase integral methods. Unfortunately, no phase integral method can claim validity for this model except in cases of trapping. In general, the Eckersley phase integral method for untrapped modes requires that the Y curve be an analytic function, and the bilinear curve obviously is not. Most of the values presented are, accordingly, the results of exact calculation. Figure 3 shows that for negative s the attenuation falls rather suddenly to very small values at a certain value of g and then quickly approaches zero. This indicates the occurrence of trapping. On the other SLOPE OF LOWER SEGMENT OF M CURVE SLOPE OF UPPER SEGMENT OF M CURVE Figure 3. Attenuation constant versus anomaly height for bilinear M curve, first mode. D, = 8, + SLOPE OF LOWER SEGMENT OF M CURVE SLOPE OF UPPER SEGMENT OF M CURVE O CHARACTERISTIC VALUE FOR G-»00 \ 1.5 (=VALUE OF g ) iAy CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE Ni sema Ficure 4. Characteristic values for the first mode. hand, for positive s, the attenuation constant approaches a finite asymptotic value. It is interesting to note that this is always definitely less than the value s2x standard, which corresponds to a single straight line of slope sa standard slope. It is also useful to know the real part B of the characteristic value. Figure 4 shows the complex D plane. For g = 0 the Y curve is just standard, and as g increases the value of D for each value of s traces out a curve; for small values of g all these — curves practically coincide. For negative s the real part decreases steadily as soon as the imaginary part becomes very small. For positive s, on the other hand, the real part as well as the imaginary approaches a finite limiting value, so that each curve has an end point. Some of the consequences of this behavior of the real part can be seen by studying Figure 5. The first row of diagrams shows the situation for fixed nega- tive s and increasing value of g. The first diagram shows the standard curve. The next shows a curve with a small superstandard section, but — B still lies in nearly the same location relative to the dotted line which marks where the origin lay for the stand- ard curve; thus B has increased. The first figure of the second line shows how the same thing happens for a small substandard section. Thus for small g the first order effect is Just to add the amount g to D, for all values of s. In the third diagram of the first row we have a case in which the superstandard has a pronounced aaa ee -BO Figure 5. Curves for negative and positive s. CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE 231 effect, but trapping has not yet set in. In such inter- mediate cases B may become positive, but the diagram shows a case in which it happens to be zero. In the fourth diagram trapping is definitely established; B has become negative, and the line — B has taken on a definite position relative to Y (0) (dotted line). This same relation is maintained for larger values of g, as in the last diagram of the top row. In the last diagram the “barrier” has become much more formidable. This means that the value of U just above the barrier is extremely small, and thus the attenuation is very small because of the small leakage. In the second row, as has been remarked, the first diagram shows a small substandard section which has only a small perturbing effect; — B lies essentially at the standard distance from the intercept of the extrapolated standard curve. The second shows an intermediate case. In the third diagram the limiting value of D has been reached, and the line at —B has taken its final position relative to the joint of the Y curve. In the last, larger, diagram g has become much larger, but —B has still the same position relative to the joint. The difference between the last two diagrams is essentially the increase in the strength of the swrface barrier. The structure of the height-gain curves near and above the joint is practically the same in the two cases. The very thick barrier in the last case causes the intensity near the earth’s surface to be extremely small. This particular kind of height-gain effect can be more suggestively referred to as depth loss. The amount of this depth loss is very large: the first 200 ft of the substandard layer produces a loss in the product U(z) U(é2) of at least 200 db (at 10 em), which is about four times the gain for a similar height in the standard case. Moreover, this loss proceeds at a rapidly accelerating rate, whereas standard height gain goes at a decreasing rate. The same situation of depth loss in thick nonstandard layers occurs in transitional cases, with s positive but less than unity. ; In general the results for the first mode for positive s can be summarized as follows: In nonstandard layers of fairly small thickness, less than 100 ft for 10-em waves, the propagation is not markedly different from standard for the sub- standard case and can have attenuation strikingly less than standard for suitable thickness of a transi- tional layer. For thick layers there is a strong depth-loss effect in the first mode in both sorts of cases, and the first mode cannot be expected to be the dominant term in W except at great distances. Some other mode, which does not suffer from the depth-loss effect, although it may have greater attenuation, will be the important mode at smaller distances. The conclusions for positive s cannot be expected to apply unless the lower part of the M curve is really sensibly straight over a considerable part of its length. For negative s (trapping) this requirement is not so important. It was mentioned that other models had been employed by various investigators in calculating field strength in the presence of a duct. The British used an index distribution given essentially by Y = (2 — z"/m), where m lies between zero and unity. When m = % the problem could be treated by a phase integral method, which Booker had done. The differential analyzers at Manchester and Cambridge had been used to obtain the characteristic values for other values of m. The linear variation of index had been studied by Hartree and Pearcey. In this case of linear exponential variation Y = z + Ae~sz, where A and B are adjustable parameters. This model offers the advantage that the index is an analytic function of z and also that the modification term approaches zero with increasing height. An alternative method (Langer’s) for joining the two parts of an otherwise bilinear M profile was brought up. This method gives a solution in terms of Bessel functions and solves the difficulty perfectly for joining two straight lines. It was inquired whether, in case of positive s it had been ascertained that for large g there were no roots of the secular equation corresponding to a linear M curve having the slope of the lower segment. There was the possibility that the root found might be one of a possible pair and that there might be another solution of the wave equation for positive s which had not yet been discovered. The author replied that the roots varied continu- ously as g varied and that the investigation had dealt with the root obtained when starting with the first standard value for g = 0. What happened with increasing g when the start was made from some other standard value of g = 0 was not known defi- nitely, but the effects were believed to be peculiar. It is expected that there may be some values lying fairly near the s squared value for the imaginary part. They are not considered to lie close to the s squared value for the real part, as they would for the simple assumption previously mentioned—that when the joint is very high the upper segment can be forgotten and the curve can be assumed to be a single line all the way. This is believed incorrect, because when the result is derived by taking only the first terms in the asymptotic expansions, com- puting a small correction from the next terms in the asymptotic expansions produces terms which are infinite compared to the first terms. This means that the value s squared times D is an impossible one. It may well be that there are results with s squared times A plus some different value of B rather than simply s squared times B, but these have not been investigated. This does not occur for the first mode, which is all that this report covers, but it may happen that some other mode goes over to that value. Any mode which does so would probably not suffer from depth-loss effect and would be the important mode close in when there was a thick layer with positive slope. The need was pointed out for stressing the differ- ence between “completely trapped” modes and “leaky”? modes. With completely trapped modes the field decreases exponentially with height, and the power carried by each mode is finite, but with leaky modes the field increases exponentially with height, and the power carried by each mode is infinite. This means that completely trapped modes may exist separately, but leaky modes may not. The expan- sions of fields in terms of leaky modes are thus essentially mathematical and from physical considera- tions it is no longer possible to anticipate that these expansions would be convergent; the question of convergence has to be settled formally. The reac- tions of trapped and leaky modes to small perturba- tions are quite different. The former are relatively insensitive and the latter are very sensitive. In considering the field at a certain distance from the transmitter, it must be ascertained whether the relevant modes are affected by changes in the dielectric constant at heights large compared with this distance; if this is the case particular care must CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE be taken in proving the sum to be still the same, since even a perfectly reflecting layer at such great heights can have little effect on the field in the region of interest. It was noted that these remarks pertained to a phenomenon which had greatly puzzled the investi- gators for several months. The trouble occasioned by the concept that infinite energy is carried by a mode does exist. This means that the formula in terms of modes is valid only if all those modes are summed that make any appreciable contribution. It becomes extremely difficult to carry out the summa- tion when there are numerous modes, as they begin to cancel each other more and more with progress into that region. This occurs in leaving the diffraction region to which this work is meant to apply and in approaching the optical region. The question of what a small departure from the shape of the curve at great heights does is something which was very troublesome during studies made some months ago. There is no doubt that a small departure from a smooth shape of the M curve has an enormous effect on the results if it occurs at a great height. If the departure is located high enough it need not amount to more than a millionth of an M unit to spoil the calculation completely. That is because it is a reflecting layer similar to the Heaviside layer, and if placed high enough it not only can reflect to enormous distances but also becomes extremely effective. It was decided not to give this effect too much concern as all these calculations are made on the basis of horizontal stratification. Doubtless all sorts of small departures from a smooth curve occur at various rather large heights, but they do not occur perfectly stratified over areas of hundreds of square miles, and only such perfectly stratified departures could cause embarrassing results. Accordingly it was decided that such fluctuations as occur probably cause fading or fluctuation but do not cause the particularly troublesome effect mentioned, because they are local disturbances which are not stratified over large areas. Chapter 20 INCIPIENT LEAKAGE IN A SURFACE DUCT 20.1 CALCULATIONS FOR THE FIRST MODE OF THE BILINEAR MODEL RECENT INTERCHANGE of ideas on problems of A mutual interest with members of the wave propagation group of the Radiation Laboratory prompted the author to investigate the variation of the attenuation constant (or space decrement) a(h) of the first mode with the duct height h and negative index gradient a of a surface duct (see Figure 1). 2.0 hsDUCT HEIGHT —Y (X) REFRACTIVE INDEX ANOMALY —> (h)/a (0) fo) a Q FIRST APPROX © SECOND APPROX 0.001 fo) ' 2 3 4 5 6 7 —=5 =h(kb)'/> Figure 1. Variation of the attenuation constant with duct height. The attenuation constant is defined as the constant a which occurs in the factor as: (1/+/d) e-@4 , giving the variation of the amplitude with range d. The results are shown in Figure 1. In this figure the attenuation constant a(h) is expressed in terms of the attenuation constant for zero duct height *By C. L. Pekeris, Columbia University Wave Propagation Group. a(Q). In Figure 1 the curve for 6 < 1 was computed from a formula developed by Freehafer and Furry of the Radiation Laboratory: a(h) aoe a 6 a) 7 1~(1+5) a a 68 ( + i) ap where 6 = h(k?b)*. Here h = duct height; a = —dM/dz inside the duct; b = dM /dz above the duct; k = 27/X. It was felt that this equation could be used up to 6 equal to about 1.3 but not beyond this value. The curves on the right for 6 > 2, for which a condition of nearly complete trapping is approached, were obtained as follows. The secular equation for the proper value of A(a ~ T,,A), is Hp) HP()T_2@) + HROHR@) _ 0, (2) H%p) HP(s)\H_ OG) + HX) HP@ where 2k 2k eine _@ q ig Ie are ON a) eh Pe (3) is transformed by the substitution ; 4 : 2k\3 gq = CPN i, Dp = (@ ar 8), B= ie) (4) into fp) — F@) =0, (5) with H®(p) f(p) = HY (p) U(ya) V(x) + V(ya) U(x) NO) ob Tae) UG) = CGe) TO) (6) U(e) = h@) +e *S14@) , Va) = Ij(a) ++ e*/*1_4(@) . (7) 233 234 Assume now that P=Ppot+A, (8) where po is a constant, which is to be chosen in such a manner that A is small in comparison to pp in the region under consideration. Expanding equation (5) in a power series in A, one obtains as a first approxi- mation for A: _ G0) = siKf00) A, = - 9 : I (po) (8) and for a second approximation / lx F(a») = Laie wn) as = as 1 TGs) ee) | These expressions can be computed with the aid of the WPA Tables (unpublished) for the J functions with real argument. The curves in Figure 1 were computed down to values of 6 such that A, did not deviate appreciably from Aj. Conclusion. From the computed attenuation for a surface duct it appears that, for the first mode, when 6(= hkb) is less than 1, trapping is less than 2 per cent and that when 6 = 3 to 5 (depending on the negative gradient a), trapping is 98 per cent complete. (For the meaning of the constants see Figure 1.) There is therefore a rather narrow range of values of the parameter 6 (1 to 4) within which a rapid transition takes place from a condition of negligible trapping to a condition of nearly complete trapping. This result may have a bearing on the observed fading which is associated with ducts. 20.2 CALCULATIONS FOR THE SECOND AND HIGHER MODES OF THE BILINEAR MODEL The Analysis Section of Columbia University Wave Propagation Group has undertaken the computation of the characteristic values and height-gain functions for the second and higher modes of a bilinear model M curve. The first mode of the bilinear model is being treated at the Radiation Laboratory. The computa- tions were carried out with the aid of tables of h functions prepared by the Harvard Computation Laboratory, under the direction of Furry. Our work to date has been mainly on surface ducts, in which the slope of the lower segment of the M curve is negative. Cases with positive slopes of the lower INCIPIENT LEAKAGE IN A SURFACE DUCT segment of the M curve have been tried but were found to involve fh functions which are beyond the range of existing tables. Some results on the characteristic values are shown in Figures 2 and 3 (for a definition of natural units see preceding articles). In Figure 2 the slope of the lower segment of the M curve is the negative of the standard slope, while in Figure 3 the ratio of the slope of the lower segment to the standard slope is i Na a a SNe yay 2 Am Ficure 2. Characteristic values of D,, for a bilinear model. s = —1. Dm = Bm + i Am. s! = ratio of slope of lower segment to standard slope = s3. g = height of joint in natural units. —+/8. The curves A; and B, for the first mode were computed at the Radiation Laboratory. An imagi- nary part A, which is proportional to the horizontal attenuation (decrement), starts at g = 0 with a value appropriate for a standard atmosphere and decreases continuously as duct height g increases. Beyond g = 3 the first mode is completely trapped. The curve A>» for the second mode decreases initially SECOND AND HIGHER MODES OF THE BILINEAR MODEL too but beyond g = 2 is seen to level off to a constant limiting value. The real part of the characteristic value Bz also approaches a constant limiting value for g greater than 3. These curves were obtained by solving the secular equation for D and also deter- mining the slope dD/dg at each point. The charac- teristic values curves can also be computed by starting first with Gamow’s values appropriate for Am—= Figure 3. Characteristic values D» for a bilinear M curve. Ss = — ¥2.g = height of joint in natural units. s3 = ratio of slope of lower segment of M curve to the standard slope. Dm = Bm + i Am. large g and continuing backwards toward smaller values of g, being careful to determine the slope of the curves at each point. It is seen from Figures 2 and 3 that, in contrast to the first mode, these branches of the curves for the second and. third modes do not join on smoothly to the other branches which start with standard values at g = 0 and approach limiting values for large g. This duplicity of the solutions, which was doubted at first, was substantiated in two ways. The values of A, and By at g = 3 and g = 5 in Figure 1 were computed at both branches with increasing accuracy (up to 10-5), and it was found that the matching of the solutions at the duct height and the degree of vanishing of the height-gain function of the ground improved ‘correspondingly in both branches. This 235 TABLE 1. Comparison of exact limiting values of D with values obtained from the asymptotic formula.* 8 Second mode Third mode —1 —0.60 + 2.802 —1.06 + 3.602 Asymptotic a —0.59 + 2.837 Exact —/2 -0.78 + 2.74 1.224 3.40i Asymptotic —0.70 + 2.70% —1.42 + 4.087 Exact —2 —1.00 + 2.60i —1.386 + 3.48: Asymptotic —0.80 + 2.447 Exact *exp (- 5 D') - (: - =) /8D? = 0. proves that both solutions satisfy the boundary conditions. As a second step in testing the reality of the limiting points, an asymptotic expression was derived for the limiting values, and the values com- “ i} @Q is} @ SS BS a es SSS eae =a sae | er ay [rae | | PN ee | a ee | Ble 00 RO a a 0 Ss Ss CS ES SS See Se eee =a z/9—=— Figure 4. Height-gain functions of the second mode for a bilinear M curve. s = — V2.2 = height above ground in natural units. g = height of joint in natural units. Us (2) = normalized wave function. 236 INCIPIENT LEAKAGE IN A SURFACE DUCT puted therefrom were found to be in fair agreement with the exact values, as is shown in Table 1. The physical nature of the duplicity of solutions seems to be as follows. The solutions approaching a limiting characteristic value for large duct height g correspond to the case where the ground sinks to great depths; the other solution corresponds, of course, to the limiting case when the height of joint rises to infinity. The relative importance of the two types of solu- tion will depend on the ranges and heights considered. At sufficiently great ranges the solutions with the smaller value of A,, will predominate, but the greater the height considered the farther must one recede from the source before the initial advantage of the limiting solution due to a greater height gain is overcome by the stronger horizontal attenuation. The greater height gain of the limiting solutions at high elevations is illustrated in Figures 4 and 5. In these figures, the height-gain functions for the limit- ing solutions are drawn in solid lines, those for the Gamow solutions in dashed lines; and the unit of height is the duct height. It should also be pointed out that the normalization condition applied was | i| UZ(2)de = g, (13) 0 : 2 : F : A —- so that, if a comparison of height-gain functions of solutions of the same class for different values of g Figure 5. Height-gain functions of the second mode for - 94 Glesiedl, ah lotted 1 Inowildl dhe cimigied| a bilinear M curve. s = —1. z = height above ground Is Ces negy 2 ONE VES NOU SNe in natural units. g = height of joint in natural units. by V9 U2 (z) = normalized wave function. Chapter 21 THE SOLUTION OF THE PROPAGATION EQUATION IN TERMS OF HANKEL FUNCTIONS* HE CALCULATION Of the field strength in the atmos- ihe depends upon finding a solution of a wave equation incorporating the propagation properties of the atmosphere and satisfying the boundary condi- tions at the surface of the earth and for large heights. This chapter shows how the wave equation, for cer- tain specified conditions, may be solved in terms of Hankel functions. Let height of receiver above earth’s surface, height of transmitter, = great circle distance between source and recelver, = wavelength, k = 27/), frequency, w = 2rf, modified index of refraction, radius of the earth. Usa ll e Su > I] Under the simplifying assumptions of horizontal stratification, slight variation of refractive index in a wavelength, smooth earth’s surface, the plane earth representation, and the use of the simplified boun- dary condition Y = 0 for z = 0, which eliminates the polarization of the source, the field of a (dipole) source is described by a scalar wave equation: A + k? M?v = 0, (1) plus appropriate boundary conditions. Separation of equation (1) in cylindrical coordinates leads to the formal expansion for the field of a dipole source: v= cit) n=) where Re (cosa,) > 0. = Oi HD (kd cos On) U,,(2) U,,(hi) D (2) Here the characteristic values sin’, and the (normalized) characteristic functions U,(z) satisfy the equation 2 — iL Piste wow =O, (3) @By Lt. W. F. Eberlein, USNR, Office of the Chief of Naval Operations. plus the boundary and normalization conditions: UO) = 0 (3a) eiwtU(z) represents an outgoing wave for large positive z . (3b) lim (3c) (Ue = il. I (k)—> 0 0 m Usually sin’a is small, kd is large, and one has H® (kd cos ay) 2 alte = —— e—tlkd cos an) atkd COS ay mw 2 3 —ikd(1 — (1/2) aint an) 4 = | Saeee ae é ( ) dka COS &, The exponential decay factor of the horizontal waves thus has the form exp [ au Tn, (sin? as) , and the sin2e, values evidently lie in the upper half of the complex plane. The problem is then to find the characteristic values and characteristic functions of the system (3) for a given dependence of modified index of refraction upon height. For a ground-based duct of height h with an M curve being made up of two line segments, the upper having standard slope, equation (3) becomes 2 TO +PIA+yOlT=0, Gi) where y(z2) = 2a(z2 —h) ,O<2z 2/2. The ambi- guity on a “Stokes line” (arg W = 7/2) apparently must be resolved by taking the mean of the two expressions when their difference is important, as it is when strongly trapped modes exist (a < 0). The nature of the results obtained is illustrated in the important case of complete inversion (a < 0). For simplicity set Then E (p + 1) >4| We il + je~2ia(e + D3 ae e271 = 2) ot (11) = 0, (F< arg p Aga I ee Lee AA A AS ea ee TAAL Vy aS Sal ae 2a Re 7 ie 7 / | ip \ { / = See ese SE = SSS eh ht hae Bes WS ee eee CES Ee Ee Se eee ees Ow Ee i ae ee BA LAE vA LE LAD), ape ee al : . x Bee AeING mene DUCT murcnneee IN FEET sT 000 Fie . Horizontal attenuation of first mode and trapping index, 3,000 mc, standard attenuation (0 M deficit): 1.23 db Be rl ‘000 yd ATTENUATION DIAGRAMS FOR SURFACE DUCTS fier TKN CTS CLL A AWAAWYANS S222 TI ANASST LS a eros a | GAAS ae ABs a a eo aa Yo 000 arbi Nes S IN FEET aeae E J REECE Fiaure 4. Horizontal attenuation of first mode and trapping index, 200 me, standard attenuation (0 M deficit): 0.498 db per 1,000 yd. Chapter 23 APPROXIMATE ANALYSIS OF GUIDED PROPAGATION IN A NONHOMOGENEOUS ATMOSPHERE* Wee MILITARY IMPORTANCE of guided or ‘anomalous” propagation in a stratified atmos- phere is now well known. Unfortunately, or perhaps fortunately, the problem cannot be treated with the ald of known and tabulated functions except in some special cases because the exact field distribution with height is a function of a function, namely a function of the distribution of the modified index of refraction. For each distribution of this index with height we should have a curve for the field distribution. These curves will look similar in a general way and yet they will differ in detail; but in this particular problem we are not much concerned with details. Even if we had exact solutions we should still want some generalized way of expressing pertinent infor- mation. An approximate analysis of field distribution in terms of master curves, depending on one, or at most, two parameters, will be discussed. For example, if we have atmospheric conditions favoring forma- tion of a guiding layer immediately above the ground or sea level, then we can try to represent the field distribution with height with the aid of the master curve shown in Figure 1. This curve depends on only one parameter, H, so chosen that in the layer between 1s) H and H, the field intensity does not deviate by more than 6 db from the maximum. fo) Oo OF Of @F8 @ Io ie 1.4 ee h/H _ 2.0 Fiagurr 1. Master curve for field distribution with height inside a duct. This particular curve is chosen for the first trans- mission mode, and it has been suggested by the exact aBy S. A. Schelkunoff, Bell Telephone Laboratories. 244. analysis of guided waves in a homogeneous layer. In this case of sharp discontinuity in the index of refraction the field distribution curves are sinusoidal in the layer and exponential outside. The position of the maximum of the sinusoidal portion of the curve and the relative rate of decay of the exponen- tial part depend on the ratio of the wavelength to the thickness of the layer and on the amount of discontinuity in the index of refraction. In Figure 2, curve 1 is identical with the curve in Figure 1; curve 2 shows what happens if the wavelength is doubled; HIMZANSe TL RVR ODS AIS NANG ee Al SNS ee ARE BASeSS (0) 0 02 04 06 08 10 12 14 16 18 20 h/H ine) 0.8 0.6 E 0.4 0.2 Figure 2. Master curves for wavelength \ (1), 2d (2), and 14 X (8). and curve 3 corresponds to the case in which the wavelengthis halved. If the wavelengthis (81+/ 2) /4& 3.3 times as large as the wavelength corresponding to curve 1 or larger, no guided waves are possible with the field intensity vanishing at the ground or sea level. The situation is different if the index of refraction is allowed to vary continuously and to diminish indefinitely. Suppose, for instance, that the lapse rate of the index of refraction is constant. We don’t expect any critical wavelength in this case; as the wavelength increases we expect the field to spread out more and more. In fact, we expect the shape of the field distribution curve to remain the same, namely to be determined by that solution of 2H is Ta = B= ote WB (a) which vanishes at h = 0. In this equation oy GUIDED PROPAGATION IN NONHOMOGENEOUS ATMOSPHERE the electric intensity; = the height; the modified dielectric constant; = the radian frequency; the phase constant in the direction parallel to the stratification. @MEa =~ & Il We can try to approximate this solution by a curve of the type shown in Figure 1 in which case the problem is to select a proper value for H. The ques- tion may be raised regarding our preference for this particular curve rather than for curve 2 or 3 in Figure 2. We shall return to this point later; for the present we shall merely point out that curve 1 occupies a “mean’’ position among other curves of this type. There are two methods for selecting H. In one method # is defined as that value of h for which the coefficient B? — wue(h) in equation (1) vanishes. This value of h separates the region in which the solution of equation (1) is “more” or less sinusoi- dal” from the region in which the solution is ‘“‘more or less exponential.”’ This definition leads to one equation connecting H and g. Next, the stratified region 0 < h < H is replaced by a homogeneous region in which the dielectric constant is equal to the average value of «(h) in the interval (0,h). If we impose the requirement that curve 1 repre- sents the exact field distribution under the new conditions, we obtain the second equation for H and B. Eliminating 8 and expressing the result in sym- bols approved by the wave propagation committee, we have 9 X 108 2 128 M. (&) af 300) dh — H? M(H) = If the lapse rate of M is constant, this equation gives 4 1 (9 aM H = 65d ( 2 7) (3) If M(h) is proportional to h?, then H = isn | | : (4) If the lapse rate of M is constant, the exact solution may be expressed in terms of Bessel functions. Figure 3 shows the exact and approximate solutions. For this comparison I am indebted to J. E. Freehafer of the Radiation Laboratory. The second method is based on the fact that the 0 O05 LO 15 20 25 30 35 40 4.5 Hy = (const) Ui [J4(U) + J_4 (U)] 8 3 U="/.\1— 3} Ey = sin p p< * Ey= glig = p> & Ficure 3. (1) Exact solution normalized to have min- imum value of unity. (2) Approximation. solutions of equation (1) minimize and reduce to zero the following function: I= Bf E? dh —wye © | (A) pe a, 0 0 €(0) + [ (8) dh . (5) In deriving this equation we should remember that we are concerned with solutions which vanish at h = Oandh = wo. Hence, if we wish to approximate this solution by a function of one parameter H, we eliminate H from the following two equations ol Die Oar = 0. (6) If, for instance, we wish to approximate the field distribution by the master curve in Figure 1, we solve 2 OES 0H 9 X_105 H 128 — HP = NM 9 (7) where H . . omh = 9 Gus Ps [atsin an th # —3nh By this variational method the numerical coefficient 246 in equation (3) is found to be 64 rather than 65. The great advantage of the variational method lies in the fact that, if we wish, we can increase the number of parameters in the approximating func- tion. For example, we can assume sin(T) 05h 2H E(h) i = sin aexp| —v S| > el, @&) without specifying that 6 = y = 37/4 as we did in obtaining the curve in Figure 1. We should then calculate H, 6, and wy from ol or LO Fe = Oey = Os However, aside from the labor of solving these equations and having to deal with more complicated (10) GUIDED PROPAGATION IN NONHOMOGENEOUS ATMOSPHERE results, we shall lose the advantage inherent in a description of the field in terms of only one easily understood parameter. The most we could hope for from an analysis of these equations is a somewhat better choice of the master curve for the type of atmospheric conditions which are the most likely to occur. The obvious general conclusion from equations (7) and (8) is this: if (A) is multiplied by a con- stant factor, the effect on H is the same as that obtained if we divide \ by the square root of this factor. If M is proportional to h”, then H is propor- tional to \”“"*”), Since the gain of the guided wave over a free space wave is proportional to \p/H?, where p is the distance from the transmitter, the gain is independent of the wavelength when M(h) is proportional to h?. For a uniform lapse rate the gain varies inversely as one-third power of the wavelength. Chapter 24 SOME THEORETICAL RESULTS ON NONSTANDARD PROPAGATION: 24.1 PROPAGATION IN THE OCEANIC SURFACE DUCT HE ANALYSIS SECTION of Columbia University Wave Propagation Group undertook a theoretical study of propagation in ease of surface ducts, which have recently been reported to be of common oc- currence in oceanic areas. The M curve chosen was M(h) = 346.4 + 0.036h + 43¢701” , (1) where the height h is expressed in feet. This curve has an M deficit of 43 units and a duct height of 48 ft and is considered to be representative of condi- tions prevailing around Saipan when the wind is of the order of 10 to 20 mph. The analysis was based on the phase integral method. The standard W.K.B. (Wentzel-Kramers- Brillouin) version of the asymptotic solutions of the wave equation!” had to be extended in two ways. One was in the adoption of Langer’s form of the asymptotic solutions,*4® which enables one to bridge the “gaps” around the turning points. The other, and more important, development was in the exten- sion of Langer’s method to handle a case with two turning points. This was accomplished by joining the solutions from each turning point at the duct height. The resulting solution agrees with Gamow’s for completely trapped modes but deviates from it when leakage begins. For leaky modes the standard Langer solution is adequate. Coverage diagrams were computed for the S and X bands and for transmitter heights of 16 and 46 ft. In case of the § band, it was found that the first mode was nearly trapped, while the second mode was considerably leaky with a decrement of about 3 db per nautical mile. The two modes were com- bined, and coverage diagrams were computed over ranges and heights such that the second mode contributed no more than 25 per cent to the total field. In the case of the X band, it was found that the first two modes were completely trapped, the third mode nearly trapped, while the fourth mode was leaky with a decrement of over 3 db per nautical mile. In computing the coverage diagrams for the X aBy C. L. Pekeris, Columbia University Wave Propagation Group, Analysis Section. band, the four modes were combined over such ranges and heights that the fourth mode did not contribute more than 25 per cent to the total field. 24.2 CHARACTERISTIC VALUES FOR A CONTINUOUSLY VARYING MODIFIED INDEX In the theoretical treatment of nonstandard prop- agation by the method of normal modes, one is confronted with the task of solving the differential equation for the height-gain function U(h) given by equation (2), which, it will be noted, is identical with equation (8) in Chapter 25. Un(h) + k? [y(h) + Am) Un(h) = 0, Qn (2) y(h) = 2 X 10-§M(h) , by asymptotic methods, the characteristic value A, 1s determined, to a first approximation, by the condition that 4 Am = —y(ha) - (4) In order to solve equation (3) one has to find a value fi, which is generally complex, such that when y(hx) is substituted in the radicand and the integral hi bi Ja Sao db = 0,25 (m a i) , (3) 0 ust V/y(h) = y(ha) dh = F(ha) (5) evaluated, the result should be purely real, and equal tO Um/k. In ease of a surface duct, F'(/1) is real and is a continuously increasing function of its argument for real values of fy ranging from zero up to the duct height h,. In order for F(h;) to increase beyond the value F(h,) and still to remain real it is found that hy must be complex; i.e., the path in the complex hy-plane along which F(h;) is real consists of the portion of real axis 0 ap eS wl s — 2b» h = dy (h 0) by 5) h ae b33 ? a (—6b3b, + 12627) h — = 5) 638 pe (120bibebs — 24b12bs — 120b.') Were by? 6 = ¢im73 30m\> os Mp te y(0) (6) 2Qkh} ’ Zs : then F 4 ip = =90n) = 90) G2 + (5) (he) 64 + 68 et (ho)? — (hs) 25 ii : £295 2 Gp) Od + Say Le, 27 BUH a 35 h hy = — hw +4 — Ww? = ar ws +. (8) where he=r, he=v,--- h h Equations (7) and (8) are of the nature of asymp- totic formulas; they should be terminated when the individual terms begin to increase, and the error in Am or hy is then of the order of magnitude of the last term retained. The following examples in Table 1 illustrate the degree of accuracy obtainable from equation (7). THEORETICAL RESULTS ON NONSTANDARD PROPAGATION As a further check, we treated the case a = +20, = 0.6356, for which Pearcey and Whitehead?* give a value A; = —10.21 + 1.07 X 10—%7. Equa- tion (7) yields A; = —10.22, while the imaginary part obtainable from Gamow’s formula is 1.24 x 10%. It must be emphasized that the value obtained from equation (7) should be verified by carrying hig area out the integration of F(hy) = [v. y(h) + Amdh. While doing so, one may as Bike ee dF _ Auk a ao)? dhy and then obtain a correction to hi by Newton’s method. The method of solving equation (3) explained above has been found especially useful in the treat- ment of substandard refraction, and to a lesser extent in the treatment of the trapped modes in case of a surface duct. In the latter case one can, of course, solve for A,, directly by computing F(h,) by numerical integration. The method is not applicable for the leaky modes in case of a surface duct. So far the discussion has centered on the solution of equation (3), which in itself is only an approximate asymptotic formula valid for large values of k. Let the value of A, which satisfies equation (3) be denoted by A,,“; then an improved value for A, can be obtained from Mn = Deo 3e'7/3(y,,)4 3 4/3 7 il iG BO 2 (i) ahr G) (CO asa) > aa) where hy : dh dy SSS = , ete. , (12 0 Vy(h) + An® dh oe and the derivatives of y are to be evaluated at h = hy. ha (7) and the verification that [ y(h) + Ai dh = 2.383.* TaBLE 1. Approximate determination of A; from equation : hi from US a On Ai from equation (7) yu) = — Ad Vuh) + Ai dh vy —20 0.6356 12.360 + 9.7757 0.3997 — 0.95187 2.370 + 0.0047 2.383 —10 0.6356 4.878 + 6.3027 0.4745 — 1.19827 2.397 + 0.0102 2.383 —5 0.6356 1.499 + 4.2577 0.5691 — 1.46927 2.393 + 0.0097 2.383 —2 0.6356 —0.246 + 2.9027 —0.764 — 4.787% 2.363 — 0.008% 2.383 * y(h) = h + ce. Chapter 25 PERTURBATION THEORY FOR AN EXPONENTIAL M CURVE IN NONSTANDARD PROPAGATION: 25.1 ABSTRACT N THIS chapter a perturbation method is developed for treating nonstandard propagation in the case when the deviation of the M curve from the standard (= the M anomaly) can be represented by a term ae~*, where z denotes height in natural units. The method is also applicable to other forms of the M@ anomaly which can be derived from an exponential term by differentiation with respect to ; in fact, in its region of convergence, it is formally applicable to the most general type of M curve, including elevated ducts. The region of practical convergence of the method ranges from standard down to cases where the decrement is a small fraction of the standard value. The procedure followed is to express the height- gain function U,(z) of the k-th mode in the non- standard case as a linear combination of the height- gain functions U,,°(z) of all the modes in the standard case. Use) = Yj ArmUm°(@) « (1) The execution of this plan hinges on the possibility of evaluating the quantities C) Bnm(A) =| U,,°(2) U,°(2) Ce « (2) It is shown that B,,(A) satisfies the differential equation den Bom — = + Ban(d) —aLoD 01D jada op 0— ),,°)2 (3) QNET oO ts AIAN ti . 4 whose solution is ® (D040, + 5 -aR = DF Bam (X) = = ; a ' mR =#@ 04m |) == 2 Ll @0=m_O2 , pee OD Sam n 4g —n mo (4) LS; Here D,,° denotes the characteristic value of the m-th mode in the standard case. For large ) the following asymptotic formula holds Bim — 2 |» +20 (Dm + Dy!) = 2+ (Da! = Db, | 8 ES + 2X (Dn® + D2) =< (Da? = Da) | ar 3 -(5) ls =F 2d (Dn° = 1D)-) =7, +5 (D,,° rea Dd.) | Having determined the Byn(A) from equation (4), or by a numerical solution of equation (8), the characteristic values D, and the coefficients A,,,, are to be solved from the infinite system of equations yy es [ = D9) ban te Bers oy | = m=1 7 = WA oo (6)? For this purpose a simple iterative procedure has been developed, which has been found to be rapidly convergent. The A,,,, are normalized by the condition Uf @)asi-s Ae OP [ucoun1-Yya @ One can also expand D, as a power series in a Dip = IDR se aD sp GIDE aE 2 2 8 2 D,© = — Bir} Dp® = e*!3 y Bx m m+zk. (Tm — Tk) ; An alternative expression for D® is given in equa- tion (65). 8By C. L. Pekeris, Columbia University Wave Propagation Group. Sam = 1n=m Oum = 0, n =m. “The integral | te@ae diverges when taken along the real axis; it converges, however, and to the same limit, when the path is a radial line in the fourth quadrant of the z plane. In the sequel, whenever an integral is divergent it will be understood that the path is suitably modified. 249 250 25.2 INTRODUCTION In the theoretical treatment of nonstandard propagation by the method of normal modes, one is confronted with the task of solving the equation CU | 0) + dn|Un=0, ©) dh? subject to the condition that U,,(0) = 0 and that at h— ©, U, should represent an upgoing wave only. Here h denotes height in feet. y(h) = N2(h) — 1 = 2 X 10-* M(h) , k = a , (9) and A,, is the characteristic value which is generally complex. It is convenient to introduce natural units of height h dN? = — i 2 Sy S = Fol = WO @ = ae Dn = An (2) D q whereby equation (8) is transformed into zZ = 2.36 X 10° cm! , (10) Um dz? ain E ar di@) se Da | U2) =O. (Mi) The term f(z) in equation (11) represents the refrac- tion anomaly and is equal to zero for a standard atmosphere. In the first instance we shall be treating the case where i@) = ee” , and we shall later generalize the treatment to deal with any M curve represented as a series of Laguerre (12)¢ functions. If the original M curve is represented by the expression M(h) = bh + ae-™, b = 0.036 ft-2, (13) then a and 2X are obtained as follows: a= 2x 10*(7) a,n = oH. (14) It is to be noted that in contrast to the constants a and ¢ in equation (13), which are independent of frequency, the constants a and ) in equation (12) are frequency dependent. For a given observed curve the constants @ and X will therefore differ with 4No confusion should arise from the use of \ in equation (12) and the standard usage of \ to denote wavelength. EXPONENTIAL M CURVE IN NONSTANDARD PROPAGATION the frequency band used, as will also the height represented by one unit of z. 25.3 FORMAL SOLUTION OF THE PROBLEM BY THE PERTURBATION METHOD In order to solve the equation GU) dz? i- E + ae? + Ds| U;,(z) = 0, (15) we seek a solution in the form U;, = AW a@) ) m=1 (16) where U,,°(z) are the height-gain functions of the m-th mode in the standard case, which satisfy the equation ae t, E 4 Dat | Un(2) = 0. (17) | | U (2) jj dz=1. The solutions of equations (17) and (18) are well known: (18) 2 3 ( ? Oe) = CP EO @) ,@ = 3s Cb D9) D3 = FOr » tie = (22) ) (21) 2 where Jy (m) +P Jn (Um) me 0 2 (22) For small z the power series development of U,,°(2) is useful: UW@) = 7 A,z* , (23) Leta ae 0 ) Ave ~ pty | Peder tans], eo (25) EVALUATION OF fnm(\) AS while for large z one may use asymptotic expansion of equation (19) 9 Hy (u) =» = ei(— ut or/12) . é TU 385 E 7 72u 10,368u? . | (26) If now the expansion (16) be substituted into equation (15), we obtain, on making use of equation (17), the condition D> Aven | = 1D)39) == ae Sal Un (2) = m=1 On multiplying this equation by U,,°(z), where n is any integer, and integrating from 0 to © we get a system of equations for the determination of D; and the A pm: m=1 (27) | = ID) On SF cant) = fi = BB 2 2 (-) Bnm(Q) -| Uno (@)) Unie) en? de . (28) (29) The characteristic values D, are then obtained as the roots of the infinite determinant. D; = D,° ar abi , aBie , aBi3 , Be, D; — D2 + ao, oes, 6 aB31, aB32 = D;° =F aB33 ) , Oe Cea aD) coe (30) Having determined D, from equation (30), the Ajm are obtained by solving the system of linear equations (28). 25.4 EVALUATION OF Bnm(\) AS AN INDEFINITE INTEGRAL The primary task in the perturbation method is the evaluation of the exchange integrals Bnm(A) defined in equation (29). We shall accomplish this by proving that B,,.(A), as a function of , satisfies a differential equation of the first order for which an explicit solution can be given. For this purpose AN INDEFINITE INTEGRAL 251 we shall study the function )) = WANA) WEIN) « (31) where Un9( (2) + le + D,,"] U,°@) = 0, (32) U,%(2) + le + D,'] U,%(2) = (33) By multiplying equation (32) by U,,°(z), equation (33) by U,,°(2) and subtracting, we obtain “ (Un? OY rs Oa! U,.) = dz ie (D,,° aa D,,°) Up Oe (34) Uno One = Us U,° > (UD; = Dat) OMe) U aa r) dz . (35) 0 Now it can be verified by direct substitution that F + 2F (D, + Dm + 22) + OF (Dr. Bar D,,°) (Un! UY = Ore U,) = — (D,,° — Daye | F(a) dx . (36)° From equation (36) it follows that P= ‘| @ 5 79,0 te 1D),0) 9 +57] + 5 (Dn! — Dy’)? / F(a) de. (37) We may also note that FO) = 2U,.°0) U,(0) = —2, (38) co oO C) le Fdz =e” (F + dF) |) + | e-* Fdz 0 0 0 (-s) | Ge Hida 0 le a: | F(a) dx = — = al F(a) dx 0 0 0 ae | e™ F@) dz =+ fi eo F(2) dz. (40) de wh -) 1 Nz d = aes eg fe (2) dz A |, This is the first occasion in the author’s experience where use is made of the fact that the product of two functions, each of which is a solution of a distinct second order ordinary linear differential equation, satisfies a fourth order linear differential equation. (39) e-2 1@) da. (Gi) 202 We now substitute equation (387) in the integrand of equation (29) and obtain C) Bom ) -| F(z) e-™ dz -| ei xX 0 0 @ F ‘ 1. {iz | @e + Da + DDR + 5% ap if (Ox — Day | Pada 0 = x (Dn? = p,» | e F(z) dz + E + Dio + Dy’) F +5 | em 4. af oe | @ +. 19,0 & D0) P 4. Fi dz 0 = jl al e-” F(z) 0 | 2r< + (D,,° + D,°) + ; AS aE = (Dn? D,°) ‘| dz D, Y) ‘| ~) (42) AB am ( d) dy = 1 — 2h Ns 1 ar Bum) ke ar D,,°) ++ 9 + DH (D 0 It follows that the exchange integral B,,,(\) satisfies the first order differential equation CBs O) _ 1 ad DD ar Bm (X) ; | at y(Dat + Dat) +9 + aha (Dat — Dat)? (43) The solution of equation (48) is Boro (A) = e2 X (vo + D9 22 @ =e 24/) X dr =

M8 ce D (OO, & 2) = B + 5 (DB — DB) D) Ne Le Dy (D2, +e iD) -~2+5 (DB — D2)? 8 | ax 4. DP (DL ++ DY) = : (D2 — ay] a 2 — py]. (49) + [as + 20 (De + DY — 2 +5 (D8 SOLVING VALUES PD, AND THE COEFFICIENTS 4;,,, An alternative asymptotic expansion can be derived from equation (44) by partial integration Bmn a 2 [»*+20 (D3 + DY) ++ (DY — m2 | 4 [ + 2h (D3 + D’) — 2 (Dg - Diy | $+ —__§ = 0) [> + 2 (Do + D8) + 5 (Dh - yy | In doing so one needs to prove that LS) 3 r 1 ¢ | dx ts 5 (DY, + D9) — F544, (Dy — Pn)” a Wo =wWv,, =. (51) We shall state here without proof that 3 Ge = ap) = Winm = —— @ m~ 12 0 Vx = FYE) hs Duta (Dn), (52) where hy and hz are Furry’s functions of the first and second kind defined as hn @ Ee ey Ve Hi (G 2) (53) he (x) = @) VJ x Hy G “) (54) Since by definition of D,,°, h2(Dm°) = 0, it follows that Vinm = 0. The proof of equation (51) for n + m is left as an exercise to the interested reader. 256 JTERATION METHOD OF SOLVING FOR THE CHARACTERISTIC VALUES D, AND THE COEFFICIENTS 4,,, In solving equations (28) and (30), which are of infinite order, one proceeds by first assuming that Aim = 0 form > p, where p is a convenient integer, and then evaluating D, and A,m, m = 1,2 --: p. Next, one assumes that A,, = 0 for m > p + 1, resolves for D,, and the A,,,, and the accuracy of the results is judged by the agreement between the values in successive approximations. The direct solu- 299 tion of equations (30) and (28) is, however, a labo- rious process which rapidly increases in complexity as p exceeds about 4. The following iterative pro- cedure has been found effective and of the same intrinsic simplicity for any value of p. To begin with, the p equations in equation (28), being homogeneous, do not determine the absolute values of all the A, but merely the ratios of (p — 1) of them to a p-th one. The absolute values are then determined from the normalization condition (OZ lz => 1 = A im? - a [vee ya @ Let therefore A km ) Cy = 1, Art ey Crm = (55) and the p equations in equation (24) are just suffi- cient to determine the (p — 1) constants C,,, and D,. We divide the equations in (28) by A,, and pick the k-th equation (n = k) to solve for D,, while the other equations are used to solve for the C;,,, as is illustrated in the scheme below for the particular case of k = 1. D,° Us Onin = Catto = ear Ed (56) a a G yea Be) Op a a = = bin = Cis B23 — Cis (fa = D (57) D 2 =e BS =F Bs ) Cis a =P B33 > Cis Bog = Cis B34 7 ) (58) D 0 (2: ae Be + Bu ) Cis a a = = $4 — Cie Bo, = Chs fax = 2 © 2 (59) As a first approximation one puts D D,° — = —t =5 Bu , (60) a a PaaS 2 (2: — + bas) (61) a a 254 aa (BBs 5.) Cy = — , ete. , (62) a where the value of D:/a obtained from equation (60) is used in equations (61) and (62). Next, one substi- tutes these values of the C’s in the right-hand sides of equations (56) to (59) and resolves for D,/a and the C’s. This procedure has been found to be rapidly convergent and is, furthermore, self-correcting in case of arithmetical errors. 25.7 EXPANSION OF D, INTO A POWER SERIES IN a When a is small, it is convenient to expand D,, into the series D, = D.© +a@D,© +02 D,2 +--+ - (63) It is known from standard perturbation theory that 2 D,© = — Bir j Dp = e'7/3 y Brak! , 7 (ip ae Tk) mtk. (64) It is possible also to derive an alternative expression for Di”: 3 0 We 5 GP BT ae Dx (d) = 5D: 24/r i: ge BET). 0 Ie 4. x) Dy (\+ 2) + Di 0) Di ) [vi de Dj) » + (43/12) =) D,© A)? + —- . Ein i ES () + (2 AR, | DOA+ ue ds. (8) Since the former expression is simpler for compu- tational purposes, we shall not give here the deriva- tion of equation (65). 25.8 APPLICABILITY OF PERTURBATION METHOD TO A MORE GENERAL CLASS OF M ANOMALIES It is possible to apply the results obtained for the case when the M anomaly is of the form f(z) = ae~” EXPONENTIAL M CURVE IN NONSTANDARD PROPAGATION to more general types of M anomalies. To begin with, if f(z) = ae” + ye“ , (66) then we merely write in equation (28) in place of OBnm(A), [eBnm(X) ate YBnm(u) 1. Once the Bnm(A) are computed as functions of \, there is no additional labor required to deal with an f(z) which consists of a sum of any number of exponential terms. If instead of f(z) = ae” we had f(z) = aze-™, then the corre- sponding B’ym(A) would be (oo) (Boars (A) -| Um (2) U,,°(2) ze? dz = = oe 0 Bum (N) .(67) Tf Bym(A) is known, dBym(A)/dd can be computed directly from equation (43). When equation (48) is integrated numerically, the derivative dBpm()/dd is computed at each point in any case. Evidently, for f(z) = azke-’, where k is a positive integer. (Bier (X) = Hl Un°(2) U,°(2) zk e—™ dz (68) By successive differentiation of equation (43), it is possible to express any high order derivative of Bnm(X) in terms Of Bym(A). From a purely formal point of view we can say therefore that by our method we can treat any M anomaly by expanding it into a series of Laguerre functions, since these functions involve only terms of the form z*e~’. It may be pointed out that a single term z*e—” vanishes both at the ground and at great height and reaches a maximum at z = k/). Such a single term is therefore suitable to represent an elevated duct. 25.9 COMPUTATIONAL PROGRAM FOR THE EXPONENTIAL MODEL The Analysis Section of the Columbia University Wave Propagation Group has undertaken the com- putation of Bpm(A) for X = 0(0.1)4.0 and n, m = 1, 2, 3, 4, 5. With these functions tabulated, it is planned to compute the characteristic values D, for such values of a and ) that the difference between the values of D, obtained from the fourth order deter- minant and from the fifth order determinant will be only about 0.01. The program also calls for the computation of the height-gain functions from equa- COMPUTATIONAL PROGRAM FOR THE EXPONENTIAL MODEL tion (2), since the coefficients A,,, will be obtained simultaneously with the D, when the iteration pro- cedure is used. This will be possible only in a limited region of low altitudes, since at great heights the U,,°(2) imerease rapidly in magnitude as m is increased. However, near the ground the U,,°(z) are all of the same order of magnitude (= zz) and du, (0) dz = oy Jee (69) m=1 If this derivative of U,(z) at the ground can be obtained with sufficient accuracy, then one may use it to integrate numerically the original equation (11). It is well known that, for a given order of the deter- minant used, the characteristic values D, are obtained with higher accuracy than the height-gain functions. It may be added here that Bu(A) computed from equation (44) agrees up to \ = 5.0 with the values given by Pearcey and Tomlin.1°5 The perturbation method will of course become inefficient when trapping conditions are approached. For such values of @ and X, asymptotic methods may provide approximate values for the D,, provided care 1s taken at each stage to estimate the order of magnitude of the error involved. It is planned to map out by a combination of these methods the real and imaginary parts of D, in the operationally relevant region of the a, \ plane. Symbols for Use in Theory of Nonstandard Propagation q = standard slope of N? curve = 2.38-10~7 m— . p = slope of lower section of N? curve in bilinear model . R =N?—-1=2M - = (kgth = Sore NOmeee h/H height in natural units (k = 2r/X) . (k?q) = 7.24 Nem! (feet) natural unit of height . 1/2 (kq?) d = d/L distance in natural units . 2 (kq?)+ = 6.69 Nen* (thousands of yards) = natural unit of distance . anomaly height (height of joint in bilinear model) . h,/H anomaly height in natural units . characteristic value (for y = Oath = h,) . (k/q)? Am = Bn + 1A» characteristic value in natural units . s-? D (abbreviation for use in computing) . eiwt — 2Qwid/\ — in/4 Dr . é ee ees, L lane wave P depends on A CS) Gt » eA m™ + iB, fe . OF (21) Un (Z2) 1 natural units only fumes. 0 slant range . d = horizontal range . Chapter 26 FIRST ORDER ESTIMATION OF RADAR RANGES OVER THE OPEN OCEAN* HE MOST STRIKING nonstandard propagation conditions are for the most part associated with meteorological conditions which can exist only over those portions of the sea which are contiguous to extensive land masses. At large distances from the coasts, however, low ducts exist which, though they never produce strongly locked modes at the usual radar frequencies, nevertheless modify radar ranges. The problem of the low duct has the great advantage that conditions are sufficiently near standard that numerical solutions can be found in convenient form by an extension of the perturbation methods of wave mechanics. At appreciable distances from land the temperature of the air is essentially that of the sea, and the air is in neutral equilibrium. Montgomery has pointed out that under these conditions there is much evidence to support a logarithmic distribution of specific humidity. The logarithmic distribution of water vapor leads to an M curve given by ffir 2 sage (Ole om 2 M Myo = 7 10 BIE inj where d is the duct thickness, z is the height coordi- nate, and a is the radius of the earth. If we plot the function in the brackets, we obtain the dashed curve of Figure 1. This type of M distribution is inconvenient because (a) the logarithmic term which represents the modi- fication does not approach zero as the height increases as a modification term should; and (b) In(z/d) becomes infinite when z = 0. Accordingly it is pro- posed to replace the function in the brackets by the first two terms of its series expansion about the minimum. This amounts to substituting for the logarithmic curve a parabolic curve which has the same minimum point and the same radius of curvature at the minimum point as the original distribution. At twice the duct height the parabola has a standard slope, and it is continued from that poimt upward as a straight line of this slope (AB in Figure 1). The modification term is now represented entirely @By J. E. Freehafer, Radiation Laboratory, MIT. 256 by the departure of the parabola from the line AB, ie., 2 Mu My = F104) 1454 i) o<2e9 al rx , : Bayh 2 M Mo = 710°" 5: 2 IA d . When the duct is low, the modes leak and are not far different from the standard ones. Thus it seems 4 Q|N 2 (yn B. qo" G Fiegure 1, Schematic M curve for ground-based duct. reasonable to employ the well-known methods of perturbation theory for calculating the characteristic values and functions of the parabolic atmosphere in terms of departures from standard. If we brush aside mathematical questions of a delicate nature, it is possible to obtain an approxi- mation for the characteristic values which leads to the following expression for the fractional change in the attenuation constant (.e., the real part of 7») Re (Fm) — Re (Ym) Re (Ym) 6 -| (¢ — 6) Im hs? ( + en)] de 66 ~ 315 5 [he’ (€m)]? Im (m) Here, Re and Im designate the real and imaginary parts, and ESTIMATION OF RADAR RANGES OVER THE OPEN OCEAN L is an abbreviation for (a\?2/672)} and is equal to 33 ft for \ = 10 em, Ym is the characteristic value for the standard case, Ym is the characteristic value for the parabolic case, Ne ae he(z) is (5) sHyo(32'), H, is the Hankel function of second kind, order 2 14, of the argument (=), €m’S are roots of ho(¢) = 0. The expression above has been evaluated for the first mode by summing the series for hy and perform- ing the integration numerically. This curve is remark- able for the considerable interval in which the ordinate is practically zero. The attenuation constant differs by less than 1 per cent from the standard for ducts below 6 = 1.2. Beyond this value the effect of the duct increases rapidly, and when 6 = 1.7 the attenuation constant is 10 per cent different from standard, and at 6 = 2 it is 20 per cent different. It seems that at least for radar purposes the condition 6 <1 is a reasonable and convenient condition for defining a negligible duct. This is equivalent to saying that L/2 is the thickness below which a duct may for practical purposes be disre- garded. For instance, at \ = 10 em, L = 33 ft, and hence we conclude that the effect of ducts less than 16 ft in thickness on 10-cm radars may be neglected. On the other hand, if the wavelength is3 m, L = 300 ft, and ducts below 150 ft in thickness are negligible. If in the interest of simplicity we neglect the effect of small variations in the characteristic values on the characteristic functions, the fractional change in attenuation constant is also equal to the fractional change in the range against surface targets. It follows that the estimation of range can be reduced to a measurement of sea temperature and specific hu- midity at masthead level; for the duct thickness d under conditions of neutral equilibrium is given by _ GHG) 0 @ - \dz/o q; 1s the saturation specific humidity at sea tempera- ture and q, the specific humidity at masthead. T is a parameter for which a representative value is 0.08, and (dq/dz)o is the gradient of specific humidity required to give zero M gradient under conditions 257 of constant potential temperature. It is taken as lo g per kg. Thus it turns out that ds = Wa = 0.29 “= 6 = 0.3 Ck = where ZL “is in grams per kg per 100 ft . If LZ is given the appropriate value for \ = 10 em ) = hy = Ge (& Joe ea) For illustrative purposes, scales of (q, — qa)/L and Ys — qa for X = 10 em have been added in Figure 2. 0.15 0.05 Aaq/t G/KG/100 FT 1.0 Aq G/KG Figure 2. Fractional drop in attenuation constant of the first mode versus duct thickness. Bottom scale for A qand A g/L corresponds to X = 10 cm. It is emphasized that the calculations are rough and are presented only in the belief that some sort of simple guiding principle may be more useful than a highly accurate and cumbersome formula. The results given are accurate out to variations in range of 1 per cent, and the determination of threshold thickness is completely reliable. Extension beyond 6 = 1.2 is a definite extrapolation. The trend indi- cating that the increase in range goes up at least as fast as the sixth power of the duct thickness for 6 > 1 is, we believe, real. Chapter 27 CONVERGENCE EFFECTS IN REFLECTIONS FROM TROPOSPHERIC LAYERS? N ELEVATED DUCT may be treated as a concave spherical mirror whose radius of curvature is a, the effective earth radius. This includes any layer that can act as a reflector to radiation incident at a sufficiently small angle. The problem is here con- sidered as one of geometrical optics only. Ray tracing methods are used, and the phases are assumed to add randomly. This assumption may introduce an error as large as 3 db in the result but is necessary to simplify the solution of the problem. If the reflec- tion coefficient is other than unity, it must be multiplied into the general relation which will be given for C=KLM the net convergence factor. 27.1 CONVERGENCE FACTOR A bundle of rays leaving a transmitter below the reflecting layer is converged on reflection from a concave surface. The convergence factor K is the ratio of the power density at the receiving antenna after convergence to the power density at the receiver that would be expected after reflection from a plane surface (essentially free space condition). Referring to Figure 1, the convergence factor can be expressed as -_ (+ pM) dh i AG a OE” @) or Se Diy \* i ( ak sin 5) ’ @) RECEIVER TRANSMITTER Ficure 1. Convergence factor K. where « = distance from transmitter to point of reflection, ®By Ensign W. W. Carter, USNR Radio Division, Consult- ant Group. 258 y = distance from receiver to point of reflec- tion, R=2+y = total range, a = effective earth’s radius (usually 4,590 nautical miles), @ = angle of incidence of radiation at reflec- tion, other angles as shown on Figure 1. Equation (2) can be deduced from equation (1) by remembering that . A. a x6 cht NOUS a a (3) and Het toy Soda Se asin The form shown in equation (2) is the more useful and is similar to the divergence factor for reflection at a convex surface that has been in use for some time. Equation (2) shows that K can grow quite large and even become infinite for certain conditions. Curve 1, Figure 2, shows a plot of the absolute value ReriticaL IN NAUTICAL MILES le} 200 400 600 800 b IN FEET ——> 1000 1200 400 1600 _ 1800 Ficure 2. Value of K for height of layer (b in ft) versus range (nautical miles). of K as a function of 6, the height of the layer above the antennas, for a total range of 80 nautical miles. This plot also assumes « = y = 40 miles, which is a necessary condition for a smooth reflector. In this case, K becomes infinite for a layer 1,100 ft above the antennas. Curve 2, Figure 2, shows a plot of CONCLUSIONS 259 the layer height b necessary to give infinite conver- gence as a function of the range (plotted on right- hand scale). U2 ROUGHNESS EFFECT The most apparent difficulty with the picture presented so far is that the layers actually are not perfectly smooth. In order to take that fact into consideration, it was assumed that the layer was composed of a large number of plates set at various small angles about the horizontal according to a Gaussian distribution. As in other parts of this problem, variations are considered only in the plane of transmission, since the effect of sideways deviation would cancel out. This reduces the problem to one of two dimensions only. Each plate is further assumed to retain its original curvature. A beam falling on a patch of these plates would be reflected in such a way as to spread the energy at the receiver in a vertical pattern similar to the Gaussian distribution of the plates. It is only neces- sary to integrate this curve over the width of the antenna to find the fraction, L, of the total energy that will be useful. Z will be a function of the probable value of the deviation of the plates, the range, and the antenna width. With the rough layer assumption, there will be some plates correctly oriented at each part of the layer to reflect energy into the receiver. Therefore, a third factor, 7, must be included that is the ratio of 7/8, where y is the total angle subtended by the layer that can reflect rays to the receiver. y would be limited by the optical horizons. 8 is the angle subtended by the receiving antenna when reflection is from a plane surface; i.e., essentially, free space conditions. The net convergence factor C must be the product of these three quantities K, L, M. In this case, K must be the mean value of K averaged for various points of reflection. In order to integrate the expres- sion for the mean value of K, it is necessary to substi- tute for sin ¢ in equation (2). Ot (oie ese Se ( POG + y nF 2) d (5) which gives oe = 8 (ay)? i Ss E R? (2ab + =| ; 6) This expression is easily integrated if the product xy is used for the variable and ay; = 11(R — 2%). Example. The preceding developments have been applied to the one-way link of the U.S. Navy Radio and Sound Laboratory at San Diego, which has been extensively studied. High subsidence layers are common for this region. The probable value of the deviation of a reflecting plate from horizontal was taken as 0.1° as an engineering approximation. In this case, C equals 43, assuming a reflection coeffici- ent of 1. If the reflection coefficient is not unity, its value as a function of angle of incidence must be multiplied into the equation. Since K, L, and M can each vary through con- siderable limits, C can vary through a very wide range of values. 28 CONCLUSIONS The statistical treatment of the roughness is not always applicable, since a finite number of plates would actually be engaged in reflecting energy. Hence, the received signal would vary almost ran- domly with time as the orientation of the plates changed slightly. This could produce marked fading and peaks of large amplitude. Primarily, however, it would explain signals of the magnitude of free space signals or higher. 7 BIBLIOGRAPHY VOLUME I Numbers such as CP-100-M1 indicate that the document listed has been microfilmed and that its title appears in the microfilm index printed in a separate volume. For access to the index volume and to the microfilm, consult the Army or Navy agency listed on the reverse of the half-title page. bo . Notes on Microwave Propagation Conference at MIT , Radiation Laboratory, Division 14 Report 42, RL, Sept. 24, 1943. CP-100-M1 . International Radio Propagation Conference [held at Inter- service Radio Propagation Laboratory, from April 17 to May 5, 1944], Report IRPL-C61, National Bureau of Standards, June 1944. CP-100-M3 . Report of Second Propagation Conference, February 10 to 11, 1944 at the Empire State Building, New York, OEMsr- 1207, NDRC CUDWR-WPG, February 1944. CP-100-M2 . Scientific Investigations on Propagation Problems in the Southwest Pacific Area, F.W.G. White, OSRD II-5- 6124(S), ATP [Australian Radio Propagation Com- mittee], July 24, 1944. CP-110-M1 . The Air Defense System of the Near Islands, Thomas J. Carroll, Report OAD-55, U.S. Army Air Forces, Eleventh Air Force, OCSO, Operational Analysis Division, Aug. 30, 1944. CP-202.1-M5 . Reviews of Progress of Ultra Short Wave Propagation Work, (USWP]: 6a. [Part] J, The Evaluation of Solutions of the Wave Equation for a Stratified Medium, D. R. Hartree, OSRD WA-2961-2, JEIA 5934, RDF 239, Report AC-7017, Sept. 26, 1944. CP-110-M2 6b. [Part] 17, Statement of Work in Progress Relevant to Investigations of the Propagation of Radio Waves Through the Troposphere, R. L. Smith-Rose, OSRD WA-3005-2, Report AC-7018, NPL, Sept. 25, 1944. CP-110-M3 6c. [Part] I1I, Microwave Propagation Research at the Signals Research and Development Establishment, OSRD WA-3156-7, JEIA 6464, Report AC-7019, SRDH, Sept. 26, 1944. CP-110-M4 6d. [Part] [V, Correlation of Radar Operational Data with Meteorological Conditions, OSRD WA-8156-8, JEIA 6463, Report AC-7020, AORG, Sept. 28, 1944. CP-110-M5 6e. [Part] V, Progress Report on Forecasting of Radar Conditions, OSRD WA-3156-9, JEIA 6462, Report AC-7021, DMO, Oct. 2, 1944. CP-110-M6 6f. [Part] VI, Vertical Temperature and Humidity Gra- dients at Rye, OSRD WA-3156-10, JEIA 6461, Report AC-7022, DMO, Oct. 2, 1944. CP-110-M7 6g. [Part] VII, The Use of Radar for the Detection of Storms, OSRD WA-3156-11, JEIA 6460, Report AC-7023, DMO, Oct. 2, 1944. CP-110-M8 6h. [Part] VIII, Present States of Theoretical Study of Radio Propagation, Through the Troposphere by the Mathe- matics Group, TRE, OSRD WA-3156-12, JEIA 6459, Re- port AC-7024, TRE, Oct. 2, 1944. CP-110-M9 6i. [Part] 1X, Review of Short-Period Experimental Studies of Centimetre Wave Propagation, Carried Out Jointly by 10. 11. 12. 13. ASEH, SRDE, and GEC, E. C. 8. Megaw, OSRD WA- 3156-13, JEIA 6458, Report AC-7025, Oct. 16, 1944. CP-110-M10 6). [Part] X, Study of Centimetre Wave Propagation over Cardigan Bay to Mount Snowden, F. Hoyle, OSRD WA- 3157-1, Report AC-7026, Oct. 14, 1944. CP-110-M11 6k. [Part] XJ, Study of Reflection Coefficient of the Sea at Centimetre Wavelengths, F. Hoyle, OSRD WaA-3157-2, Report AC-7027, Oct. 14, 1944. CP-110-M12 6l. [Part] XII, Some K-, X-, and S-Band (Llandudno) Trials, General Summary of the Experimental Results Ob- tained which are Concerned with the Dependence of Radio Propagation on Meteorological Conditions, OSRD WA- 3157-3, Report AC-7028, TRE and RRDH, Oct. 14, 1944. CP-110-M13 6m. [Part] XIII, Progress Report on 369 Trials by Di- rector, Naval Meteorological Service, OSRD WA-3156-1, JEIA 6466, RDF 240, Report AC-7029, Oct.14, 1944. CP-110-M14 6n. [Part] XIV, Survey of Progress in the United Kingdom on the Electromagnetic Theory of Tropospheric Propagation, OSRD WA-3157-4, Report AC-7030, RRDE, Oct. 16, 1944. CP-110-M15 60. [Part] XV, Study of Meteorological Factors Responsible for the Refractive Structure of the Troposphere, OSRD WA- 3157-5, Report AC-7031, RRDE, Oct. 16, 1944. CP-110-M16 . Report No. 1 of Project SWP-3.2 of the Office of Field Service, Paul A. Anderson and P. Squires, OHMsr-728, Research Project PDRC-647, Washington State College, Novy. 2, 1944. CP-335-M3 . Data on Super Refraction Supplied by Australian Radar Stations, J. W. Reed, Report RP-229/1, CSIR-RL, Dec. 6, 1944. CP-223-M11 . Report No. 2 of Project SWP-3.2 of the Office of Field Service, Paul A. Anderson and P. Squires, OKMsr-728, Research Project PDRC-647, Washington State College, Jan. 7, 1945. CP-335-M3 Third Conference on Propagation, Washington, D. C. [on] November 16 to 18, 1944, NDRC CUDWR-WPG, 1945. CP-100-M4 Survey of Field of Radio Propagation and Noise with Special Reference to Australia, F. J. Kerr, OSRD II-5- 6572(S), JEIA 8641, Report RP-231, CSIR, Nov. 27, 1944. CP-110-M17 Fourth Conference on Propagation, Washington, D. C. [on] May 7 [to] 8, 1945, NDRC CUDWR-WPG, 1945. Notes on Microwaves based upon a Series of Lectures by W. W. Hansen, Samuel Seely and Ernest C. Pollard, Division 14 Report T-2, RL, Oct. 20, 1941, Chaps. 1 to 3. CP-201.1-M1 261 262 14. 15. bo — iw) bo 23. 28. 29. 30. BIBLIOGRAPHY— VOLUME 1 An Introduction to Microwave Propagation, Donald E. Kerr and Pearl J. Rubenstein, Division 14 Report 406, RL, Sept. 16, 1943. CP-201.1-M2 Electrical Communication Systems Engineering, General Information, Technical Manual TM-11-486, U. 8. War Department, Feb. 25, 1944. CP-204-M1 Superseded by TM-11-486, Apr. 25, 1945 and Electrical Communication Systems Equipment, TM-11-487, Oct. 2, 1944. . Anomalous Propagation and the Army, Thomas J. Carroll, Report ORB-P-18-1, OCSO, Mar. 4, 1944. CP-221-M12 . Principles of Radar, Staff of MIT Radar School, June 15, 1944. CP-202-M1 . Radar Performance Testing Manual, Manual 28, USAAF, Second Edition, July 1944. CP-202.31-M1 . Effects of Site Conditions on Operation of Ground Radar Installations on Aerodromes, J. L. Putnam, OSRD WA- 4172-12, Report T-1805, TRE. CP-202.31-M2 . “The Diffraction of Electro-magnetic Waves from an Electrical Point Source Round a Finitely Conducting Sphere, with Applications to Radiotelegraphy and the Theory of the Rainbow,” H. Bremmer and Balth. Van Der Pol, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 24, July 1937, Part I, pp. 141-176; Supplement, 24, November 1937, Part II, pp. 825-864; 25, June 1938, Part III, pp. 817-837; 27, March 1939, Part IV, pp. 261-275. . Ultra Short Wave Propagation Curves, 0.1 to 10 Meters, OSRD WA-1502-1a, Marconi Handbook, Marconi, Ltd., Mar. 28, 1940. CP-211-M1 . Report on Signal Strength Curves Within the Visual Range, OSRD WA-1463-1, Pamphlet RD-456, Marconi, Ltd., November 1940. CP-211-M2 “The Effect of the Harth’s Curvature on Ground-Wave Propagation,” Chas. R. Burrows and Marion C. Gray, Proceedings of the Institute of Radio Engineers, 29, Jan- uary 1941, pp. 16-24. CP-231.12-M5 . “Ultra Short Wave Propagation,” I. C. Schelling, Chas. R. Burrows, and E. B. Ferrell, Proceedings of the Institute of Radio Engineers, 21, March 19383, pp. 427-463. (See reference 447.) . Propagation Curves for Wavelengths of 13 Meters, Swpple- ment to U. S. W. Propagation Curves RD-456, Appendix RD-456A, Marconi, Ltd., November 1941. (See refer- ence 22.) . “The Calculation of Ground-Wave Field Intensity over a Finitely Conducting Spherical Earth,” Kx. A. Norton, Proceedings of the Institute of Radio Engineers, 29, Decem- ber 1941, pp. 623-639. . Siting of Stations for Maximum Range, H. G. Booker, OSRD II-5-1188, Report M/36, TRE, Feb. 9, 1942. CP-231.11-M2 Microwave Interference Patterns, J. A. Stratton, Division 14 Report C-1, RL, Mar. 7, 1942. CP-232.1-M1 Theoretical Field Strength of Ten-Centimeter Equipment over a Spherical Earth, H. G. Booker, OSRD WA-210-3), Report M/45/HGB, TRH, July 1, 1942. CP-231.12-M1 Atmospheric Refraction and Height Determination by RDF, 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. E. Hastwood, OSRD II-5-6511, JEIA 7773, Calibration Memorandum 54, RAF, July 6, 1942. (See reference 63.) CP-211-M3 Dependence of Range of Submarine Radar Equipment on Wave Length, Case 20564, Chas. R. Burrows, Technical Memorandum MM-42-160-70, BTL, July 9, 1942. CP-212-M1 Transmission on 8000 Mc. over Sea Water, J. A. Stratton, Division 14 Report C-2, RL, July 14, 1942. CP-232.1-M2 Transmission on 100 Me. over Sea Water, J. A. Stratton, Division 14 Report C-3, RL, July 14, 1942. CP-232.1-M3 Transmission on 200 Mc. over Sea Water, J. A. Stratton, Division 14 Report C-4, RL, July 14, 1942. CP-232.1-M4 Transmission on 500 Mc. over Sea Water, J. A. Stratton, Division 14 Report C-5, RL, July 14, 1942. CP-232.1-M5 Interim Report on Propagation Within and Beyond the Optical Range, C. Domb and M. H. L. Pryce, Report M-448, ASE, September 1942. Theoretical Ground Ray Field Strengths and Height Gain Curves for Wavelengths of 2 to 2000 Megacycles, OSRD II-5-5274, Technical Report 383, Section E, BRL, Sep- tember 1942. CP-211-M4 Siting for Long Range Aircraft Detection, Thomas J. Carroll, Technical Report T-13, CESL, Revised Oct. 17, 1942. CP-202.11-M1 V.H.F. Field Strength Curves for Propagation within the Line of Sight, G. J. Camfield, OSRD WA-570-3, Report Radio/279, Radio/s.2111/OPE 16, RAE, October 1942. CP-211-M5 Relation of Radar Range to Frequency and Polarization, J. A. Stratton and Richard A. Hutner, Division 14 Report C-6, RL, Nov. 3, 1942. CP-212-M2 Propagation Curves [of] 1 to 10 Cm, G. Millington, OSRD WA-1502-1c, Report TR-460, Marconi, Ltd., January 1943. CP-211-M6 Properties of the Diffracted Wave Field Intensity, Richard A. Hutner and Elizabeth M. Lyman, Division 14 Report C-8, RL, Feb. 12, 1943. CP-233-M7 The Effect of Earth Curvature on the Performance Diagram of an RDF Station, Report 29/R102/LGHH, TRH, Feb. 25, 1948. Radar Height Finding, Richard A. Hutner, Helen Dod- son, Jocelyn Gill, Bernard Howard, Francis Parker, and J. A. Stratton, Division 14 Report C-9, RL, Apr. 6, 1943. CP-202.311-M1 Technical Requirements of Ground Communications Inter- ceptor Search Systems, Technical Requirements for Early Warning Radar Systems, L. J. Chu and N. H. Frank, Division 14 Report TCAW-1 and -2, RL, May 10, 1943. , CP-202.1-M1 Low-Angle Coverage of Early Warning Radar Systems, N. H. Frank, Division 14 Report TCAW-3, RL, July 26, 1943. CP-202.1-M2 Factors Relating to the Design of an RDF Air Warning Set, F. J. Kerr, OSRD II-5-5721, Report RP-187, CSIR-RL, Aug. 11, 1948. CP-202.1-M3 48. 49, 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. BIBLIOGRAPHY—VOLUME 1 A Graphical Method of Computing the Bending of Radio Beams by the Effective Earth Radius Method, Harry Ray- mond, Technical Report T-14, CESL, Aug. 27, 19438. CP-231.12-M2 Transmission at Low Altitudes over Sea Water, Richard A. Hutner, Francis Parker, Bernard Howard, Helen Dodson, and Jocelyn Gill, Division 14 Report C-10, RL, Sept. 1, 19438. CP-232.1-M6 . Radio-Frequency Propagation Above the Earth’s Surface, Paul F. Godley, Jr., OEMsr-895, Division 15 Report 895-5, RCA, Sept. 11, 1948. CP-231.12-M3 . Field Intensity Formulas, Richard A. Hutner, Helen Dod- son, Jocelyn Gill, Francis Parker, and Bernard Howard, Division 14 Report C-11, RL, Sept. 28, 1943. Div. 14-111-M8 . Note on Field Intensity Computations for Elevated An- tennas, Case 20878, Marion C. Gray, OSRD WA-1463-23, Technical Memorandum MM-43-110-28, BTL, Oct. 9, 1943. CP-211-M7 The Calculation of Expected Vertical Coverage Diagrams by Max Sherman, February 19, 1943, revised by Walter S. McAfee, Technical Report T-17, CESL, Oct. 15, 1943. CP-211-M8 Charts for Use in Field Intensity Computations, K. Bull- ington, OEMsr-1018, Research Project C-79, NDRC Division 13 Preliminary Report 3460-KB-NF, Western Electric Company, Inc., Nov. 2, 1943. CP-211-M9 Notes on Visibility Problems, Taking Account of the Cur- vature of the Earth, OSRD WA-1368-19, Report 152, AORG, Dee. 1, 1943. CP-231.12-M4 Simplified Methods of Field Intensity Calculations in the Interference Region, William T. Fishback, Division 14 Report 461, RL, Dee. 8, 1948. CP-211-M10 Field Strength Near and Beyond the Horizon for Wave- lengths of Ten and Thirty Cms., M/Report 53/WW, TRE, Dee. 24, 1948. Theoretical Field Strength Near and Beyond Horizon for Orthodox Propagation of Fifty Centimeter Waves, OSRD WA-1976-5, Report T-1635/WW, TRH, Feb. 24, 1944. CP-211-M11 The Propagation Functions for an Atmosphere with Uni- form Lapse-Rate of Refractive Index, T. Pearcey, OSRD WA-2985-1, Research Report 256, RRDE, Sept. 1, 1944. CP-211-M12 Propagation Curves (third edition), NDRC Division 15 Report 966-6C, October 1944. CP-211-M13 Field Strength Calculator for Vertical Coverage Patterns and Propagation Curves, Clarence R. White, Technical Memorandum 154-H, CESL, Dec. 20, 1944. CP-211-M14 Theory of the Vertical Field Patterns for RDF Stations, J.C. Jaeger, OSRD I1-5-4297, Report RP-174, CSIR-RL, Mar. 17, 1943. CP-213-M1 Height, Range \and| Alpha Tables, Tables Relating to the Height, Range and Angle of Elevation of an Aircraft, OSRD II-5-6512, JEIA 7766, Radar Memorandum 50, ORS- ADGB, Aug. 10, 1944. (See reference 30.) CP-213-M2 The Calculation of Field Strength for Vertical Polarization over Land and Sea on 20 to 80 Megacycles per Second, A. M. Woodward, OSRD WA-4395-11, Report T-1704, TRE. CP-211-M15 65 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 263 . Field Intensity Contours in Generalized Coordinates, Helen Dodson, Jocelyn Gill, and Bernard Howard, OK Msr-262, Division 14 Report 702, RL, May 2, 1945. CP-211-M16 The Limiting Ranges of RDF Sets over the Sea, ¥. Hoyle and M. H. L. Pryce, O9SRD WA-1514-17, Report M-395, ASE, 1948. CP-232.2-M2 The Theory of Anomalous Propagation in the Troposphere and Its Relation to Waveguides and Diffraction, H. G. Booker, OSRD WA-599-10, Report T-1447, M/60/HGB, TRH, Apr. 12, 1943. CP-221-M2 The Tracing of Rays in the Refracting Atmosphere, T. Pearcey, OSRD WA-645-42, Report AC-3878, ADRDE- USW, Apr. 21, 1943. CP-222-M2 Graphical Construction of a Radar Radiation Pattern in a Stratified Atmosphere, Lloyd J. Anderson and F. R. Abbott, BuShips Problem X4-49CD, Report WP-4 [for the period from] March 1, 1943 to May 1, 1943, NRSL, May 1, 1943. CP-232.2-M3 Improved Tropospheric Propagation, Curves Embracing Anomalous Propagation, H. G. Booker, OSRD II-5-4950, Report T-1482, M/65/HGB, TRE, July 6, 1943. CP-221-M3 Radiation Patterns under Cases of Anomalous Propagation, T. Pearcey, OSRD WA-830-8, Report R-35/TP, ADRDE, July 19, 1943. CP-221-M5 Effect of Humidity Gradients in the Atmosphere on Pro- pagation at RDF Frequencies, Operational Research Re- port 22, AORG, July 28, 1943. CP-222.1-M2 The Calculation of Field Strength Near the Surface of the Earth under Particular Conditions of Anomalous Propa- gation, T. Pearcey, OSRD WA-931-6, Research Report 203, ADRDE, Oct. 28, 1943. CP-221-M6 Anomalous Propagation over the Earth, Case 23703, 8. A. Schelkunoff, OSRD WA-1463-50, Report MM-43- 110-33, BTL, Oct. 30, 1943. CP-221-M7 The Effect of Atmospheric Refraction on Short Radio Waves, John HK. Freehafer, Division 14 Report 447, RL, Noy. 29, 1943. CP-222-M5 Radar Ray Patterns Associated with Normal and Anoma- lous Propagation Conditions, F. P. Dane, R. U. F. Hop- kins, and Lloyd J. Anderson, BuShips Problem X4-49CD Report WP-6 [for the period from] November 1 to De- cember 6, 1943, NRSL, Dec. 10, 1943. CP-221-M8 Transmission of Plane Waves Through a Single Stratum Separating Two Media, John B. Smyth, BuShips Problem X4-49CD, Report WP-9, NRSL, Dec. 22, 1943. CP-221-M9 Notes on Theoretical Coverage Diagrams for Anomalous Propagation, Donald E. Kerr, OSRD WA-1464-9, TM/ Memorandum/14/AMW, TRE, Jan. 1, 1944. CP-221-M11 The Dependence of Microwave Propagation over Sea on the Structure of the Atmosphere, J. M.C. Scott and T. Pearcey, OSRD WA-1591-9, Memorandum 40, ADRDH, Feb. 4, 1944. CP-232.2-M8 Improved Tropospheric Propagation, Curves Embracing Superrefraction (revised edition), OSRD WA-1666-27, Report T-1625/WW, TRH, Feb. 18, 1944. CP-223-M1 264 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. OTE 92. 93. 94 95. 96. 97. BIBLIOGRAPHY— VOLUME 1 TRE Requirements for Propagation, Curves Embracing Superrefraction, OSRD WA-1666-26, Report M/Memo- 16/HAB, TRE, Feb. 25, 1944. CP-223-M2 The Mechanical Determination of the Path Difference of Rays Subject to Discontinuities in the Vertical Gradient of Refractive Index, F. R. Abbott, BuShips Problem X4-49CD, Report WP-10, NRSL, Mar. 10, 1944. CP-222.1-M3 Improved Tropospheric Propagation, Curves Embracing Superrefraction, OSRD W A-2026-2, Report T-1626/WW, TRE, Mar. 28, 1944. CP-223-M3 Interservice Propagation, Curves Embracing Superrefrac- tion, Dependence of Mathematical Parameter L on Physical Entities, Report M/Memo-18/WW, TRE, Apr. 3, 1944. CP-223-M4 Theoretical Coverage-Diagrams for 10 Cm. Radars Em- bracing Superrefraction, JEIA 3229, Report T-1634, TRE, Apr. 14, 1944. CP-223-M5 Theoretical Coverage-Diagrams for 50 Cm. Radars Em- bracing Superrefraction, OSRD WA-1992-4, JEIA 3230, Report T-1659, TRE, Apr. 14, 1944. CP-223-M6 Theoretical Coverage of Navigational Aids Embracing Superrefraction, OSRD WA-1992-6A, Report T-1660, TRE, Apr. 14, 1944. CP-223-M7 The Theory of Propagation of Radio Waves in an Inhomo- geneous Atmosphere (Part I), T. Pearcey, OSRD WA- 2251-5, Research Report 245, ADRDE, April 1944. CP-221-M10 Reflection Coefficient of Layers of Varying Refractive Index, G. Millington, OSRD WA-2562-13, JEIA 4644, Report TR-483, BRL, April 1944. CP-222.1-M4 Evaluation of the Solution of the Wave Equation for a Stratified Mediwm, D. R. Hartree, P. Nicholson, N. Hyres, J. Howlett, and T. Pearcey, OSRD WA-2341-4, Memorandum 47, ADRDE, May 24, 1944. (See reference 108.) CP-221-M13 Transmission of Plane Waves Through a Single Stratum Separating Two Media (Part II), John B. Smyth, Bu- Ships Problem X4-49CD, Report WP-13, NRSL, June 23, 1944. CP-221-M9 Waves Guided by Dielectric Layers, 8. A. Schelkunoff, Re- port MM-44-110-52, BTL, July 5, 1944. CP-221-M14 Microwave Transmission in Nonhomogeneous Atmos- phere, S. A. Schelkunoff, Report MM-44-110-53, BTL, July 5, 1944. Contour Diagrams of the Radiated Field of a Dipole under Various Conditions of Anomalous Propagation, T. Pear- cey and F. Whitehead, OSRD WA-2985-2, Research Report 257, RRDE, July 15, 1944. (See reference 110.) CP-221-M16 Theoretical Coverage-Diagrams for 114-Meter Radars Em- bracing Super-refraction, A. M. W. Woodward, OSRD W A-2854-2, Report T-1708, TRE, July 23, 1944. CP-223-M9 Propagation Curves Embracing Super-refraction: SS Duct, Profile-Index 0.2 (Preliminary Hdition), H. G. Booker, M/Memo-23/WW, TRH, Sept. 7, 1944. CP-223-M10 A Note on the Reflection Coefficient of an Isotropic Layer of Varying Refractive Index, G. Millington, OSRD WA- 3172-1, JEIA 6481, Report TR-497, BRL, Oct. 5, 1944. CP-222.1-M5 CP-221-M15 © 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. Predicted Low Level Coverage of S-Band Shipborne Radars as Affected by Weather, F. R. Abbott, L. L. Whittemore, L. W. Cross, and E. J. Wyrostek, BuShips Problem X4-49CD, Report WP-14, NRSL, Nov. 1, 1944. CP-232.2-M9 Predicted Low Level Coverage of 200 MCS Band Shipborne Radars as Affected by Weather, F. R. Abbott, L. L. Whit- temore, L. W. Cross, and E. J. Wyrostek, BuShips Prob- lem X4-49CD, Report WP-15, NRSL, Nov. 4, 1944. CP-232.2-M10 Variational Method for Determining Eigenvalues of Wave Equation of Anomalous Propagation, G. G. Macfarlane, Report T-1756, TRE, Nov. 18, 1944. Wave Propagation Analysis with the Aid of Non-Euclidian Spaces, Benjamin Liebowitz, OEMsr-1207, Report WPG-7, CUDWR, December 1944. CP-221-M18 Atmospheric Waves, Fluctuations in High Frequency Radio Waves, L. G. Trolese and John B. Smyth, BuShips Prob- lem X4-49CD, Report WP-18, NRSL, Feb. 1, 1945. CP-225-M1 The Relation Between the Wave Equation and the Non- Linear First Order Equation of the Riccati Type, T. L. Eckersley, OSRD WA-4223-7, JEIA 9104, Report TR- 501, BRL, January 1945. (See reference 111.) CP-221.1-M1 A Report on Transmission of Waves over the Earth, T. L. Eckersley, OSRD WA-4002-13, Report TR-504, BRL, January 1945. CP-221.1-M2 New Convergent Integrals, T. L. Eckersley, OSRD, WA- 4002-11, Report TR-509, BRL, February 1945. CP-221.1-M3 The Effect of a Subrefracting Layer of Atmosphere upon the Propagation of Radio Waves, T. Pearcey and M. Tomlin, OSRD WA-4016-28, JEIA 8371, Memorandum 83, RRDE, Feb. 12, 1945. CP-223-M13 Theory of Characteristic Functions in Problems of Anoma- lous Propagation, W. H. Furry, OEMsr-262, Division 14 Report 680, RL, Feb. 28, 1945. CP-221-M19 The Evaluation of the Solution of the Wave Equation for a Stratified Medium ({Part] IZ), D. R. Hartree, OSRD WA-4424-11, Research Report 279, RRDE, Mar. 12, 1945. (See reference 90.) CP-221-M20 Theoretical Coverage Diagrams for 3-Meter Radars Em- bracing Super-refraction, W. Walkinshaw and R. Hens- man, OSRD WA-4320-7, JEIA 9198, Report T-1815, TRE, Mar. 18, 1945. CP-223-M12 The Radiation Field of a Dipole under Various Conditions of Anomalous Propagation, T. Pearcey, M. Tomlin, and F. Whitehead, OSRD WA-4392-7, Research Report 275, RRDE, Apr. 13, 1945. (See reference 94.) CP-221-M21 Notes on the Solution of a Non-Linear First Order Equation of the Riccati Type, T. L. Eckersley, OSRD WA-4428-7, JEIA 9725, Report TR-502, BRL, May 1945. (See refer- ence 103.) CP-222.1-M6 Perturbation Theory for an Exponential M-Curve in Non- Standard Propagation, C. L. Pekeris, OEMsr-1207, Re- port WPG-12, CUDWR, July 1945. CP-221.1-M4 Graphs for Computing the Diffraction Field with Standard and Superstandard Refraction, Pearl J. Rubenstein and William T. Fishback, OEMsr-262, Division 14, Report 799, RL, Aug. 13, 1945. CP-222-M11 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. BIBLIOGRAPHY—VOLUME 1 265 Radio Interpretation of Meteorological Observations in the First Two Meters of Atmosphere Above Grass at Harling- ton, Middlesex, January to June, 1940, OSRD WA-861-3, Report T-1471, M/63, TRE, June 1940. CP-222.1-M1 Anomalous Echoes Observed with 10 Cm C.D. Set, A. E. Kempton, OSRD_ II-5-564, Research Report 119, ADRODE, Oct. 8, 1941. CP-623-M1 Centimeter Wave Propagation over Sea Between High Sites just within Optical Range, F. Hoyle and E. C. 8. Megaw, OSRD WA-171-12, ASE-GEC, June 12, 1942. CP-232.2-M1 Centimeter Wave Propagation over Land (Part II), Meas- urements within and beyond Optical Range, G. W. N. Cobbold, H. Archer-Thomson, and E. C. 8. Megaw, Re- port AC-2917, Com. 1386, SRDE-GEC, Oct. 16, 1942. Radar Wave Propagation, Lloyd J. Anderson, John B. Smyth, F. R. Abbott, and R. Revelle, BuShips Problem X4-49CD, Report WP-2, NRSL, Nov. 30, 1942. CP-623-M2 Very Short Wave Interception and D.F., T. L. Eckersley, OSRD II-5-5276, Report TR-438, BRL, 1943. CP-224-M2 Anomalous Propagation of 10 Cm R.D.F. Waves over the Sea (February 6, 1948); First Swpplement to Report 87 (July 26, 1943), OSRD WA-909-21, Report 87, AORG, July 26, 1943. CP-232.2-M5 Investigation of Propagation Characteristics of A.W. Sta- tions, Report 17, AORG, Mar. 9, 1943. CP-332-M1 “A Study of Propagation over the Ultra-Short-Wave Radio Link between Guernsey and England on Wave- lengths of 5 and 8 Meters (60 and 37.5 Mc/s),” R. L. Smith-Rose and A. C. Stickland, The Journal of the In- stitution of Electrical Engineers, OSRD WA-1463-31, NPL, Vol. 90, No. 9, March 1943, Part III. CP-224-M3 The Effect of Atmospheric Refraction on the Propagation of Radio Waves, A. C. Stickland, OSRD WA-623-19, Report RRB/S-10, NPL-RRB, Mar. 20, 1948. CP-222-M1 Propagation of Ultra-Short Waves, H. C. Webster, OSRD I1-5-4575(S), Report 354, Australia, Apr. 17, 1943. CP-224-M4 Report on Radar Wave Propagation, Atmospheric Refrac- tion, A Qualitative Investigation, Lloyd J. Anderson and John B. Smyth, BuShips Problem X4-49CD, Report WP-5, NRSL, May 7, 1943. CP-222-M4 Radio Interpretation of Meteorological Observations in the First 400 Feet Above Cardington, 1942, OSRD WA-861-1, Report T-1413, M/61, TRE, May 14, 1943. CP-321-M1 Centimeter Wave Propagation over Sea (Part IT), Measure- ments from Shore Sites Near and Beyond Optical Range, G. W. N. Cobbold, A. J. Jones, H. A. Bonnett, E. C. S. Megaw, H. Archer-Thomson, and H. M. Hickin, OSRD WA-792-10, Report 8180, GEC, May 27, 1943. CP-232.2-M4 Preliminary Observations on Radio Propagation at 6 Centi- meters Between Beer’s Hill, New Jersey, and New York, Case 37003-4, File 36691-1, G. W. Gilman, Report MM-43-160-87, BTL, June 12, 1943. CP-224-M6 Some Observations of Anomalous Propagation, Report T-1483, M/64, TRE, July 6, 1943. 130. 131. 134. 135. 136. 137. 138. 139. 140. 141. 143. 144. Application of Anomalous Propagation to Operational Problems at Home and Abroad, H. G. Booker, JMRP 3, Report T-1484, M/66/HGB, TRE, July 7, 1948. CP-221-M4 Propagation of Signals on 45.1, 474 and 2800 Mc from Empire State Building to Hauppauge and Riverhead, L.I., New York. G. S. Wickizer and A. M. Braaten, OEKMsr- 691, NDRC Research Project 428, Division 14 Report 179, Report 1, RCA, July 20, 1943. CP-631-M1 . Propagation of Ultra Short Waves, T. L. Eckersley, OSRD WA-1463-3, Report TR/476, Marconi, Ltd., August 1948. CP-224-M7 . The “K” Effect in Anomalous Propagation of Ultra-Short Waves, F. Syer (RAAF), JMRP 11, Australian Paper 266, Report AC-4496, Australia, Aug. 10, 1943. CP-224-M15 The Propagation of 10 Cm Waves over Land Paths of 14, 52, and 112 Miles, Paul A. Anderson, C. L. Barker, K. E. Fitzsimmons, and 8. T. Stephenson, OEMsr-728, Re- search Project PDRC-647, Division 14 Report 202, Report 4, Washington State College, Oct. 26, 1943. CP-224-M8 The Propagation of 1-Cm Waves over the Sea as Deduced from Meteorological Measurements, J. M. C. Scott and T. Pearcey, OSRD WA-1339-6, JMRP 4, Research Report 227, ADRDEH, Noy. 11, 1948. CP-232.2-M6 Centimeter Wave Propagation over Land, A Preliminary Study of the Field Strength Records between March and September 1943, R. . Smith-Rose and A. C. Stickland, OSRD WA-1514-6, JMRP 10, Paper RRB/S-13, DSIR- NPL, Nov. 15, 1943. CP-333-M1 The Propagation of 10 Cm Waves over an Inland Lake, Correlation with Meteorological Soundings, Paul A. Ander- son, K. E. Fitzsimmons, and S. T. Stephenson, OEMsr- 728, Research Project PDRC-647, Division 14 Report 212, Report 5, Washington State College, Nov. 12, 1943. CP-232.2-M7 Measurements of Radar Wave Refraction and Associated Meteorological Conditions, Lloyd J. Anderson and L. G. Trolese, Report WP-7, NRSL, Dec. 10, 1943. CP-222-M6 Anomalous Propagation in India, Preliminary Report on Overland Transmission in Bengal, H. G. Booker, OSRD TI-5-6555(S), Report S-5, ORS-SHA, Dec. 30, 1943. CP-334-M1 Atmospheric Physics, Summary of Investigations on Anom- alous Propagation of Radar Signals Carried Out by the Australian Operational Research Growp During 1942-43, D. F. Martyn, AORG, 1943. CP-221-M1 The Cause of Short Period Fluctuations in Centimeter Wave Communication, J. M. C. Seott, OSRD WA-1962-7 Memorandum 42, ADRDE, Mar. 8, 1944. CP-224-M10 . Anomalous Propagation in the Persian Gulf, Naval Officer in Charge, Hormuz, OSRD WA-2146-23, Report AC- 5975, USW, Received Mar. 20, 1944. CP-331-M4 Effect of Super-refraction on Surface Coverage on Enemy 50-Cm and 80-Cm Radar Sets, OSRD WA-2284-3, Report M/Memo-19 GGM, TRE, April 1944. CP-223-M8 K-X-S Experiments, News Letter No. 1, T. Gold, MK. 12201, ASE, May 3, 1944. CP-333.2-M1 266 BIBLIOGRAPHY—VOLUME 1 145. 146. 147. 148. 154. 155. 156. 157. 158. 159. Abnormal Radar Propagation in the South Pacific, An Investigation into Conditions in New Zealand and Nor- folk Island on 200 Mc/s. with Notes on Fiji, New Cale- donia and Solomon Islands, Air Department Wellington, File 1385/14/10, Report 119, ORS-RNZAF, May 4, 1944. CP-335-M1 Procedure and Charts for Estimating the Low Level Cover- age of Shipborne 200-Mc Radars under Conditions of Pronounced Refraction, F. R. Abbott, Lloyd J. Anderson, F. P. Dane, J. P. Day, R. U. F. Hopkins, John B. Smyth, L. G. Trolese, and A. P. D. Stokes, BuShips Problem, X4-49CD, Report WP-11, NRSL, Revised May 10, 1944. CP-202.32-M1 Centimeter Propagation over Land, A Study of the Field Strength Records Obtained During the Year 1943-1944, A. C. Stickland and R. W. Hatcher, JEIA 4789, Re- port RRB/S-18, NPL-MO, DSIR, May 11, 1944. CP-224-M11 K-X-S Experiments, News Letter No. 2, T. Gold, MK. 12201, ASE, May 18, 1944. CP-333.2-M1 . Atmospheric Propagation Effects and Relay Equipment, Thomas J. Carroll, Report ORB-PP-12-1, OCSO, May 18, 1944. CP-311-M2 . Low-Level Coverage of Radars as Affected by Weather, Procedures and Charts, Report IRPL-T2a, May 25, 1944. (Reference 146 reprinted.) NRSL, . Variations in Radar Coverage, Report JANP-101, Joint Communications Board, June 1, 1944. CP-202.4-M4 Earlier edition: IRPL T-1, CUDWR-WPG, May, 1944. CP-202.5-M1 . Effect of Atmospheric Refraction on Range Measure- ments, G. G. Macfarlane, OSRD I-A-320, Report T-1688, TRE, June 12, 1944. CP-222-M7 . Microwave Transmission over Water and Land wnder Various Meteorological Conditions, Pearl J. Rubenstein, I. Katz, L. J. Neelands, and R. M. Mitchell, OEMsr- 262, Division 14 Report 547, RL, June 13, 1944. CP-311-M4 Abnormal Propagation in W. A. C. for May and June, 1944. Report 10, Canadian ORS-WAC, July 27, 1944. Propagation of Signals on 45.1, 474 and 2800 Me from Empire State Building, N.Y.C. to Hauppauge and Riverhead, L.J., N.Y., G.S. Wickizer and A. M. Braaten, OEMsr-691, NDRC, Research Project 423, Division 14 Report 298, Report 2, RCA, July 31, 1944. CP-631-M1 The Structure of the Electromagnetic Field During Con- ditions of Anomalous Propagation, T. Pearcey and F. Whitehead, OSRD WA-3070-1, Research Report 258, RRDE, Sept. 19, 1944. CP-221-M17 Tropospheric Propagation and Radio-Meteorology, Re- port WPG-5, CUDWR-WPG, September 1944. “Some Factors Causing Super-refraction on Ultra High Frequencies on South West Pacific,’ (Daily Report on Abnormal Echoes, RAAF Form 146 included in ATP 821), D. F. Martyn and P. Squires, Australian Iono- sphere Bulletin, October 1944, Section 1.2. CP-224-M14 Atmospheric Refraction, A Preliminary Qualitative Inves- tigation, Lloyd J. Anderson, F. P. Dane, J. P. Day, R. U. F. Hopkins, L. G. Trolese, and A. P. D. Stokes, BuShips Problem X4-49CD, Report WP-17, NRSL, Dec. 28, 1944. CP-222-M9 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. . Propagation Anomalous Propagation with High and Low Sited 3 Cm Ship Watching Radar Sets, G. C. Varley, OSRD WA- 4238-2, Report 250, AORG, Mar. 20, 1945. CP-232.2-M12 Anomalous Propagation at English Coastal Radar Sta- tions, March to September, 1944, D. Lack, OSRD WA- 4491-12, JEIA 9946, Report 258, AORG, May 30, 1945. (See also reference 6d.) CP-232.2-M13 Lebanon-Beer’s Hill Transmission on Wavelengths of 2.0 Meters, and 80 Centimeters, Case 20564, A. B. Crawford, Report MM-39-326-98, BTL, Dec. 5, 19389. CP-224-M1 Centimeter Wave Propagation over Land; Preliminary Trials, G. W. N. Cobbold, H. A. Bonnett, A. J. Jones, E. C. 8. Megaw, H. Archer-Thomson, A. S. Gladwin, and E. M. Hickin, Report 8045, GEC, Aug. 21, 1942. The Propagation of 10-Cm Waves on a 52-Mile Optical Path over Land, The Correlation of Signal Patterns and Radiosonde Data, Paul A. Anderson, C. L. Barker, S. T. Stephenson, and K. EK. Fitzsimmons, OEFMsr-728, NDRC Research Project PDRC-647, Division 14 Report 151, Report 1, Washington State College, June 10, 1943. CP-224-M5 Centimeter Wave Propagation over Sea Within and Be- yond the Optical Range, EK. C. S. Megaw, H. Archer- Thomson, EH. M. Hickin, and F. Hoyle, Report M-582, ASE, July 1943. Aden-Berbera V.H.F. Experiments, Final Report on Propagation Aspects, E. W. Walker and S. R. Bicker- dike, OSRD WA-2187-14, Report MS-4, SRDE, De- cember 1942 and July 1948. CP-331-M1 (Ultra Short Wave Communication], Investigation No. 369, Trish Sea Experiment, OSRD WA-2146-18, -19, -20, -21, and -22; WA-2379-2, WA-2797-36, WA-3158-13; WA- 3822-30; and -31. Or, as identified in Progress Reports AC-5970 Sept. 1, 1948, AC-5971 Dec. 14, 1948, AC- 5972 Jan. 15, 1944, AC-5973 Feb. 9, 1944, AC-5974 Mar. 20, 1944, AC-6334 May 14, 1944, AC-6828 Aug. 12, 1944, AC-7206 Oct. 19, 1944, AC-7465 Nov. 10, 1944, and AC-7668 Jan. 4, 1945, British Ministry of Supply. CP-224-M9 Experience with Space and Frequency Diversity Fading on New York-Neshanic Microwave Circuit, Case 87003-4, G. W. Gilman and F. H. Willis, Report MM-43-160- 152, BTL, Sept. 18, 1948. CP-240-M1 Investigation of Changes in Direction of Transmission during Periods of Fading in the Microwave Range, Case 3870038-4, File 86691-1, A. C. Peterson, Report MM-43- 160-183, BTL, Oct. 30, 1943. CP-240-M2 Radar Calibration Report, New York Region, R. C. L. Timpson, Mitchell Field, N.Y., Nov. 30, 1943. CP-202.1-M4 Aden-Berbera VHF Experiments, Meteorological Con- ditions and Possible Correlations, E. W. Walker, OSRD WA-1614-1, JMRP 14, Report AC-54938, USW-SRDE, Dee. 20, 1943. CP-331-M3 . Propagation over Short Paths and Rough Terrain at 200 Mc/s, A. B. Vane and D. G. Wilson, OEMsr-262, Di- vision 14 Report 468, RL, Jan. 18, 1944. CP-231.2-M1 and Reflection Characteristics of Radio Waves as Affecting Radar, William G. Michels and 174. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. BIBLIOGRAPHY—VOLUME 1 William C. Pomeroy, Service Project (M-38) lla, U.S. Army Air Forces Board, Jan, 31, 1944, © CP-531-M1 Microwave Propagation Measurements (Conference of February, 1944), ¥. H. Willis, Report MM~44-160-55, BTL, Mar. 10, 1944. (See reference 3.) . An Estimation of the Incidence of Anomalous Propa- gation in the Cook Strait Area of New Zealand from Jan- uary 1948 to January 1944, F. BE. 8. Alexander, OSRD II-5-5849(S), Report RD-1/373, RDL-DSIR, NZ, May 2, 1944. CP-332-M2 . K-Band Radar Transmission, A Preliminary Report of Tests Made Near Atlantic Highlands, N.J. between De- cember 1948 and April 1944, G. C. Southworth, A. P. King, and S. D. Robertson, Report MM-44-160-115, BTL, May 19, 1944. CP-202.2-M1 Report on Cross Channel Propagation of British No. 10 Set, K. R. Spangenberg, Report OAB-2, OCSO, Aug. 26, 1944. CP-224-M12 Radar Range and Signal Strength, L. Jofey and A. C. Cossor, Report MR-142, Research Department, Myra Works, London E10, August 1944. Results of Microwave Propagation, Tests on the New York-Neshanic Path, Case 37003-4, File 36691-1, A. L. Durkee, Report MM-44-160-190, BTL, Aug. 28, 1944. CP-224-M13 Height-Gain Tests in the Troposphere, G. A. Isted, JEIA 5560, JMRP 36, Report TR-488, BRL, September, 1944. CP-312-M1 Interim Report on Investigation of 120 Mc/s and 50-Cm Propagation Across the English Channel, W. R. Piggott, OSRD WA-3157-6, Report AC-7081, USW, Oct. 4, 1944. CP-333-M5 Measurements of the Angle of Arrival of Microwaves in the X-Band, Case 20564, W. M. Sharpless, Report MM- 44-160-249, BTL, Nov. 7, 1944. Overwater Transmission Measurements, 1944-Part I: Preliminary Analysis of Radio and Radar Measure- ments, Pearl J. Rubenstein, OEMsr-262, Division 14 Report 649, RL, Dec. 15, 1944. CP-222-M8 The Vertical Distribution of Field Strength over the Sea Under Conditions of Normal and Anomalous Propa- gation, J A Ramsay and P. B. Blow, OSRD WA-3870-1, Research Report 267, CAEE-RRDE, Jan. 5, 1945. CP-232-M1 Centimetre Wave Propagation over Sea, A Study of Signal Strength Records Taken in Cardigan Bay, Wales Between February and September, 1944, R. L. Smith- Rose and A. ©. Stickland, OSRD WA-4297-9, JMRP 50, Paper RRB/C-114, NPL-DSIR, Feb. 28, 1945. CP-333-M3 Over-Water Tests of S-Band Early Warning for Ships, Vertical Coverage of the CXHR (SCI) Search System, Walter O. Gordey, Donald T. Drake, and M. Kessler, OPMsr-262, Service Project NS-194, Division 14 Re- port 703, RL, Mar. 5, 1945. CP-232.2-M11 Preliminary Report on S- and X- Band Propagation in Low Ducts Formed in Oceanic Air, Martin Katzin, Prob- lem $411.2R-S, Report R-2493, NRL, Mar. 24, 1945. CP-222.2-M2 188 189 190. 192. 193. 194. 195. 196. 197. 198. 199. 200. 201. 204. 267 Atmospheric Refraction under Conditions of a Radiation Inversion, Lloyd J. Anderson, J. P. Day, C. H. Freres, R. U. F. Hopkins, John B. Smyth, and A. P. D. Stokes, BuShips Problem X4-49CD, Report WP-19, NRSL, Apr. 21, 1945. CP-222-M10 Radio-Meteorological Relationships, E. C. 8. Megaw and F. L. Westwater, OSRD WA-4594-15, Report AC-8140, USW-138, May 4, 1945. CP-222.2-M3 Calculated Relationship Between Signal Level and Uni- form Gradient of Refractive Index for the Trish Sea Paths, E. C. 8. Megaw, OSRD WA-4594-13, GEC Report 8656, AC-8225, USW-141, GEC-USW, Apr. 19, 1945. CP-222.1-M8 . Radio-Meteorological Relationships, General Summary of Papers AC-8140/USW.138 and AC-8225/USW.141, EH. C. S. Megaw and F. L. Westwater, OSRD WA-4618-1, Report AC-8336, USW-149, USW, 1945. (See references 189 and 190.) CP-222.2-M4 General Summary Covering the Work of the KXS Inter- Service Trials, Llandudno, 1944, J. R. Atkinson, JMRP 64, Report T-1770, TRE, May 1945. CP-333.2-M2 X-Band Trials at Rosehearty, J. R. Atkinson, OSRD WA-4596-11, JEIA 10401, Report AC-8228, USW-142, May 28, 1945. CP-222.3-M1 S- and X- Band Propagation in Low Ocean Ducts (Fourth Conference), R. W. Bauchman and W. Binnian, Report R-2565, NRL, July 5, 1945. (See reference 12 and 187.) KXS Llandudno Interservice Trials, Summer 1944, JMRP 68, Report T-1865, TRE, 1944. Survey of Radio Meteorological Information Available at TRE, JMRP 67, Report M/98 (T-1888)/JWH, TRE, August 1945. The Diffusive Properties of the Lower Atmosphere, O. G. Sutton, OSRD WA-670-9a, Report MRP-59, Chemical Defense Experimental Station, Air Ministry Meteoro- logical Research Committee, Dec. 29, 1942. CP-3823-M1 A Study of the Effect of the Meteorology on the Refraction of Radio Beams, H. Raymond, Technical Report T-2, CESL, May 4, 1943. CP-222-M3 The Rapid Reduction of Meteorological Data to Index of Refraction, Lloyd J. Anderson and F. R. Abbott, Report WP-8, NRSL, Dec. 10, 1943. Application of Diffusion Theory to Radio Refraction Caused by Advection, P. M. Woodward, OSRD, WA- 2047-4, Report T-1647, TRE, Apr. 6, 1944. CP-323-M2 Qualitative Survey of Meteorological Factors Affecting Microwave Propagation, 1. Katz and J. M. Austin, OEMsr-262, Division 14 Report 488, RL, June 1, 1944. CP-311-M3 . The Influence of Ground Contour on Air Flow (Trans- lation), P. Queney, Translated by Walter M. Elsasser, OEMsr-1207, Report WPG-4, CUDWR, September 1944. CP-322-M1 . Radio-Meteorological Tables, P. M. Woodward and J. W. Head, OSRD WA-3401-1, JMRP 30, Report T-1724, TRE. CP-222.1-M9 Modified Index Distribution Close to the Ocean Surface, R. B. Montgomery and Robert H. Burgoyne, OEMsr- 262, Division 14 Report 651, RL, Feb. 16, 1945. CP-222.2-M1 BIBLIOGRAPHY— VOLUME 1 207. 209. 211. bo — or . Tables for Computing the Modified Index of Refraction M, E. R. Wicher, Report WPG-8, CUDWR, March 1945. . Nomograms for Computation of Modified Index of Refrac- tion, Robert H. Burgoyne, OEMsr-262, Division 14 Re- port 551, RL, Apr. 6, 1945. CP-222.1-M7 Meteorological Report in Connection with V.H.F. Wireless Experiment Between Aden and Berbera, 1943, Ronald Frith, OSRD WA-1746-2, JMRP 18, Report AC-5492, USW, Oct. 30, 1943. CP-331-M2 . Meteorological Measurements, Irish Sea Experiments: Meteorological Observations [taken] on [Board] the Ship Glen Strathallan in the Irish Sea for the Period November 1, 1948 to October 23, 1944, OSRD WA-1759-14, WA-1935-1, WA-1951-1, WA-2131-5, WA-2131-C5, WA-2152-13, WA-2131-5A, WA-3180-1, WA-2242-4, WA-2315-1, WA-2364-13, WA-2587-5, WA-2623-18, WA-2843-13, WA-~4079-1, WA-2905-4, WA-3029-2, WA-3180-1A, WA- 3180-1D, WA-3322-1, and WA-3584-3, NMS. CP-333.1-M1 Meteorological Observations [taken] on [Board] the Ship Coila in the Irish Sea for the Period December 15, 1943 to October 26, 1944, OSRD WA-2131-5B, WA-2843-11, WA-2748-12, WA-4079-2, WA-3305-5, WA-3322-2, and W A-3584-2, NMS. CP-333.1-M2 Meteorological Measurements [taken] on [Board] the Ship St. Dominica in the Irish Sea for the Period May 19, 1944 to August 29, 1944, OSRD WA-2587-6, W A-2645-4, WA- 3143-9, WA-3991-2, WA-3180-1B, and WA-3180-1C, Inter-Service Cm. Wave Prop. Research NMS. CP-333.1-M3 Tables of Temperature and Humidity Observations at Rye, OSRD WA-1463-13A, Report JMRP-5, MO, November 1943. CP-333.3-M1 . Low Altitude Measurements in New England to Determine Refractive Index, 1948, Robert H. Burgoyne and I. Katz, Division 14 Report 42, RL, Feb. 22, 1944. CP-336.2-M1 Climate in Relation to Microwave Radar Propagation in Panama, Arthur E. Bent, Division 14, Report 476, RL, Feb. 25, 1944. CP-336.1-M1 . The Vertical Distribution of Temperature and Humidity at Rye on the Night of January 14-15, 1944, JEIA 10318, Report JMRP 6, MO, Feb. 26, 1944. JEIA 10319, Report JMRP-7, MO, February 1944. CP-333.3-M3 . Radio Climatology of the Persian Gulf and Gulf of Oman with Radar Confirmation, H. G. Booker, Report T-1642, TRH, Mar. 15, 1944. CP-331-M5 . Stations in the Western Hemisphere with Conditions in the Lower Layers of the Atmosphere Similar to Those at Selected Stations in the Eastern Hemisphere, Report 729, U.S. Army Air Forces, Weather Division, March 1944. CP-337-M1 . Some Values of the Refractive Index of the Atmosphere at Rye, 8.100958, JEIA 10322, Report JMRP 23, MO 8, June 1-6, 1944. . Low-Level Meteorological Soundings and Radar Correla- tion for the Panama Canal Zone, K. E. Fitzsimmons, 8. T. Stephenson, and Robert W. Bauchman, OEMsr-728, CP-333.3-M2_ . Analysis of Temperature and Humidity Records at Rye, 218. 219. 221. 222. 225. 227. No i) oO 229. 230. NDRC Research Project PDRC-647, Report 6, Wash- ington State College, June 12, 1944. CP-336.1-M2 Wave Propagation Report No. 3, Report 413.44/R113, Naval Research Group, Intel. Br. OCSO Canal Zone, July 1, 1944. Preliminary Analysis of Height-Gain Tests in the Tropo- sphere, R. F. C. McDowell, OSRD WA-2930-2, JEIA 5777, Report TR-494, BRL, September 1944. CP-333-M2 . Diurnal Variation of Temperature and Humidity at Var- tous Heights at Rye, 8.100958, JEIA 10323, Report JMRP 26, MO 8, Oct. 21, 1944. CP-333.3-M4 Report on General Climatic and Meteorological Conditions in Banda Sea, 4°-7° S., 126°-131° E., Report List 2, Sec- tion IT, Series 7, No. 18, RAAF, Directorate of Meteoro- logical Services, November 1944. CP-335-M2 Hourly Values of Modified Refractive Index M for Meteoro- logical Office [at] Rye, May, 1944, JEIA 10325, Report JMRP-31, MO, Dec. 28, 1944. CP-333.3-M5 . Temperature and Humidity Measurements Made with the Washington State College Wired Sonde Equipment at Kai- koura, New Zealand, Between Sept. 22, 1944 and Oct. 19, 1944, F. B.S. Alexander, Report RD-1/482, RDL-DSIR, NZ, Jan. 15, 1945. CP-332-M3 4. Highlights of the December, 1944 Typhoon Including Photographic Radar Observations (Part I), A Distant Ob- servation of a Warm Front Including a Photograph of Cloud Forms and Slope of Front (Part II), George F. Kkosco, Fleet Weather Central Paper 10, U.S. Navy, Third Fleet, Feb. 10, 1944. CP-336.3-M1 Results of Low Level Atmospheric Soundings in the South- west and Central Pacific Oceanic Areas, Paul A. Anderson, K. E. Fitzsimmons, G. M. Grover, and 8. T. Stephenson, OEMsr-728, NDRC Research Project PDRC-647, Re- port 9, Washington State College, Feb. 27, 1945. CP-335-M4 . Centimeter Wave Propagation over Sea, Correlation of Radio Field Strength Transmitted Across Cardigan Bay, Wales with Gradient of Refractive Index Obtained from Air- craft Observations, R. L. Smith-Rose and A. C. Stickland, OSRD WA-4459-9, JEIA 9813, Paper RRB/C-121, DSIR, May 10, 1945. CP-333-M4 Balloon Psychrometer for the Measurement of the Relative Humidity of the Atmosphere at Various Heights (and Ad- dendum), S. M. Doble and S. Inglefield, OSRD II-5- 5079(S) and OSRD II-5-5080(S8), ICI, Apr. 1, 1943; Addendum Sept. 25, 1948. CP-344-M1 . The Captive Radiosonde and Wired Sonde Techniques for Detailed Low-Level Meteorological Sounding, Paul A. Anderson, C. L. Barker, K. E. Fitzsimmons, and S. T. Stephenson, OEMsr-728, NDRC Research Project PDRC-647, Division 14 Report 192, Report 3, Washing- ton State College, Oct. 4, 1943. CP-341-M1 Instruments and Methods for Measuring Temperature and Humidity in the Lower Atmosphere, I. Katz, ORMsr-262, Service Project SC-8, Division 14 Report 487, RL, Apr. 12, 1944. CP-344-M2 Anomalous Propagation, Adaptation of Model RAU-2 Radio Sonde Receiving and Recording Equipment for Use as Low Level Sounding Device, Navy Dev. Project Unit 1, 234. 236. 237. 238. 241. 242. 243. 244. 245. 246. BIBLIOGRAPHY—VOLUME 1 Friez Instrument Division, Bendix Aviation Corpora- tion, May 31, 1944. CP-342-M1 . Meteorological Investigation at Rye, Instrumental Lay- oul for Recording Gradients of Temperature and Relative Humidity (Part I), Report JMRP-17, - Instruments Branch, MO 4, May 1944. CP-344-M3 2. Noles on Operational Use of Low-Level Meteorological Sounding Equipment, IX. E. Fitzsimmons, 8. T. Stephen- son, and Robert W. Bauchman, OEMsr-728, NDRC Research Project PDRC-647, Report 7, Washington State College, June 15, 1944. CP-342-M2 . Microwave Propagation Studies, Detection of Tropo- sphere Stratification by Means of Sound Echoes, Pre- liminary Trial, Case 37003, H. B. Coxhead and F. H. Willis, Report MM-44-160-148, BTL, June 21, 1944. CP-344-M4 Operating Instructions for the WSC Low-Level Atmos- pheric Sounding Equipment, Paul A. Anderson, OEMsr- 728, NDRC Research Project PDRC-647, Report 8, Washington State College, July 10, 1944. CP-342-M3 . Meteorological Equipment for Short Wave Propagation Studies, Walter M. Elsasser, Report WPG-3, CUDWR August 1944. Wired Sonde Equipment for High Altitude Soundings, Lloyd J. Anderson, BuShips Problem X4-49CD, Re- port WP-16, NRSL, Nov. 17, 1944. (See reference 238.) CP-341-M2 A Note on the Resistance of Electric Hygrometer Ele- ments, Lloyd J. Anderson and S. T. Stephenson, Report ABRO-1, NRSL, May 8, 1945. CP-343-M1 Improvements in USNRSL Meteorological Sounding Equipment, Lloyd J. Anderson, S. T. Stephenson, and A. P. D. Stokes, BuShips Problem X4-49CD, Report WP-21, NRSL, July 3, 1945. (See reference 236.) CP-341-M3 . Forecasting of R. D. F. Conditions, JMRP 2, Memoran- dum 103, AORG, May 31, 1943. CP-410-M1 . The Meteorological Aspects of Anomalous Propagation, Short Wave Radio, R. W. Hatcher, Report JMRP 1, [Great Britain] June 1943. CP-410-M2 Oboe Propagation, August-October, 1943, H. G. Booker, OSRD WA-1464-5, Report T-1605, TRE, 1943. CP-422-M1 “Naviprop” Forecasts, E. Gold, OSRD WA-2255-1Q, Report SIS 45, MO, Nov. 8, 1943. CP-422-M2 Issue of Anoprop Forecasts, Synoptic Instruction Special No. 39, OSRD WA-2255-1R, Report SIS 39, MO, Feb. 11, 1944. CP-422-M3 Elements of Radio Meteorological Forecasting, H. G. Booker, Report T-1621, Mathematics Group, TRE, Malvern, Feb. 14, 1944. CP-410-M3 Preliminary Instruction Manual, Weather Forecasting for Radar Operations, Report 614, U.S. Army Air Forces, Weather Division, March 1944. CP-410-M4 Tropospheric Weather Factors Likely to Affect Swperre- fraction of VHF-SHF Radio Propagation as Applied to the Tropical West Pacific, E. Dillon Smith and R. D. Fletcher, Report RP-1, U.S. Department of Commerce, Weather Bureau, July 1, 1944. CP-424-M1 247. 248. 249. 252. 253. 254. 258. 259. 260. 261. . American 269 Preliminary Instruction Manual of Weather Forecast- ing for Radar Operations in South West Pacific Area, D. F. Martyn and P. Squires, Report RP-220, CSIR- RL, Sept. 4, 1944. CP-424-M2 Outline of Radio Climatology in India and Vicinity, H. G. Booker, JEIA 6061, Report JMRP-25, Report T-1727 (M/85), TRE, Sept. 12, 1944. CP-423-M1 Notes on TRE Report T-1727, JMRP No. 25, Radio Climatology in India and Vicinity, C. 8. Durst, JEITA 10324, Report JMRP-27, MO, Nov. 7, 1944. (See refer- ence 248.) CP-423-M2 . A Rough Sketch of World Radio Climatology over Sea, H. G. Booker, Report T-1730, TRE, Oct. 31, 1944. CP-424-M3 Continents Meteorological Counterparts of Western Pacific and Indian Ocean Areas as Applied to Tropospheric Radio Propagation, J. H. Brown, J. L. Paulhus, and E. Dillon Smith, Report RP-2, U. S. Weather Bureau, Nov. 15, 1944. The Possibility of Investigating the Fohn Wind and Sea Breeze Phenomena in N. Z. with a View to Elucidating Certain Problems of Radio-Meteorological Forecasting in Other Parts of the World, M. A. F. Barnett and F. B.S. Alexander, JEIA 7469, Report RD-1/471, RDL-DSIR- NZ, Dec. 1, 1944. CP-421-M1 Determination of a Suitable Method of Forecasting Radar Propagation Variations over Water, Tests Conducted by 26th Weather Region, Orlando, Florida, J. R. Gerhardt and William EH. Gordon, Service Project 4252R000.77, U.S. Army Air Forces, Mar. 10, 1945. CP-425-M1 A Qualitative Outline of the Radio Climatology of Aus- tralasia, H. G. Booker, JMRP-53, Report T-1820 (M/95), TRE, Apr. 19, 1945. CP+421-M2 . Determination of the Practicability of Forecasting Me- teorological Effects on Radar Propagation, Tests Con- ducted by AAF Tactical Center, Orlando, Florida, John R. Gerhardt and William E. Gordon, Service Project 3767B000.93, U. S. Army Air Forces, June 13, 1945. CP-425-M2 . Absorption of 1-Cm Radiation by Rain, M. G. Adam, R. A. Hull, and C. Hurst, Mise. Report 3, CVD-CL. . The Absorption of Ultra-Short Wireless Waves in the Water Vapour of the Earth's Atmosphere, J. A. Saxton, OSRD II-5-210, Paper RRB/C-18, NPL, Feb. 14, 1941. CP-510-M1 Echo Intensities and Attenuation Due to Clouds, Rain, Hail, Sand and Duststorms at Centimeter Wavelengths, J. W. Ryde, OSRD WA-81-25, Report 7831, GEC, Oct. 18, 1941. CP-511-M1 The Atmospheric Absorption of Microwaves (in Third Conference Report of CP), J. H. Van Vleck, Report 175 (48-2), RL, Apr. 27, 1942. (See reference 10.) < Div. 14-121.1-M4 The Effect of Rain Upon the Propagation of 1-Cm Elec- tro-Magnetic Waves, Case 22098, 8. D. Robertson, Re- port MM-42-160-87, BTL, Aug. 1, 1942. CP-511-M2 The Effect of Rain on the Propagation of Microwaves, Case 22098, A. P. King and 8. D. Robertson, Report MM-42-160-93, BTL, Aug. 26, 1942. CP-511-M3 270 262. 263. 265. 267. 272. 273. 274. 275. 276. BIBLIOGRAPHY— VOLUME Il Comparison of Theoretical and Experimental Values for the Atlenuation of 1-Centimeter Waves in Rain, Case 22098, S. D. Robertson, Report MM-43-160-2, BTL, Jan. 5, 1943. CP-511-M4 An Investigation on the Number and Size Distribution of Water Particles in Nature, Josef Mazur, F/Lt. Polish Air Force, OSRD II-5-6306(S), Report MRP-109, Meteoro- logical Research Committee, Great Britain, June 1943. CP-511-M5 4. Report on the Absorption and Refraction of Electro-Mag- netic Waves by the Liquid Water, Water Vapour and Fog or Rain, N. F. Mott, OSRD II-5-4936, Reference 43/2881, CRB, Sept. 2, 1948. CP-510-M2 Report on the Absorption of Electromagnetic Waves in the Wavelength Range 1-100 Cm by Water in the Atmosphere, N. F. Mott, OSRD II-5-4937, Reference 43/2882, CRB, Sept. 2, 1943. CP-510-M3 . Verification of Mie Theory, Calculations and Measure- ments of Light Scattering by Dielectric Spherical Particles (Progress Report), Victor K. LaMer, OSRD 1857, OEMsr-148, Service Project CWS-1, Division 10, NDRC, Columbia University, Sept. 29, 1943. CP-512-M1 The Absorption of Centimetric Radiation by Atmospheric Gases, J. M. Hough, ADRDE, USWP-WC, Apr. 27, 1944. CP-510-M4 . Attenuation Due to Water Drops in the Atmosphere, J. M. Hough, ADRDE, USWP-WC, Apr. 28, 1944. CP-511-M6 . Propagation of K/2 Band Waves, G. E. Mueller, Report MM-44-160-150, BTL, July 3, 1944. CP-511-M7 . Preliminary Note on Secure Communications on Muilli- metre Waves, OSRD WA-2868-3, JEIA 5597, Report L/M40/WBL, TRE, Sept. 11, 1944. CP-510-M5 . Rotational Line Width in the Absorption Spectrum of At- mospheric Water Vapor and Supplement, Arthur Adel, OEMsr-1361, NDRC Division 14 Report 320, University of Michigan, Oct. 10, 1944; Supplement Feb. 1, 1945. CP-510-M6 The Absorption of One-Half Centimeter Electromagnetic Waves in Oxygen, E. R. Beringer, OEMsr-262, Service Project AN-25, Division 14 Report 684, RL, Jan. 26, 1945. CP-510-M7 The Effect of Rain on Radar Performance, 8. C. Hight, Report MM-44-170-50, BTL, Oct. 17, 1944. CP-511-M8 Measurements of Wave Propagation, G. E. Mueller, Report MM-45-160-17, BTL, Feb. 5, 1945. CP-511-M9 Further Theoretical Investigations on the Atmospheric Ab- sorption of Microwaves, John H. Van Vleck, OEMsr-262, Service Project AN-25, Division 14 Report 664, RL, Mar. 1, 1945. CP-510-M8 Measurements of the Attenuation of K-Band Waves by Rain, G. T. Rado, OF Msr-262, Service Project AN-25, Division 14 Report 603, RL, Mar. 7, 1945. CP-511-M10 . Altenuation of Centimetre and Millimetre Waves by Rain, Hail, Fogs, and Clouds (Draft), J. W. Ryde and D. Ryde, OSRD WA-5181-10, Report 8670, GEC, May 18, 1945. CP-511-M11 278. 279. 280. 282. 283. 284. 285. 286. 287. 288. 290. 291. 292. 293. The Relation Between Absorption and the Frequency De- pendence of Refraction (Fourth Conference), John H. Van Vleck, OEMsr-262, Division 14 Report 735, RL, May 28, 1945. (See reference 12.) Div. 14-122.24-M4 Absorption and Scattering of Microwaves by the Atmos- phere (Fourth Conference), Louis Goldstein, Report WPG-11, CUDWR, May 1945. (See reference 12.) C.V.D. Progress Report for May, 1945. The Absorption of K-Band Radiation in Gaseous Ammonia (Part I), Progress Report, CVD-CL, May 1945. . K-Band Attenuation Due to Rainfall, Lloyd J. Anderson, J. P. Day, C. H. Freres, John B. Smyth, A. P. D. Stokes and L. G. Trolese, Report WP-20, NRSL, June 8, 1945. CP-511-M12 A New Method for Measuring Dielectric Constant and Loss in the Range of Centimeter Waves, S. Roberts and Arthur R. von Hippel; Wave Guides with Dielectric Sections, L. J. Chu, Report 102, MIT, March 1941. CP-521-M1 The Electrical Properties of Ice, T. A. Taylor and Willis Jackson, OSRD W-126-42, Report AC-1516, RDF 110, Com. 78, RDF, Dec. 22, 1941. CP-522.13-M1 The Dielectric Constant and Loss Factor of Water Vapor at a Wavelength of 9 Cm, Frequency 3380 Mc/s, J. A. Sax- ton, OSRD W-203-2, Paper RRB/S-1, NPL-DSIR Mar. 31, 1942. CP-522.12-M1 The Dielectric Constant of Water Vapour and its Effect wpon. the Propagation of Very Short Waves, A. C. Stickland, OSRD WA-175-7, Paper RRB/S-2, NPL-DSIR, May 11, 1942. CP-522.12-M2 Progress Report on Ultrahigh Frequency Dielectrics, Arthur R. von Hippel, OEMsr-191, Division 14 Report 121, MIT, Laboratory for Insulation Research, January 1948. CP-521-M2 Conductivities of Sea, Tap and Distilled Water at }=10 Cm., L. B. Turner, OSRD WA-649-1, Report M-496, ASE, April 1943. CP-522.11-M1 The Measurement of Dielectric Constant and Loss with Standing Waves in Coaxial Wave Guides, Arthur R. von Hippel, D. G. Jelatis, and W. B. Westphal, OHMsr- 191, Division 14, Report 142, M1T, Laboratory for Insu- lation Research, April 1948. CP-521-M4 . The Dielectric Constant and Absorption Coefficient of Water Vapour for Wavelengths of 9 Cm and 3.2 Cm, Frequencies 3,330 and 9,350 Mc/s., J. A. Saxton, Paper RRB/S-11, NPL-DSIR, June 14, 1943. CP-522.12-M3 “Electrical Measurements on Soil with Alternating Cur- rents,” R. L. Smith-Rose, Journal of the Institution of Electrical Engineers (London), NPL, Vol. 75, August 1943, pp. 221-237. CP-522.3-M1 Memorandum on an Electrical Method of Measuring the Dielectric Constant of Atmospheric Air, and Recording it Continuously, OSRD WA-1464-7, Report JMRP-8, Report M/Memo-15/PEC, TRE, Jan. 6, 1944. CP-522.2-M1 The Dielectric Constant and Absorption Coefficient of Water Vapour for Radiation of Wavelength 1.6 Cm, Frequency 18,800 Mc/s., J. A. Saxton, Paper RRB/S.17, NPL-DSIR, Apr. 22, 1944. The Dielectric Constant of Water and Ice at Centimetre Wavelengths (Working Committee), J. M. Hough, ADRDE, USWP-WC, Apr. 28, 1944. CP-522.1-M1 294, 295. 298. 299. 300. 301. 302. 303. 304. 305. 306. 307. 308. 309. . Dielectric Properties of Water and Ice BIBLIOGRAPHY—VOLUME 1 Preliminary Report on the Dielectric Properties of Water in the K-Band, C. H. Collie, Report CL Mise. 25, CVD, May 1944. Recent Dielectric Constant and Loss Tangent Measure- ments on X-Band (Radome Bulletin No. 5), Elizabeth M. Everhart, ONMsr-262, Division 14 Report 483-5, RL, July 14, 1944. CP-522.4-M1 Div. 14-234.5-M5 at K-Band, B. L. Younker, OHMsr-262, Service Project AN-25, Division 14 Report 644, RL, Dee. 4, 1944. CP-522.1-M2 . The Interaction Between Electromagnetic Fields and Di- electric Materials, Arthur R. von Hippel and R. G. Breckenridge, OEMsr-191 Division 14 Report 122, MIT, Laboratory for Insulation Research, January, 1943. CP-521-M3 The Dielectric Properties of Water at Wavelengths from 2 Cm to 10 Cm and over the Temperature Range 0° to 40° C, J. A. Saxton, OSRD WA-4340-5, Paper RRB/C-115, NPL-DSIR, Mar. 20, 1945. CP-522.11-M2 The Dielectric Properties of Water in the Temperature Range 0° C to 40° C for Wavelengths of 1.24 Cm and 1.58 Cm, J. A. Saxton and J. A. Lane, JEIA 9811, Paper RRB/C.116, NPL-DSIR, Mar. 7, 1945. The Anomalous Dispersion of Water at Very High Radio Frequencies in the Temperature Range 0° to 40° C, J. A. Saxton, OSRD WA-4459-8, JEIA 9812, Paper RRB/C- 118, NPL-DSIR, Apr. 6, 1945. CP-522.11-M3 Centimeter Wave Propagation over Sea Within the Op- tical Range, H. Archer-Thomson, J. C. Dix, F. Hoyle, E. C. 8. Megaw, and M. H. L. Pryce, OSRD W-157-16, Report M-398, ASE, January 1942. CP-532.2-M1 Preliminary Report on the Reflection of 9-Cm Radiation at the Surface of the Sea, H. Archer-Thomson, N. Brooke, T. Gold, and F. Hoyle, OSRD WA-1131-2, Report M-542, ASE, September 1943. CP-532.2-M2 Comment on the Reflection of Microwaves from the Sur- face of the Ocean (Part II), S. O. Rice, Report MM-43- 210-6, BTL, Oct. 18, 1943. CP-532.2-M3 S-Band Measurements of Reflection Coefficients for Var- tous Types of Harth, BH. M. Sherwood, Report 5220.129, Sperry Gyroscope Company, Oct. 29, 1943. CP-532.1-M1 Special Report on the Determination of the Coefficient of Reflection of Radio Waves at the Ground by Means of Radar Observations, W. Sterling Ament, Report RA- 3A-212A, NRL, Nov. 10, 1948. CP-532.1-M2 Scattering, T. L. Eckersley, OSRD WA-2255-1F, JEIA 3904, Report TR-481, BRL, November 1943. CP-512-M3 Preliminary Measurements of 10 Cm Reflection Co- efficients of Land and Sea at Small Grazing Angles, Pearl J. Rubenstein and William T. Fishback, Division 14 Report 478, RL, Dec. 11, 1943. CP-532-M1 Further Measurements of 3- and 10-Cm Reflection Co- efficients of Sea Water at Small Grazing Angles, William T. Fishback and Pearl J. Rubenstein, OHMsr-262, Di- vision 14 Report 568, RL, May 17, 1944. CP-532.2-M4 Microwave Propagation Studies, The Reflection of Sound Signals in the Atmosphere, Case 37003, File 36691-1, 310. 311. 313. 314. 315. 316. 317. 318. 319. 320. 321. 322. 323. 324. 325. 326. 271 I. H. Willis, Report MM-44-160-156, BTL, July 3 1944, Interim Report on Experiments on Ground Reflection at a Wavelength of 9 Cm, L. H. Ford, JEITA 4899, Paper RRB/C.101, DSIR, July 7, 1944. An Experimental Investigation of the Reflection and Ab- sorption of Radiation of 9-Cm Wavelength, L. H. Ford and R. Oliver, OSRD WA-3386-2, Paper RRB/C-107, DSIR, Oct. 27, 1944. CP-532-M2 2. The Measurement of High Reflections at Low Power (Radome Bulletin No. 7), Raymond M. Redheffer, OEMsr-262, Division 14 Report RL-483-7, RL, Nov. 20, 1944. CP-531-M3 Ground Reflection Coefficient Experiments on X-Band, Case 20564, W. M. Sharpless, Report MM-44-160-250, BTL, Dee. 15, 1944. CP-532.1-M3 The Reflection Coefficient of a Linearly Graded Layer, OSRD WA-34388-5, Report TR-492, BRL, December 1942. CP-531-M2 Reflection and Scattering, T. L. Eckersley, OSRD WA- 4002-12, Report TR-506, BRL, January 1945. CP-532.2-M5 Reflection from an Inversion, L. BH. Beglian and F. J. Northover, OSRD WA-4494-14, JEIA 9997, Report AC-8210, USW-140, USW, May 24, 1945. CP-531-M5 Notes on the Comparison of Vertical and Horizontal Po- larization in Ground Wave Propagation, G. Millington, OSRD WA-1463-5, Report TR/442, BRL, January 1940. CP-540-M1 Horizontal and Vertical Polarization, T. L. Eckersley, OSRD II-5-5280, Report TR-441, BRL, July 1942. CP-540-M2 The Investigation of Horizontally and Vertically Polar- ized Direction Finding on Frequencies of the Order of 20 to 70 Megacycles per Second, T. L. Eckersley, OSRD TI-5-5284, Report TR-451, BRL, September 1942. CP-540-M3 Polarization Effects and Aerial System Geometry at Cen- timeter Wavelengths, BH. C. S. Megaw, H. Archer-Thom- son, and E. M. Hickin, Report 8101, GEC, Nov. 26, 1942. Change of Polarization as a Means of Gap Filling, Richard A. Hutner, Francis Parker, Bernard Howard, and Joc- elyn Gill, Division 14 Report C-7, RL, Dec. 28, 1942. CP-540-M4 Vertical Polarization vs Horizontal Polarization, Ralph C. Loring, Tentative Technical Report T-1, CESL, Oct. 22, 1948. CP-540-M5 The Depolarization of Microwaves, M. Kessler, C. B. Mandeville and E. L. Hudspeth, Division 14 Report 458, RL, Nov. 1, 1948. CP-540-M6 Polarization Studies at S and X Frequencies, O. J. Baltzer, W. M. Fairbank, and J. D. Fairbank, OEMsr-262, Division 14 Report 536, RL, Mar. 14, 1944. CP-540-M7 Screening by Hills, H. G. Booker, OSRD WA-1105-3C, Report T-1015, TRE, May 1941. CP-231.222-M1 Diffraction Round a Sphere or Cylinder, G. Millington, OSRD II-5-5703, Report TR-433, BRL, March 1942. CP-231.21-M1 272 327. 328. 330. 331. 333. 334. 335. 336. 337. 338. 339. 340. 341. BIBLIOGRAPHY— VOLUME 1 Centimeter Wave Transmission Measurements from an Ur- ban Site, H. Archer-Thomson, EH. M. Hickin, and E. C.S. Megaw, Report 8034, GEC, July 28, 1942. Report on an Investigation of the Propagation of Centimeter Waves over Ridges and Through Trees, R. L. Smith-Rose, OSRD WA-772-19, Report AC-4345, Com. 181, NPL, June 2, 1943. CP-231.22-M1 . A Note on the Propagation of K-Band Waves Through Trees, Case 22098, S. D. Robertson, Report MM-43-160- 129, BTL, Aug. 13, 1943. CP-231.221-M1 Report on Further Experiments on the Propagation of Centimeter Waves Through Trees in Leaf and over Level Ground, OSRD WA-1837-3, Report AC-5059, Com. 197, NPL, Sept. 6, 1943. CP-231.221-M2 Centimeter Wave Propagation, Notes on the Effect of Ob- struction by a Single Tree, R. E. Jennings, H.C. 8. Megaw, H. Archer-Thomson, and E. M. Hickin, OSRD WA- 1356-6, Report M-565, ASE, October 1948. CP-231.221-M3 2. An Hxperimental Investigation on the Propagation of Radio Waves over Bare Ridges in the Wavelength Range 10 Centimetres to 10 Metres, Frequencies 30 to 3000 Mc/s, J. S. McPetrie and L. H. Ford, OSRD WA-1463-17, Paper RRB/S-12, NPL-DSIR, Oct. 1, 1948. CP-231.222-M2 Some Observed Effects of Trees wpon Microwave Propaga- tion, Case 37003, File 36691-1, A. C. Peterson, Report MM-43-160-150, Sept. 17, 1948, Revised Oct. 15, 1948. CP-231.221-M4 Effect of Hills and Trees as Obstructions to Radio Propaga- tion, Delmer C. Ports, OSRD 3070, OEMsr-1010, Jansky and Bailey, November 1943. CP-231.22-M2 Report on Some Further Experiments on the Effect of Ob- stacles on the Propagation of Centimetre Waves, L. H. Ford, A.C. Grace, and J. A. Lane, JEIA 3157, Report AC-5876, NPL-RD, USW, Jan. 20, 1944. Addendum, R. L. Smith-Rose, OSRD WA-3822-12, Re- port AC-5876a, NPL, Jan. 1, 1945. CP-231.223-M1 The Propagation of Ultra Short Waves Round Hills and Other Obstacles, T. L. HWekersley, OSRD WA-2884-3, JEIA 5674, Report TR-479, BRL, May 1944. CP-231.222-M3 Scattering of Radio Waves by Metal Wires and Sheets, F. - Horner, JEIA 7793, Paper RRB/C-110, DSIR, Jan. 1, 1945. Some Experiments on the Propagation over Land of Radi-~ ation of 9.2-Cm Wavelength, L. H. Ford, OSRD WA- 4297-8, Paper RRB/C-113, NPL-DSIR, Feb. 15, 1945. CP-231.22-M3 A Preliminary Study of Ground Reflection and Diffraction Effects with Centimetric Radar Equipment, J. S. Hey, F. Jackson, and 8. J. Parsons, OSRD WA-5062-2, Report 274, AORG, June 28, 1945. CP-231.21-M2 Diffraction at Coast Line, Sloping Site, H. G. Booker, OSRD WA-986-6c, Report 10, TRE, May 1, 1941. CP-233-M2 Mixed Land and Sea Transmissions, T. L. Eckersley, OSRD II-5-5515, Report H-16, BRL, October 1941. CP-233-M3 342. 343. 344. 345. 346. 347. 348. 349. 350. 351. 352. 353. 354. 355. 356. 357. 358. 359. 360. Diffraction at Coast Line, Further Numerical Examples, H. G. Booker, OSRD WA-92-5d, Report M-35, TRE, Feb. 5, 1942. CP-233-M4 Coastal Refraction, OSRD II-5-5281, Report TR-436, BRL, May 1942. CP-233-M5 Propagation of Wireless Waves over Ground of Varying Earth Constants (Part Land and Part Sea), G. Millington, OSRD II-5-5277, Report TR-440, BRL-Marconi, Ltd., July 1942. CP-233-M6 Transmission over Ground of Varying Earth Constants, OSRD II-5-5457, Report TR-473, BRL, July 1943. CP-233-M8 Diffraction at Coast Line (Appendix to Report on Siting of RDF Stations), H. G. Booker, OSRD WA-986-6b, Report 6, TRE, Jan. 27, 1944. CP-233-M1 Siting and Coverage of Ground Radars, E. J. Emmerling OEMsr-1207, Report WPG-10, CUDWR, May 1945. (See reference 12.) CP-202.4-M6 Scattering and Spurious Echoes, T. L. Eckersley, OSRD II-5-5275, Report TR-437, BRL, April 1942. CP-621.7-M1 Reflection of 10-Cm Radiation by Model Aircraft, A. F. Phillips, Christchurch Report 174, ADRDE, Sept. 8, 1942. Elementary Survey of Scattering and Echoing by Elevated Targets, H. G. Booker, Report M/48/HGB, TRE, December 1942. The Resolution of Composite Echoes with Centimeter Wave R.D.F., J. R. Benson, J. A. Ramsay, and P. B. Blow, OSRD WA-1789-2, Report 4070/C/104, CAEH, Feb. 10, 1943. CP-623-M3 Microwave Radar Reflection, J. ¥. Carlson and S. A. Goudsmit, Division 14 Report 43-23, RL, Feb. 20, 1943. CP-623-M4 Reflection of Radar Waves from Targets of Simple Geomet- ric Form, Lloyd J. Anderson, John B. Smyth, and F. R. Abbott, BuShips Problem X4-49CD, Report WP-8, NRSL, Feb. 24, 1948. CP-612.4-M1 Radar Echoes from Periscopes, John E. Freehafer, Divi- sion 14 Report 42-1, RL, Mar. 1, 1948. CP-622.1-M1 Radar Echoes from Atmospheric Phenomena, Arthur E. Bent, Division 14 Report 42-2, RL, Mar. 13, 1943. CP-621.1-M1 Echoes Produced by Perfectly Conducting Objects of Certain Simple Shapes in Free Space, R. BH. B. Makinson OSRD II-5-5691, Report RP-173, CSIR, Mar. 25, 19438. CP-622.5-M1 Gratings and Screens as Microwave Reflectors, Division 14 Report 54-20, RL, Apr. 1, 1948. CP-611-M1 Report on an Investigation into the Nature of Sea Echoes, OSRD WA-1142-8, Report T-1497, TRE, May 12, 1943. CP-621.6-M1 The Application of Corner Reflectors to Radar (Theoreti- cal), R. D. O’Neil, F. S. Holt, and Prescott D. Crout, Division 14 Report 48-31, RL, May 14, 1943. CP-611.1-M1 The Application of Corner Reflectors to Radar (Experi- mental), R. D. O'Neil, Division 14 Report 55-4, RL, July 1, 1948. CP-611.1-M2 361. 362. 363. 364. 365. 366. 367. 368. 369. 370. 371. 372. 373. 374. 375. 376. 377. 378. 379. BIBLIOGRAPHY—VOLUME 1 Measurement of the Effective Echoing Areas of Various Aircraft, Ross Bateman, Report ORG-P-8-1, OCSO, July 2, 1943. CP-622.3-M1 Overwater Observations al X and S Frequencies on Surface Targets, O. J. Baltzer, V. A. Counter, W. M. Fairbank, W. O. Gordy, and E. L. Hudspeth, Division 14 Report 401, RL, July 26, 1943. CP-612.3-M1 Towed Radar Targets, G. A. Armstrong and G. H. Beech- ing, OSRD WA-1012-2, Research Report 212, ADRDE, Aug. 6, 1948. CP-612.2-M1 Corner Reflector Tests at Langley Field, C. M. Gilbert, Division 14 Report 402, RL, Aug. 6, 1943. CP-611.1-M3 Properties of Corner Reflectors, Case 22098, S. D. Robert- son, Report MM-43-160-130, BTL, Aug. 12, 1943. CP-611.1-M4 Use of Corner Reflectors as IFF on Ships, OSRD II-5- 5680, Operational Research Report 24, Australian ORS and CSIR-RL, Aug. 30, 1948. CP-611.1-M5 An Investigation into the Nature of Sea Echoes, A. C. Cossor, Ltd., JEIA 1221, Report MR-109, Research De- partment Myra Works, London E10, Sept. 8, 1943. The Scattering of Radiation from Rectangular Planes, Half-Cylinders, Hemispheres, and Airplanes, Contract W-2279sc-551, Item 3, Moore School of Engineering, University of Pennsylvania, Oct. 12, 1948. CP-512-M2 On the Appearance of the A-Scope when the Pulse Travels Through a Homogeneous Distribution of Scatterers, A. J. F. Siegert, Division 14, Report 466, RL, Nov. 9, 1943. Div. 14-124.2-M2 On the Fluctuations in Signals Returned by Many Inde- pendently Moving Scatterers, A. J. F. Siegert, Division 14 Report 465, RL, Nov. 12, 1943. Div. 14-122.113-M7 The Use of Permanent Echo Amplitudes for Monitoring S-Band Radar Equipment, F. J. Kerr and J. F. McCon- nell, OSRD II-5-5750, Report RP-177/2, CSIR-RL, Dee. 7, 1943. CP-623-M5 The Range Calculator, S. J. Mason, Division 14 Report 497, RL, Dec. 20, 1943. CP-202.4-M2 The Performance of 10-Cm Radar on Surface Craft, B. F. Schonland, OSRD WaA-1570-39, Report 155, AORG, Jan. 3, 1944. CP-202.312-M1 Special Report on Radar Cross Section of Ship Targets, Martin Katzin, Report RA-3A-213A, NRL, Jan. 24, 1944. CP-612.1-M1 Observations of Life Rafis Equipped with Corner Re- flectors, Emmett L. Hudspeth and John P. Nash, Divi- sion 14 Report 533, RL, Feb. 15, 1944. CP-611.1-M6 Radar Cross Section of Ship Targets (Part II), W. Sterling Ament, Martin Katzin, and F. C. MacDonald, Report R-2232, NRL, Feb. 18, 1944. CP-612.1-M1 Optical Theory of the Corner Reflector, R. C. Spencer, OEMsr-262, Division 14 Report 433, RL, Mar. 2, 1944. CP-611.1-M7 Observations on Signal Stability at S and X Frequencies, Otto J. Baltzer, Jr., William M. Fairbank, and J. D. Fairbank, OEMsr-262, Division 14 Report 537, RL, Mar. 14, 1944. CP-632-M1 Interim Report on the Recognition of Radar Echoes, F. E. S. Alexander, OSRD II-5-5796(S), JEIA 3401, Report RD-1/353, RDL-DSIR, NZ, Mar. 20, 1944. CP-623-M6 380. 383. 384. 385. 386. 387. 388. 389. 390. 391. 392. 393. 394. 395. 396. 273 Screened and Unscreened Radar Coverage for Surface Targets, W. Walkinshaw and J. E. Curran, OSRD WA- 2284-2, Report T-1666, TRE, March 1944. CP-612.3-M2 . The Performance of Naval Radar Systems Against Air- craft, F. Hoyle, OSRD WA-2255-1lo, Report JEIA-3902, ASE, Apr. 3, 1944. CP-202.11-M2 2. Preliminary Report on the Fluctuations of Radar Signals, H. Goldstein and Paul D. Bales, OEMsr-262, Division 14 Report 569, RL, May 16, 1944. CP-632-M2 Radar Ranging on Land Targets, OSRD II-5-6178(S), Memorandum 101/G-36/ALH, TRE, May 18, 1944. CP-202.4-M3 The Radar Echoing Power of Conducting Spheres, T. Pearcey, and J. M. C. Scott, OSRD WA-2334-6, Report CR-228, ADRDE, May 24, 1944. CP-623-M7 Use of Corner Reflectors in Beaconry, F. J. Kerr, OSRD II-5-6145(S), JEIA 5180, Report RP-200, CSIR-RL, June 8, 1944. CP-611.1-M8 Calibration and Standardization of Land Based Radars by the Use of Small Plane Targets, F. R. Abbott, BuShips Problem X4-49CD, Report WP-12, NRSL, June 10, 1944. CP-612.5-M1 Test of the Pre-Production Model Corner Reflector, Final Report of Project E-44-37, Alvin E. Hebert and C. B. Overacker, AAF Board Project (M-3) 69-Eglin Field, Fla., Report 413.44/R387.1, Intel. Br. OCSO-USA, June 17, 1944. CP-611.1-M9 Radar Cross Section of Ship Targets (Part III), W. Sterl- ing Ament, Martin Katzin, and F. C. MacDonald, Re- port R-2295, NRL, June 27, 1944. CP-612.1-M1 Notes on Echoes and Atmospherics from Lightning Flashes on P Band, J. L. Pawsey, OSRD II-5-6144(S), JEIA 5177, Report RP-49-2, CSIR-RL, July 11, 1944. CP-621.3-M1 Theory of Ship Echoes as Applied to Naval RCM Opera- tions, T. S. Kuhn and Peter J. Sutro, OKMsr-411, Re- search Project RP-186, Report 411-93, Harvard Uni- versity, RRL, July 14, 1944. Div. 15-221.11-M2 Radar Echoes from the Nearby Atmosphere, Case 37003-4, Millard W. Baldwin, Jr., Report MM-44-150-2, BTL, July 18, 1944. CP-621-M1 Radar Cross Section of Ship Targets (Part IV), W. Sterl- ing Ament, Martin Katzin, and F. C. MacDonald, Re- port R-2332, NRL, July 21, 1944. CP-612.1-M1 Radar Echoes from the Nearby Atmosphere, Second Report, Case 37003-4, Millard W. Baldwin, Jr., Report MM-44- 150-3, BTL, July 31, 1944. CP-621-M1 Reflecting Properties of Metal Gratings, J. S. Gooden, OSRD II-5-6230(S), Report RP-215, CSIR-RL, July 31, 1944. CP-611-M2 Theory of the Performance of Radar on Ship Targets (ADRDE and CAEHE Joint Report), M. V. Wilkes, J. A. Ramsay, and P. B. Blow, OSRD WA-2843-10, ADRDE Reference R04/2/CR252, CAHE Reference 69/C/149, July 1944. CP-612.1-M2 Corner Reflectors for Life Rafts, Emmett L. Hudspeth and John P. Nash, OEMsr-262, Division 14 Report 608, RL, Aug. 1, 1944. CP-611.1-M10 274 BIBLIOGRAPHY—VOLUME Il 397. 398. 399. 400. 401. 403. 404. 405. 406. 407. 408. 409- 410. 411. The Characteristics of S-Band Aircraft Echoes with Par- ticular Reference to Radar A.A. No. 3 MK. II. G. H. Beeching and N. Corcoran, OSRD WA-2812-13, Re- search Report 253, ADRDH, Aug. 4, 1944. CP-622.3-M2 Radar Echoes from the Nearby Atmosphere, Third Report, Case 37003-4, Millard W. Baldwin, Jr., Report MM-44- 150-4, BTL, Aug. 11, 1944. CP-621-M1 Considerations Concerning Radar Coverage Diagrams, J. L. Pawsey, OSRD II-5-6229(S), Report RP-217, CSIR-RL, Aug. 14, 1944. CP-202.4-M5 RDF Echoes to be Expected from Objects of Various Shapes, OSRD WA-6-21, Extra Mural Res. F.72/80, Report 26, Ministry of Supply, DSR. CP-622.5-M2 Radar Echoes from Shells Bursts at 4 Meters and 50-Cm Wavelengths, S. M. Taylor and F. E. W. Bugler, Research Report 260, RRDE, Oct. 9, 1944. CP-622.4-M1 . Summer Storm Echoes on Radar MEW, J. S. Marshall, R. C. Langille, William M. Palmer, R. A. Rodgers, G. P. Adamson, and F. F. Knowles, Report 18, CAORG, Nov. 27, 1944. CP-621.1-M2 The Cancellation of Permanent Echoes by the Use of Co- herent Pulses (Interim Report), H. Grayson, O8SRD WA- 3482-7C, Technical Note RAD-253, RAE, November 1944. CP-623-M8 The Fading of S-Band Echoes from Ships in the Optical Zone, R. I. B. Cooper, OSRD WA-8677-8, Research Report 265, Dec. 12, 1944. CP-622.2-M3 Rotating Corner-Reflectors for Ship Identification, Julian M. Sturtevant, OEMsr-262, Division 14 Report 654, RL, Jan. 1, 1945. CP-611.1-M11 Reflection from Smooth Curved Surfaces, R. C. Spencer, OEMsr-262, Division 14, Report 661, RL, Jan. 26, 1945. CP-531-M4 Analysis of Over-Water Tracking, Elizabeth J. Campbell, OEMsr-262, Service Project NO-166, Division 14 Report 695, RL, Feb. 12, 1945. CP-202.12-M1 Technical Report on the Maximum Range of Detection of the German Early Warning Radar Equipment, Especially when Viewing Large, Tight Formations of Bomber Air- crafl, W. E. Bales and K. A. Norton, Report OAD-13, ORS, VIII Bomber Command OCSO, Sept. 13, 19438. CP-202.4-M1 Performance Checks and Estimation of Vessel Size on Short-Based 10-Cm Radar Sets, D. Lack, OSRD WA- 1992-3, JEIA 3124, AORG, Mar. 30, 1944. CP-622.2-M1 Report of Trials to Determine the Variations of the Appar- ent Reflecting Point of Plain 10-Cm Waves from a Destroyer, J. F. Coales and M. Hopkins, OSRD WA-3702-1, Report M-627, ASE, July 1944. CP-622.2-M2 The Reflection of Electromagnetic Waves by Long Wires and Non-Resonant Cylindrical Conductors, J. M. C. Scott and T. Pearcey, JEIA 7286, Research Report 259, RRDE, Noy. 18, 1944. . Theory of Radar Return from the Schnorkel, P. M. Marcus, OEMsr-262, Division 14 Report 671, RL, Jan. 15, 1945. CP-622.1-M2 “Sea Returns and the Detection of Schnorkel, G. G. Mac- farlane, OSRD WA-4196-8, JEIA 8643, Report T-1787, TRE, Feb. 18, 1945. (See reference 418.) CP-622.1-M3 414. 415. 416. 417. 418. 419. 420. 421. 422. 423. 424. 426. 427. 428. 429. 430. 431. Interservice KXS-Band Radar Trials; Over Water Per- formance Against Surface Targets, J. A. Ramsay, P. B. Blow, and H. J. Worsdall, JEIA 8820, Report M-688, ASE, February 1945. CP-612.3-M3 An Observation of Diffuse Cloud-Like Echoes, J. LL. Paw- sey and F. J. Kerr, OSRD II-5-7007(S), Report RP-246, CSIR-RL, Mar. 6, 1945. CP-621.4-M1 The So-Called Standard Target, A. H. Brown, OEMsr- 262, Division 14 Report 8-48, RL, Mar. 10, 1945. CP-612.6-M1 Radar Cross Section of Ship Targets (Part V), F. C. Mac- Donald, Report R-2466, NRL, Mar. 12, 1945. CP-612.1-M1 Radar Results Against Schnorkels: A Commentary on TRE T-1787, Sea Returns and the Detection of Schnorkel, OSRD WA-4276-5, JEIA 9111, Report 338, ORS/CC, Mar. 16, 1945. (See reference 413.) CP-622.1-M4 Radar Echoes from Clouds of Water Droplets, F. Hoyle, Report AC-7930, Report 128, USW, Mar. 16, 1945. Comments on Radar Echoes from Water Droplets, (Paper AC-7930, USW Report 128), R. G. Ross, OSRD WA- 4149-10, Paper AC-7931, Report 129, USW, Mar. 16, 1945. CP-621.2-M1 Radar Cross Section of Ship Targets (Part VI) W. J. Barr, Report R-2467, NRL, Apr. 10, 1945. CP-612.1-M1 S-Band Radar Echoes from Snow, R. C. Langille, J. S. Marshall, William M. Palmer, and L. G. Tibbles, Report 26, CAORG, June 14, 1945. CP-621.5-M1 Surface Coverage of Some Shipborne Radar Sets on S, X, and K Bands, J. D. Fairbank and W. M. Fairbank, OEMsr-262, Service Projects NS-234 and NS-175, Divi- sion 14 Report 720, RL, June 15, 1945. CP-202.4-M7 Echoes from Tropical Rain on X-Band Airborne Radar, Arthur E. Bent, OEMsr-262, Division 14 Report 728, RL, June 15, 1945. CP-621.2-M2 . Analysis of Storm Echoes in Height Using MHF, J. S. Marshall, L. G. Eon, and L. G. Tibbles, Report 30, CAORG, June 25, 1945. CP-621.1-M3 See also: Radar Camouflage, Division 14 Report 766, RL, July 16, 1945. CP-633-M1 3000-Megacycle Communication, H. H. Beverage, OEMsr-32, NDRC Projects SC-13 and PDRC-90, RCA, Mar. 10, 1942. CP-203.1-M1 Microwave Telephone, Part I Omnidirectional, Part IT, Directional, OEMsr-442, NDRC Projects C-42 and SC-18, RCA, Mar. 22, 1943. CP-203.1-M2 Factors Determining the Range of Radio Communications in the Various Theaters of Operation, Jack W. Herbstreit, Report ORG-P-14-1, OCSO, June 3, 1948. CP-732-M1 Radiotelephone Communication on 3000 Megacycles, Paul A. Anderson, K. E. Fitzsimmons, C. L. Barker, and 8. T. Stephenson, OEMsr-728, NDRC Research Project PDRC-647, Division 14 Report 152, Report 2, Wash- ington State College, June 12, 1948. CP-203.1-M3 An Analysis of the Effect of Frequency on Short Distance Radio Communications, Ross Bateman and William Q. Crichlow, Report ORB-P-15-1, OCSO, Aug. 18, 1943. CP-732.1-M1 Use of the 25- to 50-Mc/s Band for Short Range Wireless Communication, OSRD WA-1022-3, Report 130, AORG, Aug. 27, 1943. CP-732.1-M2 432. 433. 434. 435. 436, 437. 438. BIBLIOGRAPHY—VOLUME 1 Zi Trials with a 250-Watt Frequency-Modulated VHP Sender Across a Sea Water Path Beyond the Optical Range, G. W. Higgins and W. H. Hill, OSRD WA-1352-5, Report 878, SRDE, September 1943. CP-712-M1 Radio Communication in Jungles, Arthur C. Omberg, Report ORG-2-1, OCSO, Sept. 1, 19438. CP-711-M1 Measurement of Factors Affecting Jungle Radio Com- munication, Jack W. Herbstreit and William Q. Crich- low, Report ORB-2-8, OCSO, Nov. 10, 1948. CP-711-M2 Methods for Improving the Effectiveness of Jungle Radio Communication, Technical Bulletin Sig. 4, U.S. War Department, Jan. 14, 1944. CP-711-M3 Survey of Existing Information and Data on Atmospheric Noise Level over the Frequency Range 1-80 Mc/s, H. A. Thomas and R. E. Burgess, OSRD WA-3201-2, JEIA 2815, Paper RRB/C-90, DSIR, Feb. 21, 1944. CP-732-M2 Methods of Reducing Radar Interference to Communication, Arthur C. Omberg, Joseph B. Epperson, and William Q. Crichlow, Report ORB-E-27-2, OCSO, Apr. 19, 1944. CP-731-M1 The Application of Passive Repeaters to Point to Point Communication at VHF and UHF, Ross Bateman, Re- port ORB-P-20-1, OCSO, Apr. 29, 1944. CP-721-M1 439a.Summary of Radio Propagation Problems in Southwest Pacific Area, W. C. Babcock, JEIA 6298, Report US/ 413.44/R118, Intel. Br. OCSO, Sept. 6, 1944. CP-713-M1 439b.Point to Point Communication in MF and Via Ground Wave Propagation, W. C. Babcock, JEIA 6770, Report 413.44/R423.4, Intel. Br. OCSO-SWPA, Aug. 15, 1944. 440. 441. 445. 446. 447. 448. 449. 450. al Measurements of Factors Affecting Radio Communication & Loran Navigation in SWPA, Ross Bateman, Jack W. Herbstreit, and Robert B. Zechiel, Report ORB-24, OCSO, Dee. 16, 1944. CP-713-M2 Field Trials of Ultra Short Wave Frequency and Amplitude Modulated Multichannel Radio Telephone Systems, A. W. Pearson, W. J. Bray, J. H. H. Merriman, R. W. White, J. G. Hobbs, C. H. Gibbs, and H. Prain, Radio Report 1115, POED, Mav. 27, 1944. 2. Physics of the Air, W. J. Humphreys, McGraw-Hill Book Co., 1940, p. 457. . Ergebnisse der Hxakten Naturwissenshaften, H. Plendl and G. Hekart, Berlin, 17, 1988, p. 334. . “Reflection of Waves in an Inhomogeneous Absorbing Medium,” P. S. Epstein, Proceedings of the National Academy of Sciences, 16, 1930, p. 627. “Penetration of a Potential Barrier by Electrons,” Carl Eckart, The Physical Review, 35, 1980, p. 1303. “The Relation of Drop Size to Intensity,” J. O. Laws and D. A. Parsons, Transactions of the American Geo- physical Union, 1943, p. 452. “Ultra Short Wave Propagation,” I. C. Schelleng, Chas. R. Burrows, and EH. B. Ferrell, Bell System Technical Journal, April 1933. (See reference 24.) Report JANP 102, Joint Communications Board. “On the Connection Formulas and the Solutions of the Wave Equation,” R. E. Langer, The Physical Review, 51, 1937, p. 670. Treatise on Theory of Bessel Functions, George Neville Watson, Cambridge University Press, Second Edition, 1944. GENERAL BIBLIOGRAPHY OF REPORTS ON TROPOSPHERIC PROPAGATION REPORT WPG-14 This Bibliography is a comprehensive tabulation of the body of scientific reports pertaining to wave propagation through the troposphere, compiled by the Columbia University Wave Propagation Group to about October 31, 1945. For convenience and clarity it has been divided into twenty sections, each dealing with a particular phase of propagation phenomena. The various headings are self-explanatory, and the list of sources and their abbreviated designations which precede the Bib- liography proper will be found helpful. In preparing the Bibliography, about 560 papers were considered. Of these, 115 were excluded as obsolete, or because their contents were included in other reports retained. An additional 46 papers dealing with doppler effect and the transmission of sound in water were also excluded as not directly relevant. It is believed that the approximately 400 titles included form a fairly exhaustive compilation of present knowledge of electromagnetic wave propagation through the troposphere. The reports are grouped and a Bibliography number has been assigned to each report. The letter to the right of the Bibliog- raphy number designates the present United States security classification. Requests for copies of the reports listed herein may be made by Bibliography number referring to this edition, but should be made through the proper channels. The Central Radio Bureau is the distributing agent for American reports in Great Britain and for propagation reports originating in Great Baddow, Chelmsford, England. All other British reports may be ob- tained from the British government department controlling the sources. The OSRD Liaison Office will, upon request, supply readers in the United States who are not in the Armed Services with all reports originating outside of the United States. They will supply Army and Navy units with all except JEIA-numbered reports. Requests for the latter should be directed to the Joint Electronics Information Agency, Munitions Building, Wash- ington, D.C. In general, application should be made to the NDRC Chairman’s Office for reports written by NDRC Divisions, Committees, or contractors, NDRC Section 6.1 being the present exception; to the Bureau of Ships for reports from Naval Research Lab- oratory, Navy Radio and Sound Laboratory, and all reports appearing in Section 20 of the Bibliography (Under-Water Sound Propagation); to the Office of the Chief Signal Officer for Signal Corps reports; to Inter-Service Radio Propagation Laboratory, Bureau of Standards for IRPL reports. Requests for case-numbered BTL reports should be sent to the Director of Research, Bell Telephone Laboratories, 463 West Street, New York, N. Y. CLASSIFICATION OF REPORTS 1.000 Conferences and Progress Reports 10:000 Radar Forecasting 2.000 General Discussions 11.000 Atmospheric Absorption and Scattering 3.000 Standard Atmosphere Propagation 12.000 Dielectric Constant and Loss Factor 4.000 Non-Standard Atmosphere Propagation—Pure 13.000 Reflection Coefficient Theory 14.000 Horizontal and Vertical Polarization 5.000 Non-Standard Atmosphere Propagation — Experi- 15.000 Effect of Hills, Trees, Obstacles, ete. ment and Theory 16.000 Transmission over Part Land-Part Sea 6.000 Propagation Experiments 17.000 Targets and Echoes 7.000 Meteorological Theory 18.000 Doppler Effect 8.000 Meteorological Experiments 19.000 Communication (Tropospheric) 9.000 Meteorological Equipment 20.000 Under-Water Sound Propagation LIST OF ABBREVIATIONS AMERICAN AMG-C. Applied Mathematics Group, Colum- MIT. Massachusetts Institute of Technology bia University NATC. Naval Air Training Center, Corpus BTL. Bell Telephone Laboratories Christi, Texas CBS. Columbia Broadcasting System NDRC. National Defense Research Committee oa : Rue Bee See es NRL. Naval Research Laboratory : ommittee on Propagation : CUDWER. Columbia University, Division of War NEEL, Neng eacte ed Stowe! LINO Research OCSO. Office of the Chief Signal Officer IRPL. Inter Service Radio Propagation Lab- OFS. Office of Field Service oratory; National Bureauof Standards ORB. Operational Research Branch; JEIA. Joint Electronics Information Agency Office of the Chief Signal Officer 277 278 GENERAL BIBLIOGRAPHY ORG. RCA. RL. RRL. SWP. TCAW. UCDWR. WD., HQAAF. WPG AORG. ATP. CSIR-RL. RAAF. A& AKE. AC. ADRDE. AORG. ASE. BAD. BCSO. BRL. CAEE. CRB. CVD-CL. DMO. DSIR. Operational Research Group; Office of the Chief Signal Officer Radio Corporation of America Radiation Laboratory, M.I.T. Radio Research Laboratory, Harvard University South West Pacific Technical Committee on Air Warn- ing, Office of the Sec’y of War; Reports distributed by Radiation Laboratory University of California, Division of War Research Weather Division, Headquarters Army Air Forces Wave Propagation Group AUSTRALIAN Australian Operational Research Group Australian Technical Paper Council for Scientific and Industrial Research, Radiophysics Laboratory Royal Australian Air Force BRITISH Aircraft and Armament Experimental Establishment Advisory Council on Scientific Re- search and Technical Development Air Defense Research and Develop- ment Establishment Army Operational Research Group Admiralty Signal Establishment British Admiralty Delegation British Central Scientific Office Baddow Research Laboratory Coast Artillery Experimental Estab- lishment Central Radio Bureau Coordination of Valve Development Committee, Clarendon Laboratory Director of Meteorological Office Department of Scientific and Indus- trial Research Bib. No. 1.001 S The Effect of the Atmosphere on the Propagation of Title GEC. ICI. JIEE. JMRP. MAP. MO. MetResCom. NMS. NPL. ORS-ADGB. POED. RAE. RRB. RRDE. SDTM. SRDE. TRE. USWP. USWP-WC. ORS-WAC. CAORG. ORS-RNZAF. RDL-DSIR-NZ. ORS-SEHA. Author or Source General Electric Company Imperial Chemical Industries Journal of the Institution of Electrical Engineers Joint Meteorological Radio Propaga- tion Sub-Committee Ministry of Aircraft Production Meteorological Office, Air Ministry Meteorological Research Committee Naval Meteorological Service National Physical Laboratory Operational Research Section, Air De- fense of Great Britain Post Office Engineering Department Royal Aircraft Establishment Radio Research Board Radar Research and Development Establishment Synoptic Divisions Technical Memo- randum Signal Research and Development Establishment Telecommunications Research Hstab- lishment Ultra Short Wave Propagation Panel of the RDF Application Committee Ultra Short Wave Propagation Panel, Working Committee CANADIAN Operational Research Section, West- ern Air Command, Royal Canadian Air Force Canadian Army Operational Research Group NEW ZEALAND Operational Research Station, Royal N.Z. Air Force Radio Development Laboratory, De- partment of Scientific and Industrial Research—New Zealand SOUTH EAST ASIA Operational Research Section, South Hast Asia 1.000 CONFERENCES AND PROGRESS REPORTS Radio Waves. First Report on American Investiga- tions. 1.002 S The Effect of the Atmosphere on the Propagation of Radio Waves. Second Report on American Investiga- tions. 1.003 C Notes on Microwave Propagation Conference at RL MIT Radiation Laboratory. 1.004 5 Report on K-Band Work in U.S.A. B. Bleaney 1.005 5 Monthly Progress Report for the Month of March, RDL-DSIR 1944 (New Zealand). NZ H. G. Hopkins H. G. Hopkins Number Date BCSO June 16 No. 201 1943 BCSO Aug. 6 No. 218 1943 RL 42- Sept. 24 1943 RL 475 Oct. 20 1943 RD 1/363 Apr. 14 1944 Bib. No. 1.006 C 1.007 C 1.0088 1.009 S 1.010 § 1.0118 1.0128 GENERAL BIBLIOGRAPHY 279 Title Author or Source Number 1.000 CONFERENCES AND PROGRESS REPORTS (continued) Report of International Radio Propagation Confer- ence. Conference on Propagation—February 10-11, 1944— Empire State Building, New York. TRE Progress Report for the Period 16th June to 15th July, 1944. Progress Report, Radio Development Laboratory, DSIR, New Zealand for Months of June and July, 1944. Scientific Investigations on Propagation Problems in the South West Pacific Area. The Air Defense System of the Near Islands. Reviews of Progress of USW Propagation Work, I The Evaluation of Solutions of the Wave Equation for a Stratified Medium. II Statement of Work in Progress Relevant to In- vestigations of the Propagation of Radio Waves Through the Troposphere. III Microwave Propagation Research at Signal Re- search & Development Establishment. IV Correlation of Radar Operational Data with Meteorological Conditions. V Progress Report on Forecasting of Radar Condi- tions. VI Vertical Temperature and Humidity Gradients at Rye. VII The Use of Radar for the Detection of Storms. VIII Present States of Theoretical Study of Radio Propagation Through the Troposphere by the Math- ematics Group. IX Review of Short-Period Experimental Studies of Centimetre Wave Propagation, Carried out Jointly by ASE, SRDE and GEC. X Study of Cm. Wave Propagation over Cardigan Bay to Mount Snowden. XI Study of Reflection Coefficient of the Sea at Centimetre Wavelengths. XII K, X, and S (LLANDUDNO) Trials—General Summary of the Experimental Results Obtained which are Concerned with the Dependence of Radio Propagation on Meteorological Conditions. XIII Progress Report on 369 Trials by DNMS. . XIV Survey of Progress in the United Kingdom on the Electromagnetic Theory of Tropospheric Propa- gation. IRPL CUDWR WPG TRE RDL-DSIR NZ F, W. G. White T. J. Carroll USWP D. R. Hartree R. L. Smith-Rose (NPL) SRDE AORG DMO DMO DMO TRE E. C. S. Megaw (GEC) F. Hoyle F. Hoyle TRE & RRDE DNMS RRDE IRPL-C61 CP NDRC MAP File Ref. No. SB 30917 RD 1/439 or JETA 5491 Australia OCSO OAD-55 AC 7017/ RDF 239 or JEIA 5934 AC 7018/ USW AC 7019/ USW or JEJA 6464 AC 7020/ USW or JEIA 6463 AC 7021/ USW or JEIA 6462 AC 7022/ USW or JEIA 6461 AC 7023/ USW or JEIA 6460 AC 7024/ USW or JETA 6459 AC 7025/ USW or JEIA 6458 AC 7026/ USW AC 7027/ USW AC 7028/ USW AC 7029/ RDF 240 USW or JEIA 6466 AC 7030/ USW Date June 1944 1944 June- July 1944 June- July 1944 July 25 1944 Aug. 30 1944 Sept. 26 1944 Sept. 25 1944 Sept. 26 1944 Sept. 28 1944 Oct. 2 1944 Oct. 2 1944 Oct. 2 1944 Oct. 2 1944 Oct. 16 1944 Oct. 14 1944 Oct. 14 1944 Oct. 14 1944 Oct. 14 1944 Oct. 16 1944 280 GENERAL BIBLIOGRAPHY Bib. No. 1.0138 1.014 C 1.015 S 1.0168 1.017 R 2.001 S 2.002 8 2.003 S 2.004 8 2.005 C 2.006 C 2.007 R 2.008 C 2.009 C 2.010 R 2.011 R 2.012 C 2.013 C 2.014 2.015 C 2.016 R 3.001 Title Author or Source Number 1.000 CONFERENCES AND PROGRESS REPORTS (continued) XV Study of Meteorological Factors Responsible for the Refractive Structure of the Troposphere. Report No. 1 of Project SWP—3.2 of the OFS. Data on Super Refraction Supplied by Australian Radar Stations. (Progress Report on Analysis of Data from 200 Mc/s. Radar Stations Mar.-Aug., 1944). Report No. 2 of Project SWP—3.2 of the OFS. Third Conference on Propagation— Washington, D.C.—Nov. 16-18, 1944. Survey of Field of Radio Propagation and Noise with Special Reference to Australia. RRDE P. A. Anderson J. W. Reed P. A. Anderson CUDWR-WPG F. J. Kerr 2.000 GENERAL DISCUSSIONS Considerations Affecting Choice of Wavelength. Notes on Microwaves. Fundamentals of Early Warning Radar. RDF Propagation at Centimeter Wavelengths. Notes on Ultra Short Wave Propagation in the United States. An Introduction to Microwave Propagation. Electrical Communication Systems Engineering. Anomalous Propagation and the Army. Radar System Fundamentals. Radio Fundamentals. Radar Electronic Fundamentals. Principles of Radar. Fundamentals of Radar. General Lecture Series on Radar Components. Radar Performance Testing Manual. Effects of Site Conditions on Operation of Ground Radar Installation on Aerodromes. See also 10.007. Kk. T. Bainbridge W. W. Hansen ORG F. J. Kerr H. G. Booker D. E. Kerr P. Rubenstein War Dept. T. J. Carroll War Dept. War Dept. War Dept. Staff of MIT Radar School Staff of Radar Fund. Sec.- NATC RL HQ, AAF J. L. Putman AC 7031/ USW Washington State Coll. CSIR-RL RP 229/1 Washington State Coll. CP NDRC CSIR RP 231 or JEIA 8641 RL- V-78 RL- T-2 OCSO ORG-E-5-1 Australia No. 284 RP 177 TRE S 4457 RL 406 TM 11-4867 OCSO Rep. No. ORB-P-18-1 TM 11-467 TM 11-455 TM 11-466 NAVAER 08- 58-108 RL T-18 Air Forces Manual No. 28 TRE T 1805 3.000 STANDARD ATMOSPHERE PROPAGATION The Diffraction of Electro-magnetic Waves from an Electrical Point Source Round a Finitely Conducting H. Bremmer Balth. Van Der Pol Phil. Mag. Vol. 24 Date Oct 16 1944 Nov. 2 1944 Dec. 6 1944 Jan. 7 1945 1945 Nov. 27 1944 Sept. 24 1941 Oct. 20 1941 Mar. 5 1943 Apr. 27 1943 Aug. 9 1943 Sept. 16 1943 Feb. 25 1944 2nd Edition Apr. 25 1945 Mar. 4 1944 Apr. 28 1944 May 22 1944 June 29 1944 1944 Nov. 10 1944 Dec. 1, 1944 July 1944 2nd Edition July 1937 Bib. No. 3.002 3.003 3.004 3.005 C 3.006 R 3.007 3.008 S 3.009 S 3.010 S 3.011 S 3.012 C 3.013 S 3.014 8 3.015 S 3.0165 3.017 8 3.018 C 3.019 C 3.020 C GENERAL BIBLIOGRAPHY Title 3.000 Sphere, with Applications to Radiotelegraphy and the Theory of the Rainbow. Part I The Diffraction of Electro-magnetic Waves from an Electrical Point Source Round a Finitely Conducting Sphere, with Applications to Radiotelegraphy and the Theory of the Rainbow. Part II The Propagation of Radio Waves over a Finitely Conducting Spherical Earth. Part III Further Note on the Propagation of Radio Waves over a Finitely Conducting Spherical Earth. Part IV Ultra Short Wave Propagation Curves (0.1 to 10 Meters). Report on Signal Strength Curves Within the Visual Range. The Effect of the Earth’s Curvature on Ground-Wave Propagation. The Siting of RDF Stations. Appendix: Screening of RDF Sets from Fixed Echoes. Propagation Curves for Wavelengths of 13 Meters. Supplement to USW Propagation Curves RD 456. The Calculation of Ground-Wave Field Intensity over a Finitely Conducting Spherical Harth. Siting of Stations for Maximum Range. Microwave Interference Patterns. Dependence of Range of Radar Equipment on Wave- length for ASV—Case 23815 and 23817. Theoretical Field Strength of Ten Centimeter Equip- ment over a Spherical Harth. Atmospheric Refraction and Height Determination by RDF. (Details and Results of a Numerical Meth- od of First Order Correction.) (See 3.050) Dependence of Range of Submarine Radar Equip- ment on Wavelength—Case 20564. Transmission on 3000 Me. over Sea Water. Transmission on 100 Me. over Sea Water. Transmission on 200 Me. over Sea Water. Transmission on 500 Me. over Sea Water. Interim Report on Propagation Within and Beyond the Optical Range. Theoretical Ground Ray Field Strengths and Height Gain Curves for Wavelengths of 2—2000 M. Siting for Long Range Aircraft Detection. Author or Source H. Bremmer Balth. Van Der Pol H. Bremmer Balth. Van Der Pol H. Bremmer Balth. Van Der Pol Marconi Marconi C. R. Burrows M. C. Gray TRE Marconi K. A. Norton H. G. Booker J. A. Stratton C. R. Burrows H. G. Booker E. Eastwood, F/O (RAF) C. R. Burrows J. A. Stratton J. A. Stratton J. A. Stratton J. A. Stratton C. Domb M. H. L. Pryce BRL T. J. Carroll Number STANDARD ATMOSPHERE PROPAGATION (continued) pp 141-176 Phil. Mag. Vol. 24 pp 825-864 Phil. Mag. Vol. 25 pp 817-837 Phil. Mag. Vol. 27 pp 261-275 Marconi Handbook Marconi RD 456 Proc. IRE Vol. 29 pp 16-24 TRE T 1430 Marconi Appendix RD 456A Proc. IRE Vol. 29 pp 623-639 TRE M/36 RL- C-1 BTL MM-42- 160-54 TRE M/45/HGB Calibration Memo No. 54 or JEJA 7773 BTL MM-42- 160-70 RL- C-2 RL- C-3 RL- C-4 RL- C-5 ASE M 448 BRL Section E Tech. Rep. 383 CESL No. T-13 281 Date Supp. Nov. 1937 June 1938 March 1939 March 28 1940 Nov. 1940 Jan. 1941 July 19 1941 Nov. 1941 Dec. 1941 Fels. 9 1942 Mar. 7 1942 June 1 1942 July 1 1942 July 6 1942 July 9 1942 July 14 1942 July 14 1942 July 14 1942 July 14 1942 Sept. 1942 Sept 1942 Oct. 17 1942 (Rev.) GENERAL BIBLIOGRAPHY 3.021 C 3.022 5 3.023 3.0245 3.025 8 3.026 8 3.0275 3.028 S 3.029 S 3.030 C 3.031 8 3.032 8 3.033 8 3.034 R 3.035 3.036 C 3.037 R 3.038 S 3.039 C Title Author or Source Number 3.000 STANDARD ATMOSPHERE PROPAGATION (continued) VHF Field Strength Curves for Propagation within the Line of Sight. Relation of Radar Range to Frequency and Polar- ization. 1 to 10 Cm. Propagation Curves. Properties of the Diffracted Wave Field Intensity. The Effect of Earth Curvature on the Performance Diagram of an RDF Station. Radar Height Finding. Technical Requirements for GCI Search Systems. Technical Requirements for Early Warning Radar Systems. Low-Angle Coverage of Early Warning Radar Sys- tems. Factors Relating to the Design of an RDF Air Warn- ing Set. A Graphical Method of Computing the Bending of Radio Beams by the Effective Earth Radius Method. Transmission at Low Altitudes over Sea Water. Radio-Frequency Propagation Above the Harth’s Surface. Field Intensity Formulas. Propagation Curves. (See 3.046) Note on Field Intensity Computations for Elevated Antennas. Case 20878. The Calculation of Expected Vertical Coverage Dia- grams. Charts for Use in Field Intensity Computations. Notes on Visibility Problems, Taking Account of the Curvature of the Earth. Simplified Methods of Field Intensity Calculations in the Interference Region. G. J. Camfield R. A. Hutner H. Dodson J. Gill B. Howard F. Parker J. A. Stratton L. J. Chu N. H. Frank RL N. H. Frank RL F. J. Kerr H. Raymond R. A. Hutner F. Parker B. Howard H. Dodson J. Gill P. F. Godley, Jr. R. A. Hutner H. Dodson J. Gill F. Parker B. Howard BTL M. C. Gray M. Sherman Revised by W.S. McAfee K. Bullington English AORG W. T. Fishback Radio/279 RAE Ref: Radio/s. 2111/ OPE 16 RL- C-6 Marconi TR 460 RL- C-8 TRE 29/R102/ LGHH RL- C-9 TCAW 1 and 2 TCAW-3 CSIR-RL RP 187 CESL No. T-14 RL C-10 RCA Lab. Rep. No. 895-5 Div. 15 OEMsr-895 RL- C-11 NDRC Div. 15 966-6.A BTL MM-43- "110-28 CESL T-17 NDRC Proj. C-79 AORG No. 152 RL 461 Date Oct. 1942 Nov. 3 1942 Jan. 1943 Feb. 12 1943 Feb. 25 1943 Apr. 6 1943 May 10 1943 July 26 1943 Aug. 11 1943 Aug. 27 1943 Sept. 1 1943 Sept. 11 1943 Sept. 28 1943 Oct. 5 1943 Oct. 9 1943 2/19/43 Revision 10/15/43 Nov. 2 1943 Dec. 1 1943 Dec. 8 1943 Bib. No. 3.040 C 3.0415 3.042 C 3.043 5 3.044 C 3.045 5 3.046 R 3.047 C 3.048 C 3.049 8 3.050 3.051 R 3.052 C 4.001 S 4.0028 4.003 C 4.004 C 4.005 S 4.006 C GENERAL BIBLIOGRAPHY Title 3.000 Tield Strength Near and Beyond the Horizon for Wavelengths of Ten and Thirty Cms. Theoretical Field Strength Near and Beyond Horizon for Orthodox Propagation of Fifty Centimeter Waves. Location of Signal Strength Maxima, Nulls, and Re- flection Areas for Standard U.S. Early Warning Radar Equipment. Cover by German Coastal Radar on Low Flying Air- craft. The Propagation Functions for an Atmosphere with Uniform Lapse-Rate of Refractive Index. Ideal Field Intensity Distribution in the Vertical Plane for Transmitting or Receiving Antennas when Each has the Same Pattern. Propagation Curves. (Issue 8—Replacing Previous Issues.) Field Strength Calculator for Vertical Coverage Pat- terns and Propagation Curves. >Theoretische Resultaten over de Voorplanting Van Radiogolven. Theory of the Vertical Field Patterns for RDF Sta- tions. Height/Range/Alpha Tables (Tables Relating to the Height, Range and Angle of Elevation of an Air- craft.) (See 3.012.) The Calculation of Field Strength for Vertical Polar- ization over Land and Sea on 20 to 80 Megacycles per Second. Field Intensity Contours in Generalized Coordinates. 4.000 The Limiting Ranges of RDF Sets over the Sea. The Theory of Anomalous Propagation in the Tropo- sphere and Its Relation to Waveguides and Diffrac- tion. The Tracing of Rays in the Refracting Atmosphere. Graphical Construction of a Radar Radiation Pattern in a Stratified Atmosphere. Improved Tropospheric Propagation—Curves Em- bracing Anomalous Propagation. Radiation Patterns under Cases of Anomalous Prop- agation. Author or Source TRE TRE R. C. L. Timpson, Major R. C. Raymond I. H. Crowne T. Pearcey J. W. Herbstreit BTL C. R. White Balth. Van Der Pol J. C. Jaeger ORS ADGB A. M. Woodward H. Dodson J. Gill B. Howard F. Hoyle M. H. L. Pryce H. G. Booker T. Pearcey L. Anderson F. R. Abbott H. G. Booker T. Pearcey 283 Number STANDARD ATMOSPHERE PROPAGATION (continued) TRE-M/ Rep. 53/WW TRE T 1635 First Air Force OCSO OAD-25 RRDE Research Rep. No. 256 OCSO ORG-PP-5 NDRC Div. 15- Report 966-6C CESL Tech. Memo No. 154-E Natuurkundig Laboratorium N. V. Philips Gloeilampen Fabrieken, Eindhoven, Holland CSIR-RL RP 174 ORS(ADGB) Radar Memo No. 50 or JEIA-7766 TRE T 1704 RL 702 NON-STANDARD ATMOSPHERE PROPAGATION—PURE THEORY ASE M 395 TRE M/60/HGB or T 1447 ADRDE AC 3878 USW NRSL WP-4 TRE M/65/HGB ADRDE R 35 Date Dec. 24 1943 Feb. 24 1944 Apr. 7 1944 Apr. 15 1944 Sept. 1 1944 1944. Oct. 1944 Dec. 20 1944 Aug. 1941 Trans. Apr. 14 1945 Mar. 17 1943 Aug. 10 1944 May 2 1945 1943 Apr. 12 1943 Apr. 21 1943 May 1 1943 July 6 1943 July 19 1943 284. Bib. No. 4.007 S 4.008 C 4.026 C 4.027 GENERAL BIBLIOGRAPHY Title 4.000 Effect of Humidity Gradients in the Atmosphere on Propagation at RDF Frequencies. The Calculation of Field Strength Near the Surface of the Earth under Particular Conditions of Anom- alous Propagation. Anomalous Propagation over the Earth, Case 23703. The Effect of Atmospheric Refraction on Short Radio Waves. Radar Ray Patterns Associated with Normal and Anomalous Propagation Conditions. Transmission of Plane Waves Through a Single Stratum Separating Two Media. Notes on Theoretical Coverage Diagrams for Anom- alous Propagation. The Dependence of Microwave Propagation over Sea on the Structure of the Atmosphere. Improved Tropospheric Propagation—Curves Em- bracing Superrefraction. TRE Requirements for Propagation—Curves Em- bracing Superrefraction. The Mechanical Determination of the Path Differ- ence of Rays Subject to Discontinuities in the Verti- cal Gradient of Refractive Index. Improved Tropospheric Propagation—Curves Em- bracing Superrefraction. Interservice Propagation—Curves Embracing Super- refraction. Dependence of Mathematical Parameter L on Physical Entities. Theoretical Coverage-Diagrams for 10 Cm. Radars Embracing Superrefraction. Theoretical Coverage-Diagrams for 50 Cm. Radars Embracing Superrefraction. Theoretical Coverage of Navigational Aids Embrac- ing Superrefraction. The Theory of Propagation of Radio Waves in an Inhomogeneous Atmosphere (I). Reflection Coefficient of Layers of Varying Refrac- tive Index. Evaluation of the Solution of the Wave Equation for a Stratified Medium. (See 4.043.) Transmission of Plane Waves Through a Single Stra- tum Separating Two Media (II). Waves Guided by Dielectric Layers. Author or Source Australian Operational Research Group T. Pearcey S. A. Schelkunoff J. E. Freehafer F. P. Dane R. U. F. Hopkins J. Anderson B. Smyth J. M. C. Scott T. Pearcey TRE TRE F. R. Abbott NRSL TRE TRE TRE TRE TRE T. Pearcey G. Millington BRL D. R. Hartree P. Nicholson N. Eyres J. Howlett T. Pearcey J. B. Smyth S. A. Schelkunoff Number NON-STANDARD ATMOSPHERE PROPAGATION—PURE THEORY (continued) Oper. Res. Rep. No. 22 ADRDE Research Rep. No. 203 BTL MM-43-110 33 RL 447 NRSL WP-6 NRSL WP-9 TRE TM/Memo/ 14/AMW ADRDE Memo No. 40 TRE T 1625 TRE M/Memo 16/ HAB NRSL Rep. No. WP-10 TRE T 1626 TRE M/Memo 18/ WW TRE T 1634 or JEIA 3229 TRE T 1659 or JEIA 3230 TRE T 1660 ADRDE Research Rep. No. 245 BRL TR 483 or JEIA 4644 ADRDE MR 47 NRSL WP-13 BTL MM-44- 110-52 Date July 28 1943 Oct. 28 1943 Oct. 30 1943 Nov. 29 1943 Dec. 10 1943 Dec. 22 1943 Jan. 1 1944 Feb. 4 1944 Feb. 18 1944 Feb. 25 1944 Mar. 10 1944 Mar. 28 1944 Apr. 3 1944 Apr. 14 1944 Apr. 14 1944 Apr. 14 1944 April 1944 April 1944 May 24 1944 June 23 1944 July 5 1944 Bib. No. 4.028 C 4.029 C 4.030 R 4.031 R 4.032 C 4.033 R 4.034 R 4.035 R 4.036 C 4.037 C 4.038 C 4.039 C "4.040 C 4.041 C 4.042 C 4.043 C 4.044 R 4.045 C 4.046 C 4.047 C 4.048 C 5.001 C GENERAL BIBLIOGRAPHY Title 4.000 Microwave Transmission in Nonhomogeneous Atmos- phere. Contour Diagrams of the Radiated Field of a Dipole under Various Conditions of Anomalous Propagation. (See 4.045.) Theoretical Coverage-Diagrams for 144 Metre Ra- dars Embracing Superrefraction. Propagation Curves Embracing Superrefraction: SS Duct, Profile-Index 0.2 (Preliminary Edition). A Note on the Reflection Coefficient of an Isotropic Layer of Varying Refractive Index. Predicted Low Level Coverage of S-Band Shipborne Radars as Affected by Weather. (Horizontal Polar- ization—Antenna Height 100 Ft.) Predicted Low Level Coverage of 200 Mes Band Shipborne Radars as Affected by Weather. (Hori- zontal Polarization— Antenna Height 100 Feet.) Variational Method for Determining Higenvalues of Wave Equation of Anomalous Propagation. Wave Propagation Analysis with the Aid of Non- Euclidian Spaces. Atmospheric Waves—Fluctuations in High F're- quency Radio Waves. The Relation Between the Wave Equation and the Non-Linear First Order Equation of the Riccati Type. A Report on Transmission of Waves over the Harth. New Convergent Integrals. The Effect of a Subrefracting Layer of Atmosphere upon the Propagation of Radio Waves. Theory of Characteristic Functions in Problems of Anomalous Propagation. The Evaluation of the Solution of the Wave Equation for a Stratified Medium (II). (See 4.025.) Theoretical Coverage Diagrams for 3 Metre Radars Embracing Superrefraction. The Radiation Field of a Dipole under Various Con- ditions of Anomalous Propagation. (See 4.029.) Notes on the Solution of a Non-Linear First Order Equation of the Riccati Type. (See 4.038.) Perturbation Theory for an Exponential M-curve in Non-Standard Propagation. ‘Graphs for Computing the Diffraction Field with Standard and Superstandard Refraction. 5.000 Radio Interpretation of Meteorological Observations in the First Two Meters of Atmosphere Above Grass at Harlington, Middlesex, January to June, 1940. Author or Source S. A. Schelkunoff T. Pearcey F. Whitehead A. M. W. Woodward H. G. Booker G. Millington BRL F. R. Abbott L. L. Whittemore E. J. Wyrostek F. R. Abbott L. L. Whittemore E. J. Wyrostek G. G. Macfarlane B L T. L. Eckersley T. L. Eckersley T. L. Eckersley T. Pearcey M. Tomlin W. H. Furry D. R. Hartree W. Walkinshaw R. Hensman T. Pearcey M. Tomlin F. Whitehead T. L. Hekersley C. L. Pekeris P. J. Rubenstein W. T. Fishback TRE Number NON-STANDARD ATMOSPHERE PROPAGATION—PURE THEORY (continued) BTL MM-44- 110-53 RRDE Research Report No. 257 TRE T 1708 TRE M/Memo 23/WW BRL TR 497 or JETA 6481 NRSL WP-14 NRSL WP-15 TRE T 1756 CUDWR WPG-7 NRSL WP-18 BRL TR-501 or JEIA 9104 BRL TR 504 BRL TR 509 RRDE Memo No. 88 or JEIA-8371 RL 680 RRDE Res. Rep. No. 279 TRE T 1815 or JEIA 9198 RRDE Res. Rep. No. 275 BRL TR 502 or JELA-9725 CUDWR WPG-12 RL 799 T 1471 TRE M/63 Date July 5 1944 July 15 1944 July 23 1944 Sept. 7 1944 Oct. 5 1944 Noy. 1 1944 Nov. 4 1944 Nov. 138 1944 Dec. 1944 Feb. 1 1945 Jan. 1945 Jan. 1945 Feb. 1945 Feb. 12 1945 Feb. 28 1945 Mar. 12 1945 Mar. 18 1945 Apr. 13 1945 May 1945 July 1945 Aug. 13 1945 NON-STANDARD ATMOSPHERE PROPAGATION—EXPERIMENT AND THEORY 1940 286 Bib. No. 5.000 5.002 S 5.003 C 5.004 C 5.005 C 5.006 C 5.007 C 5.008 S 5.009 5.010 C 5.0118 5.012 C 5.013 C 5.0148 5.015 S 5.016 C 5.0178 5.018 C 5.019 5.020 8 5.021 C 5.022 S GENERAL BIBLIOGRAPHY Title Author or Source Number Date NON-STANDARD ATMOSPHERE PROPAGATION—EXPERIMENT AND THEORY (continued) Anomalous Echoes Observed with 10 Cms. CD Set. Centimeter Wave Propagation over Sea Between High Sites just within Optical Range. Centimeter Wave Propagation over Land, II. Meas- urements within and beyond Optical Range. Radar Wave Propagation. Very Short Wave Interception and DF Anomalous Propagation of 10 Cm. RDF Waves over the Sea, Also: First Supplement. Investigation of Propagation Characteristics of AW Stations. A Study of Propagation over the Ultra-Short-Wave Radio Link between Guernsey and England on Wave- lengths of 5 and 8 Meters (60 and 37.5 Mc/s.). The Effect of Atmospheric Refraction on the Propa- gation of Radio Waves. Propagation of Ultra-Short Waves. Report on Radar Wave Propagation. Atmospheric Refraction—A Qualitative Investigation. Radio Interpretation of Meteorological Observations in the First 400 Feet Above Cardington, 1942. Centimeter Wave Propagation over Sea, II. Measure- ments from Shore Sites Near and Beyond Optical Range. Preliminary Observations on Radio Propagation at 6 Centimeters Between Beer’s Hill, New Jersey, and New York—Case 37003, File 36691-1. Some Observations of Anomalous Propagation. Application of Anomalous Propagation to Operation- al Problems at Home and Abroad. Propagation of Signals on 45.1, 474 and 2800 Mc. from Empire State Building to Hauppauge and Riverhead, L.I., New York. Propagation of Ultra Short Waves. The “K” Effect in Anomalous Propagation of Ultra- Short Waves. The Propagation of 10 Cm. Waves over Land Paths of 14, 52, and 112 Miles. The Propagation of 1-Cm. Waves over the Sea as Deduced from Meteorological Measurements. A. EK. Kempton F. Hoyle E. C. 8. Megaw G. W. N. Cobbold H. Archer-Thomson E. C. S. Megaw L. Anderson J. B. Smyth F. R. Abbott R. Revelle T. L. Eckersley AORG Australian ORG R. L. Smith-Rose A. C. Stickland NPL A. C. Stickland NPL H. C. Webster L. Anderson J. B. Smyth TRE . W. N. Cobbold . J. Jones . A. Bonnett . C.S. Megaw mS @ . M. Hickin . W. Gilman Qe he TRE H. G. Booker G. 8. Wickizer A. M. Braaten RCA T. L. Eckersley F. Syer, Flying Officer, RAAF P. A. Anderson C. L. Barker K. E. Fitzsimmons S. T. Stephenson J. M. C. Scott T. Pearcey . Archer-Thompson ADRDE Research Oct. 8 Rep. No. 119 1941 ASE June 12 GEC 1942 SRDE Oct. 16 GEC 1942 AC 2917/ Com. 136 NRSL Nov. 30 WP-2 1942 BRL TR 4388 1943 AORG 2/6/43 No. 87 Supplement. 7/26/43 Oper. Res. Mar. 9 Rep. No. 17 1943 JIEE Mar. 90 1943 RRB Mar. 20 /S 10 1943 Australia Apr. 17 Rep. No. 354 1943 NRSL May 7 WP-5 1943 TRE M/61 May 14 or T 1413 1943 GEC May 27 No. 8180 1943 BTL June 12 MM-43- 1943 160-87 TRE M/64 July 6 or T 1483 1943 TRE M/66/HGB July 7 or T 1484 or 1943 JMRP No. 3 NDRC July 20 Proj. 423 1943 Rep. No. 1 Marconi Aug. 1 TR/476 1943 ' Australia Aug. 10 No. 266 or 1943 JMRP No. 11 Wash. State Oct. 26 Coll. Rep. 1943 No. 4 NDRC PDRC-647 ADRDE Nov. 11 Res. Rep. 1943 No. 227 or JMRP No. 4 Bib. No. 5.000 5.023 8 5.025 C 5.026 C 5.028 S 5.029 S 5.030 S 5.031 8 5.032 8 5.033 C 5.034 S 5.039 5 GENERAL BIBLIOGRAPHY Title NON-STANDARD ATMOSPHERE PROPAGATION—EXPERIMENT | Centimeter Wave Propagation over Land. A Pre- liminary Study of the Field Strength Records be- tween March and Sept., 1943. The Propagation of 10 Cm. Waves over an Inland Lake. Correlation with Meteorological Soundings. Measurements of Radar Wave Refraction and Asso- ciated Meteorological Conditions. Anomalous Propagation in India—Preliminary Re- port on Overland Transmission in Bengal. Atmospheric Physies—Summary of Investigations on Anomalous Propagation of Radar Signals Carried out by the Australian Operational Research Group Dur- ing 1942-43. The Cause of Short Period Fluctuations in Centi- metre Wave Communication. Anomalous Propagation in the Persian Gulf. Effect of Super-refraction on Surface Coverage on Enemy 50 Cm. and 80 Cm. Radar Sets. K-X-S Experiments, News Letter No. 1. Abnormal Radar Propagation in the South Pacific. An Investigation into Conditions in New Zealand and Norfolk Island on 200 Mc/s. with Notes on Fiji, New Caledonia and Solomon Islands. Procedure and Charts for Hstimating the Low Level Coverage of Shipborne 200 Mes. Radars under Con- ditions of Pronounced Refraction. Centimeter Propagation over Land. A Study of the Field Strength Records Obtained During the Year 1943-1944. K-X-S Experiments, News Letter No. 2. Atmospheric Propagation Effects and Relay Equip- ment. Low-Level Coverage of Radars as Affected by Weath- er. Procedures and Charts. (5.033 Reprinted.) Variations in Radar Coverage. Earlier Editions have Appeared As: Radar Operation and Weather. Weather Influences in Radar Wave Propagation. Effect of Atmospheric Refraction on Range Measure- ments. Author or Source R. L. Smith-Rose A. C. Stickland NPL P. A. Anderson Kx. E. Fitzsimmons 8. T. Stephenson L. J. Anderson L. G. Trolese South East Asia D. F. Martyn J. M. C. Scott Naval Officer in Charge, Hormuz TRE T. Gold ASE ORS-RNZAF Air Dept. Wellington F. R. Abbott L. J. Anderson F. P. Dane J. P. Day R. U. F. Hopkins J.B Ens. A. P. D. Stokes A. C. Stickland (NPL) Number 287 Date AND THEORY (continued) DSIR RRB/S 13 or JMRP No. 10 Wash. State Coll. Rep. No. 5 NDRC PDRC-647 NRSL WP-7 ORS-SEA Rep. No. 8 5 Aust. Oper. Research Group ADRDE Memo 42 AC 5975/ USW TRE M/Memo 19 MK 12201 RNAZAF Rep. No. 119 File 135/ 14/10 NRSL WP-11 (Rev.) BuShips Prob. No. X4-49CD DSIR: RRB/ Flt. Lt. R. W. Hatcher S 18 or (MO) T. Gold ASE T. J. Carroll OCSO NRSL Joint Communi- cations Board CUDWR- WPG CUDWR- WPG G. G. Macfarlane JEIA 4789 MK 12201 ORB-PP- 12-1 IRPL T2a JANP 101 IRPL T-1 NAVAER 50-IT-16 TRE T 1688 Nov. 15 1943 Nov. 16 1943 Dee. 10 1943 Dec. 30 1943 1942- 1943 Summary Mar. 8 1944 Ree’d Mar. 20 1944 April 1944 May 3 1944 May 4 1944 May 10 1944 Revised May 11 1944 May 13 1944 May 18 1944 May 25 1944 June 1 1944 May 1944 May 1944 June 12 1944 288 GENERAL BIBLIOGRAPHY Bib. No. 5.000 5.040 C 5.041 S 5.042 C 5.043 C 5.044 C 5.045 C 5.046 5.047 C 5.048 S 5.049 S 6.001 6.002 C 6.003 C 6.004 C 6.005 S Title Author or Source Number Date NON-STANDARD ATMOSPHERE PROPAGATION—EXPERIMENT AND THEORY (continued) Microwave Transmission over Water and Land under Various Meteorological Conditions. Abnormal Propagation in WAC for May and June, 1944. Propagation of Signals on 45.1, 474 and 2800 Me. From Empire State Building, N. Y. C. to Hauppauge and Riverhead, L. I., N. Y. The Structure of the Electromagnetic Field During Conditions of Anomalous Propagation. Tropospheric Propagation and Radio-Meteorology. Some Factors Causing ‘‘Superrefraction’” on Ultra High Frequencies in South West Pacific. (Daily Re- port on Abnormal Echoes—RAAF. Form No. 146 Included in ATP 821.) Aeroplane Tests. Atmospheric Refraction—A Preliminary Qualitative Investigation. Anomalous Propagation with High and Low Sited 3 em. Ship Watching Radar Sets. 4Anomalous Propagation at English Coastal Radar Stations, March-September, 1944. 6.000 Lebanon-Beer’s Hill Transmission on Wavelengths of 2.0 Meters and 30 Centimeters—Case 20564. Centimeter Wave Propagation over Land: Prelimi- nary Trials. The Propagation of 10 Cm. Waves on a 52-Mile Opti- cal Path over Land. The Correlation of Signal Pat- terns and Radiosonde Data. Centimeter Wave Propagation over Sea Within and Beyond the Optical Range. Aden-Berbera VHF Experiments—Final Report on Propagation Aspects. P. J. Rubenstein I. Katz L. J. Neelands R. M. Mitchell Canadian G. 8S. Wickizer A. M. Braaten (RCA) T. Pearcey F. Whitehead CUDWR- WPG D. F. Martyn F/Lt. P. Squires BRL R. F. Opies L. G. Trolese Lt. A. P. D. Stokes G. C. Varley D. Lack PROPAGATION EXPERIMENTS A. B. Crawford = . N. Cobbold . Bonnett . Jones . S. Megaw rcher-Thomson . Gladwin M. Hickin A. Anderson L. Barker S. T. Stephenson Kk. E. Fitzsimmons (8 Babee E. C. S. Megaw H. Archer-Thomson E. M. Hickin F. Hoyle Lt. E. W. Walker Lt. S. R. Bickerdike RL 547 ORS-WAC Rep. 10 NDRC Proj. 423 Rep. No. 2 RRDE Res. Rep. No. 258 CUDWR WPG-5 Australian Ionosphere Bul. Sect. 1.2 or ATP 821 JMRP No. 35 or BRL TR 488-A NRSL WP-17 AORG Rep. No. 250 AORG Rep. No. 258 or JEIA 9946 BTL MM-39- 326-98 GEC No. 8045 Washington State Coll. Rep. No. 1 NDRC-PDRC- 647 ASE M 582 SRDE MS 4 June 13 1944 July 27 1944 July 31 1944 Sept. 19 1944 Sept. 1944 Oct. 1944 Dee. 21 1944 Dec. 28 1944 Mar. 20 1945 May 30 1945 Dec. 5 1939 Aug. 21 1942 June 10 1943 July 1943 Dee. 742 July ’43 Bib. No. 6.006 5 6.007 5 6.008 C 6.009 C 6.0108 6.0115 6.012 C 6.013 S 6.014 S 6.015 S 6.016 S 6.017 C 6.0185 6.019 S 6.020 S GENERAL BIBLIOGRAPHY Title 6.000 PROPAGATION EX Investigation No. 369 (Irish Sea Experiment). Experience with Space and Frequency Diversity Fad- ing on New York-Neshanic Microwave Circuit— Case 370034. Investigation of Changes in Direction of Transmis- sion during Periods of Fading in the Microwave Range—Case 37003-4, File 36691-1. Radar Calibration Report—New York Region. Aden-Berbera VHF Experiments— Meteorological Conditions and Possible Correlations. Propagation Measurements on Polo Pony R/T Equipment. Propagation over Short Paths and Rough Terrain at 200 Mc/s. Propagation and Reflection Characteristics of Radio Waves as Affecting Radar. Microwave Propagation Measurements— Report Pre- sented at NDRC Conference of Feb. 10-11, 1944. Army Air Force Cold Weather Tests, Fairbanks, Alaska, Winter 1943-1944. An Ultra-Short-Wave Field, Array Polar Diagram, and DF Survey (North Devon and Cornwall—Sept.- Oct., 1943). An Estimation of the Incidence of Anomalous Propa- gation in the Cook Strait Area of New Zealand from Jan., 1943 to Jan., 1944. K-Band Radar Transmission—A Preliminary Report of Tests Made Near Atlantic Highlands, N. J., be- tween December, 1943 and April, 1944. Effect of Pulse Length on System Performance and Operation. Report on Cross Channel Propagation of British No. 10 Set. 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