THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL ENGINEERING Radiation Laboratory TV AND FM INTERFERENCE BY WINDMILLS FINAL REPORT 1 January 1976 - 31 December 1976 February 1977 Contract No. E(11-1)-2846 by: Thomas B.A. Senior, Dipak L. Sengupta and? Joseph E. Ferris ' Prepared for: Energy Research and Development Administration 20 Massachusetts Avenue, N.W. Washington, D.C. 20001 14438-1-F = RL-2273 Ann Arbor, Michigan

014438-1-F TV and FM Interference by Windmills by Thomas B.A. Senior, Dipak L. Sengupta and Joseph E. Ferris The University of Michigan Radiation Laboratory Ann Arbor, Michigan 48109 Final Report 1 January 1976 - 31 December 1976 February 1977 Contract No. E(11-1)-2846 Prepared for Energy Research and Development Administration 20 Massachusetts Avenue, N. W. Washington, D.C. 20001

A BSTRACT The report describes a preliminary but wide ranging investigation of te effects of a horizontal axis windmill on the reception of TV and FM signals mits vicinity. It is shown that the rotating blades produce a time varying amplitue modulation of the total signal received, and that for an antenna so located as bt pick up the specular or forward scattering off the blades, the modulation can produce severe distortion of the video portion of a TV signal reproduction. Thedistortion is worst at the higher frequencies, and therefore poses more of a prc&lem at UHF than at VHF. No interference to the audio signal nor to any FM tranmission has been observed. Based on laboratory studies as well as field tests, a moilation level has been established at which the video interference is judged "setee" (or objectionable), and this threshold of interference is substantially indepeuant of the primary field strength. A theory has been developed to compute the interference zone about a windmill for any given TV transmitter, and the results are in good agreement with those obtained from field tests using the operational iwndmill - at the NASA Plum Brook Facility. i

TABLE OF CONTENTS Page No. Introduction...................... 1. Background.................. 2. Purpose and Nature of the Study......... 3. Task Summary................ 3.1 Signal Analysis of TV Reception (Appendix I). 3.2 Windmill Modulation (Appendix HI)..... 9 0 0 0 0 0 9 0 0 0 3.3 Propagation and Scattering Analysis (Appendix 3.4 Computer Program (Appendix IV)....... 3.5 Laboratory Simulation (Appendix V)..... 3.6 Field Tests (Appendix VI)......... 3.7 Analysis of Results (Appendix VI)..... 4. Conclusions................. 5. Recommendations for Future Work....... 6. Acknowledgements.............. 7. References................. Appendix I - Signal Analysis of TV Reception...... I. 1. Introduction................. I.2. Basic TV Detection Process.......... I. 3. Artificially Corrupted TV Signal....... I. 4. Multipath Effects............... I. 5. Discussion.................. Appendix 1 - Signal Modulation by a Windmill II.1. Introduction................ II.2. Rotating Point Scatterer............; III) * * * * * * * * * * 1 1 5 10 10 10 11 11 11 12 12 13 14 14 15 16 16 17 19 20 23 1.3. Rotating Linear Scatterer 0 0 0 0 0 0 a 0 0 0 1. 4. Further Discussion of the Modulation Waveform H.5. Experimental Investigation.......... 11.6. Discussion................. I. 7. Windmill Modulation............ 0 0 0 9 0 0 0 a 24 25 31 37 41 48 50 ii

TABLE OF CONTENTS (Continued) Page No. Appendix III - Propagation Analysis................... 52 11. 1. Introduction....................... 52 III. 2. The Primary Field..................... 53 I. 2.1. General Expressions................ 53 m.2.2. Check with Berry's Formulation........... 57 I. 3. Field Expressions for the Present Problem.......... 61 11. 3.1. Geometry of the Problem.............. 61 m. 3.2. Field Incident at B.................. 64 I1. 3.3. Induced Dipole Moment on the Blade........... 66 II. 3.4. Scattered or Secondary Field at the Receiver..... 67 1. 3.5. Direct Field at the Receiver............. 70 11. 3.6. Total Field at the Receiver............. 70 II. 4. Discussion........................ 71 In. 5. References............72 Appendix IV - Computer Program...................... 73 Appendix V - Laboratory Simulation Studies of Modulation Effects....... 101 V. 1. Introduction....................... 101 V. 2. Experimental Arrangement.........101 V. 3. Presentation of Results........103 V.4. A Mechanical Simulator............................ 105 V. 5. Discussion.................116 Appendix VI - Field Tests................. 117 VI. 1. Introduction..................... 117 VI. 2. The Wind Turbine..................... 117 VI. 3. Test Procedures..................... 119 VI.4. Exploratory Tests..................... 121 VI. 5. Scattering Tests........................ 122 VI. 5.1. Scattering Test Results............... 124

TABLE OF CONTENTS (Continued) VI. 6. Operational Tests and Results. VI.6.1. Test Procedures... VI. 6.2. Operational Test Results VI. 7. Discussion......... VI. 8. Reference........... Appendix VII - Analysis of Results.... VII. 1. Introduction......... VI. 2. Field Strength Variation... VII. 3. Total Received Field..... VII. 4. Modulation Function..... VII.4.1. Determination of f (t) m VII.4.2. Nature off (t)... m VII. 4.3. Rotating Beam Concept VII. 5. Interference Zone of a Windmill VII. 5.1. Simplified Model.. 0 9 0 a * * ft * * * * * a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0 0 0 0 0 0 0 0 0 a 9 0 0 0 0 0 0 0 0 a 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a 0 0 127 127 131 134 134 135 135 135 136 142 143 145 147 147 149 151 154 157 157 159 160 VII.5.2. Improved Model. * * * VII.5.3. Interference Zone Calculation. VII. 6. Comparison of Calculated and Observed Results VII. 6.1. Scattering Tests............ VII. 6.2. Operational Tests........ VII. 7. Discussion........... 0 9 0 0 iv

TABLE OF FIGURES Page No Figure 1. Figure I. 1. Figure I. 2. Figure I. 3. Figure II. 1. Figure I. 2. Figure II. 3; Figure 1. 4. Model of 100 kW wind turbine generator....... ~.. 4 Block diagram of the first detection system in a TV receiver................... 18 Block diagram of the first detection system for an artificially corrupted signal................... 20 Block diagram of the first detection system in the presence of multipath interference............. 23 Transmitter and receiver in the presence of a rotating point scatterer.................... + cos (kp sin gst) versus 0s = st for k = 60, F=0.5, =0 and 0 = 7r/4............... Frequency spectrum diagram for the modulation produced by a rotating point scatterer, kip = 20..... av or - versus I/X for the rotating point s 5 scatterer: S/4 scatterer: ~ =0 and ~ = 7r/4............. s 25 29 30 32 Figure I1.5. 1+ rS (L psin ft)versus O = f t for kL = 60, a 5 s s s S.. 34 Figure 11. 6. Figure II. 7. Figure II. 8. Figure 11. 9(a). Figure I. 9(b). Figure HI. 10a. Figure H. lOb. Frequency spectrum of the modulation function produced by a rotating extended scatterer of length L... Spectral distribution curve for the rotating linear scatterer. n = 1 corresponds to the frequency f = 2f, f is the rotation frequency.............. A single modulation pulse.......... Sketch of the experimental set-up............ Block diagram of the receiving system.......... Modulation waveform for L = 0.5k, 0 = 60 degrees, fs = 30.83 Hz. Vertical scale 10 mv/division; horizontal scale 5 ms/division............. Modulation waveform for L = X, 0 = 60 degrees, f = 30.83 Hz. Vertical Scale 10 mv/division; horizontal scale 5 ms/division...... 36 38 40 42 42 44 44

TABLE OF FIGURES (Continued Page No. are II. 1 la. are II. lb. are II. lc. are II. lid. ure II. 1 e. Modulation waveform for L = 6.32X, 0 = 60 degrees, f = 6.1 Hz. Vertical scale 50 mv/division; Horizontal scale 20 ms/division.......... Modulation waveform for L = 5.32X, 0 = 60 degrees, fs = 5 Hz. Vertical scale 20 mv/division; horizontal scale 20 ms/division............. Modulation waveform for L = 4.32X, 0 = 60 degrees, f = 5 Hz. Vertical scale 20 mv/division; horizontal scale 20 ms/division............. Modulation waveform for L = 3.32X, 0 = 60 degrees, f = 5 Hz. Vertical scale 20 mv/division; horizontal scale 20 ms/division............. Modulation waveform for L = 2.32 X, 0 = 60 degrees, f = 5 Hz. Vertical scale 10 mv/division; horiotal scale 2 m/d zontal scale 20 ms/division............. 45 45 46 46 47 ure 11.-1. ure 1I. 2. ure III. 3. ure III. 4. ure III. 5. Coordinate system used for the primary field calculations.......................... 54 Geometry of the flat earth case............58 Geometry of the problem in the interference zone..... 59 The geometry and the coordinate system used for the windmill, transmitter and receiver located above a spherical earth................ 63 Reflected path and grazing angle for the transmitterreceiver combinations.........................65 ure IV.1. ure IV.2. ure V. 1. ure V. 2. ure VI. 1. ure VI. 2. ure VI. 3. Flow diagram for windmill program............ Flow diagram for subroutine GRWAVE.......... Equipment and arrangement used in simulated modulation studies............... Rotatable reflector in front of TV antenna........ 74 75 102 115 100-kilowatt experimental wind turbine generator....... 118 Test equipment set up......................120 Wind turbine test sites........................ 123 vi

TABLE OF FIGURES (Continued) Page No. Figure VI. 4. Figure VI. 5. Figure VI. 6. Figure VI. 7. Figure VI. 8. Figure VI. 9. Figure VI. 10. Figure VII. l(a) Figure VII. l(b) Figure VII. 1(c) Figure VII. 2. Figure VII. 3. Figure VII.4. Figure VII. 5. Figure VII. 6. Figure VII. 7. Wind turbine control center strip chart recordings during site 6 measurements...... WWV time code and scattered Channel 24 signals observed at site 6................ Wind turbine control center strip chart recordings during site 5 measurements........... WWV time code and scattered Channel 24 signals observed at site 5................ TV receiving antenna pattern (600 MHz)...... Wind turbine control center strip chart recordings during the operational test at site 14....... WWV time code and received Channel 43 signals during operational test at site 14........... 125.... 126.... 128.. 129... 130.... 132.... 133 IE(R)i vs. d(= d12) for f = 50 MHz....... IET(R)| vs. d(= d12) for f = 100 MHz....... ET(R)I vs. d(= d12) for f = 500 MHz..... E(R)I vs. d(= d32) iad lE0(R) vs. d(= d32) for f 647MHz, h 300m, h 10 m, d3 =79.7km, =15, a = 0.lS/m........... Scattering problem for a rectangular plate.... Simplified model for interference zone calculations. Interference zone based on the simplified model: A A A - A 1 mx( mXD 2 mX mXD ) = Interference zone for incidence normal to the plane of blade rotation................ The specular ( ) and forward ( ----) scattering portions of the interference zone of a windmill..... 137.... 138.. 139... 140.... 143.... 150.... 151.. 152 153

TABLE OF TABLES Page 'o. Table II. 1. Table II. 2. Table I. 3. Appendix IV Table V. 1. Table V.2. Modulation pulse widths produced by a rotating linear scatterer: ~ 60 degrees............ Measured frequency spectrum of the modulation waveform produced by a linear rotating scatterer: 0-60 degrees, f = 5 Hz............. Modulation pulse widths produced by a linear rotating scatterer of length L = 30.48 m (= 100')...... Computer Program Table of Contents (sequential).. Channel 2 picture quality with sine wave modulation at indicated modulation frequency in Hz. Video carrier frequency = 55.25 MHz, audio carrier frequency = 59.75 MHz. Test receiver is Zenith model No. 17GC45................... 43 ~.. 49... 51... 76 106 Table V.3. Table. V.4. Table V. 5. Table V. 6. Channel 13 picture quality with sine wave modulation at indicated modulation frequency in Hz. Video carrier frequency = 211.25 MHz, audio carrier frequency = 215.75 MHz. Test receiver is Zenith model No. 17GC45................... Channel 2 picture quality with sine wave modulation at indicated modulation frequency in Hz. Video carrier frequency = 55.25 MHz, audio carrier frequency = 59.75 MHz. Test receiver is Magnavox model No. CD4220...................... Channel 13 picture quality with sine wave modulation at indicated modulation frequency in Hz. Video carrier frequency = 211.25 MHz, audio carrier frequency = 215.75 MHz. Test receiver is Magnavox model No. CD4220...................... Modulation index required to produce minimum observable video distortion at Channel 2. Video carrier frequency = 55.25 MHz, audio carrier frequency = 59.75 MHz. Test receiver is Zenith model No. 17GC45..................... Modulation index required to produce minimum observable video distortion at Channel 7. Video carrier frequency = 175.25 MHz, audio carrier frequency = 179.75 MHz. Test receiver is Zenith model No. 17GC45...................... 107 108 109 110 111

TABLE OF TABLES (Continued) Page No. Table V. 7. Table V. 8. Table V. 9. Table V. 10. Modulation index required to produce minimum observable video distortion at Channel 13. Video carrier frequency = 211.25 MHz, audio carrier frequency = 215.75 MHz. Test receiver is Zenith model No. 17GC45................ Modulation index required to produce minimum observable video distortion at Channel 2. Video carrier frequency = 55.75 MHz, audio carrier frequency = 59.25 MHz. Test receiver is Magnavox model No. CD4220................. Modulation index required to produce minimum observable video distortion with sine wave modulation at Channel 13. Video carrier frequency = 211.25 MHz, audio carrier frequency = 215.75 MHz. Test receiver is Magnavox model No. CD4220................. Modulation index required to produce minimum observable video distortion with pulse modulation at Channel 7. Video carrier frequency = 175.25 MHz, audio carrier frequency = 179.75 MHz. Test receiver is Zenith model No. 17GC45.............. 112 112 113 113 -A

INTRODUCTION, 1. Background It is possible that in the years to come large windmills will be used to generate power not only for rural communities but as input to the National Grid, thereby bringing about a revival of one of mankind's earliest methods of harnessing nature. Although the first conversion of wind power is lost in antiquity, a sailboat is depicted on a Egyptian urn circa 4000 BC and there were references to millwrights in Persia some 1300 years ago. Among the westerners sent back to Mongolia by Genghis Kahn were Persian millwrights and Mongolia has maintained its interest in wind-generated power since that time. Horizontal shaft windmills appeared in northwestern Europe 900 years ago and then spread rapidly, remaining common-place throughout the entire continent for over 700 years. It was mostly the power of win d water that fed the early stages of the industrial revolution, but with the advent of the steam engine and the abundant, reliable and inexpensive power that it provided, the wind soon lost its 'major role, and windmills lingered on only in regions where steam was unobtainable or impractical, principally for pumping water. Nevertheless, prior to the construction of area-wide electrical power grids in the U. S., propeller-type mills consisting of 20 to 24 galvanized steel blades mounted around a wheel were often used in rural areas to power small electrical generators. These charged batteries that in turn supplied electricity to the house and farm, and by the early 1950's, such units were commonly available in sizes up to 10 kW. Although winds at ground level come and go in a most unreliable way, even places without strong prevailing surface winds may have strong winds at rather low altitudes, and measurements at three Texas towers off the eastern U. S. have shown annual average wind speeds as high as 20 mph at 100 m above the sea. The World Meterological Association has estimated the wind power in those parts of the lower 1

atmosphere accessible to man and his machines to be 20 TW, ten times the estimated total power available from flowing streams. But hydro generating capacity in the U.S. is presently around 53 GW, from approximately 30 percent of the potential sites that are available, whereas the wind is contributing nothing. Experimental work on large scale electrical energy conversion from wind began in France in the 1920's with the construction of a 20 m diameter two-bladed propeller. Work next developed in Russia, Mongolia and Western Europe, but one of the most successful models to date was that constructed in 1941 under the Smith-Putnam project [i. It was a 53 m diameter, to-bladed propeller mounted on top of Grandpa's Knob near Rutland, Vermont and usedto power a 1.25 MW electrical generator. Once a mechanical difficulty associated with a main bearing had been overcome, the machine ran successfully for four years, but when one of the blades failed, the experiment ended for lack of financial support. For all practical purposes, the subject of power generation from the wind lay dormant in the U. S. through two decades of ever increasing power consumption, but was revived by Heronemus as a means of providing power for New England. His initial concept was the placement of wind power systems on offshore banks and in floating positions off the coast, and in 1972 he proposed [2] the construction of 83 clusters of offshore stations to generate an annual average power of 38.2 GW. Each cluster would be 55 km in diameter and consist of 165 towers, with each tower supporting three 60 m diameter rotors driving a 2 MW generator, to produce an average of 900 kW. Heronemus also proposed a wind-generator network for Eastern Wisconsin to achieve an annual average output of 7.4 GW by extracting about 0.25 percent of the available wind energy over the area. Some of the stations would be floated offshore in Lakes Michigan and Superior, while most would be tower-mounted straddling highways. Were it not for the power shortages of the last few years and the rapidly increasing costs of fuel, many of these schemes would have remained the pipedreams of an inspired visionary, but as the costs of other power sources escalated, the "clean' energy that is available in the wind has seemed ever more attractive. In 1973 a wind 2

energy program was initiated jointly by the National Science Foundation and the NASA Lewis Research Center and in 1975 the responsibility for planning and executing a sustained wind energy program was transferred from NSF to the newly formed Energy Research and Development Administration. As part of the program, a 100 kW wind turbine (or windmill) generator has been designed and fabricated, and is now in operation at the Plum Brook facility near Sandusky, Ohio. The rotor consists of two blades of aerofoil shape with a total diameter of 37. 5 m and a fixed coning angle of 7 degrees. The rotor is mounted atop a tower;30 m in height (see Figure 1) and is intended to produce 133 kW of power (100 kW at the actual generator) when rotating at 40 rpm in an 18 mph wind(3, 4] With the knowledge gained from this prototype machine, other and larger generators are being developed, and the national goal of energy sufficiency by the 1980's could well see the rapid deployment of this nonpolluting and not visually unattractive system of electrical power generation throughout the United States. Even as presently conceived these windmills could have two or three-blade rotors up to 60 m in diameter C[5. The blades themselves may be twisted and tapered from root to tip, consisting of a metallic skin on a framework of girders or made of fiberglass, and with their aerofoil shape, they would be rather similar to the wings of an aircraft. It is therefore obvious that blades such as these could produce the same type of radio 'interference as a low-flying aircraft, and could adversely affect both TV and FM reception. Indeed, the problem may be more severe. Whereas aircraft interference is a transitory phenomenon, a windmill would be fixed in its location, and since the blades would be in a plane which is close to the vertical, any windmill could drastically interfere with all forms of radio and TV in that sector of space where signals are received that are specularly reflected from the surfaces of the blades. If a windmill is to be effective it must be elevated, and to obtain the full advantages of the distributed means of power generation that windmills could provide, most should be located close to the communities which use the power to minimize transmission losses. Communities, bath rural and urban, could then find themselves exposed to windmills in the same manner that they are now exposed to radio and TV (transmitting) antennas and at the outset of this study it was not obvious how compatible the two are.

Figure 1. Model of 100 kW wind turbine generator.

2. Purpose and Nature of the Study Based on preliminary analyses we had performed as well as the observed fact that an aircraft passing nearby could distort a TV picture, it seemed possible that the rotating blades of a windmill could interfere with TV reception. If this was indeed so, it could impact on the allowable siting of a windmill vis-a-vis the community it was desigmed to serve, and the main objective of the study were therefore as follows: (i) determine if such interference could exist, (ii) quantify the levels of interference that were found, and (iii) assess the impact of these levels on the siting of windmills. Since the time-varying multipath attributable to the blades would be a source of both amplitude and frequency modulation of the total signal received, it was required that we also consider the possibility of interference with FM (radio) transmissions. To meet these objectives a rather comprehensive program was developed involving laboratory measurements and simulation, field testing using the existing windmill at the NASA Plum Brook Facility, and rigorous analyses and computations. To complete the investigations within a time span of one year required that many of the tasks be carried on in parallel, but it was nevertheless our hope that by careful coordination each task could be timed so that its findings would have maximum impact on the others. In this at least we were not entirely successful. Due in part to adverse wind conditions, the windmill was seldom in full operation throughout the first half of the year, and it was not until the tenth month of our study that we were able to obtain data with the blades rotating. Several months prior to this our laboratory simulations had indicated that interference did exist and was of sufficient magnitude to pose a problem. This added urgency to the completion of the analytical investigations, and by late summer the computer programs that had been developed were being fully exercised in the assessment of the interference levels at various (potential) windmill sites. It is not inappropriate to add that when the operational tests were finally carried out at Plum Brook, the interference observed was in excellent agreement with the prediction. 5

In a later part of this report we summarize the work performed in several different categories and cite the main conclusions reached, but to better appreciate how the various tasks impacted upon one another, it may be helpful to start with a chronological survey. At the beginning of the program it seemed probable that the frequency modulation attributable to the rotating blades of the windmill would be the prime source of interference, and that the problem would be most severe in fringe areas of reception where the primary (direct) signal was already weak. At large distances from a transmitter, the presence of the earth has a substantial effect on the field strength, and it was therefore decided that all calculations would be carried out for the transmitting and receiving antennas and the windmill located on or above a homogeneous smooth spherical earth of arbitrary electrical properties. This required the development of a computer program adequate to determine the field at any point due to a transmitter at another, and though we were fortunate to obtain a program previously compiled by Berry [6], substantial time was taken to 'de-bug' the program and get it working foi the situations of concern to us. Meanwhile a series of laboratory simulation experiments had commenced using two identical 1976 Zenith color television sets selected because of their highly rated [7] capability for interference rejection. A simple signal analysis had indicate the general character of the phase (or frequency) and amplitude modulations which a windmill could impose on the signal reaching the antenna of a TV receiver. The impact that this has on the quality of reception obviously depends on the receiver characteristics, and though there is a high degree of commonality among. the receiver in use today, the complexity of their circuitry is such that it is difficult to predict the degradation of the receiver output from a knowledge of the input signal perturbation. We therefore chose to rely on measurements using devices attached to the input terminals of one television set to simulate the modulation that a windmill would provide. Phase and amplitude modulation devices were constructed capable of imposing an adjustable level and frequency of modulation on any VHF channel TV signal received. Reception with and without modulation was compared for a sequence of modulation levels and for frequencies of the (sinusoidal) modulation that would be reasonable for 6

a windmill to generate. It was immediately found that phase (or frequency) modulation had almost no effect. Not surprisingly (since the video signal is in the form of amplitude modulation), the TV picture was quite immune, and only at the very highest levels of modulation was it possible to detect some audio interference in thlle [olrl ol "clicking". This finding was later substantiated by a signal analysis of Ihe basic TV reception process. It also suggested that the interference would not be a problem with FM (radio) transmissions and, indeed, no interference of any magnitude was found then or later. On the other hand, amplitude modulation did have a noticeable effect on the TV picture. Even at quite low levels, distortion of parts of the picture could be seen with (depending on frequency) grey bands moving up the screen. As the modulation level increased, the bands darkened with (perhaps) "snow" accompanying them, and it was now painful to try to watch the picture. Occasional flipping of the picture occurred due to the breakdown of the vertical hold, and with further increase of modulation the picture disintegrated completely. It was now evident that the time-varying amplitude modulation produced by a windmill could be a source of major concern to TV reception. Further simulation tests were performed with a unidirectional rectangular pulse type of amplitude modulation and, in particular, a detailed series of measurements was carried out as the level and width of the pulses were increased in steps. At each step the quality of the TV picture was rated by two or more observers. It was found that the modulation level at which the distortion became severe (and "unacceptable") remained reasonably constant at about 20 percent and showed no significant dependence on the TV signal strength. The pictures were also recorded on video tape, but unfortunately the concept of a ' reference tape' proved less effective than we had hoped because of the degradation introduced by the video recording system. These findings added urgency to our theoretical investigations. The sensitivity of a TV receiver to time-varying amplitude modulation was confirmed by a detailed signal analysis and we also pushed forward with our analysis of windmill scattering in the presence of the earth. A computer program to find the field at any point due to a transmitter at another point was now in operation. This could also serve to find the field incident on the windmill and by using a simple (physical optics) scattering 7

model in which a windmill blade was approximated by a plane rectangular metal plal of equivalent dimensions, the windmill-scattered field could be found. According tc this model, the scattering is significant only in directions near those of specular an forward scattering from the blades. A program was developed to compute the prim (direct) field of a linearly-polarized transmitting antenna as well as the secondary (windmill scattered) field, and to do so at a sequence of distances -from the windmil] in front and behind. Based on the conclusion that the interference would be objectio able for a modulation index m > 0. 2 and the fact that, in the large, m is a decree ing function of distance from the windmill, the (maximum) distances from the windn at which m = 0. 2 could be found. The distances correspond to a receiving antenna the same great circle path as the transmitter and the windmill and either nearer or further from the transmitter than the windmill. The average then serves to specify the radius of an equivalent circular zone of interference about the windmill. There are, however, three points that should be noted. Firstly, the computations were carried out on the assumption of an omnidirectional receiving antenna, it is possible that in any given situation the interference could be substantially redui by using a high performance directional antenna. Secondly, the interference zone i not actually circular (see Appendix VII) and this also could reduce the practical con sequence of the interference; and lastly, the interference level is computed on the assumption that the windmill is so pointed as to direct the maximum blade-scattere signal to the receiving antenna. It therefore follows that even within the interferen zone, TV reception will be affected only when the winds are from the appropriate direction. This could be a small fraction of the total viewing time for that channel. This program was our basic tool for interference prediction but it was still rather inefficient one requiring the manual comparison (and interpolation) of long strings of computer outputs which were themselves costly to obtain. It had not beet our intent to use it in this form, but this was forced by the urgent need to assess potential windmill sites for interference. In practice, it remained our only tool throughout the entire study and has been used to survey more than a dozen different locations for as many as 20 TV channels in each case. 8

This effort was carried out in parallel with field tests at the NASA Plum Brook Facility, but our hopes to coordinate the field tests with the laboratory simulations and computer analyses proved largely unattainable. By late Spring we had mapped out a series of field tests whose objective was to develop data for comparison with the findings of the laboratory work. Sites were physically located at Plum Brook, the necessary equipment assembled in a portable package, and a sequence of visits made. It was confirmed that the blades did act as specular reflectors as regards the TV signals incident upon them, and that the magnitude of the scattered signal was comparable to that predicted by our simple scattering model. These were only static tests and, unfortunately, mechanical difficulties prevented the full speed operation of the windmill. By the time these difficulties were overcome, the wind no longer cooperated, and such windy times as did exist were so ephemeral that we were unable to catch them. In this manner, Summer dragged on to Fall, and the overall program advanced only through analytical studies of, for example, the modulation spectrum of rotating point and distributed scatterers. It was not until late September that the wind conditions improved. Fearing that we might now have only a single opportunity to observe the interference, we therefore selected a site where our theory has predicted that the interference would be significant for a given TV channel with the windmill slewed appropriately in azimuth. On our next visit, we went immediately to this site (number 14), and interference was indeed observed at a level comparable to that predicted. When the windmill was driven out of the azimuthal plane that would direct a scattered signal to the receiving antenna, the distortion disappeared. Video tape recordings were made of the distorted and undistorted pictures. The output of a spectrum analyzer was also recorded to show the modulation waveform, which was a series of sinc-like pulses occurring with every half-revolution of the blades. Since most of our laboratory simulations had been carried out using sinusoidal modulating waveforms, it is noteworthy (and not a little fortuitous ) that the predicted interference based on the selection m = 0. 2 for the modulation index was in such good agreement-with observation. For the most part the rest of the program was anti-climatic. The field test data were analyzed and their implications determined as regards the calculation of 9

interference zones. The nature of the modulation waveform was confirmed using a small blade rotating in an anechoic room, and preliminary analyses performed to determine what effect such modulation might have on other microwave systems. Suffice to say that the main objectives of the study had been achieved. 3. Task Summary In the appendices to this report we detail the work performed in seven different areas constituting the main lines of investigation. These are summarized in the following. 3.1 Signal Analysis of TV Reception (Appendix I) For a TV signal corrupted by arbitrary amplitude and phase modulation such as may be introduced by a windmill, the output of the first detector of a TV receiver is analyzed. It is shown that amplitude modulation has the most effect. It could therefore cause video distortion, whereas the audio information, being transmitted using frequency modulation, will be relatively unaffected. 3.2 Windmill Modulation (Appendix II) The amplitude modulation of the signal scattered by a slowly rotating object is studied analytically using two simple models: (i) A rotating point scatterer for which the modulation waveform is sinusoidal with variable frequency. Only a few discrete frequency components have significant magnitude. (ii) A rotating linear (extended) scatterer for which a scalar analysis indicates that the modulation waveform consists of sinc-type pulses in time whose spectrum is (ideally) a band of equal amplitude frequencies. The dominant frequencies can be many times larger than the rotation frequency, and the highest frequency (for the point scatterer) and spectral width (linear scatterer) are determined by the largest (effective) dimension of the scatterer. The implications of these results on the modulation produced by a windmill are discussed. 10

3.3 Propagation and Scattering Analysis (Appendix III) Expressions for the primary (direct) field of the transmitter at the receiver are taken from the work of Fock [8] and Wait [93 on the diffraction of electromagnetic waves by a homogeneous smooth spherical earth, and these also serve to determine the field falling on the windmill. The blades LIareC treated as rectangular metal pl:lltes lying in the (vertical) pla:ne of rotation: a more realistic approximation wvould have them twisted out of this plane and, indeed, sonme such defornmation is necessary to account for the observed modulation. The scattered field can be attributed to induced electric dipoles whose moment(s) are obtained using the physical optics approximation, and a further application of the propagation equations then leads to an expression for the secondary (scattered) field at the receiver. The approach is quite general and valid for arbitrary transmitter and receiver locations with respect to both the location and pointing direction of the windmill. The implications as regards the magnitude and modulation of the scattered field are discussed. 3.4 Computer Program (Appendix IV) An available [6] computer program has been adapted and extended to compute the primary and secondary fields at the receiver in accordance with the expressions in Appendix III. The program is completely general, and from a knowledge of the primary and secondary field strengths at the receiver, the modulation depth (or index) can be found. This is required to determine the maximum distance from the windmill at which interference may occur. 3.5 Laboratory Simulation (Appendix V) Laboratory simulation tests demonstrated that amplitude modulation of the general level that a windmill could create does produce video distortion of TV reception. The modulation waveform was initially a sinusoid whose frequency and amplitude were adjustable, but later we also used unidirectional rectangular pulses. Based on these experiments it was concluded that a modulation index m > 0.2 would cause "objectionable" video interference, regardless of the incident field strength. 11

);. (6 Field Tests (AppendLx VI) The tests were all conducted at Plum Brook and were of two main types. For the scattering tests the windmill blades were locked in a horizontal position and the entire turbine was then rotated in azimuth. Using one of the Cleveland or Toledo TV transmitters as the signal source, the field that was scattered off the blades was observed. It was found that the scattering was primarily in the specular direction and that the blades contributed singly. The field strengths were in good agreement with those predicted using the physical optics approximation. As a result of the theoretical and scattering test data, a site was selected to observe the signals when the windmill was in operation. The site was approximatcl 0.5 km from the windmill. Using TV Channel 43 (whose transmitter is 79 km away) and with the windmill slewed to direct the specular scattering to the receiver, video distortion was observed and recorded. This was in spite of using a directional receiv ing antenna pointed towards the transmitter, thereby discriminating against the source of interference. 3.7 Analysis of Results (Appendix VII) As a consequence of the laboratory simulations it was concluded that a modulation index m > 0.2 would cause video distortion that was judged "objectionablet". On the assumption that for any given location of the receiver the windmill is so oriented as to direct the maximum blade scattering to this point, the region where m > 0.2 is defined as the interference zone. That portion of the zone which is produced by specular reflection off the blades is a cardioid centered on the windmill and with its maximum directed towards the transmitter. There is also a narrow lobe directed away from the transmitter resulting from forward scattering, and this generally provides the maximum distance from the windmill at which objectionable interference can occur. In site surveys we have usually quoted a single interference distance equal to the average of the maximum distances ascribed to the cardioid and the forward lobe The field test results have been analyzed in the light of the theoretical predictions. The key findings are: 12

(i) the blade scattering is predominantly specular with the blades contributing singly: however, the sites used were not such that any forward scattering would have been observed; (ii) the rotating blades produce impulsive ('sinc-type') modulation; and (iii) the threshold of modulation for severe video distortion with impulsive modulation is approximately m = 0.1. Overall, the agreement between the calculated and observed results is remarkably good. The theory has been found capable of predicting all of the major features of the observed phenomena, and is quantitatively accurate as regards the interference zones associated with windmills. 4. Conclusions The dominant conclusion is that the rotating blades of a horizontal axis wind turbine or windmill can interfere with TV reception by producing video distortion. The interference is predicted theoretically and has been measured experimentally using the operating windmill at Plum Brook. It increases with increasing frequency and is therefore worst on the Upper UHF channels. It decreases with increasing distance from the windmill, but in the worst cases could still produce objectionable video distortion at distances up to a few miles. There does not seem to be any significant dependence on the primary field strength, and no audio distortion has been observed. Using the theory that has been developed, it is possible to compute the distance from a windmill at which the interference to reception of a given TV channel changes from "severe" to "acceptable": in effect, to compute the zone of interference about a windmill. These calculations are based on a windmill having metallic blades of the same size as the Plum Brook machine. For blades of smaller size or made of a material which does not reflect all of the energy incident upon it, the interference zone would be proportionately smaller. We also remark that the receiving antenna has been assumed omnidirectional with the windmill blades so positioned as to direct the max imum scattered signal to the receiver. In circumstances other than this, the 13

interference will be less, and the local topography about a given site could also reduc, (or increase) the actual level of interference experienced. 5. Recommendations for Future Work The study that has been carried out is only the first step, and in order to explore ways of reducing the interference that a windmill will produce, it is necessary to have as much information about the interference as possible. To this end and confining attention to the problem only as it relates to TV reception, the following are recommended: 1) Laboratory simulation tests should be performed with sinc-type modulation pulses to establish threshold modulation levels for a number of commercially available TV receivers, old as well as new. These tests should also explore the dependence (if any) on primary field strength. 2) More extensive field tests should be conducted using the existing windmill at Plum Brook and, if possible, a completely mobile receiving system, to trace the interference zone with particular reference to directions near back and forward scattering from the blades. The effects of blade coning and rotation speed should also be explored. 3) To better understand the modulation produced by a rotating scatterer, theoretical and (small scale) experimental investigations should be initiated. 4) The reduced scattering that would result from blades which are not metallic should also be explored, and attempts made to minimize the scattering by appropriate choice of blade material and/or treatment. 6. Acknowledgements It is a pleasure to acknowledge the assistance of the following members of the Radiation Laboratory who participated in various phases of the study: Professors R.E. Hiatt and E.L. McMahon, Messrs. W. F. Parsons and F.P. Rhine; and Dr. V. V. and Mrs A. Liepa. We are also grateful for the support, moral as well as 14

financial, of the ERDA Wind Energy Projects Office, and the advice and encouragement of Drs. L.V. Divone and D. D. Teague was much appreciated. Mr. J. Glassco of the NASA Lewis Research Center was instrumental in coordinating our field tests, and we acknowledge the assistance provided by Messrs. D. Cooksey and H. Phanner of the Plum Brook Facility. 7. References 1. Putnam, P.C. (1948), Power from the Wind, Van Nostrand Co., New York. 2. Heronemus, W.E.(1972), "Pollution-free Energy from Offshore Winds", 8th Annual Conference and Exposition, Marine Technology Society, Washington, D.C. 3. Puthoff, R. L. and P.J. Sirocky (1974), "Preliminary Design of a 100 kw Wind Turbine Generator", NASA Technical Memorandum X-71585. 4. Thomas, R., R. Puthoff, J. Savino and W. Johnson (1975), "Plans and Status of the NASA-Lewis Research Center Wind Energy Project", NASA Technical Memorandum X-71701. 5. ____ (1975), "A 3-MW Windmill that would blow good", Electronic Design 23(1), p. 68. 6. Berry, L.A., Fortran Program for Calculating Ground Wave Propagation over Spherical Earth, National Bureau of Standards, Boulder, Colorado. 7. (1976), Consumer Report 1976 Buyer Guide, p. 221; Consumers Union, Mount Vernon, New York. 8. Fock, V.A. (1965), Electromagnetic Diffraction and Propagation Problems, Pergamon Press, New York. 9. Wait, J.R. (1964), "Electromagnetic Surface Waves", in Advances in Radio Research, (edited by J.A. Saxon), Vol. 1, pp. 157-217, Academic Press, London. 15

Appendix I SIGNAL ANALYSIS OF TV RECEPTION I. 1. Introduction The present chapter discusses theoretically the general mechanisms by which a windmill may produce undesirable interference effects on television (TV) reception. In the neighborhood of a windmill, a TV receiver would receive the signals scattered by the windmill in addition to the desired direct signals. If sufficiently strong, the former may produce adverse effects on reception. To investigate the problem rigorously, it i> necessary to have a detailed knowledge of the scattering behavior of the windmill and the detection characteristics of a TV receiver. To simplify the analysis, it is assumed that the windmill acts as a time varying multipath source producing both amplitude and phase (or frequency) modulation of the signals at the input of the receiver. In the following sections, we discuss the general effects of such extraneous modulations on the output of the first detector of a TV receiver. The principles of operation of a TV receiver receiving only the direct signals from a desired TV station are well known. Nearby stationary multipath sources like buildings, water-towers, bridges, even static windmills, and other large reflecting objects may cause time delayed signals to reach the receiver. If sufficiently strong, these signals would produce multiple images or so-called "ghosts" on the TV screen, even when the receiving antenna is matched. However, the use of matched directional receiving antenna usually corrects the situation unless the receiver is located in a region of strong multipath sources or such interfering sources lie in the general direction of the desired TV station. For this reason, the present analysis ignores the effects of stationary windmills on TV reception. It is clear from the discussion that the time varying nature of the windmill scattering makes it a potential source capable of producing adverse effects other than "ghosts" on TV reception. 16

2. Basic TV Detection Process In the absence of multipath sources, the composite signal at the input a TV receiver may be represented by: y(t) = [+ fV(t)]cos (wt + 01) +B cos[(w + Ci)t + A(t) + 02] (I. 1) here f (t) is the video information transmitted in the form of amplitude modulation of a carrier of radian frequency w~, OA(t) is the audio information transmitted in the form of frequency modulation of an audio carrier of radian frequency (w +Au); c Au is called the audio subcarrier and normally/A = 4.5 MHz, 2rT B is the amplitude of the audio carrier with respect to that of of the video carrier, usually B < < 1, 1 022 are the phases of the video and audio carriers respectively and are assumed to be constants for the present. The first detector of a TV receiver envelope detects the signal given by q. (I. 1). The output of the first detector consists of the video information f (t) and a V requency-modulated audio subcarried signal which on second detection yields the esired audio information 0A(t). To see this process clearly, let us rewrite Eq. (I. 1) a the following form: y(t) = r(t) cosLW t + + a(t) (1.2) 0 1 1/2 'here r(t) = [A(t)2 + B2 + 2A(t)B cos ( wt + 0A(t) + 02 - 1 ], (1.3) tan Q(t) Bsin (wt + OA(t) + 02 - 1 (I.4) A(t) + B cos (Awt + A(t) + 02 - A(t) = 1 +f (t). (1.5) V 17

From the transmitted TV signal characteristics it is known that B<<A(t) and thus we can approximate Eqs. (I. 3), (I. 4) as follows: r(t) - A(t) + B cos (Atwt + OA(t) + 02 - 01 1 + fv(t)+ B cos Awt + 0A(t)+ 02 - (I.6) (At A(t) sin At + (t) + 02 -=1+ f (t) Sm wt + PA(t) + 02 - 01 (I.7) Under these approximations, the signal at the input of the first detector may be written as: y(t) = [l+f (t) +Bcos(Awt+ A(t)+ 2- ][cos (at+O +a(t (I.8) It is now easy to see that the envelope detection of Eq. (1.8) yields the video signal f (t) and a constant amplitude subcarrier signal frequency modulated by the audio signal 0A(t). A low pass and a band pass filter at the output of the envelope detector separates the video and audio signals and directs them to the appropriate channels of the TV receiver for further processing. The basic first detection system may be shown in the form of a block diagram given by Figure I. 1. Note that the output of the low pass filter is the undistorted video signal, as it should be. In the present case, the phase term (0 2 - 01) in the output signal of the band pass filter is constant. Consequently, the undistorted audio signal would be recovered from it on second detection at a later stage.,VAudio Channel B cosQut + +A(t) + 02 - 1. Video Channel Figure 1.1. Block diagram of the first detection system in a TV receiver. 18

1.3. Artificially Corrupted TV Signal In this section we investigate the outputs of the first detector when the input signal is artificially corrupted. Some of the results of this section may be useful to explain the few observations made during the experiment on the sensitivities of TV receivers to laboratory-injected modulations applied to the input signals. For generality, it is assumed that the video and audio carriers are amplitude and phase modulated by fml(t), 0l(t) and fm2(t), 02(t) respectively. These modulations may be artificially introduced at the input of the receiver in a laboratory environment in which case fml(t) = fm2(t) and 0l(t) = 02(t). In the general case, the corrupt signal at the input of the first detector may be written as: y (t) = [1 + fv(t) + f (t) + B(1 + fm (t)) cos( t + A(t)+ (t) - 01(t))} * cos( Wt + 1(t) + '(t)) (I. 9) where B1 +f(t)) mi (t) 1 + + f (t) sin( wt + OA(t) + 02(t) - 01(t)) * (I. 10) The following observations can be made from a study of Eq. (I. 9): (i) The video channel output consists of fv(t) + fml(t) which implies a possible distortion of the picture signal. The artificially injected phase modulations have no effects on the video output. (ii) The audio channel output is B[1 + fm2(t)]x cos (wt + OA(t) + 02(t) - l0(t)). The audio subcarrier is now also amplitude modulated; the implication of this is that if fm2(t) is sufficiently large it may affect the efficiency of the second detection and thereby affect the audio signal output. If 01(t) = 02(t), the phase modulation will not affect the audio signal output. If 01(t) # 02(t), the audio signal will be distorted as indicated above. 19

yl (iii) In the special case when fm(t) = fm2(t) = 0 and 0l(t) = 2(t) # 0, both the video and audio signal outputs are unaffected by the extraneous phase modulations. The above observations are summarized in the block diagram given in Figure 1.2.. Audio Channel Bandpass Filter B( + f (t) cosAwt (t) yc(t)... Detector + 2 Lowpass Video Channel articial modul tions Filter f (t)+ f (t) fml(t) ) --- 1 [m (t)j 2(t) Figure I. 2. Block diagram of the first detection system for an artificially corrupted signal. I. 4. Multipath Effects In this section we study the first detector outputs when the input signal consists of the direct TV signal and a multipath signal. We need not concern ourselves here about the nature of the multipath sources. It is assumed that the multipath source introduces both amplitude and phase modulations to the signal incident on it and the delayed multipath signal then enters the input of the receiver. Thus, the combined direct and simulated multipath signal at the input of the first detector may be written as: yd(t) = y(t) + ym(t) = A(t) cos c t + B cos() t + Awt + 0A(t)} + [ A'(t) cos (wct + l(t)) + B (t) cos{( t + Awt + A(t) + 2(t)) ] (I. 11) 20

where A(t) = 1 + f(t) V A'(t)= l+f (t)+f (t) B'(t) = [1 + f (t) B 2 9 B may be identified with the amplitude of the scattering coefficient of the multipath source, f (t), f (t) are the equivalent amplitude modulations introduced by the multipath source, 01(t), p2(t) are the equivalent phase modulations introduced by the multipath source; note that 0l(t) and p2(t) may contain static terms to account for the phase delay of the multipath signal, and the other symbols are as explained before. As before Eq.(I. 11) may be rewritten in the following approximate form: Yd(t)r [A(t) + B cos ({wt + OA(t) ] cos(w t + e(t)} + A'(t) + B'(t) cos {Awt + OA(t) + 02(t) - 01(t)} ] * cos act + 01(t) + c2(t)}, (1.13) where B sin {Awt0 (t) tan l(t) A(+) +B cos Awt+ 0A(t)} or aI(t)- A(t) sin tt+A(t (14) B'(t) sin( Awt + A()(t) + 2t) (t)) tan a (t) = A'(t) + B'(t) cos( wt + (t) + (t) (t)) (1.15) A. A + 25) 2 A'(t) sin wtAAt + a( + 2 ( t) - (t)} Finally, we express Eq. (I. 13) in the following form: yd(t) = [F(t) + G(t) cos ((l(t) + 2(t) - a(t)) ] cos (act + l(t) + a3(t), (1.16) 21

where F(t) = A(t) + B cos( wt + A(t)) (1.17) G(t) = [ A'(t)+ B'(t) cos (wt + 0A(t) + 2(t) - (t))] (1.18) G(t) sin (l(t) + 2(t)- al(t)) tan 3 F(t) + G(t) cos 0l(t) + a2(t) - a (t)) (I. 19) r GF(t) s in1(t)0 + 2(t)- al(t 3 F(t) 1 Grouping the video and audio components in the amplitude of Eq. (I. 16) we obtain the input signal in the following form: yd(t) =A(t) + (t) cos (t) + 2(t)- (t))) + (B cos (Att + OA(t)) +3B'(t) cos (0 (t) + a2(t) - al(t) )) cos (Awt + OA(t) + 02(t) - 01(t) )] cos (w t + l(t) + c3(t) ). (1.20) The first detection of the signal given by Eq.(I.20) yields the video and audio channel outputs denoted by fvio fa respectively and are given by: video audio ideo= f (t)+ ( + f(t)+ f (t)) cos 01(t) + 2(t) - al(t)) (.21) audio =B cos (wt + OA(t)) +B (1 + fm2(t)) cos( (t) + (t) - r (t) cos {Awt + OA(t) + 02(t) - 01(t). (1.22) In particular, if f (t) = f (t) = f (t) << f (t) and l(t) = (t) then m m2 m v 1 2 it can be seen from (I. 14 and 15) that r (t) ^- a2(t). Under these conditions it is found that the video and audio channel outputs are: deo= f(t) +( + f(t)+ f ( os 01(t) (1.23) audio 1 +, 1 + fn(t cos l(t)]Cos^Wt + A(t)} (I.24) 22

Aq. (I. 24) indicates that audio channel output is amplitude modulated due to the multi)ath effects. If the amount of this modulation is not strong enough, the audio channel signal on second detection would yield undistorted audio output. However, the video )utput, as given by Eq. (. 23), appears to be affected by both the amplitude and phase nodulations due to the multipath source; the effects of amplitude modulation would be iominant. The block diagram given in Figure I. 3 summarizes the main effects of multipath. Bandpass Audio Channel Filter _ B cos (Awt + 0A(t) Y) (t) Envelope -+ mB + f2 o (t) + a2(t) - (t ect e cosFwt + OA(t) + 02(t)- 01( Lowpa.. ite e Filter multl ath f(t)+ l e(t)sf (t) signal v v m1 cos (1(t) + a2(t) - el(t) Figure I. 3. Block diagram of the first detection system in the presence of multipath interference...5 Discussion The present analysis indicates that the extraneous amplitude modulation of the 3ignals is more serious and is liable to produce distortion in the picture reception. Po the first order, the phase modulation effects may be neglected. Unless the interering signals are very large, the audio reception maybe assumed to be unaffected. rhus it is important to study the nature of amplitude modulation produced by a windmill. 23

Appendix II SIGNAL MODULATION BY A WINDMILL II. 1. Introduction Generally the scattering effect of windmill blades is to produce both amplitude and phase modulation of the incident signal. In Appendix I it has been found that extraneous amplitude modulation is likely to distort video reception. The present Appendix is therefore addressed to the general nature of the amplitude modulation caused by a windmill. Physically it is clear that such modulation is primarily due to the rotation of the windmill blades. The blades rotate at a variable speed, the typical speed being 1 30 rpm (- Hz). If the blade rotation were to produce continuous amplitude modulation 2 only at the rotation frequency, the AGC circuit in the TV receiver might be able to handle such low frequency modulation, in which case there would not be any appreciable video distortion. But if the modulation waveform is discontinuous (like some sort of repetitive pulse waveform), it may contain larger frequencies which could then adversely affect the video reception. It is therefore of considerable interest to ascertain the modulation waveform produced by the windmill. The nature of this waveform and its frequency spectrum depend, in a complicated manner, on the electri magnetic scattering properties of the windmill blades. The geometry of the problem characterizing the scattering of TV signals by windmill blades is a difficult electromagnetic boundary value problem and will be discussed in Appendix III. Here, we shall adopt a simpler approach. We first discuss theoretically the scattering characteristics of some idealized rotating scatterers illuminated by electromagnetic waves. Emphasis is given to the time waveforms and the frequency spectrum of the scattered fields. Secondly, the results of an experimental investigation of the scattered fields produced by a rotating linear scatterer are discussed. From these results some of the characteristics of the modulation wav form produced by the windmill are ascertained. 24

II. 2. Rotating Point Scatterer We start by examining the scattering of a scalar wave by a rotating isotropic point scatterer. Although this is a highly idealized model, the results will have relevance to the windmill problem when the scattering centers are associated with the windmill blades. Consider a transmitter T located on the negative y-axis at y = -y0 and a receiver R located in the x-y plane at (r, 0, 0) with respect to a spherical coordinate system with origin 0 as shown in Figure II. 1. Assume an isotropic point scatterer S located at (1 Qs, 0 ) and rotating in the plane 0 =s at an angular frequeny Q such that = 5 t = 27rf t. s s s (1. 1) It is assumed that both T and R are in the far zones with respect to each oofor and with respect to S. For simplicity it is assumed that the transmitter is ar iotropic source producing a spherically symmetric field. v R(r, ea A,) To - y^ - - - O / ---— y n Figure H. 1. Transmitter and receiver in the presence of a rotating point scatterer. 25

The distalnce 1) between the transmitter and the receiver is given by D = r + +2ry0sin (I. 2) and the other two distances D1 and D2 in Figure II. 1 may be approximated as follows: D1 = TS- y + sin sin, < < ( 3) D2 = SR r - sin 0 cos (0- 0 < < r. (II. 4) The field at the receiver consists of the direct field and the field scattered by S, and can be expressed as E(R) = E + rFe1 - ip s (nI.5) i(ct - D) where E= K D (K is a constant), (I. 6) w is the radian frequency of the video carrier, k = 27r/X is the propagation constant at the carrier frequency, Fe is the scattering coefficient of the scatterer S, and p = sin0 -cos(0 - ). (.7) S S The complete expressions for the amplitude and phase of the received signal may be obtained from (II. 5) and are |E(R)I = |E 1 [+ r + 2r cos(kp sin 0 - 6), (II. 8) -1 sin(ktp sin 0s -6) arg E(R) = arg E + tan 1 ros(p sin -6) (. 9) Assuming 6 =0, < < 1 and using (1. 1) we can write (II. 8) as |E(R) = |E [ + fm(t) (n. 10 26

where the amplitwde modulation introduced by the scatterer is f At) - rcos(kip sin 2 t) (I. 11) Note that if the center of rotation of the scatterer, the transmitter and the receiver are in line, thertf (t) becomes independent of time for all values of 0. It can be m s seen from (II. llcthat as a function of time f (t) varies at a variable angular frequency given by j 0t) = kePIS cos t = kf2s |sin 0s - cos(0 - 0s)I Cos n t. (II. 12) in S s By considering rt average number of oscillations of f (t) in a time equal to the period of the rotation frequency %, it can be shown from (II. 11) that the average frequency of oscillations i.jrf (t) is approximately m v =;k1Ipk2 (II.13) Observe that (I, t3) may also be obtained by taking the average of v (t), given by (II. 12), over a,tlf-period of fS In fact, f (t) contains an infinite number of components whose frequencies are harmonically retated to 2. The characteristics of these components may be underS stood clearly if 3e- express (II. 11) in the following form: 00.t) = rJ0(kep)+2F Z J 2(kp) cos 2n t, (1. 14) n=1 where J is theLBessel function of the first kind and order n. The number of significant n terms for different values of klp can be found from plots of the Bessel functions, from which it is seen that J2 (kep) decreases rapidly for 2n> k |p,. particularly if kA p >>~ 1. Thus, for large)values of kep, the significant frequencies of amplitude modulation are n =2n, n= 1, 2,......, 1 kep, (I. 15) mn s 2 27

whose amplitudes are A = 2 |j J2 (kip), (II. 16) with n varying as before. For large kd p, only a few components at the upper range of n will be significant. From this it follows that the frequency and amplitude of the largest frequency component in the amplitude modulation are approximately _ = ki p = |Isin S - cos(0 - 0) |, (1. 17) A = 2rJ 2n' ) n (II.18) where 2n' I-kI| p is the even integer nearest to kt pi. It is interesting to observe that the largest frequency n given by (H. 17) is exactly equal to the maximum frequency of variation predicted by (I. 12). n may be many times larger than the rotation frequencq of the scatterer if k) is large. For example, if 0 = 0 and 0 = 7r/4, s s where A is the wavelength corresponding to the carrier frequency w. Figure II.2 shows a plot of [1 + f m(t) versus O, as obtained from (II. 10) for 0= = 7r/4, ke = 60 and r = 0.5. This large value of F may be unrealistic and it is assumed here for ease of computation and to enhance the effects. Note that the spacings between the maxima and minima in Figure 11.2 are not uniform, showing that a single frequency cannot be assigned to the oscillations. However, from Figure I.2 av /Qs = 28, whereas f2 /Q2 -27 as predicted by (H. 13). Figure 11. 3 av s av s shows a plot ofk2 (20) versus n which may be considered as the frequency spectrum diagram for the case when klp = 20. Observe that the frequency components are 2nhS and are negligible for n > 10. The edge of the frequency spectrum is approximately at 2n = klp = 20, i.e. at n = 10. Within the frequency band only selected frequencies have significant amplitudes, and in the present case the frequency component for 28

= -7 / _I Figure 11. 2. + I'cos(Mp sin Q t versus 0 = Q. t for ki = 60, I' = 0. 5, 0 = 0 and 0 S S S S i.5 '.O 1.0 "I.. 4-a WI r —4 0.5 - - - - -- -- - - - - L.- -1 - --- I -j ONWANOWA& -. -- - - -- -. -- - I e " I,, 30 60 90 120 I 3i I 30 es = 0st(degrees)

dominant frequency. 25 0. component 0.20 KJ(2n)I -- approximate edge o: frequency spectri 0.15 0.10 0.05 0 5 10 15 n Figure 1. 3. Frequency spectrum diagram for the modulation produced by a rotating point scatterer, kip = 20. f the um 30

n = 9 seems dominant. For future reference the largest frequency of amplitude modulation normalized to the rotating frequency is Tr ( i s2v lsinA - cos( - 0) (1. 20) s s Figure II.4 shows the plots of (II.20) versus i/A for the case = 0 and 0 = 7/4. For Os = the maximum values of the normalized frequencies are obtained when 0 = 0 or s and are ~2' times the values shown in Figure 11.3. For example, if 0 or 7r,.4 x 44.4 = 62.8, and av = 1.4x28.3 40.02 for /AX = 10. s tS s I. 3. Rotating Linear Scatterer We now turn to the scattering of a scalar wave by a rotating linear scatterer. Consider a scatterer consisting of a continuous distribution of point scatterers along a length L, centered on S and aligned along S as in Figure II. 1. The linear scatterer is assumed to rotate in the plane 0 = 0s at the angular frequency (II. 1). After rede5 i8 i6 fining the scattering coefficient per unit length as - e where Fe is now the total scattering scattering coefficient of the scatterer, it can be shown that the scattered field at R for the geometry shown in Figure II. 1 is given by I+ L/2 E(R) e-ikipsin9 E (R) =E re sin 0 e I- L/2 -ikip sin 0 = E Fe e sinc( p sin O ) (II.21) where sinc(x) =, (II.22) 7TX and the other parameters are as before. The total field at R is then E(R) = E + E (R) 0 s = E + e e sinc(- p sin ) O (n. 23) 31

140 120?I 0 s 0 z= 601 10 Figure 11.4. P%72 S av or - si versus t/X for the rotating point scatterer: Os= 0and0 =7T/4. 32

Assuming. = 0 and r<< 1, the amplitude modulation function introduced by a linear scatterer of length L is i (t) -sie p.l sill 12 l) (o.s ( if sill S2 1). (11.2 ) Note that for L O0, (11. 24) reduces to the point scatterer result given in (II. 1 I). For i = L/2, i.e. a linear scatterer extending from i = 0 to I = L, the modulation function is f (t) = rsinc (kLp sin Q2 t). (11.25) For I = 0, i. e. if the scatterer is symmetrically located with respect to the origin 0, the modulation function is f (t) = rsinc( -p sin Q t). (II. 2() m2s (II. 26) may be identified with the modulation produced by a pair of rotating windmill blades. Figure II.5 shows a plot of 1 +f (t) versus s = QSt, with f (t) given by m s s m (n.26), for kL = 0, 0 = = = T/4 and r = 0.5. Notice that 1 + f (t) repeats s m itself for 0 = n7T. This is because f (t) is a periodic function of period T /2 = 7T/ns i.e. its frequency is 2s. To obtain the frequency spectrum of f (t) we assume that s m it may be approximated by the following: kL f (t)~ rPsinc (2 P Qst) (II. 27) and f (t + T /2) = f (t), i.e. f (t) is a periodic function with period T /2. For m s m. m s large values of the argument this approximation should be good. kL The Fourier transform of sinc( -p Q t) is (1. 28) kL s sc(kL t W ) inc( — p 0St = sinc(-p ftse dt-) 33

kL + f (t) Figure 11.5. 1 + rS t- p sin I2 t) versus 0 =!Q t for kL = 60, r = 0.5, 0 = 0 and 0 = /4 + a 2 S S S s 1.5 a 1.0 0.5 0 I I 6I I I1 0 30 60 90 120 130 180 1 80 s = st (degrees) S S

where the gate function G (w) is defined as W1 o<T GT(W) = 0O w > T. (II.29) Using the concepts of the Fourier series expansion of a periodic function we obtain the following expansion of f (t): o^ 'Tr Gin 0t - G (nQ )e f (t) =r (II. 30()) m 27T L.i -00 -oD kL where 20s, 2 = T p Q (II. 31) As p - 0, GT(nnQ 2(n) (1.32) implying -00 f( t)r 2 s 27T( )e deOx= r -OD For convenience we rewrite (II. 30) as follows: f m(t) =r GT(2nIs)ei st. (.33) -Oo Eq. (II.33) indicates that the modulation contains even harmonics of 2 each of con1 kL stant amplitude of, and that the spectrum extends up to 2n-s-p 2. A sketch of the spectral components of f (t) is shown in Figure II. 6. In contrast to the point scatterer case, the results in Figure II. 6 show that all the frequency components within the band are of equal amplitude and theoretically no frequency component kL exists beyond the value -p QS s The modulation frequency spectrum shown in Figure I. 6 is based on the kL is small this maybe a poor approximation even when - is large. 2 35

A 1 kL 2 Pas a."' iplitude '- + 4- l X -o-r-r-s - -d.. s s - S, -Ir, II.-,. 2 iqlIu-l'-: y Figure II. 6. Frequency spectrum of the modulation function produced by a rotating extended scatterer of length L. Under such conditions the modulation function f (t) given by (II. 26) should be examined more carefully. To do this we use the following expansion: kL sin(- -p sin Q t) = 2 2 s 00 J2n + 0 ( 2 p)sin(2n + 1) nSt~, (II. 34) to obtain CD f (t) = 2r m o kL (-p) 2n + 1 2 kL 2P sin ((2n + 1) st) sin ' t s (I. 35) For integral values of n, sin (2n + 1) st) n -sins = 1 + 2 cos 2m t. sin t m= s s m=1 (I. 36) 36

and (II. >:) then gives 2n + i 2 2m 4 + 1 2 f t 2 2) cos 2nQ2 t. (II. 37) t)kL kL s f~ o p n=1 m=n ( — p) 2 2 The amplitudes of the various modulation frequency components are therefore 4J 2 P) 2m+l 2 A = L -, l, 2, 3,.... (11.38) n kL P P k. m=n - 2 P As expected, the calculation of the frequency spectrum from (1I.38) is much more complicated than in the approximate case discussed earlier. However (II. 38) does indicate the existence of a band of frequencies, the highest frequency being determined kL kL by the parameter - p, as before. Figure II. 7 shows m + ( — ) versus 2 2m Y +1 2 m=n kL n for two values of —p. The band-limited nature of the modulation waveform is evident in Figure II. 7. In contrast to the ideal case (Figure II. 6), the amplitudes of the various frequencies within the band now fluctuate about some constant value and the band-edges are less sharp. H. 4. Further Discussion of the Modulation Waveform For the purpose of the present section the modulation function f (t) given m by (I. 26) is rewritten as sin [- -cos 0 sin ts f (t)= r L' (n. 39) m. L2 cos0sin s t where it is assumed that the rotating scatterer is in the xz plane and the receiver is in the xy plane and at an angle 0 from the x-axis. (II. 39) indicates the f (t) is a periodic function of period Ts/2 where Ts( = 2Tr/Qs) is the time period of rotation of the kL scatterer (see Figure II.5). More importantly, for large — cos 0 and small Q f(t) consists of a series of pulses (of s xform) repeating at intervals of Ts/2 n x 37

0).7 0.6 0.5 0.4 k L, T7P 20 \ I,, y Oa L LI J.1 'N VI A 0.3 0.2 0.1 0 4 8 12 n Figure II.7. Spectral distribution curve for the rotating linear scatterer. n = 1 corresponds to the frequency fl = 2f, f is the rotation frequency. 38

k L one of these modulation pulses is sketched in Figure 11.8. For large values of — cos 0 the pulse width may be defined as 2t, (see Figure 11. 8) whe re __ _ 5 1 1.5,X tsin (11.40) 1 27 27t7r (I. C S 4 S S L for cos >> 1, f being the rotation frequency. As discussed earlier the modulaforE s tion function f (t) contains a band of frequencies harmonically related to the rotation frequency. The largest modulation frequency is determined by the parameter - cos 0 and the amplitude of the various frequency components fluctuate about some constant value. The above expression for the modulation function needs to be modified by taking into account the vector nature of electromagnetic waves. Assume that a zpolarized electromagnetic field is incident on the linear scatterer rotating in the xz plane. The current induced on the scatterer is proportional to the component of the incident field parallel to the scatterer. Assuming that the induced current distribu7rTI tion on the scatterer is of the form cos -, it can be shown that the modulation waveform at the z-polarized receiver, located in the x-y plane and at an angle 0 from x-axis is: sin -(cos7 + — f (t) =C (1 + cos 22 t) - L (S 4 L (cos Y + 2L A.X 2L sin — (cos ( 2AL ) ( cos 2L 71L cos os ( os) =C (1 +cos 22 t) TTr (n.41) s 2 22 4 7T 7r L 2 - 2 cos 'y 4 2 where cos Y = cos 0 sin f t. (1n.42) s 39

p 1 a f m a I f (t) =S(at) 37r \1 2a /6> t Figure 1. 8. A single modulation pulse. 40

(f.41) is again a periodic function of period T /2. For sufficiently large cos 0 and small Qs, f (t) will consist of a series of pulses repeating at Ts/2. The general shape of the pulse is as sketched in Figure II. 8 but the width of the pulse will be wider than that given by (II.40). For sufficiently large - cos 0 the width of the pulse may be obtained from: _ 1 - i1 L 2 (H.43) tl 27Tf sin L cos 0 (. S L L valid for - cos >> 1. For small and intermediate values of - cos 0, t can be obtained by numerically computing (I. 41). The general nature of the frequency spectrum of f (t) given by (II. 41) is similar to that in (1. 39) except that the fundamental component of frequency 2f now has much larger amplitude than the others. It can also be seem from (11.41) that as the length of the scatterer is reduced, the modulation waveform changes from repetitive pulse type to a continuous sinusoidal waveform of frequency 2f. I. 5. Experimental Investigation The present section discusses the results of an experimental investigation of the amplitude modulation produced by a rotating linear scatterer illuminated by linearly polarized electromagnetic waves. Figure II. 9(a) is a sketch of the complete experimental arrangement. A rectangular metallic scatterer of length L = 6.32X, widthw = 0. 173A and thickness d = 0.028X at x = 21.4 cm (f = 1.4 GHz) rotates in the xz plane at an angular frequency 2. A transmitting horn illuminates the scatterer s at an angle 0 with z-polarized electromagnetic waves. A similar horn receives the scattered field at an angle (Tr - 0) as shown. The center of the rotating scatterer and the two horns are placed in the xy plane. The two horns are located 12'4" from the center of the scatterer and are displaced 14'4" in the x direction. Figure I. 9(b) gives the block diagram of the receiving arrangement. The received signal is first fed to a spectrum analyzer, the output of which is connected to the vertical input to an oscilloscope where the modulation waveform in the received scattered field is observed. The output of the spectrum analyzer is then fed to a cascade of two band pass filters whose output is in turn connected to an oscilloscope. This arrangement 41

z Linear N' t scatterer \^ jI Receiving horn / / / / / I~ 0 = Q t S S / 0 -O' / / / \ / / 4 Transmitting horn x Figure II. 9(a). Sketch of the experimental set-up. - Figure II. 9(b). Block i::agram of the receiving system. 42

is used to measure the amplitude of the various frequency components of the mlodulation waveform. The desired frequency component is selected by properly adjusting the band width and the center frequency of the two bandpass filters. Figures II. 10(a) and (b) show the observed modulation waveforms for L = \/2 and X when the scatterer is rotating at f = 30. 83 Hz. Note that the repetition period of 16.2 ms in Figure 9(a) is exactly half the time period (32.4 milliseconds) of rotation. For = 0.5 the observed modulation waveform is sinusoidal as predicted by L the theory. For- = 1.0 the lower halves of the waveforms are distorted (Figure II. 10(b)) indicating the existence of harmonics. Figures II. ll(a) - (e) show the observed modulation waveforms for some selected values of- Observe that in case (a) the rotation frequency is f = 6.1 Hz and in all A. s other cases the rotation frequency is 5 Hz. The repetitive pulse-like nature of the modulation waveforms is particularly evident for larger For large values of X X the waveforms resemble the shape sketched in Figure II. 8. The width (2t ) of the modulation pulses (defined as the time interval between the two minima of the mainlobe of the waveform) obtained from Figures II. 10(a) - (e) are shown in Table II. 1. The corresponding pulse widths obtained numerically from (II. 41) are also shown in Table II.1. Considering the approximate nature of the theory the overall agreement between the measured and theoretical results in Table II. 1 is L very satisfactory. The somewhat poorer agreement between the results for - = 6.32 is due to the fact that the receiving and transmitting horns were not located in the far zone of the scatterer in this case. L Measured 2tl Theoretical 2tl X in milliseconds in milliseconds 6.32 50 39 5.32 58 50 4.32 65 62 3.32 70 78 2.32 95 100 Table II. 1. Modulation pulse widths produced by a rotating linear scatterer: 0- 60 degrees. 43

Figure II.lOa. Modulation waveform for L = 0. 5k, 0 = 60 degrees, f = 30. 83 Hz Vertical scale 10 mv/division; Horizontal scale 5 ms/division. Figure II. lob. Modulation waveform for L = X, 0 = 60 degrees, f = 30.83 Hz Vertical scale 10 mv/division; Horizontal scale b ms/division. 44

Figure I. lla. Modulation waveform for L = 6.32X, 0 = 60 degrees, f = 6.1 Hz Vertical scale 50 mv/division; Horizontal scale 20 ms/division. Figure II. lib. Modulation waveform for L = 5.32X,. = 60 degrees, fs = 5 Hz Vertical scale 20 mv/division; Horizontal scale 20 ms/division. 45

Figure II. 1 l. Modulation waveform for L = 4.32X, 0 = 60 degrees, fs = 5 Hz Vertical scale 20 my/division; Horizontal scale 20 ms/division. Figure II.lld. Modulation waveform for L = 3.32X, 0 = 60 degrees, fs = 5 Hz Vertical scale 20 mv/division; Horizontal scale 20 ms/divisioi 46

Figure I.lle. Modulation waveform for L = 2.32X, 0 = 60 degrees, fs = 5 Hz Vertical scale 10 mv/division; Horizontal scale 20 ms/division. 47

As mentioned earlier the modulation waveform was fed to a cascade of bandpass filters to single out the harmonic content of interest. The peak-to-peak amplitudes, in millivolts of the harmonic output from the filters were measured using an L oscilloscope, and Table II.3 lists the results for different-. The maximum peakto-peak amplitude values in millivolts are also shown in Table I1.2. Due to diminished accuracy, results below 0.5 millivolts have not been included. Because of the response characteristics of the filters and the oscilloscope and the low rotation frequency (5 Hz) used, the determination of the amplitudes of the frequency components near the fundamental was quite difficult. The results in Table II. 2 show that the waveform contains a band of frequencies harmonically related to the rotation frequency. There are also certain general trends: L the band becomes wider as - is increased, and the frequency components near the L L fundamental become stronger as - is decreased. For large - there exists a group A. A of higher frequency components which are of approximately equal amplitudes. Qualitatively at least, the measured data are in agreement with the theory. II. 6. Discussion The scattering of electromagnetic waves by a rotating linear scatterer has been studied both theoretically and experimentally. Based on the results discussed in the earlier sections, the following observations are made about the general effects produced by such scatterers. (i) The rotating scatterer produces amplitude modulation of the incident signal. The waveform of the modulation depends L L critically on the parameter -. For A 1/2 the modulation waveform is pure sinusoid having a frequency twice the roL tation frequency of the scatterer. For large - and sufficiently low rotation frequency the modulation waveform becomes pulse-like, repeating at twice the rotation frequency. 48

L 6.32 5.32 4.32 3.32 2.32 V - - 74.0 80.0 100.0 110.0 150.0 PP __. pp 1 41.4 51.7 48.3 113.8 131.0 2 38.5 41.3 37.3 16.0 11.5 3 9.6 13.9 17.4 15.2 8.7 4 6.8 5.5 5.5 7.3 12.7 5 4.8 4.4 4.4 8.9 12.7 6 2.9 2.9 5.4 9.6 9.6 7 2.5 3.6 5.4 7.1 4.6 8 3.2 5.0 5.4 5.4 3.1 9 4.1 4.8 4.5 3.1 1.7 10 5.2 4.1 3.5 2.1 1.1 11 5.0 2.7 2.3 1.3 0.5 12 4.5 2.1 1.5 0.9 ---- 13 3.1 1.2 1.0 0.5 ---- 14 2.2 0.7 0.7 --- --- 15 1.5 0.6 0.6 ---- --- 16 1.2 0.5 0.5 --- --- 17 0.8 ---- ---- --- - 18 0.7 ---- --- --- 19 0.5 --—...... 20.................... Table II.2. Measured frequency spectrum of the modulation waveform produced by a linear rotating scatterer: p - 60~, f = 5 Hz. s Note: Vpp is the maximum peak-to-peak amplitude of the waveform in millivolts. app is the peak-to-peak amplitude of the harmonic in millivolts. n is the harmonic number: n = 1 corresponds to 10 Hz. 49

L (ii) The width of the modulation pulse decreases with increasing- cos 0, L implying that for a given -, the pulse width will decrease with increasing observation angle 0. The theory we have developed is only approximate, but it has been found to be sufficient to obtain an engineering understanding of the scattering of an electromagnetic wave by a rotating object. The simple theory explains, with reasonable accuracy, the behavior of the modulation waveforms produced. It is recommended that further theoretical and experimental work be performed to develop a better quantitative understanding of the problem. II. 7. Windmill Modulation If a pair of windmill blades is replaced by a rotating linear scatterer of equivalent area, the above results can be applied to study the modulation waveform produced by the windmill. On the basis of the rotating linear scatterer model of the windmill blades the following comments can be made about the general nature of the modulation waveform produced by the windmill: (i) The modulation waveform is a series of pulses repeating at intervals Ts/2 where T is the rotation period of the blades. For s s sufficiently large T the frequency spectrum of the waveform will s be a band of discrete frequencies harmonically related to the rotation frequency of the blades. The spectrum will extend from 2L DC to a maximum angular frequency= s A --- cos. Depending L on the parameter - cos 0, the maximum modulation frequency maybe many times larger than the blade rotation frequency. (ii) The width of the modulation pulse becomes smaller at higher frequencies. Thus in the UHF band the modulation waveform will contain a substantial number of high modulation frequencies. It is also expected that at UHF frequencies the scattering from the windmill blades will be large. This would imply that the interference problem is strongest at the UHF channels. 50

(iii) For receivers located in a direction normal to the plane of rotation of the blades the modulation waveform will contain very low frequency components and hence the interference effects will be less severe. For future reference we give in Table II, 3 the widths of the modulation pulses at three selected TV channel frequencies produced by a rotating linear scatterer of length L = 30.48 m (100'). The dimensions and frequencies are those appropriate to the windmill at Plum Brook. The pulse widths have been obtained using (1. 43). The missing values in Table 11.3 are when (II. 43) cannot be used to obtain the modulation pulse widths. It implies that at these points the modulation waveform is almost sinusoidal at a frequency 2f. s TV Fr Wave- Pulse width in Pulse width in TV Wave- milliseconds for milliseconds for Channel quency length f = 1/2 f No. MHz Xinm 0 0 No. MHz in m = 60 0 = 75 0 = 60 0 = 75 43 647 0.46 66.3 38 74 57 111 11 200 1.5 20.3 126 249 189 373 4 70 4.29 7.1 381 --- 571 ---,I....____________ ______________ ______________............. ______ Table II. 3. Modulation pulse widths produced by a linear rotating scatterer of length L = 30.48 m (= 100'). 51

Appendix III PIOPAGATION ANALYSIS III.. Introduction The present Appendix develops the theoretical expressions necessary for computing the TV signals received by a given antenna in the presence of a large windmill. It is assumed that the transmitting antenna is an elementary electric dipole and the receiving antenna is isotropic. The present results can be easily adapted to the case of non-isotropic receiving antennas. In general, the field which reaches the receiving antenna consists of two distinct parts: the primary or direct field of the transmitting antenna in the presence of the earth, and the field originating from the transmitter and scattered by the windmill, also with the earth present. The latter field will be referred to as the scattered or secondary field. It is assumed that the transmitter, the receiver and the windmill are located in the far zones of each other. Theoretical expressions for the primary fields are obtained from the work of Fock [1] and Wait [2 on the propagation of radio waves over a smooth homogeneous spherical earth with arbitrary ground constants. As these results are well-known, we shall merely quote the appropriate expressions without derivation. Since the time varying portions of the windmill scattered fields are of interest, we seek the fields scattered by the windmill blades only. To simplify the electromagnetic scattering problem, each windmill blade is replaced by a narrow rectangular metallic plate of equivalent area. The method of obtaining the scattered fields is as follows. Concepts of physical optics are used to determine the dipole moments induced on the metallic plate by the incident (direct) field. The windmill blades are then replaced by a dipole of equivalent moment, and the secondary field which this produces are found by re-applying Fock theory. 52

A detailed computer program has been dcvelolped by i t.','y L:; to (tetlclrinc the fields of elementary electric dipoles located above a homogeneous spherical earth. In the following sections, expressions for the primary and secondary fields are presented that can be used directly in the computer program developed in 3. The computer program itself is discussed in Appendix IV. III. 2. The Primary Field III. 2.1. General Expressions Ide Consider a current element Idi of dipole moment p = located at T and oriented either along the z-axis or the x-axis (vertical or horizontal) as shown in itot Figure III. 1. It is assumed that the time dependence is e. The origin of the spherical coordinate system (r, 6, 0) is taken to be at the center of the earth of radius a. The electric and magnetic fields at R may be obtained from the following: E = xVx 7 r, (III.1) H = i Vx7T, (III. 2) where E is the permittivity of the medium and g is the Hertz vector produced by the source at the receiving point R. It can be shown [1, 2] that the Hertz vector is given by the following: -* -ikae 1/2 - pe ' ixt 7 /2 = F(t, Y1, y2 q)dt (III. 3) 4-nrca( sin 8)1/2 r2 2 where k = 27' is the propagation constant, F2 consists of the straight line segments from me / to the origin and out along the real axis to oo in the complex t-plane, and the other parameters are defined as follows: F = - wl((-t - Y ) + B(t)w (t - Y ] (III.4) w2(t) - qw2(t) B(t) = -, (III. 5) Lwl(t) qwl(t)

z (transmitting dipole) T a R (receiving point) x Figure III. 1. Coordinate system used for the primary field calculations. 54

Y1 j kh1l'Y y a h2 1/3 6) ( 2 v)(III. ( 6) - a1 /= 3 k1/3& 2. ) 6. fI - 1/r] for vertical polarization r - 1 for hirozontal polarization (III. 7) 7 1.8x10 ca = 1 — f where f is the frequency in KHz, a is the ground conductivity in mho/m and c is the permittivity of the ground relative to that of free space. w (t) and w2(t) are the Airy integral function and the associated Airy integral function respectively defined as follows: 1 r 3 1 w (t) = exp(st - s /3)ds (III. 8) w (t) = exp(st - s /3)ds r 2 where Fr consists of straight line segments in the complex s-plane from ooe73 t the origin and out along the real axis to oo and F2 is as defined before. The expression (. 3) is valid for y2> y (i.e., h1); if y1 > y2 the quantities y1 and y2 in the expression (m. 4) for F are to be interchanged. In Wait's notation [2], (m. 3) may be written as follows: -Pe -ikaa / 4 1/2 -, ixt e e F (q t)dt, (III. 9) 47rca (Tsin e q w I2 55

\Vherc1e 1I )II,) ''( I! (h )ll.(h.),' (, lt). 1... w (t) w (t-y )wl(t- y1) Hl(hl) = wl(t) H2(h2) = 0.5 C(w1(t) - qw1(t))w2 (t - y2) -(w 2 (t) -qw2 (t) - Y2)]. For a z-directed dipole IT = zTr, where Z (111. 10) (in. I 1) and (III. 12) -ika0 1/2 pe Pz v 1Tz 4rrea T nrsin 0 ie'/4 e e r2 xtF (q, t)dt (III. 13) Idi with z= - and q given by the form of (HI. 7) appropriate for vertical polarization. The far zone fields can now be obtained from (III. 1) and (I. 2) and are E - sin (k2r ) C Z (III. 14) HO =/%o where r0 is the intrinsic impedance of free space. Similarly, for an x-directed dipole, 7 = x7r with x -ikaO 1/2 pe x ( v ) -ir/4 -ixt. 7x 47rtea Trsin 0 e F (q, t)dt W (III. 15) ICdl where P = -and q is given by the form of (1. 7) appropriate for horizontal polarization. The far zone fields of interest in this case are [1] 56

2 E - k 7r sin 0 x (111. IG) H - — Tr sin r 1 x fII. 2.2. Check with Berry's Formulation: For computational purposes Berry [3] takes a contour F = - r2 in (III. 9) and writes the Hertz vector in the form - a ( v ) 1/2 -i3/44 -ixt (III. 17) where FI(q, t) = -iF (q, t). With this notation H2(h2) is given by (III. 12) with - i in front of the right hand side. Thus, in Berry's notation the components of the z- and x-directed Hertz vectors are -ikaO ip e 1/2 7rz= -a ( o v ) e-i3r/4 e-iF(q t)dt (1.18) "z 47rca 7rsm 0 x r with q having the appropriate value. The far fields can now be obtained from (III. 14) or (HI.16). Berry's computer program computes the z-component of the field, E, for vertical polarization and the x-component of the field, E, for horizontal polarization, and the transmitting dipole moment is also expressed in terms of the effective radiated power in free space. For a current element IdN (of moment p = IdM/iw) located above a conductive half-space, it can be shown [4] that the total effective power radiated in free space is P - =5k2 (III. 19) f Peff = P where P is expressed in kW, then Idl can be expressed as Id = 5 (III. 20) k ' 57

To compute the fields it is convenient to divide the entire space into regions. The location and extent of these regions depend on the transmitter and receiver positions, the ground constants and the operating frequency, and are chosen so as to permit different approximations to be made to evaluate the integral in (III. 18). Overall there are four regions where four different versions of the potential function obtained from (III. 18) are employed to compute the fields. After making use of (1I. 20), we write below the modified forms of (III. 18) appropriate to the four regions, listed in the order of increasing distance from the transmitter. The radio waves propagate as a surrace wave if both antennas are located near the earth. For short distances between the two antennas it is possible and convenient to assume that the earth is flat, enabling the flat earth approximation to (III. 18) to be made. The geometry of this situation is shown in Figure III. 2. The appropriate expressions for the Hertz vector components are [2] TT 300 WP z = A(z), (III.21) x k 2d where A(z) is the flat earth attenuation function defined as 2 A(z) = 1 - R 5 eZ erfc(z) (III. 22) Transmitter Receiver 2 Figure III. 2. Geometry of the flat earth case. 58

where is the surface impedance of the ground (sec III. 7) R T e7/4 rkD, (III. 123) 0 ) D (d +(h1 - h2) (III. 24) h1 + h2 z eir/4 5+ D (III. 25) 2 00 2 erfc(z) = 2 e dt. (II. 26) 7T z Geometrical optics approximations can be used to simplify (III. 18) if the receiving point is located well above the radio horizon when viewed from the transmitter. The geometry of the problem in this region, called the interference region, is sketched in Figure III.3. The Hertz vector components then have the expression[l, 2] 300VP- e- ik(D- +D d) 7 2 2D I +R e 1 2 ) (III. 27) x k Transmitter Receiver Spherical earth Figure 1I.3. Geometry of the problem in the interference region. 59

where s in.-, (III.28) g sin^,+ o - cos 2/ri for vertical polarization -, (III.29) r - cos A for horizontal polarization fr2 2 2 1/2 D 2a + 2a(h + h) (1- cos 0) + h + h -2h h cos (III. 30) a + 1 2 h 2 h h2os D.=(a sin A +A. - asinA, i = 1, 2, (m.31) 2 A. =2ah. + h2 i = 1, 2, (III.32) (D1 + D)2 + 4 D1D2 sin2 A - D2 = 0. (III. 33) 1 2 12 Observe that (III. 27) assumes the divergence factor to be unity. The next region is known as the transition region where the receiving point is near but not beyond the radio horizon of the transmitting antenna. This is the most difficult region in which to compute the fields since the integral in (III. 18) must now b, evaluated numerically. For this purpose (III. 18) is written in the following modified form: 300 ikaO v 1/2 i37/4 - ixt t)t 47r sin Fe x k a where q is given the value appropriate to the polarization. The shadow region is farthest from the transmitter and corresponds to a receiving point located beyond the radio horizon of the transmitting antenna. The integral in (I. 18) can then be evaluated using its residue series to give 60

300) Tr -ikaO( v 1 - i7/4 'Tr -" e e z 2 a 7Tsin 0 x k \ - ixt. J Hl(h )H (h2) tj_11I (III. 35) where t. are the poles of FI(q, t), J] i.e. the solutions of w, (t) - q wI(t) = o (III. 36) The exact conditions under which the various approximations are employed will be discussed along with the computer program in a later Appendix. After using (III. 14) and (III. 34) the z-component of the E-field in the transition zone produced by a vertically polarized (2-directed) electric dipole is obtained as 1/2 2 300o o - ika0 & v E =kz = -- e z z a \47rsinO/ e - i7r/ -ixtF qst) dt (111. 37) where q corresponds to vertical polarization. Similarly in the horizontal polarization case, the x-component of the E-field in the transition zone produced by a horizontally polarized (x-directed) electric dipole may be obtained using (III. 16) and (III.34) and is 2 300 VP - ikaO / v 2 E = k e x x a 47r sin 0 e- Fi37r14 ( t)dt r (11. 38) - ikaO where q corresponds to horizontal polarization. Apart from the term e, (III. 37) and (m.38) agree with Berry's expressions [3]. III. 3. Field Expressions for the Present Problem III.3.1. Geometry of the Problem A spherical polar coordinate system (r, 0 p) is chosen with its origin 0 located at the center of the spherical earth of radius a and its polar axis z aligned along 61

the windmill tower (see Figure II1.4). The windmill tower height is C'C = p. It is assumed that the windmill blades lie and rotate in the x-z plane. The location of a typical blade area element dS' at B is identified by the coordinates Q, 2 where 2 is measured from the z-axis and i is the distance from the top of the tower to the center of the area element. With this choice of coordinates, the rotation of the windmill blades can be simulated by making the parameter Q2 time varying. The locations of the phase centers of the transmitting and receiving antennas are at T and R respectively. With respect to the basic spherical coordinate system, the coordinates of 13, R and T are respectively (a + h3, 0., 0), (a + h2, 02, ) and (a + h, 1, '[) where h3, h2 and hI are as shown in Figure III. 4. The various great circle distances between these three points, measured along the surface of the earth are represented by: transmitter-to-receiver: d = a0 transmitter-to-windmill blade point: d = aO (III. 39) windmill blade point-to-receiver: d = a023 where 0 12 013 and 023, as shown in Figure III.4, are given by cos 012 = cos 01 cos 02 + sin 0 sin 02 cos (0 - 02 cos 013 = cos 01 cos 03 + sin 01 sin 03 cos 0 (III. 40) cos 023 = cos 02 cos 03 + sin 02 sin 03 cos 2 with sin0 x= sin.Q (i1.41) [a+p) + 0 2 +2(a + p)cos2 /+ The parameter h3 for the area element dS' is obtained from the following relation: h3 =-a + \a + p0) + +2(a+p0) cos 62

dS' = dx'dz' z B R a y Figure III.4. The geometry and the coordinate system used for the windmill, transmitter and receiver located above a spherical earth. 6 3

If T, R and B are within the line-of-sight of each other, the three relevant line-ofsight distances D12 (transmitter-to-receiver), D13 (transmitter-to-windmill blade point) and D2 (receiver-to-windmill blade point) are given by 23 D12 =(a + hi) +(a + h)2 - 2(a + hl)(a + h) cos 0 (l.43) 12 1 2 1 2 12( 2 I9 a + h)2 + [i(p + 2)2 + 2 1 2(p() + a) cos 2 - 2(a - h1)2 [e sill S2 sin 0 ccos ( os S2 I;i)cos 0 (111. 11) D =(a+ h2)2 + [(p +a)2 + 2 + 2(p0 + a) cos n] - 2(a + h2) 2[ sin. sin 02 cos 2 + (i cos n + p + a) cos 02] (II.45) To find the reflected fields it is necessary to know the length of the reflected path and the grazing angle. This is shown in Figure II. 5 for the transmitter and receiver combination where the reflected path length is D1 + D2 and the grazing angle is A. These parameters may be obtained from the following: 2 2 2 D1 22ah1 + hi + a sin A - a sin A (III. 46) 2 2 2 D2 = 2ah2 +h a sin A- a sinA (III. 47) 2 2 D12 =(D1 + D2) - 4D1D2 sin A. (III. 48) For TB and BR combinations the required parameters may be obtained from (HI. 46) - (III.48) by appropriate change of subscripts. III. 3.2. Field Incident at B ^ Idt Assume that an x-directed current element IdL of moment xp x — is loTx w cated at the transmitter point T. The fields produced by the transmitter at the windmill blade point B may be obtained using (I. 16) and (m. 18) and are 64

R 0 Figure 1I. 5. Reflected path and grazing angle for the transmitter-receiver combinations. k2 sin- ikae 1/2 \13 v E (B)= - 47rea iPTxe sin 13 1 T T E( ((. H (B) = (III. 50) r t0 vhere I eC ix13t I4 j FI(q, t)dt, (III.51) r 65

with q specified appropriately for horizontal polarization. In terms of the ct'ective rad(li'tltl I)owe;r P1 (in k\V), (111. 1)) may be written as 1B 300 1Fsin l - i l:tl E (B) --- i( a 47TY Sin / t T T The incident field E (B), H (B) will induce currents on the windmill blade at B which r in turn will produce the scattered or secondary field at the receiving point. The induced current density and hence the induced dipole moment on the blade surface is discussed in the next section. III. 3.3 Induced Dipole Moment on the Blade It is assuime( that the windmill blades are perfectly conducting. The induced surface current density on the windmill blade at the point B can be approximated as I(B) = 2(n x ), (III. 53) where n is the unit outward vector normal to the blade surface at the point B and A H is the incident magnetic field at that point. For the present case n = y and H = E (b)/rl and from (II. 53) we then have 2ET K(B) = () os 03 - z sin 03. (m.54) The current on the surface element dS' induces a dipole of moment PB which may be written as K(B) A A B dS= PBxx + Bz, (111.55) PB = BxiBz where 2E (B) Bx = cos 03 dS, (m. 56) P~x ~r0 2E (B) Bzsin 3 dS'. (I. 57) 66

It can be seen from (III. 55) to (III. 57) that the field of a horizontally polarized transmitter induces both horizontally and vertically polarized dipoles on the windmill blade. This indicates that the scattered field will contain both horizontal and components in general. However, in a practical situation 0 3 0 and hence the contributions due to the vertical dipole are negligible. We shall therefore confine our attention to the horizontally polarized scattered field. mI. 3. 4. Scattered or Secondary Field at the Receiver The horizontally polarized secondary field at the receiver is produced by the x-directed dipole induced in the windmill blade. Using (III. 16), (I. 18) and (III. 56), the secondary field at a receiver R located at (a + h2, 93, 03) is B 2ET (B) sin 02 cos 03 - ika032 v ) 1/2 E (R) 3 dS' e... Xa 47rsin 32 (mI.58) i3 /4 e ix32t e e Fi(q, t) Jr where ka 1/3 X32 =2) 032 V32 (III.59) and the other parameters are as defined before. The total scattered field produced by the windmill blades can be obtained by integrating (III. 58) over the surface area of the equivalent rectangular plate. This integration is difficult to carry out exactly. However, considering the orders of magnitude with respect to the large parameter a of the various parameters identifying the metallic plate, we can make some approximations so that the total scattered field may be estimated with sufficient accuracy without actually carrying out the integration. The incident field being x-polarized, it is expected that the blades will produce strong scattering when they are parallel to the x-axis (i.e., Q = 7r/2 in Figure III. 4.). 67

Under this condition, the maximum scattering will occur in a direction normal to the x-axis, and the maximum value of the total scattered field can be obtained by replacing dS' in (H. 58) by the area A of the metal plates. The directional characteristics of the total scattered field can be approximated from the following considerations. The linear dimensions of the blades are small compared to the radius of the earth. Because of this the horizontally polarized incident electric field induces predominantly x-direcled dipoles on the metallic plate (see Section nI. 3.:). Under the physical optics apl))roxination the total scattere(l field produced by the rectangular plate can be obtained from (II. 58) and is written in the following form: B 2E (B) sin 02 cos 03 E(R) = - 0 dS'1, (I.60) 0 Xa where ika032 v 1/2 f eT D -ix32t I eika 32 ) / 37T/4 3 F(q, t)dt, (III. 61) 2 47T sin 632 sin 1 (in os sin 0c cos 0 sin4L2 (cos 0 + cos 0 n 1 2 21 2 gS' =A -. 1 (sin 01 cos 1 + sin cos 0 2 (cos 0j + cos 02) 1' 2 (III. 62) from the z-axis of a local spherical coordinate system with center at C (Figure III. 4). L1, L2 are the linear dimensions of the rectangular plate in the x- and zdirections respectively, and A = L1 L2 is the physical area of the rectangular plate. Because the radius of the earth is large compared to other parameters involved, it can be seen from (III.39) and (HI.40) that 01, 02 are usually very small. Also, in a practical situation, it is most important to know the scattered field variation in a 68

ine normal to the plane of rotation of the blades (i.e. 0- 0 ' T/2'), and it is then sufficient to use the following expression instead of (III. 62): dS' = A sin 2 (cos 01 + cos 2) 2 — (cos 01 + cos 02)} (III. 60) indicates that the source of the scattered field at the receiver is the T electric field E~ (B) produced by the transmitter at B as given by (III. 52). For computational purposes it is convenient to first obtain the field produced at It by an x-directed electric dipole of known strength located at B and then obtain the desired scattered field from this with the help of an equivalent dipole strength depending on T the incident field E0 (B). Let an x-directed electric dipole with effective radiated power PB (in kW) be located at B. The field produced at R by this dipole is given by: 300 PB E(R)=- sin 1 (II. 64) a 2 2 where 12 is as defined before. From (III. 60) and (III. 64) the equivalent strength of the dipole at B (or the normalizing constant) is B T E (R) 2 dS1' cos 03 E (B) N=. (III.65) E (R) 300 X P~ Its maximum value for a given ET (B) is 2A E T4(B)I 30m0 A- __ (IH. 66) and the maximum value of the scattered field amplitude at R is therefore and the maximum value of the scattered field amplitude at R is therefore 69

2AE (EB) / — E (R) E ((R) (III.67) max 300 X III. 3.5. Direct Field at the Receiver The direct field at the receiver may be obtained by using (III. 1(i), (III. 18) and (mT. 20) and is T 300'. 1/2 ikaO12 -L a sin 47r sin 012 i37r]4 - ix12t ei. e Fi(q, t)dt, (III.68) where 1/3 X12 = ) 012 (III.69) sin 02 cos 2 - sin 01 cos 1 cost = cos 2 (I - sin 0 sin 02 cos(01 - 02) - cos 0 c 2)01 (III. 70) and the other parameters are as defined before. III. 3.6. Total Field at the Receiver The total field at the receiver is obtained by adding (1. 58) and (m. 68) and is T B E E(R) = E ( R) (II. 71) where it has been assumed that Ep (R) now denotes the total scattered field. Observe that the scattered field given by (m. 60) depends on the windmill blade parameter Q through the parameters 03, 032 etc. For a rotating blade f will be a function of time, implying that the scattered field amplitude and phase will also be functions of time. It is therefore expected that the scattered field will be both amplitude and phase modulated by the rotating windmill blades. The modulation characteristics can be found 70

by studying the time behavior of (111. 58) as a function of the parameter Q, and an approximate analysis of the modulation of the total receiver signal was presented in Appendix II. We shall not repeat any of this here, and will merely indicate how the T B amplitude modulation index can be determined from a knowledge of ET (R) and E (R). The windmill scattered signal is modulated by the rotating blades, and assuming that the maximum value of the scattered signal at the receiver is small compared with the direct one, the modulus of the total signal reaching the receiver can be written as |EQ (R t)| = IE5 (R)[ [1 + m(t)] (11. 72) T where E (R) is as before, f (t) is the normalized modulation function of amplitude unity, ind m is the amplitude modulation index: E B(R) B m = (III. 73) TE(R) where E (R) is the maximum scattered field at R. Using (II. 67) the expression for the modulation index becomes 2 300 (B)w B m P E (R), (III. 74) where Ep (R) is the field produced at R by an electric dipole located at B and radiating an effective power PB in kW. III. 4. Discussion The theoretical expressions have been derived which are necessary to obtain the primary and secondary signals received by an isotropic receiving antenna in the 71

presence of a1 windmill. The field expressions include explicitly the directional properties of the transmittinrg antenna and Ihe winm(iill bll(de scatte.rer. The dilreetional characteristics of a receiving antenna can be included by niultiplying each received signal by the appropriate pattern function of the receiving antenna. In the present study we are mainly interested in obtaining the maximum scatterer signal relative to the direct signal at the receiving antenna. For this purpose it is sufficient to ignore the directional characteristics of the transmitting and receiving antennas and the windmill blade scatterer during the initial calculations of the various field quantities. This is justified also by the following practical considerations. Although the transmitted TV signal is horizontally polarized, it is not known a priori exactly what the polarization of the incident signal is in a given situation. Also the vertical plane of rotation of the windmill blades is arbitrarily oriented with respect to the incident field polarization. Under these conditions it is more appropriate to carry out the initial field calculations on the basis of non-directional transmitting and receiving antennas and the maximum of windmills scattered fields. The assumption of isotropy will therefore yield the maximum values of the various field quantities of interest in a given practical situation. III. 5. References 1. Fock, V.A. (1965), Electromagnetic Diffraction and Propagation Problems, Pergamon Press, New York. 2. Wait, J.R. (1964), "Electromagnetic Surface Waves", in Advances in Radio Research, (edited by J.A. Saxon), Vol. 1, pp. 157-217, Academic Press, London. 3. Berry, L.A., Fortran Program for Calculating Ground Wave Propagation over Spherical Earth, National Bureau of Standards, Boulder, Colorado. 4. Stratton, J.A. (1941), Electromagnetic Theory, McGraw-Hill Book Co. Inc., New York, p. 437. 72

COMPUTER PROGRAM In this Appendix we describe the program used to compute the field of a iorizontal (or vertical) electric dipole transmitter when a large windmill is present. rhe transmitter, receiver and windmill are assumed located above a homogeneous smooth spherical earth of arbitrary electrical properties. The program is based on;hat developed by Berry, but with the modification necessary to take account of the Iffects produced by the windmill. The various field expressions derived in Appendix j1 have been implemented in an IBM-compatible FORTRAN program which is capable Af providing the following information: (i) Primary field at the receiver in the absence of the windmill: complex, amplitude and phase. (ii) Incident field at the windmill: complex, amplitude and phase. (iii) Secondary, i.e. windmill-scattered, field at the receiver as a function of the blade position: complex, amplitude and phase. (iv) Total (primary plus secondary) field at the receiver: complex, amplitude and phase. The above information is obtained for any transmitter and receiver heights and ocations, and for a windmill of arbitrary size and location; however, the program isting presented later shows only those parameters of direct interest in the present;tudy. Most of the notations used are explained there, and Appendix III should be "onsulted for any that are not clear. On the Amdahl 470 V/6 computer at The Univer-,ity of Michigan, the C.P.U. time to compute a single field quantity averages 0.1 sec. Plow charts of the entire program are shown in Figures IV. 1 and IV. 2, and a program isting follows. 73

NO NO YES *GRWAVE is a subroutine to compute the ground wave field strength. A flow diagram follows in Figure IV. 2. Figure IV. 1. Flow diagram for windmill program. 74

Enter Compute FTEST if kl(h + h ) |s > 1/10, FTEST -(). otherwise FTEST = max(5., 437/' 3 ). ok r W- - -I p- N - - - NO i / -1 a -1 a \ Distance > a(cos- a+ + cos -? \a+h a+h / NO Use geometric optics formulas and compute sina,, Compute E.?YEuS — t using residue / series equation ( NO Compute E using geometric optics equation, - i,, Figure IV. 2. Flow diagram for subroutine GRWAVE. 75

TABLE OF CONTENTS (Sequential) Page No. ICOM, Cornpex Lunction............................................ 7 GRWAVE, Subroutine......................... 81 DOWN, Subroutine.....................................................88 UP, Subroutine........................................................88 OMCOS, Function......................................................89 ZEXP, Subroutine......................................................89 AIRY, Complex Function................................................ 89 AI, Entry in Module AIRY............................................93 AIP, Entry in Module AIRY...................... 93 WI, Entry in Module AIRY...................... 93 WIP, Entry in Module AIRY............................... 94 WIP, Entry in Module AIRY......................... 94 WIP, Entry in Module AIRY............................... 94 WI2, Entry in Module ARY......................... 94 WI2P, Entry in Module AIRY......................... 94 RGW, Complex Function...................... 97 TW, Subrountine........................... 98 CWAIRY, Subroutine......................... 99 76

rHIS PROGFAM COMPUTES THE PRIMARY AND SECONDARY FIELDS AT A RECEIVIN6 POINT PRODUCED BY A TRANSMITTER AND T I THE PRESENCE OF A LARGE WINDMILL. INPUT DATA CARD 1 1 F C A P1 R( H:H CARD 2 P U p 0:O 0 E L L N: CARD 3 REQ OND PS LFA OWE OEO 1 2 HI 1 FORMAT (5F5. C, 3F10. 5) = FREQUENCY IN MHZ = GROUND CONDUCTIVITY IN MHO/n = GROUND PERMITTIVITY RELATIVE TO FRE2 SPACE = EFFEC IVE EARTH RADIUS FACTOR R = EFFECTIVE RADIATED POWER IN KILDOATTS = WINDMILL TOWER HEIGHT IN METERS = HEIGHT OF THE TRANSMITTER IN METERS = HEIGHT OF THE RECEIVER IN METERS FORMAT (6F5., 2F10.5,I2) I HI2 MEGAI irINC IL A-ST LI = AZIMUTHAL ANGLE OF THE TRANSMIrrER WITH RESPECT TO THE PLANE OF ROTATION 3F THE BLADE = AZIMUTHAL ANGLE OF THE RECEIVER (SEE PHI1 ABOVE) = INITIAL ANGLE OF THE BLADE AREA ELEMENt MEASURED FROM THE Z-AXIS =ANGLE INCREMENT OF OMEGA = FINAL ANGLE OF THE BLADE AREA ELEMENT = DISTANCE IN METERS FROM THE TOP OF THE rOWER TO THE CENTER OF THE BLADE AREA ELEMENT = LONGER DIMENSION OF THE BLADE IN METERS = SHORTER DIMENSION OF THE BLADE IN METERS = GROUND WAVE POLARIZATION = VERTICAL POLARIZATION = HORIZONTAL POLARIZATION RMAT (6F10. 2) 1 2 POL 1 2 FCF D 1I = INITIAL GREAT CIRCLE DISTANCE IN KM BETWEEN TRANSMITTER AND BLADE ELEMENT D1INC = DISTANCE INCREMENT D1F = FINAL GREAT CIRCLE DISTANCE BETWEEN TRANSMITTER AND BLADE ELEMENT D2I = INITIAL GREAT CIRCLE DISTANCE BETWEEN RECEIVER AND 3LADE ELEMENT D2INC = DISTANCE INCREMENT D2F = FINAL GREAT CIRCLE DISTANCE BETWEEN RECEIVER AND BLADE ELEMENT OUTPUT DATA D31 = GREAT CIRCLE DISTANCE BETWEEN TRANSMITTE3 AND WINDAILL BLADE POINT D32 = GREAT CIRCLE DISTANCE BETWEEN WINDMILL BLADE POINT AND RECEIVER D12 = GREAT CIRCLE DISTANCE BETWEEN TRANSMITTER AND RECEIVER 77

C IN TIHE FOLLOW-ING TBBPT&R REPRESENT: C TB = TRANSMITITER~-TO-WINDMILL BLADE POINT BP = WINDMILL BLADE POINT-TO-RECEIVER c TR = TRANSMITTER-TO-RECEIVER C AM'PT[3,AMPBRAMPTR = AMPLITUDES OF FIELDS IN VOLIS/METv&R AT A IC RECEIVING POINT C DBTB,.DBBP,,DBTE = AMIPLITUDES IN DB OF FIELDS AE A RECEIVIN- PC C MTBMYBR,!'!T.P AN INTEGER (1o,2g,30,4) DESI3NAIILNG THE C 1*'ETHOD USEED TO CDmjPJIE THE FIELD: IC 1 =FLAT EARTH C 2 = GEOMIETRIC OPTICS C 3 = NUMERICAL INTEGRATI)lI C 4~ = RESIDUE SERIES C REAL"*PR THiFT.A1,THETA2,COST1,rSINT1,pCOST2 vSINT2,pANGfCOSPl1,COSP2, &SINT3,COST43,COSPI2,SINPl2,PIRADCON1lCON2,COS:-INE, 03lD32,Dl PEAL*8 AC3SB, SINB, RHOOf WAVE#ELr ROOTvAN3O REAL LAMDAL1,L2 INTEGER VEBP COMPLEX EETBrEI3RrETRvSQPBX DATA PI/3.114159265358379/, DS/1.O0/ DATA VEBF/2/ RAD=PI/180. D)C READ (5,1l) FiFQ0,CDJND.,EPS,,ALFAPOW"R,,ROE2,Hl1,H2 50 READ(5,2) PHIlPHI2,rOL~EGAIOM~INCOMLASTpELILlfL2,NPOL READ (5,;3) DlIDlINCoDlFD2ID2INCD2F WRITE (6,,9) 1 FO RMAT (5FP5.0, 3 F 15) 2 FORMNAT (6 F5.0, 2F 10. 5,1I2) 3 FORMAT(biF1O.2) 9 FO RMAT (i HI1) L AMID A3=CC. /F RFQ A=6. 3b7309D6*ALFA WAVE=2.*PI/LAMDA FREQ=1. E3*F FEQ WRITE(6,1O) POWER IF (NPO_.EQ. 1.OR.VEBP.E'rQ.j) WRITE(60,15) FREQ IF (NPOL -EQ. 2) WEITE(6,1l3) FREQ WRITE(b,1l4) EPSfC0NDU1lH2vALFA RHOQ = ROY ( WA VEL 1=WA VE*Ll1/2. WAVEL2= WAVE*L2/2. Dl=DlI CLOOP ON TPANSMITTrR-BLADE DISTANCE STARTS HERE CENDS AT STATEME1NT 1br 80 CONTINUE THEv~TAl-=1.D34'Dl/A CoST1=DCOS (rHETAl1) SINT1=DSIN (TH'ETAl1) D2=D2I 78

ON RE-CEIVER-BLADE DISTANCE STARTS HERE AD AL ST A TE NT 150 CONTIN~uE A'HETA2=1. D3*D 2/A" co0r52 =DCC S (T HET A2) sIN1q-l~.=D SIN (THETA2) ANG=PHI11*RAD COSPI=DCOS (ANG) sIN? =DSIN (ANG) IF (ABS (SIN? 1).LE. 1. E-L4) SINP1=0. ANG=PHI2*RAD COSP2=DCOS (ANG) SINP2e-DSINT (ANG) IF (ABS (SINP2).LE, I.,E-4s) SINP220. ANG= (PHI 1-PHI2) *PFAD COS?12-=DCOS (ANG) SINP1I2=DSIN (ANG) P?=-SQPT (POWdER) *SINPl COSB=(ST.NT1*COSPl-SINT2*COSP2)/(DSQRT(2.iO* (l.D3-SINT1* &SINT2*COSP12 -COSTl*,COST-.2) ) SI 13BDS ~ (1. D'- COSB *COSB) Ppp=-SQFT (PO WER) *S5li PBXCON=-SINP2/ (1 51.0. *LAMDA) C.ON,1=(A+ RHOO) *(A+RHOO) 4.EL*ELi C0N2' 2.D0* (A+RHO,) *EL WIRI T E(6 1 7) D 1,D 2,rEL# RHOO0,PH 1P HI:2, 1L 2 c COMPUTE E FOR TRANSMITTER DIRECT TO RE."EIVER COSI'NE=COSTI *COSIL2+SINT1*SINT2*COSP12 D12=A*DARCOS (COSINE) D3=Dl2/1. D3 CALL GEWAVE (FR-EQCONDEPS,ALFAD3,H1lH2,NPOLENTP) vET-`=F-*PPP*CDEL-XP (DCMPLX (0. DO,-WAVE*D12)) AMPTR =CA BS (E TP) PH ASTR= ATANi2 (AILIAG (ETR),REAL (ETR)) D B S lF 2C.A LOG 1G (AlIPT R) 0't:.iEGA=0MEGAI."'LOOP ON OMEGA START.S HERE - ENDS AT STATEMENT 140 100 mmr=mumi+l ANGO=OME'GA*R AD ROOT=DSQ-RT (CON 1+CON2*DCOS (ANGO)) "COMAPUTE E FOR TrRAiNSMITTEA.R TO BLADE HP=-A+ROOT SINT3=DSIN (ANGO) IF (DABS(SINT3).LE.l.D-4S) SINT3=0.DO SINT3=E~L.*DABS (SI NT3) /RCOT C0ST3=.DSQRT (l.DO-SINT3*SINT3) COSINE=COST3*COST14+SINT3*SINT1*COSP1 D3 1=A*DARCOS (COSI.NE) 79

D1C=D31/1. D3 SINSIN=WAVEL1* (SINT1*COSP1+SINT2*COSP2) COSCOS=WAVEL2* (COST 1+COST2) DS=L1*L2* (SIN (SINSIN)/SINSIN * SIN (COSCDS) /-OS~D3S) COSINE=CO0T3*COST2+SINT3*SINT2*COSP2 D32=A*DARCOS (COSINE) D2C=D32/1.D3 IF (PP.NE.0.) GO TO 104 ETB= (C.,0.) AMPETB=C. DBSETB=1. E-75 MTB=C. GO TO 103 104 CONTINUE CALL GE WAVE (FREQ, COND, EPS, ALFA, D 1C,H1, HP, NPD L, E,!TB3 ETB=E*PP*CDEXP(DCMPLX (O.DO,-WAVE*D31)) AMPETB=CABS (ETB) DBS ETB=20. *ALOG1C (AMPETB) SQPBX=PBXCJN *ET3*COST3*DS 103 CONTINUE C COLPUTE E FOR BLADE TO RECEIVER IF (VEBB.EQ. 1) GO TO 105 IF (AMPETB.EQ.X..OR. PBXCON.EQ.0.) GO TO 106 CALL GRWAVE(FREQ,COND,EPS, ALFA, D2C, HP, H2, LP)L, EBR) EBR= E*SQPBX*CDEXP(DCP1PLX(0.DO,-WAVE*D32)) GO TO 120 CCOM.PUrE VEFTICAL EBF 105 CONTINUE IF (SINT3. N.0..OR.A3PETB.NE.O.) GO TO 113 106 EBR= (0.,C.) AMPBR=0. PHASBR=C. MBR=0 DBSBR=1.E-75 GO TO 130 110 CONTINUE CALL GRWAVE (FREQ,COND,EPS,ALFA,D2C,HP,H2, VEBR,E, 1BR) EBR=-E*ETB*SINT3-DS*CDEXP (DCMPLX (0.DO,-WAVE*D32)) / & (15C0.*LAMDA) 120 CONTINUE AMPBR=CABS (EBR)?HASBPR=ATAN2 (AIMAG (EBR),REAL (EBR)) DBSBR= 20.*ALOG1C (AMPBR) 130 CONTINUE WRITE (6,20) OM.GA,D1C,D2C,D3 WRITE(6,21) AMPETB,DBSETB, TB IF (VEBR.EQ. 1) WRITE (6,23) AMPBR, PHASBRB, DBSBft, BR IF (VEBR.NE. 1) WRITE (6,22) AMPBR,DBSBR,MBR WRITE (6,24) AMPTR, D3STR,MTR DIFFDB=DBSBR-DBSTB ETRBR= 1C.** (DIFFDB/20.) 0OEGA=OMEGA+OMINC 80

(CD.'I G A.E. O rLA S3T) GO0 T0 1~C D 2 2 +D INC iSO F (D,2) A.,ED2F) G) TO ')() Dl1=D1 +DI1INC ibO IF (D1.L1E.D1F) GO TO 30 io FOR SA T( 1O0X,'GPO9U N D W A VE F I ELD S TR FN G TH F D R 'F"R.3, K~W S FF ETIIV E &RADIATED POWER') Fi 0?P~~lA T (lHO0 lX, D 1 =,FS8. 2,r3 X, D2 =,F 8.2,f3 X rL =* 92 f &/12.X,'HOO =',F8.2,5X,'PHI1 =',F5.1,3Xr1PH12 ='4F5.1f &2,LI1 'F 5.01, 3X,'IL 2 =' 5,F.1) 13 FOP AT (17X,'HOR IZO NTAL — PO LAR IZAT"ION, FREQU EN CY =,F9IQ,2, KHZ,) is FRMA (1xIRTCALPOTLARIZAI'ION,FREQLUENCT =1fF9.2r' KHZ, 14 FORMAT (1 4X r tPER ITT I VITY =',F7. 2,', EJAR H ZNDUCTIVITY F'E7. 3 &' MHOS/M,' 1/i25K r 'HEIGHT OF THE T RANSMI TT&R I,F71, 'f1,'/22X, & 6 X,"'HEIGHT OF THE, RECEI VER ='I, F7. 1,'M i /22 K i & ' (EFFECT~IVE RAD)IUS)/(TRUE RADIUS) =, F7. 3//) 20 FO RI-0AT (1 Ht0,3X,'OMEGA =',FB. 1 /14X, I'D31 ', F1O0. 4 & 2Xi 1D32 ='#F1P. 4, 2X,'D1 2 =',rFl10.4) 21 FO3MAT(1H, 3X,'#At'PTB ='E 1 4, 7i5X,'1DBTB ='F9,PS2o,5X,'MIB =',2) 22 FORMAT(lH, 3 Xr'AMPBR ='E4.7,r5X f#DBBR t ',F 2, 5-X, ABP ', I2) 23 FORF l AiT ( 1 I,3X I' AMPB3E ',E114. 7,f5X,' PHASE BZR f ='FS3.3,5Xo, DBBZ.R =,F9. 2 f g 5X, 'IMBZR =1,I2) 24 FORMA T ( 1H I 3X ' AMPTE ='EIl4.7,SX,'IDBTE? -'F8. 2, 5X,'TR ='12) 30 F3RMAT(1H,52-X ' DIFF f FS. 2v5Xr #ETRBR = o, E114,7) GO TO 5C EN D SUBROUTINE GRWAVE(FREQCONDEPS,.ALFA,DMIN,Hr,HRNPOLEMCASE —) C *** CALCULATION OF THE GROUND WAVE OVER A FNTLODZI& C SPHERIZ".AL EARTH. C C ****INPUT C FE.Q = FREQUENCY IN KILOCYCLES/SECOND. C COND = GROUND CONDUCTIVITY IN MHO/METER (SIEMENS/MErER). C EPS = DIELECTRI.C CONSTANT RELATIVE TO FREE SPACE. C ALFA = EFFECTIVE-~ EARTH RADIUS FACTOR. C DMIN = THE- ftINIAUi4 DISTANCE' IN KILOMETERS BETWEEN THE TRANSMITT.ER C AND RECEIVE.R. C H.T = HEiIaHT- OF THE TRANSMITTER IN MET&ERS. C HR = HEIGHT Of THE RECEIVER IN METERS. C N POL = 1,, THE GROUND WAVE FOR VERTICAL POLARIZATION. C NPOL = 2, THE GROUND WAVE FOR HORIZONTAL PJLARIZATIJN. C ******* OUTPUT C E = FIEL.D ST"RENGTH IN VOLTS/METER. C MCASE = THE METHOD USED IN CALCULATING E. C I = FLAT EAPTH C 2= GEOMETRIC OPTICS C 3 = NUMERICAL INTEGRATION C = RESIDUE SERIES 81

CO MMON /W(WI AKlI, VjfYl ~ O~SHIXiT~H ~F~~~MaW CO> PIPL E X E TArD ElTAQFo,UFCZWEECOMtz2,RRRJ-W,?T(96),ro(96),tWl(96 &W2 — (96), DW1 (96) fDW2 (96) fWX (96), WWl (960) r WW2 (9-3). rs,.ZZTZoWYlWY2 2-.OMPLvEX EE~KEAKECKZRZTRSZCCZZO?FAL*8 Al,A2,HT-2,,HR2,,D,,D1,D2,SD2,SD,S,SSQ,AS —Q, S-,SSE,sA,Dr DD~ENSION G-(48),W(L48),M,1(96),NM2(96-),MDl(96),1i~D2(96),f1PT(96) M1R G WD=2 G(l) =~-.9987710V73 G (2) =-.9935301723-4 G (3) =-, 9841 245837 G (4) -~.9705915925 G (5) =-95298770' 3 Ie G (6) M. 9313866907 G(7) =-m9058791367 G (8) =-. 876 572020 3 G(9) =-.6435882616 G (10) =~.M807""662040 G(ll) =.-.7671590325 G (12) =.724'3141 309 IS (13) =-6778723796 G (14)=-.628P673968 G(15) =-.5772247261 G (16) =. 5231609747 G (17) =-.'4669029048 G (18) -~. 4086864820 G(19) =~-.3487558863 G (20) =.,28736214974 G (21) =-22476379C4& G (22) =.1612223561 G (23) =-09700L469 92 G (214) =-M.03238C 17096 G(25) =.C3238017096 G(26) =.C970C469921 Cs(27) =01612223561 G (283) =221476 37934 G (29) =02873624874 G (30) =3487558363 G (3 1) =40 8686L4820 G (32) * 4669C29C48 G,(33) =052316097147 G (34) =.577224726C G (35) =06288673968 G (36) =6778723796 G (37) =7214034130 9 G (38) =07671590325 G (39) =*801706 62040, G (40,)=. 8435882616 G(41) =.876572(0203 G (42) =09C58791367 G (43) =9313866907 G (44) =9529877032 82

( (45)=.G7C5 15925 (46) =.9841 245337 G (47) =.99353C 1723 1(48) =. 998771CGC73 W (1) =.CC3153346J52 W(2) =.CC73275539C1 W(3) =.C1147723458 W (4) = C1557931572 W (5) =.01961616C146 W(6) =. 2357076084 W (7) =.02742650971 W(8) =.03116722783 W (9) =.03 477722256 W(10)=.03824135107 W( 1 1) =.0415 4508294 W (12) =.C 4467 4560 86 ( 1 3) =.04761665849 W (14) =.05035903555 W(15) =.C5289018949 W (16) =.C551995037C W(17) =.C572772921C W(18) =.C5911 48397C W(19) =.C607C443917 W (20) =.062039423 16 W(21)=.C6311419229 W(22) =.C6392423858 W (23) =.6446 6 16444 W (24) =. C6473769681 W(25) =.C 6 473769681 W(26) =,C66446616444 W(27) =.C6392423858 W (28) =.C6311419229 W(29) =.06203942 -16 W(30) = C607: 443917 W(31) =.C591148397C W(32)=. C5727729210 W (33) =.C5519950370 W (34) =. 5289018949 W(35) =.C5035903555 W (3) =. C 4761665849 W(37) =.C4467456086 W (38) =.04154508294 W(39) =C3824135107 W (40) =.C3477722256 W(41) =.03116722783 W (42) =. 0274265n971 W (43) =.02357076084 W (44) =.C 1961616046 W(45) =.,1557931572 W (46) =.01147723458 W(47) =.007327553 90 W (48) =.CC3153346052 83

POWER=1. A=6. 36739F3*ALFA W A VA-=FREQ*. "" 20'9584~ V= (AK1/2. )**C. 33333333 V2=V*V Z. 5/v 2 ZC=2. 5*Z FLF=300. *SQRT (POWE,"R) ETA=CM'PLX (EPS,,-l8. E6*COND/FREQ) DELT.k.A=CSQRT (ETA- 1. ) IF (NPOL.EQ. 2) GO TO 35 D -'JTA =DE L TA/ETA 35 Q=CMiPLX (0.,v-V) *DELTA MMO= MGW =1 TFST=0. IF (HR.GE.HT) GO TO 50,.w= 1 TEM1P=HR HR=HT HTT '=EM P 5O CONTAINUE HTK M= HT/1 0.0 HRKM=HR/1000. YIl=WAVE*HTKM/V Y2=WAVE*HP KM/V IF (HT+HF) 70,f7C, 65 65 B=A+HTKMl R=A+EIRKM TEST = A* (APCOS ( A/P.) + APCOS( A/B)) CONTAINUE FTEST=ArMAX1I(5.,#437./ (FRr&Q**. 38)) IF (WAVEA* (HTKM+EIRKM) *CABS (DELTA).GT..1)Frpsr =o. THETA=D['IN/A X= V*TH.T-A STH= SIN (THETA) COTH =CCS (THETA) /STH E= (G.,rO.) IF (DLI~I.LE, FTEST) GO TO 100 IF(DMIN.GT, TEST) GO TO 400 GO TO 2C0 100 CONTINUE C COMPUTE. GROUND WAVE ASSUMING A FLAT EARTH* C USED FOR SHORT DISTANCES. R=SQRT (DMIN*DMIN*1.E6+ (HT-HR) **2) PO= (. 886227,. 886227) *SQRT (WA VE*R*1.E-3) U=R-*DELT"A* (1.+ (HT+HR)/(DELTA*R) ) 84

CZWU=r (C. 5,~'. 5) *SQR:- (WA VE! (P*1. E- 3) ) *00 V= (1.-RO* DELT A*E CO ol(CZ W) )*FLF/ (1%C'0. *D MIN) GO TO 6CC 200 CNIU c * C3OMPUTE GROUND WAVE WITH GEOMETRICOTIS C USED FOR HIGH ANTENNAS WELL WITHIN THE LINOE-07SIl-iT. HT2=HTKM*HrKM' HR2= H PKY * HR KM A 1 =2. * A *HT"KM +HT 2 A22'. *A*HRKM+HP2 D=DSQRT ( (2.*A*A4+2.*A* (HT.Ktr+HRKM) ) *QtaC5 (THETA) +HT!2+HR2 & -2. *HTKM*HKM*COS (THETA)) IF (HT.NE. 0.) GO TO 210 Dl=O.DO D2=D CISQD (((A+HR KM) *SIN (THEETA) ) /D) **2. SD2= 1. DC-CSQD SD=DSQRTA (502) GO TO 25C 210 CONTINUE KOUNT1l S 1. DC/SQPT ( 1. (DMIIN/ (HfTK.%f*HRKM) )**2) SSQ=S*S ASQ=A*A Dl=DSQRT (ASQ*SSQ+Al) -A*S rD2=DSQR~1 ( ASQ*SS-Q+A2) -A*S S")E= (Dl+D2) **2-t4. DO*Dl*D2*SSQ-D*D SD=S +DSIGN(.1DO,S) SD2=50* SD C*** START INTERATLION TO FIND RAY PATH DISTANCES. 220 Dl=DSQPT ( ASQ*S'D2*Al) -A*SD D2=DSQRT L( kSQ*SD2+A2) -A*SD SSq-F= (Dl +D2) **2-14. DO *D1*D2')*SD2-D*D KOUNT=KCUNT+ 1 IF (KOUNT.GT. 20) GO TO25 SA=SD+ (S-SD) *SSE/ (SSE-SE).S=SD 55Q= S*S SE=SSE SD=SA SD2=SD*SD IF (DABS( SSE).GE..62831 853/WAVE) GO TO 220 CSQD=1. DO-SD 2 250 CONTINUE C*** NEAR THE HORIZON(SMALL SD),r USE NUMERICAL INTESYRATtON. IF (SD.LT. 2./V) GO TO 300 Z2=CSQRT (ETA-CSQD) IF (NPOL.EQ. 1) Z2=Z2/ETI '4R= (SD-Z2) /(SD+Z2) DT=~4.DO*Dl*D2*SD2/ (Dl+D2+D) Er=FLF*CDEXP( DCMPLX(O.DOo,-WAVE*(D-DMiIN)))/(2000.*D)* & (1.+RR*CDEXP (DCMIPLX (ODC,%rWAVE*.DT))) 85

MC AS F= 30 0 CONTINUE C*** C0MPU7E GROUND WAVE, WITH GAUSSIAN NUMERICAL IMIEGRAIION. CAL.L TW (N,Q,TZEv-EKMZEAKMAfECKMZE-CKMZI BOT.'.5*AI~lAG(TZ) YONE=BOT-" XONE=REAL (TZ) TOP = AMIN1( -AM~IN1(6./'X,100.)c,-SQRT(Yl)hS2EIT(f2)) FTX=.5* (TOP- BOT) KK=O SGN1l. DO 310 1=1,2 SGN=-SGN DO 310 K=1lf48 KK=KK+l TX= ((TOP-B3T) *G(K) +TOP+BOT) *,5 0 (KK) =CMPLX (XONE+SGN * (TX-YONE),TX) 313"j CONTINUE DO 365 K1,f96 IF(ABS(REAL(O(K) )-Y2).GT. 5..AND.Yl.GT.q-o..AND. &CABS (O (K) ).G4T. 5.) GO TO 340 CALL CWAIRY(loO(K),Wl1(K),lwl(K),W2 (K) tM2(K)) CALL CWAIRY (2,0 (K),DW1 (K),MD1 (K),DW2 (K),f1D2 (K)) F=2. 71 82 81 8** (MAD1 (K) - M 1 (K)) WX(K)=F*DW1 (K)/W1l(K)-Q 330OCALL CWAIRY (1,0(K) -Y2,WY 1a, MYl, EEK,f~M) MIPT (K) = MY 1- M 1 (K) PT(K)=WYl/WIl(K) /WX(K) IF(Yl.LE.O.) GO TA"O 365 WW2(K)=2,7182818**(MD2(K)-M2(K))*DW2(K) -W2(K)*Q CALL CWAIRY(10,0(K)-Yl,WY1,M~YlWY2,L~Y2) F=2-.7182818** (MY`1+t~2 (K)) FF=2.7182813**(M'Y2+M1 (K)) PT (K) =(C. -. 5) *(FF*WY2*WW1 (K) F*WY1*WW2 (K)) *PI!(K) GO TO 1365 340 MPT( K) = 0 IF(K.GT.L48) GO TO 350 TS=CSQRT (0(K)) Zo=. 66666666 7* 0 (K) *TS ZR=CSQRT (O(K)'-Y2) ZT..=CSQRT (O(K).Y1) ZZ=CSQRT (ZR*ZT) ZR=.666666667*ZR* (0 (K) -Y2) ZT=.666666667*ZT* (0(K) -YI) PT (K)=. 5*CEXP (ZR-ZT) *(1,+CEXP (2e* (ZT-ZO)) & (TS+Q)/(TS-Q))/ZZ GO To 365 86

3 50:S=CSQR' (-D (K) zc=_.66~6b66567*0(K)*TS ZP=CSQET (Y2-O0(K)) ZT=CQPT(Yl-O (K) ZZ=CSQET (ZR*ZT) ZR=. 66666666-0 7*7R* (Y2-0 (K) ZTm=. 6666666'67*ZT* (YI-O (K) PT (K) =. 5*CEX(P ( (C.,- 1. ) * (ZR-ZT) )*(.+CEXP ( (0. -2.) & (ZT-ZO) )*(011. *TS+Q) / (0.11. *TS-+Q) ) ((0. 1. *ZZ) 365 CONTINUE 380 KK=O S GN =1. DO 385 1=1,2 SGN=-SGN: *INTEGRATE FOR THIS DISTANCE DO 385 KLo48 KK=KK+l1 CALL ZEXP(X*AI.MAG(O(KK)),-X*REAL(O(KK)),TX,TY,'~T) F=2. 7182 82** (M.T+ MPTI (KK) ) 38 5 E=E+W "(K) *FT"X*F*CMPLX (T"X,TY) *CMIPLX (1.,SGN) *PT (KK) E=FLF*SQRT (V/(6. 2831853*STH) )/(2000. *A) *E* (.1.,,1.) MCASE =3 GO TO 600 140 0 CONTINUE ' *COMPUTE GROUND WAVE WI"TH THE RESIDUE SERIE.S. E.=RGW (MGW):**RGW IS SUBROUTINE TO COMPUTE GROUND WAVE WITH FOK~-WAIT SERIE"S. -"C A S E = 14 600 CONTINUE IF' (MM.EQ.0) RETURN HT=HR HR=TE"-MP PRjT UR N END COMPLEX FUNCTION EECOM (Z) **ECOM (Z) =EXP (Z**2) *ERFC (Z). ERFC IS THE COMPLEMENTARY ERROR FUNCTI3N. COl1PLEX Z, ZP IF (REAL(Z)) 4,3,3 3 CALL UP (ZEJCOl) RETURN14 CALL UP (-Z,,ZP) ECOM= (2.C,O. 0)*CEXP (Z**2) -ZP RETURN '*'EN D 87

S uB3ROJIINE- DOWN (A,,')P Cr* CP U T'.S E "P (7**E) *EF ()ULGPOWER SER IFS. CGO1PLEX AE,U IF(CABS(A)- 3.5) 2,20,1 I CALL UP (A,LJ) E= 2Ex2K?(A**2) - U REE T P N 2 Z=PEAL (A) ZI=AItIAG (A) C R= 1. 12".8-3`79 16 7 *Z CI=1. 128379167*ZI BI=CI Z21R = Z*Z-ZI*zI Z21 = 2.*Z*ZI E-; m=l1. S 6 PR= Z2fl*CR-Z2I*CT PI = Z2?*CI + Z2I*CR CP = PR/S EL CI=Plf/EM~ BP=BF+CP BI=BI+Cl I F ((C R *C P,+CI *C I)/(B R*B BI*BI)~1.E - 1 q,9,r8 ~3 EfM=EM1+1.C GO TO 6 91 ER=BR EITBI 7'>CMPLX (EREI) R ET UR N END SUBROUTINE UP (AE) C C*** COMIPUTES EXP(Z**2)*ERFC(Z) USING" ASYMPTOTIC S2RIES. C COM"PLEX AEZEjP,z2,GN Z=A IF (CAi3S(Z)- 3.5) 1,1l,2 1 CAL'A DOWN (ZEP) E.=CEXP (Z**2) -H'l R EAT1URP.N 2 Z2=-Z*Z ZB2=CA3S (Z2) GN=(C.564-189580,O.O)/Z EP=GN 5 GN=EN*GN/Z2 EP=ED+GN IF(C'-ABS(GN/EP).-l*OE-005) 7s,7,6 6 EN=r.N+1.0 IF (FN-ZB2) 5,7,7 7 E=rP RAPTURjpN END 88

KN "~Cr7ITON, - DICJS (X) O~2O -3(X) = 1 - COS(X) IS ACCURATE FOR ALL X INC —LUDING X NEAR 1 IF(AiiS( X).13T..15) GO TO 140 IF(X.ET-aQ.C.) GO T10 50 IF X IS SMALL, SUM TAYLORS SERIES FOR 1 -Z-OS (X) S = X*X T=. 3*S JMCOS = T P = 4 10 T=-T*S/ (R* (P-1.) OMCOS=OMCOS + T IF (ABS (T&/OMCOS).LE..5E- 9) GO TO 51 GO TO 10 4L% ONCOS = l.-COS(X) RETURN 5) OMCOS = 0. 51 RE.TURN END SUBROUTAlINE ZEXP(A,D,BXYMAGTUD) *SCAl.'ED EVALUATION OF THE EXPONENTIAL FUN'%'rION IN THE COMPLEX PLANE. INPUT: (A+IB)= THE COMPLEX EXTPONENT. OUTPUT: vXP(A+IB) =(X+IY)*(E**M.AGTUD) MAGTUD=A SCALE= MAGTUD E="E4XP( A-SCALE) X=E*COS( B) Y=E*SIN( B) RETLURN END CO%"ALEX FUNCTA.ION AIRY (ZZ) C*** COMPUTES HUFFORDS NORMALIZATION OF THE AIR FUNCT1)NS. COMNMON/MEX P/ti COM~PLEX ZZZ,ZIAAP~tJZTZAZBZEZRBO,B1l B2, B3 COMPLEX Al, AIP, WIWIlfWIP, WIlP, WI2,WI2P DIMENSION X(2),Xl(2),XT(2) LOGICAL LG(3) EQUIVALENCE (XZ), (XlZl),i (XTZT) DATA Zl/CC),A/(O.35502805389j.,.)f DATA AP/(-0 25881940379,o.)/ DIMiENSION AV( 70) COMPLEX AV 89

DATA AV/ &, (-3.2914517363E-C001, C. 4OGOOC0E+' D), & (-2.678f^'35625E+) IC, 1. 4774589547E+900 ), & ( 3. 5C761C 9')3E-001, C. %COCO O0COE+OOG), & ( 2.4122262158E+CCC, 6.9865124448v3-01), F. ( 3.3635531189E+C 1,-3.4600959696F+00), & ( 3.4449739613E+002,-3.3690890250E+On2), & (-7.026553295DE-C'02, 0.CO000COOOOE+000), & (-5. 481821929GE-C01,-1.92736599E5+05 ), & (-1. 3383395342E+C 1,-1.6022590802E+001), 6 (-2. 2967795901E+?.C2,-3. 2072452637E+001), 5 (-1. 8C478P476E+0C3, 2.1917675036E+0n 3), & (-3.7881429368E-0n1, O. nOCO(0D00CE+Cv),), & (-1.3491836060E+O(C, 8.4969077213E-001), & (-6.0453339320E+000, 1.0623175540E+001), 6 ( 3. 1169621695E+001, 9.8813517650E+0C1), & ( 9.8925349347E+002, 1.39052860(8E+002), f, ( 2.274n742820E-'u01, 0.00000 OOCOOE+003), 6 ( 7.1857403459E-001, 9.7809094170E-001)/ DATA AV(19),AV(26),AV(21),AV(22),AV(23),AV(24) &,AV(25),AV(26),AV (27),AV(28),AV(29),AV(30),AV(31) / & ( 6.0621D88063E+000, 2.7203014866E+000), & ( 3.63C7084828E+u01,-2.r961355813E+00t1), 6 (-6.7139789190E+l001,-3.0904638708E+002), & (-2.8CC 1653691E+303, 4.6649365984E+0C2), 6 ( 5.3556088329E-n01, 0.0000000000E+000), 6 ( 9.2407365385E-001,-1.9106560052E-OP1), & ( 1.8716185961E+0C0,-2.5743310394E+000), & (-7. 218.9436328E+nOC,-1. 29242C 1 90E+0rf1), & (-8. 1787377840E+OC1, 3. 20870138391!++00 1), F& ( 2.9933948552E+002, 5.6922179258E+002), & ( 3. 55028'5389E-001, 0. 0OOOOOCOQ0E+000), & ( 3. 12034381C.4E-001,-3. 8845385098S-0n1), & (-5.2839999360E-OO1,-1.09764 1 1 220E+009) / DATA AV(32),AV(33),AV (34),AV(35),AV(36),AV (37)/ & (-4.2CO9351585E+000, 1.1940151191E+300), & ( 7. 1858832892E+00C, 1.9600912513E+001), & ( 1.C129121011E+002,-7.5951233292E+001),, ( 1.3529241631E-001, 0.OOOO0,000E+00), & ( 3.2618478398E-CO2,-1.7084872785E-001), & (-3. 4215381(05E-001,-8. 9067646330E-002) / DATA AV(38),AV(39),AV(4C),AV(41),AV(42),AV (43), &AV (44),AV (45), AV (46),AV (47),AV (48), AV (49), &AV (50),AV(51),AV (52),AV(53)/ & (-1.4509641493E-001, 1.0328015748E+003), & ( 4.1C01968523E+000,-6.8936911760E-001), & (-1.3030124036E+C01,-1. 6910541453E+001), & ( 3.4924130423E-002, 0.00000OOOOOE+000), & (-8. 4464726625E-003,-4.2045154421E-002), & (-6.9313268963E-002, 3.5364798705E-002), & ( 1.5227622646E-001, 1.2848454470E-001), & 1 1.0681373184E-001,-6.7766153503E-001), 90

& (~-2.6193L432727.E+CCC, 1.5699859905E+lfMD), & ( 6.59,1139357L4E-CC3, C.OCC00OOCOOOE+OCO), g, (-3.94439855OE-OC-3,-6.d8(6O196117E.-003), & (-5. 982013 1079E-003, 1. 17993iC10L49E-C?1)2), & ( 2. 9922t499L4n(6E-'CC2,-5. 977293C737E-'203), & (-7. 7461413O231E-OU2,-5. 22921402759E-0(02), & ( 1. 12765e58396E-OC1,1 3. 5112442L4311,-)C1), & ( 9.5156385121lE-04, 0.C0G000lQO0F>+0f)/) DATLA AV (5L1), AV (55),AV (56),AV (57),AV (5Bq) / & (-8.08L429Q5655E-0G4,-7. 65901 3269CE-C'L4) &, ( 1.6147816(065E-OO04, 1.7661755136E-303), & ( 2.0138718363E-00O3,-.3.1976716632E-10'f3), & (-9. 5n%'8673144&40E-003, 4. 5377832L492v"-OO3) & ( 3.756fl191819E-002, 5.73619168614E-.Or4)/ DATA AV (59),AV (60),AV (61),AV (62),AV (63), AV(614) &'AV(65),AV(66),AV(67),AV(68),AV(69),AV(71)/ & (1.083L4442814E-OOL4, Q.0ooLOOOCOCE+0OO), & (-1.096960,6L480E-.-004,-5.99C2329668E-005), & ( 1.0778191327E"-004, 1.5771596227E-OO0s), & (-6. 89809378893E-flO05,-3. 7626457370OE-(V1)4), & (1.61 66 126 17t4E-'00L4, 9 7457773280E-OO14), & (9.94~769Ls3603E-006, 0.0O0000 00C+00O), & (-1.09568323939E-005,-2,9508799638E-3nl6), & ( 1.L470,9074502E-005s, 8.10142089702E-006), & (-2.L44460151R0E-0O5,-2.063811431O8Ew-005) & ( 7.14921288614GE-007f C.OOOOOOOGOOOE+OOO), ~ (-3q.4619'~68946E-007,-3.6807338399E.,-O08), & ( 1.218396338L4E-006j, 8,3589199402E-O08) / DIM1ENSION APV( 70) COMiPLEX APV DATA APV/ & ( 3. 45.9354~8728E-001, o0.COUOOOO00E+OO0),f & ( 4.1708876594E+')OO, 6.2L414L437707E+0OCY~), & ( 3.2719281855E-001, 0o.OOCOOCC00E+(nO), & ( 1.08287f42735E+00C,-5,49283n~2529E+O00), &, (-2.3363517933E+QC1, —7.,49018481&OE+OC1),f & (-1.C26~4877-579E+OC3,r-5.67C,7940O802E+002),r F& (-7.9(,62857537E-001, O.COG0O~(;onofG'+00EQ), & (-3.8C85833358E+Oco,r 1,512960l5192E+r)O(),I & (-2.6r86379c8IE+00,1,r 3.55L40709915E-Dnl), &l.C761838222E+002, 5.1239914L494E+910 2), &(6. 65977971 97E+003,r 1.8096186253E+003), & (3. 1458376921 E-001,v O.OOOOOOOOOO0E*OfO) & (1. 871 5425L470E+OOO, 2.0544836557E4'OOO) r & (2.2591736932E+001,r 4. 8562995L474E+0OO), & (1.61629978719E+0)2o,-1.4335597185E.+U02), & (-8. 0C471 61665E+002,r-2. 1527454270wi.003), & (6.18259020714E-Oo1e, O.(COOOO0OOE+OOO), &(1.3('1960389OF+0OOO,-1.229077149'544.m+OO)/ DATA APV (19),APV (20),APV (21),APV (22),APV (23,, 91

&AP V(24) p AP V(25),APV (26),AP V(27) A PV (28),APV (29)/ & ( 1. 5f3611 874~5E-QO1j,-l,100O8O92874E4'O01), & (-7.0116800393E'OO10,-4.0L480822759Ev+001) p & (.-4. 83 171 6691)2E+002,r 4.s9692755 71BE+002), & ( 14.BP970655652E4003,r 4. 862729O801F,+003), & (-1.0160567116E-002l O.Of'nO000OO0E+000), & (- 5,482663 6454E-nOO1, -7. 1365288t46 3?.001) & (-4. 67491314088E+OOO,-1.*1924245293E-0O1), & (-l1.0536397828E+00 10, 2.14943711387E+001), & ( 1.o6333770696E*+0029 9.0394910688E*Ofll), & ( 5,64149455285E+C02,-1,42483214426E+003), & (-2.58819410380E-001$ 0.OOOOOODOOOE+000)/ DATA APV(30),APV(31),rAPV(32),APV(33),FAPV(34),pAPV(35),r &APV(36),,APV(37),APV(38),APV(39),APV(140),APV(L41)/ & (-L4.86207541C9E-0O1, 1.5689924913E-0O1), & (-4.73148131897E'-OO1, 1.7093438130E+OtlO), 7,( 703738L40765E+OCO, 3.628182491'3E4+OOD) I & ( 17739586372E+001f-4.O036O422L4O2E+OO1) v & (-2.979151195bE*002g,3.o84U8892977E+0O1) I & (1. 59 1L47144130 E-001, O.O OOOO000E+OOO) 0, & (1,13 40423572E-0O1, 1.f1*97305014925E-011),r & 4 0 12623)9154E'00 1 3.le9222995820S-001),f & (, 13348652430E+%0O0,#-1,4377272421E+0OO), & (-7. 9C22~494720E+00Cq-4.s2063644605E+000), & (-1. 3892752107E+000r 5. 1229L416787E+0O1) v & (-.5. 3C. 90 38 4434 E-C02, 0, OOOOOOOOOOE+000) / DATA APV (42), APV (43),APV (44) tvAPV (45), APV (146) APV (47J, & APV (48),APV (49), APV (50), APV (51)sAPYV(52), APYV(53)/ & (- 1 *683296 5528E-00 3, 6. 8366967 859E-002)4v & ( 1.3789401334E-0Gl,-l.1613804016E-002), & (-1. 471 373 0621 E-00 1, -3.71 51985747E-001), & (1,3C 701964 9512 +OCOf 1.*1 591348425E+OOO), & (, 75045049133E*000, L4*6913115383E'001), & (-i. 1912976706E.-002, C.OOOOOOOOOOE+OOD), & ( 5.11468574932E-003, 1*3660891236E-002), & ( 1.8309710537E-CD)2,-l.8808588497E-002), & (-6.14461593156E-002l,.1.3611794i718E..002), & ( 1.0516239905E-001p 1.9313053560E-O01), & ( 2.0520346212E-O01,-9.1772617372E-001),1 & (-1.95864095C2E-003, 0.00OOOOOOOOOE+000)/ DATA APV (514),APV (55),APV(56),APV (57),APV(58),APV(59)/ & ( 1.'4695649526E-003,r 1.8086384633E-003),p & ( 5,97099'47951E-0040,-3.8332699216E-003)p & (-6. 891089 3004 E-003, 5. 4467425272E-003), & ( 2.6167927738E-002,-8.4092000294E.-004). & (-8,8284474&192E-0O2,,-4,6475312179E-on2) v & (-2.4741389087E-004,, O.OOOOOOO0010E000)/ DATA APV(6~f'),APV(61),rAPV(62),pAPV(63),APV'(6L), &APV(65),APV (66),APV(67),APV(68),APV(69),APV(70)/ & ( 2.37C7837404E-0014, 1.6461109527E-OOL4), & (-1.71465569860E-004,-4.20267839815E-00.4), 92

g(1.C,39451 61 UE-OCL4, 9. 4761844375-O(P4), &(-2. 476c52C0397E-n~O5, C. n'OCOOOQOOOE+OOO) & (2".6 71 4870 932E.-OC 5,r 9. 869 1 565027E- )')6), & (3. 353 9774 178EO 05 2.7 1 132384942~'CC.'-, 5), & ( ~.9 1973L4 3 1 $OE- CG5, 6. 934 90 920 91 E-0QS), & (-2. OC 815 8 9f47E-006, O. nnCOOODOOOEtCQC), &C 2.267124~4519E-61O6, 2.7848508382E-D0,7)0, &(3. 269213 2725E-COr6 -7. 394 3L488682E-007)/ DIIFNSICN ASLT (17) DATA ASLT/ 1. 1407E+0021 1. 15149E4'002, & 1. 1779E~nO2,I 1. 21 2LE+00 2, 1. 261 9E+T'2, 1. 33 19E4I)%2l & 1.43C7E+002, 1.5716E+On)2, 1.7774E+rY)2,-. 2.0884E+I"2, & 2.5832E4'(02f 3.4~29l4E+(dC2, 5.0339E*QC2, B.5678E*3)2, & 1.8336E+C03, 5.7270E+003, 3.5L401E+00L4/ DIMENSION ASV(21) D AT'!A ASV/1. 83357669L42?+O1O, & 1.9293755496E+009,, 2. 1428303701E*008, 2.5198919876E~+OD7, & 3. 1482574 185-&A+006,I 4&.l1524~87519E+OD5, 5. 9q9 251 3580E+014, & 9. 2372nd66015E+C0(.3, 1, 533169L4323E+0O3, 2. 73650808~4E+0OO2, & 5.5622785377E+0OO1, 1. 234s1573335E+Oel, 3.395,1)E00 & 8.7766696967P-)"O1, 2.9159139927E-OO1, 1.16O991)6'404E'-)1, & 5.7614919nL421rE-CO2, 3.7993059132E-Onr2, 3,7133L487657E-002t & 6.9 4444t~4448E-OO2, 1.0OGOCOOOOOOE+0OO/ DIMENSION APSV(21) D AT A A PS V/-1.%8643 93 1 093 EJ+ 0C1 & 1. 9635237894~E+C,09,-2. 1e2934&2O88E+QO8,~-2. 56979383B9E+OD,)7, & -3. 21L4536522CE+OC,6,-L4.28952(4OQ48E+005,-~6.13357%14678E+0O4, & -9. 44635L4825C(E+rCO3,-1. 5763573O37E+O03, -2. 870332371 7E+002., &-5.75C830352L4E+001,-1.2807293083E+OD1)f,-3.2104935853E+OO(), &.-9.2047999257E-CO1,-3.0825376496E-001,-1. 241~5896O5E-O,)l, & -6. 26621635OOE'-002,-4. 246283379L4E-rO2,-4(. 38851,3O868E-002, & -9. 7222222227E-)02, 1.,COOOOOOQOO 0 0E +OOQ/ DTIIENSION NQTT (1 5) j,NQT (8) '7QUIVALENCE (NQTT (8), NQT (1) DAT A NQTT-/1, 3,7, 12, 17,23,29, 35, 4 1,'47, 53, 59, 64, 68, 71/ ANMi(Z)=ABS( PEAL(Z))+ABS( AIMAG(Z)) ENR ''-~Y Al (ZZ) LA=O GO TO' 1 ENTRY AIP(ZZ) LA=O GO TO 2 ENTR Y WI ( ZZ) 93

ENTRY WI 1(ZZ) LA= 1 GO TO 1 ENTRY WIP (ZZ) ENTRY WI 1P (ZZ) LA=1 GO TO 2 ENTRY WI2(ZZ) LA=-l GO TO I ENTRY WI2P(ZZ) LA=GO TO 2 1 LB=0 GO TO 3 2 LB=1 GO TO 3 3 Z=ZZ IF (LA) 5,7,4 4 U=(-O.5,O.866C2540378) GO TO 6 5 U= (-O. 5,-O. 8 66C,2540 378) 6 Z=rJ*Z 7 LC=O IF (X (2)) 8, 9, 10 B LC=1 X(2)=-X(2) GO TO IC 9 X(2)=O. 10 CONTINUE CO** COMPARE WITH PREVIOUS IF (X(1).NE. X1(1).OR, X(2).NE, X1(2)) -23 TO 29 IF (LG(LB+1)) GO TO 400 IF(LB) 2200,21C,220 400 CONTINUE CLc** EXIT IF(LB) 4#2,1401,402 401 ZT=A IF (LC.EQ.1) XT(2)=-XT(2) IF(LA) 404,411,1403 94

C2 1,T=A P I F (LC. Er0Q. 1) XT (2) =X:(2) I F(L A) $C 3,f4 1 1,4L&) 4 LC 3U tJ(1., -1.7 32O050.3C 76) GO TO'' L4 1C ls4 4U =( 1.,1.7 32'50 8 076) GO TO 4~1C uao ZT-=IJ*ZT4 1 1ATrRY=ZT, AI=AIPY AIP-=AIRY WI=AIRY W I 1=A I RY WIP=AIRY WIl1P=AIEY WI2=AIRY WI2P=AIEY RFTURN 20 CONTINUE C*** AFFINE COORDINATES IM=0) Zl=Z LG (1) =. FALSE. LG (2) =.FALSE. LG (3).FALSF. '-rF(X(1).LE.-7..OR.X(1),GT..r7..OR. X(2),GGT.6.9282'W3232) & GO TO 2C0 IP=7.-X (1) IP=7-IP P=IP IQ=0. 86662540378*X (2) +Q* 5* (P-X (1)) Q=I Q N=NQT- (IP) +IQ IF(N.GE.NQT(IP+1)) GO TO 200 100 CONTINUE C** SER.IES XT. (1) =P XT (2) =1. 15470053 8L*Q U=Z~-ZT Bl=AV (N) B3=Bl1*ZT*U ArP.=APV (N) B2=AP*U A=B2*Bl AP=AP+83 A N= 1. DO 110 1=2,3 AN=AN+ 1. B3=E13*U/AN A=B3+A Bn=Bl 95

3 1 = B2 32=B33 B3I= (ZT*IB 1+U*BO) *U/AN A P = B 3 + A P IF (AN.Ni(B2).GTI.O.5E-10*ANM(A).AN~D. & ANM (B3). GT. 0.5E- 1O*ANU! (AP)) 1=0 11e CcN:7INUE LG (1)=0 TIU(JE. LG (2) =.FUE.I GO TO 4C0 2('IO CONTINUE C*i** ASYMPTOTICS ZA=CSQRT (Z) ZB=U. 28209479 177/CSQRT (ZA) ZT-=-O0. 6666666666 7*Z*ZA T=XT.n (1) **2+XT (2) **2 C A LL Z EX P(XT (1 ),X T (2.) pSX S YiM) ZE=CM~PrLX(SX0,SY) ZML=EXP (-FLOAT (M+N)) ZR =l. /Z7 IF(XT(2).GT. no.AND. XT(I).LT, 11.8595) LG(3),TaUEJE DO 201 NT=2,18 IF(T.LT, ASLT(NT-1)) GO TO 202 201l CONTINUE NT=1 9 202 IF (L B) 220, 2 10, 220 2_10 CONTINUE C*** A ZT=ASV (NT-I) DO 211 I=NT,21 211 ZT=ASV(I)+ZTA*ZR A=ZT*ZF IF (,NOT-. IG(3)) GO TO 216 212 ZT=ASV(NT-1) DO 42 13 I= NT f2 1 2 13 ZT=ASV(I)-ZTri*Z? A=A+ (0., ~*ZT/ (ZE) *7Zj 216 A=ZB*A LG (1) A.TtE GO TO 401 220 CONTINUE C*** AP ZT=AkPSV (NT-I) DO 221 I=NT,21 221 ZT=APSV (I) +ZT*ZR AP=-ZT*ZE IF (.NOTr. LG(3) GO TO 226 222 ZT=APSV(NT-1) DO 223 I=NT,21 223 ZT=APSV (I) -ZT*Zii AP=AP+ (0., 1. *ZTr/(ZE) *ZM~ 226 AP=ZA*ZB*AP LG (2) =. TRUE. GO TO 1402 END 9

COMPLEX FUNCTION RGW (MM) C c*** CA-iCtJLATPON O1F THE GROUJND WAVE c IN P UT c DMIN DISTANCE BETWEE-N TRANSMITTER AND RECEIVER IN KM c Hi = HFIGHT OF THE TRANSMITTER IN KM c H2 HEIGHT OF THE RECEIVER IN KM c OUTPUT C RGW= THE GROUND WAVE CALCULATED WITH THE RESIDUE SERIES COMMON /WG/ AKil VQYlY2,COTHSTH,XHlH2,FLFAMR&-WD COM~PLEX T(200),W(200)fGRl2,SDQWlDW1,WYlIWY2,GW,S2 COMPLEX TJY1,rTJY2,DWYI G W=-O. GO TO(6C,125)rMM C*** MM=l MEANS THIS IS A NEW CASE. FIND SOLUTIONS TO MODE EOUATI)N. C*** riM%=2 M4EANS ONLY THE DISTANCE HAS CHANGED& 60 J2=1 C*** LOOP Oh TFRMS OF RESIDUE SERIES. 65 DO 100 J=J2,200 c*** TW FINDS T'HE SOLUTION OF ~"HE MODE EQOUATION C AND GETS AIRY FUNCTIONS. CALL TW( J-1 Q, T(J), Wl, MWl, DWl, MD1, S,MfS,Mb) TJY1=T (J) -Yl TJY2=T (J) -Y2 IF(HI.GT.O)GO' TO 80 lF (H2.GT.O) GO TO 75 W (J) =1. GO TO 85 C*** COMPUTE HEIGHT GAIN FACTORS 75 CALL CWAIRY (1FT (J)-Y2,WY2,,MY2 Sj,4) W (J) = 2.71 828 18** (~1IY2~-r WI) *WY2/Wl GO TO 85 CONTINUE IF (MR-GWD.NE. 1) GO TO 81 C*** COMPUTE DERIVATIVE OF Wl ( 7-Yl) CALL CWAIpY(2,TJY1,rDWYlM`Y1,54M) WY1=-DWY1 GO TO 82 81 CALL CWAIRY(1,T(Jh-YlWYIyl,~LlSM) CONTINUE W (J) =2. 71828 18** (MY1-~tWl) *WYl/Wl IF(H2.LE. 0.) GO TO 85 CALL" CWAIRY (1 T (J) -Y21 WY`2,MY2, StM) S=2. 7182818** (MlY2-MW1) *WY2/Wl w (J) =W (J) *S 85 W (J)= W (J) /(T (J) -Q*Q) C*** W (J) IS THE COEFFICIENT orF THE DISTANCE -FA-.TOR 97

C FOii ~'HE J-ZHLl T"RY1." GW=GW+G IF(J.EQ.1)GO TO 100 IF( CAi3S(G/G"W).GT. 0.0005) GO To 100 Jl=J GO TO 110 100 CONTINUE J 2=2 D00 GO TO 165 110 IF(Jl.LrE.J2)GO TO 165 J2=J1 GO TO 165 C**** SUM THE RESIDUE SERIES FOR THItS DISTAN%3E. 125 00 140 J=1,J2 G=W(J)*CEXP( (C.,o-1.)*X*T(J)) G W =%;W +G IF(J.EQ.1)GO TO 140 IF( CAi3S(G/GW).LT. 0.0005) GO TO 165 14')1 CONT-INUE IF (J2. GE*.200) GO TO 16 5 J2J2+1I GO TO 65 5 RGW=GW*(FLF*3.14'15927 *SQRT(2.*V/(3.1415927#STFI)) & /(2000.*A))*(1o..1.) RETIURN END C SUBROUTINE TW( I, Q, To W1,MW1, DWIMD1, W2,MW2, DW2,MD2) C CT IS THE I-TH ROOTA OF W-SUB-ONE-PRI'LIE - Q*W-SUt3-1 =0* C (W IS THE AIRY FUNCTION.) CTHE FOOTS ARE COUNTrED IN ORDER OF INCREASING MiGNITUDE, C W-SUJB-ONE (T) = EXP (MW1) *W1, W-SUB-ONE-PRIME = EXP (MD1) *DW1,f C W-SUB-'TWO = EXP (MW2) *W2,o ET11C. C DI ME NSIO N TZ E"RO(1 1), TINFI N(1 1) COMPLEX QW1rDW1,W2,DW2r PH, A,T W-SUB-ONE-PRIME (TZERO (1)) =0. DATA TZERO/ 1.018793, 3.2481975p, 4. 8200992, 6. 1633074,r 1 7. 3721773,r 8. 4884868, 9. 53544 90, 10.e52766, 11.o4750570, 12. 3847 88 2 13.262219/ W-SUB-ONE (TINFIN (I)) =0. DATA TINFIN / 2.3380997, 4.0879494, 5.5205598, 6.7867081, 1 7.91441336, 9.0226508, 10.040174, 11.008524, 11.936)16, 12.82877 2 13.691489/ DATA PH /(O.5,r -0*8660254)/O, CON/ 1.17809724/ 98

IF ( REAL (Q) **2.' AIMAG (Q) **2. GT. 1.) GO TO 50 IF(I.GT. 10) GO TO 10 TZ = TZERO(I+l) GO TO 20 10 YS= ((4*I+1)*CON)**2 TZ= YS**0.3333333*(1.-.1L4583331YS) 20 T = TZ*PH C T IS NOW SOLUTION FOR Q =0. T = T+Q/T GO TO 100 53 IP(I.GT. 10) GO TO 60 TZ = TINFIN (1+1) GO TO 70 60 YS= ((4*1I.3) *CON)**2 TZ= YS**0.33333333*(1.+.1)41667/YS) 70 T = TZ*PH C T IS SOLUTION FOR Q=INFINITY. T = T+1./Q 100 K=0 NOW, USE NEWTONS ITERATION TO CONVERGE ON S0LUTIONI. C CWAIRY COMPUTES W(T) AND W PRIME(T) C10I CALL CWAIPY(1,T$,W1,MW1,W2o, MW2) CALL CWAIRY (2,TDW1,I~D1,rDW2,rMD2) A= (2. 718281828** (1MD1-MWl) ) *D~W1/W A = (A-'Q)/( T -A*Q) T = T~-A K=K+l1 IF(K.GT. 15) GO TO 150 IF(CABS(A/T).GT. O.5E-5) GO TO 101 RETURN WRITE(6,155) ITA FORMAT('- FAILED TO CONVERGE ON T(tvI,20)o, T= 1', I (E14,6,rEl4.6), LAST CORRECTION =1, (E1L496,E14.6~) RETURN EN D SUBROUTINE CkoWAIRY(KKsTFlM1,F2,M2) C C CALCULATION OF THE V(T) AIRY FUNCTIONS. C INPUT: C KK=l, W (T) OF KIND 1 AND W (T) OF KIND 2 ARE COMPUTED. C KK=2v THIE DERIVATIVE OF W(T) OF KIND I AND rHE DERIVATIVE C OF W (T) OF KIND 2 ARE COMPUITED. C T = THE COMPLEX ARGUMENT* c OUTPUT: c F1*(E**Ml) = W(T) OF KIND 1 O)R THE DERIVATIVE OF W(T) C OF KIND I AS INDICATED BY KK. C F2*(E**ti2) = W(T) OF KIND 2 OR THE DERIVATIVE OF W(T) c OF KIND 2 AS INDICATED BY KK. NOTE. F1 AND F2 ARE COMPLEX, E2.*718281828..., AND C Ml AND N2 ARE EXPONENTS. 99

COMM'ON/MEXP/M COMPLEX Fl, F2, WI Iv W12, WI I P, W122Pt T GO TQ(lCO,200),KK 100 F2=WI1(T) Mi2=i% F1=WI2 (T) N11 M GO TO 300 202 F2=WIlP(T) M2=M Fl=WI2P CT) Ml=M 300 Fl=1.77245385fn9* (O.f-1.) *Fl F21.o 7724538509* (O.,+1.o) *F2 RETURN END 100

Appendix V LABORATORY SIMULATION STUDIES OF MODULATION EFFECTS V. 1. Introduction In the present Appendix the effects on TV reception of extraneous modulations of the received signals are investigated by laboratory simulation techniques. The primary purpose of the simulation tests was: (i) to observe and characterize the nature of the interference effects produced and (ii) to establish any possible relationships between the onset and amount of distortion produced and the characteristics of the modulation applied. We have seen earlier that the amplitude modulation of the signals caused by rotating windmills is capable of producing adverse effects on reception, and during the simulation tests emphasis was placed on this type of modulation. The simulation studies were carried out early in the program prior to the actual field tests at Plum Brook, and yielded results providing some understanding of the effects of the modulation of received signals on TV reception in a controlled environment. The test results proved useful in the design and optimuzation of the methods used in the later field tests, and they also provided important guidelines as to the effects to look for in the field testing of TV reception in the presence of a windmill. V. 2. Experimental Arrangement Figure V. 1 gives the block diagram of the equipment arrangement used in the measurements. A directive antenna with a gain of about 10 dB over an isotropic radiator was mounted on the roof of a five story building. A rotator enabled it to be directed towards the TV transmitter of interest. Laboratory simulators were designed and built such that the amplitude and phase of the input signals to a TV receiver could be modulated at any of the VHF 101

Phase Modulator. L -- -- Switch 'I Modulator Input Output 2 Switch Sync. Out Figure V. 1. Equipment and arrangement used in simulated modulation studies. 102

-hannel frequencies. An amplifier was included in the amplitude modulator thus making it possible to control the level of the input signal to the receiver. The ampli-:ude modulator applied a continuous sine wave modulation to the incoming signal. The level of amplitude modulation introduced was variable over a 30 dB range at modulation frequencies ranging from zero to one MHz. The phase modulation provided for a ~ 45 degree phase change at low modulation frequencies and up to t 90 iegrees at higher modulation frequencies. The phase changes over the above ranges could be made slowly or at rates up to several hundred KHz. The pulse generator provided unidirectional repetitive pulse modulation of the received signals. The modulation pulse width and repetition frequencies were variable. Aside from these, the components used were standard and are identified in the block diagram in Figure V. 1. Most of the data were obtained using a 1976 Zenith TV receiver. A few tests were also made using a 1974 Magnavox TV receiver. V. 3. Presentation of Results With the phase modulator in the position shown in Figure V. 1, there appeared to be no significant effect as the phase was varied. Hence no data will be presented on the effects of simulated phase modulation. However, it is recommended that further studies be made using a type of phase modulation which would more closely simulate that caused by the rotating windmill. The results obtained in the amplitude modulation tests are given in a series of tables. For a given TV receiver, tests were performed to determine the received picture quality as the modulation index was increased from zero to a value which resulted in severe distortion. To determine the modulation index, we used the change in amplitude of the level of the audio signal. This is ordinarily constant since the audio information is transmitted with frequency modulation. For sine wave amplitude modulation the modulation index m is obtained from the observed change in the audio signal level using the relation -1 dB - 1 m = - (V. 1) dB + 1 103

where dB1 = 10 (V.2) L is the observed change in the audio carrier signal level expressed in dB. The pulse modulation produces positive pulses only and in this case the modulation index is obtained from m = 0l o\ 20 1, (V.3) where L is as defined before. Data were obtained at several TV channel frequencies and as a function of the level of the input signal power, the modulation index and the frequency of modulation. The method of obtaining the data was as follows. The given TV receiver was tuned to the TV channel frequency of interest and the spectrum analyzer, with its resolution set at 300 KHz, was tuned to the audio carrier frequency of the same channel. To determine the modulation index, the output level of the spectrum analyzer was noted, first with zero modulation and then with the audio oscillator (or the pulse modulator) set at the desired level. The resulting chance L in dB of the audio carrier signal level is used to compute the modulation index. The received picture quality was then studied as a function of A. The audio reception was not appreciably effected by the modulations. The amplitude modulation interferes with the video reception in the form of horizontal dark bars moving vertically through the picture on the TV screen. When the modulation frequency approaches a multiple of the TV vertical sweep frequency, a zero beat is observed, i. e. the bars become stationery. The observed TV pictures are rated qualitatively as follows: A unimpared video. D intolerable black bars and B onset of faint black bars. vertical mirage effects. E pulsating snow caused by signal excursions into the noise level; unacceptable. 104

Tables V. 1 and V. 2 show the observed picture quality for sine wave modulation as a function of the input signal power level, the modulation index and frequency for a Zenith TV receiver tuned to Channels 2 and 13 frequencies. The corresponding data for the Magnavox TV receiver are presented in Tables V. 3 and V. 4. In both sets of data it is seen that the modulation frequency at which picture distortion begins to occur tends to become lower as the modulation index increases. One would expect that video distortion would occur more readily with a decrease in the level of the input TV signal but this is not indicated by the data. Tables V. 5 through V. 9 show the threshold of modulation defined to be the modulation index required to produce minimum observable video distortion (Case B) as a function of the input signal level and the modulation frequency. The first three tables are for the Zenith TV receiver and the last two are for the Magnavox. There is a fairly consistent trend in these results showing an earlier incidence of video distortion as the modulation frequency increases, but there is no consistent variation with the level of the input power. Table V. 6 gives results for very low modulation frequencies. This case is of interest in that is shows that the TV receiver is vulnerable to modulation frequencies much lower than had been expected. No significant difference was noted in the performance of the Zenith and the Magnavox receivers. All of the data shown so far has been for sine wave modulation. Table V. 10 shows results obtained with pulse modulation of received signals. The modulation pulses were unidirectional rectangular pulses of width T repeating at tini intervals T. Compared to the sine wave modulation data, the present results indicate that video distortion occurs at a much lower level of modulation. The threshold modulation is found to be independent of the signal level. As discussed earlier the windmill does produce a pulse-like modulation of the incident signals. Although the modulation pulses produced by a rotating windmill are approximately siax/x shape, it is expected that their effect on video reception would be similar to that found here. V. 4. A Mechanical Simulator Since there was no opportunity early in the program to do any field testing using the actual windmill at Plum Brook, a low -cost substitute was developed to 105

Level of m m m m audio carrier i dB over 0 0.058 0.112 0.226 in dB over.. milliwatt Frequency of Modulation (Hz) and Picture Quality -35 A 460 B 190 B 120 B 8000 C 600 C 360 C 600 D -40 A 400 B 150 B 100 B 2000 C 550 C 300 C 430 D -45 A 210 B 170 B 50 B 1500 C 540 C 300 C 450 D -50 A 200 B 120 B 85 B 1300 C 300 C 300 C 400 D -55 onset of snow 210 B 170 B 115 B 1200 C 400 C 170 C 380 D -60 snow 400 B 185 B 145 B 1000 C 420 C 250 C 360 D -65 very snowy 330 B 260 B 190 B 800 C 490 C 300 C 600 D Table V.1. Channel 2 picture quality with sine wave modulation at indicated modulation frequency in Hz. Video carrier frequency = 55.25 MHz, audio carrier frequency = 59.75 MHz. Test receiver is Zenith model 17GC45. 106

audio carrier Level of mB m m m vi indBover 0 0.058 0.112 0.226 0. 330 milliwatt | Frequency of Modulation (Hz) and Picture Quality -50 A 340 B 160 B 120 B 60 B >10K C 350 C 180 C 140 C 1100 D 420 D 290 D -60 A 187 B 162 B 92 B 47 B 420 C 350 C 130 C 74 C 4500 D 1180 D 360 D 235 D -65 onset of snow Table V. 2. Channel 13 picture quality with sine wave modulation at indicated modulation frequency in Hz. Video carrier frequency = 211.25 MHz, audio carrier frequency = 215.75 MHz. Test receiver is Zenith model 17GC45. 107

Level of m m m m m audio carrier udio carrier 0 0.058 0.112 0.226 0.330 in dB over......... milliwatt Frequency of Modulation (Hz) and Picture Quality -35 A 300 B 183 B 60 B 40 B 2000 C 600 C 290 C 200 C 1100 D 450 D 260 D -40 A 185 B 160 B 110 B 66 B 1000 C 350 C 365 C 170 C 680 D 380 D 294 D -50 A 420 B 190 B 165 B 103 B 550 C 600 C 290 C 232 C 730 D 380 D 253 D -60 onset of 250 B 185 B 170 B 110 B snow 600 C 420 C 310 C 175 C ______635 D 395 D 305 D -70 snow 180 B 120 B 120 B 490 C 300 C 250 C ___650 D 375 D 310 D Table V.3. Channel 2 picture quality with sine wave modulation at indicated modulation frequency in Hz. Video carrier frequency = 55.25 MHz, audio carrier frequency = 59.75 MHz. Test receiver is Magnavox model CD4220. 108

Level of m m m m m audio carrier 0 0.058 0.112 0.226 0.330 milliwatt Modulation of Frequency (Hz) and Picture Quality -40 A 240 B 120 B 115 B 70 B 775 C 350 C 250 C 240 C 1100 D 500 D 300 D -50 A 270 B 195 B 186 B 168 B 1100 C 550 C 350 C 240 C 920 D 440 D 340 D -60 A 190 B 170 B 125 B 111 B 410 C 280 C 250 C 190 C 650 D 260 D 200 D -70 onset of 165 B 120 B 120 B snow 425 C 165 C 165 C 600 D 300 D 275 D Table V.4. Channel 13 picture quality with sine wave modulation at indicated modulation frequency in Hz. Video carrier frequency = 211.25 MHz, audio carrier frequency = 215.75 MHz. Test receiver is Magnavox model CD4220. 109

Level of Frequency of modulation (Hz) audio carrier in dB over 30 50 100 200 milliwatt In m m im -35 0.82 0.60 0.24.- I I --. I I ii I IIi l 2 -40 0.60 0.52 0.20 -45 0.56 0.24 0.20 - -50 0.45 0.23 0.14 - -55 onset of snow 0.48 0.24 0.17 -60 snow 0.52 0.43 0.27 -65 very snowy 0.59 0.52 0.48,.... — Table V. 5. Modulation index required to produce minimum observable video distortion at Channel 2. Video carrier frequency = 55.25 MHz, audio carrier frequency = 59.75 MHz. Test receiver is Zenith model 17GC45. 110

Level of Frequency of Modulation (Hz) audio carrier indBover m 1.5 1.0 2.0 4.0 8.0 16.0 20.0 25.0 30.0 35.0 50.0 64.0 milliwatt 0 m m m m m m m m m m m m -30 A 0.82 0.75 0.82 0.75 0.59 -35 A 0.71 0.85 0.59 0.78 0.63 -40 A 0.80 0.70 0.48 0.48 0.48 -45 A 0.56 0.48 0.36 0.33 0.28 -50 A 0.80 0.68 0.50 0.58 0.43 -55 A 0.70 0.67 0.67 0.73 0.94 0.78 0.48 0.48 0.37 0.33 0.23 0.33 -60 C 0.60 0.52 0.45 0.43 0.37 -65 C 0.33 0.28 0.23 0.23 0.52 0.48 0.75 0.67 0.61 0.56 0.48 0.38 -70 D 0.89 0.75 0.73 0.70 0.56 Table V.6. Modulation index required to produce minimum observable video distortion at Channel 7. Video carrier frequency = 175.25 MHz, audio carrier frequency = 179.75 MHz. Test receiver used is Zenith model 17GC45.

Level of Frequency of Modulation (Hz) audio carrier 10 50 100 200 in dB over__ ____ milliwatt m m m -45 0.60 0.52 0.23 -50 0.63 0.52 0.24 -55 0.17 0.17 0.16 -60 0.20 0.20 0.11 -65 0.52 0.33 0.17 Table V.7. Modulation index required to produce minimum observable video distortion at Channel 13. Video carrier frequency = 211.25 MHz, audio carrier frequency = 215.75 MHz, Test receiver is Zenith model 17GC45. Level of Frequency of Modulation (Hz) audio carrier in dB over m = 0 50 100 200 milliwatt m m m r -35 A 0.23 0.14 0.14 -40 A 0.52 0.43 0.17 -45 A 0.67 0.59 0.23 -50 A 0.71 0.56 0.23 -55 A 0.87 0.59 0.28 -60 onset of snow 0.75 0.56 0.25 -65 snow 0.73 0.52 0.30 -70 snow 0.69 0.52 0.38 -75 snow 0.52 0.43 0.23 Table V. 8. Modulation index required to produce minimum observable video distortion, with sine wave modulation at Channel 2. Video carrier frequency = 55.75 MHz, audio carrier frequency = 59.25 MHz. Test receiver is Magnavox model CD4220. 112

Level of Frequenc of Modulation audio carrier 00 50 100 200 in dB over m = 0 ________ milliwatt mm rm -40 A 0.43 0.38 0.17 -45 A 0.59 0.52 0.17 -50 A 0.78 0.48 0.23 -55 A 0.87 0.48 0.11 -60 A 0.84 0.48 0.23 -65 A 0.63 0.48 0.17 -70 onset of snow 0.67 0.43 0.14 -75 snow 0.48 0.33 0.23 Table V. 9. Modulation index required to produce minimum observable video distortion with sine wave modulation at Channel 13. Video carrier frequecy = 211.25 MHz audio carrier frequency = 215.75 MHz. Test receiver is Magnavox model CD4220. Level of T= 20 msec =30 msec T = 40 msec T = 60 msec udio carrier = 1 sec T = 1.5 sec T = 2 sec T = 3 sec in dB over____.._______ milliwatt m m m m -30 0.14 0.15 0.18 0.16 -40 0.14 0.15 0.18 0.16 -50 0.14 0.15 0.18 0.16 -60 0.14 0.15 0.18 0.16 -70 0.14 0.15 0.18 0.16 -80 0.14 0.15 0.18 0.16 Table V. 10. Modulation index required to produce minimum observable video distortion with pulse modulation at Channel 7. Video carrier frequency = 175.25 MHz, audio carrier frequency = 179.75 MHz. Test receiver used is Zenith model 17GC45. 113

provide a mechanical simulation of at least some of the effects of a windmill on TV performance. The device consisted of a 58.5 cm diameter grid of horizontal metal rods whose spacing was close enough to produce almost complete reflection at VHF and UHF frequencies. The grid could be rotated about a vertical axis at any chosen rate up to about 1500 rpm, the limit being set by excessive vibration. The rotating mechanism was 6 feet high and rested on a 6 foot high platform so that the center of the rotating vane was at the level of the axis of the TV antenna. A photograph of the arrangement is shown in Figure V. 2. It was recognized that the rotating grid,was far from an exact simulator of a large windmill, but it did have the ability to modulate the amplitude and phase of the signal received by the TV antenna at rates which were comparable to those that a windmill would provide. With the grid rotating, no effects were observed on the VHF channels regardless of the position of the grid relative to the antenna. This is not too surprising since the entire grid is electrically small at these frequencies. However, very pronounced effects were seen on the UHF channels. These occurred when the rotating vane was about five feet in front of the end of the antenna with the antenna pointing about 30 degrees away from the direction of the transmitter. As the vane rotated through 180 degrees, the quality of the picture varied from good to completely unacceptable. This behavior was observed with rotation rates which varied from 5 Hz or so up to the highest rates achievable (approximately 25 Hz). There are, of course, two cycles of change for each revolution of the vane, and when the (net) received signals were examinedona spectrum analyzer and associated oscilloscope, it appeared that the modulation index was about 50 percent. No effects were observed when the vane was moved back to 25 feet from the front of the antenna. It was possible to receive Channel 24 on the back lobe of the antenna, and when the vane was placed in the forward beam of the antenna, there was again a pronounced effect on the TV picture. In yet another arrangement, the antenna was pointed directly at the transmitter, and then the rotating vane had no effect even when placed only five feet in front. 114

,AO * i,.x t lee > 1*-, - i 'g ''. -'=: Z Figure V.2. Rotatable reflector in front of TV antenna. 115

In all of these tests video distortion occurred only when the major portion of the TV signal was being received indirectly via reflection off the rotating vane. A similar effect was later observed with the windmill at Plum Brook in the field tests, and when it became possible to make field tests, we ceased any further study of the mechanical simulator. V. 5. Discussion The laboratory simulations demonstrated conclusively that extraneous amplitude modulation of received signals can produce video distortion of TV reception, but no audio distortion was observed with any of the types of modulation used. The level of the observed video distortion depends on the amount and nature of the modulation introduced. Both sinusoidal and pulse modulations appear to produce similar types of video distortion, but the modulation index required for the threshold of distortion is much lower in the latter case. Also, the distortion produced by pulse modulation appears independent of the signal strength, implying that a TV receiver is more vulnerable to pulse modulation. This tends to be true for sine wave modulations also. Based on these results, the nature of the observed video distortion has been characterized and classified subjectively. In addition, the pulse modulation data served to specify the choice of modulation index for the threshold of distortion to TV reception in the presence of rotating windmill. 116

Appendix VI FIELD TESTS VI. 1. Introduction Field tests associated with the NASA-ERDA 100 kW wind turbine located at the NASA Lewis Plum Brook facility were carried out during the period May to October 1976. The initial tests were made before the laboratory simulations and theoretical calculations were complete and were exploratory in nature. Later tests were aimed at obtaining scattering and operational data, but because of the very intermittent wind conditions throughout the summer, the turbine was in operation for only a few of the tests. In the following sections we give a brief description of the windmill with particular reference to those features which are important to the field tests. We then indicate the test set-up and procedures used and follow this with a discussion of the three types, i. e., exploratory, scattering and operational, of tests performed. The final section summarizes the results obtained. VI. 2. The Wind Turbine The windmill has been described in detail in several NASA documents and a sketch of the turbine and tower is shown in Figure VI. 1. Of particular importance to our tests are the yawing motion of the turbine, the blade pitch adjustment and the blade rotation. There are two modes of operation for controlling the yaw, i.e., the azimuthal rotation of turbine nacelle and blades. In the manual mode the turbine can be rotated clockwise or counter-clockwise at a uniform rate of 0.167 revolutions per minute, and this mode was used for all of our scattering measurements. Alternatively there is the auto mode in which the pointing direction is controlled via a servo system. The angular difference between the direction of the nacelle and the wind direction obtained from a sensor on top of the nacelle is used to generate an error signal which activates 117

37.5 M (125 FT) WIND - 30M (100 FT) Figure VI. 1. 100-kilowatt experimental wind turbine generator. 118

the yaw drive mechanism to align the nacelle with the wind. A calibrated voltage readout indicates the actual pointing direction at any time. The auto mode was used in all other tests. With both modes of operation a braking system is available to stop the nacelle in any desired (azimuthal) direction. Manual and auto modes also exist for controlling the pitch angle of the blades from that for zero power to that for maximum power. In the scattering measurements the blades were manually set for maximum power to provide the largest surface for specular reflection of the incident field. The auto mode is based on a servo control system in which the error signal is proportional to the difference between the actual and a pre-set (variable from 0 to 40 rpm) blade rotation speed. The actual blade pitch angle can be obtained from a calibrated voltage readout. The wind velocity must be at least 6 mph to obtain blade rotation, and the maximum allowable rotation rate is 40 rpm. However, for mechanical reasons, all of our exploratory and operational tests were made with the blades rotating at no more than 20 rpm. A voltage pulse is generated whenever a blade passes through 360 degrees (the zero being when the blade is vertical) and this pulse is available for recording. For the scattering measurements the blades were locked in position parallel to the ground using the blade braking system. VI. 3. Test Procedures The basic set-up for carrying out the field tests is shown in Figure VI. 2. where we have indicated only those instruments which are pertinent to the data gathering. The sources of the RF energy were the television transmitters located in Cleveland (Channels 3 and 43) and Toledo (Channels 13 and 24). With any given station some of the energy was reflected off the turbine blades and this, together with the 'direct' signal, was picked up by the field site antenna and fed simultaneously to a TV monitor and a spectrum analyzer. The audio portion of the signal was taken from the analyzer and recorded on paper tape for later evaluation. The video signal was detected by the TV receiver and fed to a video tape recorder whenever the data was felt worth preserving. At both the field site and the wind turbine control center the WWV time 119

Wind turbine WWV antenna TV transmitting antenna.____ __. Fr- -- eoef - TV Re Ote fiel dsite TV transmitter o / receiving I I / / antenna | wWV / TV | Videol antenna - tape monitor x i antennarecorder Spectral analyzer I Paper _tape I V ecorder receiver a) I` I~ Figure VI. 2. Test equipment set up.

code was also received and recorded to permit a subsequent correlation of the field data with the turbine state, i.e., azimuth, blade position, etc. Additional procedures peculiar to a given type of test will be described in conjunction with those tests. VI. 4. Exploratory Tests These were conducted at the Plum Brook facility on May 12 and 26, 1976. Being the first tests performed, and carried out ahead of any predictions obtained from the theoretical analyses, the objective was to see if the rotating turbine blades provided any detectable TV interference, and if they did, to examine the nature of the interference. On the first trip the blades were rotating at approximately 20 rpm and the receiving antenna was positioned only 200 feet from the turbine. This close distance was chosen to maximize the possibility of interference, and when the (directional) antenna was pointed towards the turbine (thereby discriminating against the direct signal), reception on all four TV channels showed periodic interference. The output from the spectrum analyzer indicated that the interference was in the form of a narrow pulse occurring whenever the blades passed through the horizontal. On the second trip the site chosen was approximately 0.25 miles from the turbine. With the antenna pointed towards the turbine, interference was again observed when viewing Channel 43 (Cleveland) and the type of interference was similar to that on the previous trip. These tests clearly showed that the turbine could interfere with TV reception. We therefore planned a series of further tests whose prime purpose was to study the manner in which the interference depended on the azimuthal orientation of the wind turbine with respect to the locations of the receiving antenna and the TV transmitter. In effect, these were concerned with the scattering of the RF energy off the blades of the turbine. 121

VI. 5. Scattering Tests Scattering tests wore carried out on June 15, July 30(), September 1 and October 26, 1976, with the turbine blades locked in a horizontal position. Prior to making the tests, 7 sites were identified and physically checked out at the Plum Brook facility. These are shown in Figure VI. 3 and care was taken to ensure that the turbine was visible from each. Six of the sites, numbers 3 through 8, are roughly on a circle of radius 0.5 miles centered on the turbine. Subsequently, two further sites were identified and given numbers 10 and 12 (there is no site 11). Site 10 is approximately 1 mile from the turbine and close to NASA Plum Brook sewage disposal area. It was selected because of its proximity to houses. Sites 12 and 14 are about 0.25 miles from the turbine and are approximately on the radials for sites 6 and 5 respectively. As a result of the theoretical analyses it had now become evident that the UHF channels would be most susceptible to interference. All of the scattering measurements were therefore made using the available UHF Channels 24 and 43 from Toledo and Cleveland respectively. The test procedure used was as follows: (i) Select one of the identified test sites. (ii) Connect the equipment as shown in Figure VI. 2. (iii) Lock the turbine blades horizontal with their pitch set for maximum power. (iv) Position the TV antenna to receive Channel 24. (v) Tune the TV receiver and the spectrum analyzer to this station. (vi) Rotate the turbine nacelle in azimuth. (vii) Record the WWV time code at the test site. (viii) Record the spectrum analyzer signal. (ix) At the turbine control center, record the WWV time code and the nacelle pointing direction. (x) Reposition the receiving antenna to point towards the turbine. 122

Site 1 6o Site 5 Site 4 3 0303 Site 14 330 2950 feet / Site 6 8~.2~ Site 3 108.5O Site 7 Figure VI.3. Wind turbine test sites.

(xi) Repeat steps (vi) through (ix). (xii) Position the TV antenna to receive Channel 43. (xiii) Repeat steps (v) through (xi). VI. 5. 1. Scattering Test Results Scattering test results were obtained at a number of selected sites using TV Channel 24 (video carrier frequency = 531.25 MHz) whose transmitter is located at Toledo as the source of RF signals. Figure VI. 4 shows the wind turbine control center strip chart recordings obtained during the site 6 measurements. The top recording gives the turbine nacelle pointing direction as a function of time for a selected interval. The turbine was rotating clockwise in the horizontal plane, and the 0 degree and 180 degree marks refer to the north and south directions respectively. The lower recording shows the WWV time code signals received during the same period. A reduction of the WWV signals [1] indicated that each division in the horizontal scale corresponds to 1 sec. The TV Channel 24 signals scattered by the wind turbine blades were received at field site 6. The receiving antenna was located 10 feet above the ground with its beam directed towards the turbine. The WWV time code signals and the received TV signals at the spectrum analyzer, observed during the same period of time as in Figure VI. 4, are shown in Figure VI. 5. The pair of sine wave-like shapes in the spectrum analyzer output are the signals scattered by the blades. Each sine wave may be identified with a turbine blade, and two sine waves appear because the blades are canted at an angle 0 of approximately 3 degrees relative to the normal to the nacelle axis (Figure VI. 1). As seen from Figure VI. 5 the two sine waves are separated by approximately 12 degrees and centered 6 degrees on either side of the nacelle axis direction. On the basis of specular reflection by the blades, the reflected ray direction for each blade would be displaced by an angle 20 from the nacelle axis in the same direction as the canting of the blade. Thus, the reflected rays from the two blades would be separated by 20 - 12 degrees, as shown in Figure VI. 5. The magnitude of the specularly reflected signal received at site 6 is compared with the theoretical values in Appendix VII, with satisfactory agreement. 124

WWV Time Code Wind Turbine Pointing Direction 1 sec. 31 1 - 00 (North) 180~ (South) 360~ Figure VI.4. Wind turbine control center strip chart recordings during site 6 measurements. 125

I L I I I I L I - + 5 dB -5 d -5dB 1 sec. Figure VI. 5. 0 ~f 12 *4 WWV time code and scattered Channel 24 signals observed at site 6.

Similar results obtained at site 5 are shown in Figures VI..6 and VE.T. Although the amplitude variations of the scattered signals are smaller than i: Figure VI. 5, we remark that at site 5 the scattered signal had to traverse a wedi to reach the receiving antenna, and the greater attenuation may be due to this. VI. 6. Operational Tests and Results VI. 6.1. Test Procedures Operational tests were conducted on October 29 and November 2, 1976 to observe and record any video distortion of TV reception caused by the rotatige blades of the turbine. The observed results were recorded on both video and paper tapes. The test procedure used was as follows: (i) Select one of the identified test sites. (ii) Connect the equipment as shown in Figure VI. 2. (iii) Position the TV antenna to receive Channel 24. (iv) Tune the TV receiver and spectrum analyzer to Channel 24. (v) Lock the turbine blades horizontal to the ground and point the turbine nacelle to 0 degrees azimuth. (vi) Make a 3-minute video tape. (vii) Allow the turbine blades to rotate. (viii) Make a 3-minute video tape. (ix) Record the WWV time code at the test site. (x) Record the spectrum analyzer signal at the test site. (xi) At the turbine control center, record the WWV time code, the nacelle pointing direction and the blade position mark. (xii) Reposition the receiving antenna to point towards the turbine. (xiii) Repeat steps (v) through (xi). (xiv) Position the TV antenna to receive Channel 43. (xv) Repeat steps (iii) through (xiii). A typical measured horizontal plane pattern of the receiving antenna used at the field test sites is shown in Figure VI. 8. Observe that the back lobe maximum of the pattern is about 15 dB down from the main lobe maximum. 127

WWV Time Windmill Pointing Direction 360~;0~ (South) 0~ (North) Ai Figure VI. 6. Wind turbine control center strip chart recordings during site 5 measurements. 128

1 sec. -^ 1 I I 1L I I I I. I I I. I I I I I I: I I I I T 0 Hd r -- - 11.5 sec. — Figure VI. 7. WWV time code and scattered Channel 24 signals observed at site 5. 129

10l 130 Figure VI. 8. TV receiving antenna pattern (600 MHz). 130

VI. 6.2. Operational Test Results Tests were carried out at sites 6, 12 and 14 (see Figure VI. 3). TV Channels 24 and 43 transmitting stations were both used as signal sources, but no video distortion was observed on Channel 24 at any of the test sites. Also, at sites 6 and 12, no video distortion was observed on Channel 43, but this was attributed to the fact that for the specific orientation of the turbine during the tests, the site and/or antenna were not positioned so as to receive signals specularly reflected from the blades. However, at site 14,Channel 43 signals specularly reflected by the rotating blades of the turbine were received with sufficient strength to produce video distortion, and we discuss below only the results obtained at this site using Channel 43. In the tests at site 14, the main beam of the receiving antenna was directed towards the Channel 43 transmitter. The locations of the site, wind turbine and TV transmitter were then such (Figure VI. 3) that signals specularly reflected off the blades were received on the back lobe of the antenna. Figure VI. 9 gives the wind turbine control center strip chart recordings obtained during the test. The top recording shows the turbine nacelle pointing direction as a function of time for a selected interval of time, and the middle recording gives the blade rotation as a function of time over the same period. The rotation period of the blades is 3 sec. The lowest recording in Figure VI. 9 is the WWV time code signal from which the time axis is determined. Note that each division in the horizontal axis represents 1 sec. Figure VI. 10 shows the strip chart recordings of the WWV time code and Channel 43 signals received in the presence of the rotating windmill blades. Each division of the horizontal scale represents 250 msec, and the pulse-like modulation of the total received signal produced by the blades is clearly evident in the lower recording in Figure VI. I0. The modulation pulses repeat every 1.5 sec (rotation period was 3 sec) and the widths of the individual pulses are approximately 75 msec. Video distortion was found to occur in synchronism with these pulses and the received pictures were recorded on video tape. No audio distortion was heard. In contrast to the scattering test data (Figure VI. 5) the signals received during the operational tests (Figure VI. 10) were modulated by single sine wave-like pulses. 131

Windmill Pointing Direction 00 (Nortn 1800 (soutb 3600 Blade Rotation -A 360~ X: -- 3WWV Time 3 sec. I- T - Figure VI. 9. Wind turbine control center strip chart recordings during the operational test at site 14. 132

I I I I I I I I I I I I I I I -— r- I I I I q I i i - -4 --- 4- i i 1 -4 — 17 -T — -f — T- - I i I I I I I I i i i i i I i t i i i i i t i i I i i i i i i i i i i i i i i i i i i - -17:: - - - I i i i -— t - i i i i i t i 1 -4- f -41 i i i i IV I I I I i A"' 1 4 -- i 1 1 1 1 1 ~-Iz f — 1 — i i i i i I-H — i t A& i i i i i i i i i -., - a i i i i i i i i 77Z — AILF —7 U El - i J- h - U~- h h klmI I lu U - I I I W — 11 -— T ----T I I -W I I V I 1 — 4 — 1 1 — Ii I 14f27z U I 1 1 1 1 1 1 I I i i i i i i i i i i i i i i i i i i i It 7K i f —i f i i I i i i + — i i i h I _-Oaiii I 4 I i i i i i i i KP i i i i - - -1377iiVti m llr P-4 a) 9 Cd 0 4j Cd P-4 Cd 0 blo.P4 cn 'IO (1) (2) O (1) P4 I I I I I i i I I I I I I -- --- I- L- I - - -t- — j- ---- I l t I1. I I I '4 -LI4 I + -1 I -I Li-::E::L-II - I I - -i —i Lb, ki. I I I f a i i i i i it A...1.. - --...a N H i i - . - h. AAS&k*M. r -1r-d -A I I I I - I I a MA LA 61 I L lrpp -t -JH iin - — F I — -E I I --- -- - I ---- LIIII I I I I I I —.L 7 '4-1 - i i i i i i f I i i i i f i f I - w I I I I~ I I 1 " ' i i i i i ---- - _r- --- I — I, -- 1 —i I I I I, I I I - --- --- -. — I I — -- - i - -- - --- T- - - F —. 250 ms Figure VI. 1 0. WWV time code and received Channel 43 signals durin operational tests at site 14. 133

During the tests it was also observed that the video distortion occurred when the turbine blades were approximately vertical. This was the first time that any distortion had been seen when the blades were vertical. Although the incident fields are horizontally polarized, the large blades (dimensions -60 x 3 feet; wavelength x. 1.5 feet for Channel 43 signals) will act as specular reflectors regardless of their orientation. When the blades are vertical, the upper and lower ones will reflect the incident field in directions approximately 6 degrees above and below the local horizon. The angle between the local horizon and the line joining the phase center of the receiving antenna to the center of the vertically oriented upper blade is approximately o tan1 R j where H1 is the height above the ground of the center of the vertically oriented blade; H2 is the height above ground of the phase center of the receiving antenna, and R is the distance between the wind turbine and the antenna. In the present case with H! 140 feet, H2 c 10 feet and R- 1, 350 feet, o< 5.5 degrees. The antenna at site 14 could therefore receive signals scattered by a vertically oriented upper blade, but not those from a lower blade since they would propagate in a direction 6 degrees above the local horizon and would miss the antenna. This explains the occurrence of single modulation pulses in the received signals. VI.7. Discussion The field test results showed that the rotating blades of a wind turbine introduce pulse-like amplitude modulations to TV signals received in the vicinity of the turbine. The modulation pulses repeat at half the rotation period of the blades. Significant effects occurred at UHF frequencies and at a distance of approximately 0.25 miles from the turbine in spite of the 15 dB reduction in the scattered signal produced by the polar diagram of the receiving antenna. Severe video distortion was observed on Channel 43 and recorded, but no audio distortion was found. VI. 8. Reference 1. Howe, Sandra L., Editor, "NBS Time and Frequency Dissemination Service", NBS Publications 432, U.S. Dept. of Commerce, NBS, Boulder, Colorado, January 1976. 134

Appendix VII ANALYSIS OF RESULTS VII. 1. Introduction In this Appendix we first examine typical results obtained by numerical computation of the theoretical expressions of Appendix III and compare them with the relevant field test data of Appendix VI. If a windmill is illuminated by such a field, energy will be scattered off the blades, and because of the rotation of the blades, the net field picked up by a TV receiver in the vicinity of the windmill will be amplitude modulated. A method is described for deducing the modulation function and index from the computed field strength data. If the modulation is sufficiently strong, it will produce video distortion, and for any given TV Channel there is a region around the windmill where distortion can occur. This will be referred to as the windmill interference zone and an approximate theoretical method is described for computing its dimensions. VII.2. Field Strength Variation In Appendix III expressions were presented for the far zone field of an antenna located above a homogeneous smooth spherical earth, and these can be used to compute the strengths of both the direct and secondary fields. It will be assumed that the antenna is a horizontal electric dipole whose effective radiated power P is 1 kW. As evident from the sin 3 factor in (I. 68), the far field is a function of the azimuthal angle referred to the dipole axis, but since it is sufficient to confine our attention to the direction for maximum field, this factor will be replaced by unity, corresponding to p = 'n/2. The resulting (maximum) field strength of the transmitter will be denoted by JE7 (R), where (as always) we are concentrating on the horizontal component. The variation of the field strength as a function of the great circle distance d 2 (see Figure 111.4) of the receiver from the transmitter is illustrated in Figures 12 la, b, c for three different frequencies. The lobing is characteristic of the VIE. la, b, c for three different frequencies. The lobing is characteristic of the 135

interference region and is due to the combination of direct and ground-reflected signals. Thl magnitudes of the peaks fall off approximately as 1/d 1. Beyond this region tho field strength decreases approximately as 1/(d19 ) and later exponontially. The distance over which the interference region extends decrea-ses with d(ecreasing frequency and transmitter and receiver heights, but otherwise the field strength behavior is similar in all of the cases shown. The smaller of the two transmitter heights in Figure VII. 1 is typical of a windmill viewed as re-radiator, i.e. the source of the secondary field, and with proper normalization the curves for h = 30 m in Figure VII. 1 show the variation in the strength of the secondary field as a function of distance from the windmill. To illustrate the manner in which the direct and secondary field strengths vary as a function of the distance d2 (see Figure II. 4) of the receiver from the windmill, 32 consider the case of TV Channel 43 (f = 647 MHz) at the NASA Plum Brook site for which the windmill is 79.75 km from the transmitter. The transmitter is assumed to radiate 1 kW effective power, and the strength of the windmill regarded as a trans2 mitter is computed using blades of total area 50 m (see Section VI. 1). The transmitter, receiver and windmill are taken to lie on the same great circle and in Figure VII. 2 curves 1 and 2 show the direct field at a receiver on the transmitter side and far side of the windmill respectively. Because the transmitter is at a large distance from the windmill, the direct field varies rather uniformly as a function of d32 and is, of course, larger in the first case, whereas the secondary field has a lobe structure out to 1 km or so from the windmill. At distances greater than this the strength of the secondary field relative to the direct one falls off more rapidly at a receiver on the near side of the windmill, implying that the interfering effects of the windmill will extend a shorter distance on this side. We will use these results in a later section. VII. 3. Total Received Field At a receiving antenna R in the presence of a windmill, the total field can be written as 136

20 h = 300 m, 1 h 10 m 2 h1 30 m, h = 10 m -20 - 0 Xe - =15 -60 ' "^ X a = O.O1/m 10 10 10 10 d in km indB Figure VII. l(a). IET (R) vs. d(= dla) for f 50 MHz.

20 / "- h = 300 m, h = 10 m r N \ h2 = 30m, h = l0rn -20 E = 15 a = 0.01 Z/m E (R)I indB } Nk \ r '\ \ -60 \ \ -100 I I\ \I 2 10- 1 10 10 103 d in km - Figure VII 1(b). |E(R) vs. d(= d12) for f = 100 MHz.

- 20 0 hi 300 m, h 10 m 1 2 Ihi= 30 mh 1 -2o1 h10 I Iii~1 a o=0. 01 U/m I ii IT TI:I ER)in dB -100 lo-' 1 10 102 103 d in km -- Figure VI.1(c). vs. d(= d12) for f = 500 MHz.

-50 -70 -90 -110 90/90 (1) dB Y -130 - R -150 - d in km ------ -170 i 5 0.O 0.5 - _ 1.0 5.0 10.0 Figure VII.2. E(R) Vs d d32 and E (R) Vs d(= d3 for f 647 Mz h = 10 m, dg= 79.7 kmi n = 32 h =00 m0 8 3 1 v E =150 0. 01 Z3 /M 30/270

I ) E (R, t) = E(R) + E(R,t) (VII. I) T where E (R) is the direct field at R B E (R, t) is the secondary field and the rf time dependence represented by a factor e has been omitted. All of the quantities in (VII. 1) are complex and the time dependence of the secondary field is due to the rotation of the windmill blades. We can separate out this time dependence by writing E (R, t) = IE(R)I f (t) e (VII. 2) where IE (R)| is the maximum value of the field amplitude during any one rotation of the blades, f (t) is the (real) modulation function whose maximum value is m unity, 6(t) is the time varying phase. If we also write the direct field as T T i6o E (R)= E(R)| e, the expression for the total field becomes E t (R ) +mf (t) ei } (VII. 3) i " ~(t) where 6(t)= b(t) - 6 (and is the rf phase difference between the scattered and direct signals) E(R) and m = - (VII. 4) E (R) 0 141

Assuming m < < 1, the amplitude of the total received signal is then IE(R)j = E(R) 1 + ( f t) cos (t)) (VII.5) and m can now be identified as the modulation index (see also III. 73). Compared with the function f (t), cos 6(t) is rapidly varying as a function of m time and achieves its extreme values t 1 many times during a single sweep of f (t). m The envelope of (VII. 5) is therefore E(R t) envelope = E (R) (1 + mf (t)) (VII. 6) I y envelope \ M I v m J and represents the total received field that is actually observed. As a function of time, the variations (in dB) above and below the ambient field amplitude E T(R) of the direct field alone are, respectively, A1 =20 log0 (1+ fm(t)) A2 =20 log10 ( - mfm(t) (VII.7) implying a maximum-to-minimum variation 1 2 = 20 log 1 - mft dB (VII. 8) m(t) VII. 4. Modulation Function The modulation function f (t) represents the time dependence of the scattered fieldamplitude IEB field amplitude IE (R)I introduced by the blade rotation. This could be determined by numerically computing the scattered field at every instance of time; however, this would be a very lengthy procedure in any practical case and would not bring out those features which are common to any rotating structure. We shall therefore use instead the physical optics approximation in conjunction with a rectangular plate model for a windmill blade. 142

VII. 4. 1. Determination of f (t) m Consider a rectangular metal plate located in the xz plane of a Cartesian coordinate system and oriented at an angle 0 with respect to the (vertical) z axis (see Figure VII. 3). The origin is also that of a spherical coordinate system and is located at the center of the plate. The plate will later be assumed rotating in the xz plane with angular frequency 0 such that any instant of time 0 = 2t. a (VII. 9) As noted in Appendix mI the transmitted field is predominantly horizontally polarized, implying that the magnetic field incident on the blade is in the z direction. It is therefore assumed that ik(x sin 0 cos ~0 + y sin 0 sin ~0 + z cos 0%) H = ~ H e (VII. 10) z y 4i H 0 Figure VII. 3. Scattering problem for a rectangular plate. 143

where, as always, a time dependence e has been assumed and suppressed. According to the physical optics approximation, the current density at an arbitrary point x', z' on the illuminated side of the plate is then. ik (x' sin 00 co. 00 + z' cos 0) J x 2H e (VII. 11) 5 0 and is zero on the back. These currents radiate to produce the scattered field and by carrying out the necessary integration, the electric Hertz vector specifying the scattered field at a distant point R is found to be 2H0 - ikr 2 {L1 4 e r L1L2sc (ps i -qcos 'L2 ) siac ( -p cos 0 + q sin 0)) (VII. 12) where p = sin 00 cos 0 + sin 9 cos,, ) (VII. 13) q = cos 0 + cos, L1, L are the plate dimensions (see Figure VII.3) sin7rX and sine X = 7r. 7rX The scattered electric field at R is given by 2 E =-k -T sin. p x It therefore has only the 0 component Er = i E ' X sin sin sincin q cos E sinn cos qsO fL2 \ *sinc{ (p cos 0s +q sin 0 ) (VII.14) 144

where EO - Ho/r and 70 is the intrinsic admittance of free space. With the blade rotating, its dependence on time is through the parameter 0 = Q2t, and since Jsinc Xj < 1, it follows that the modulation function is f (t) = sine (p sin st - q cos ft) sinc (p cos Pt + q sint) (VII. 15) VII.4.2. Nature of f (t) m Equation (VII. 15) shows that for a given incident field direction (00, ) the nature of f (t) is strongly dependent on the scattering or receiving direction (0, p). m For a plate in the xz plane, the specular and forward scattering directions are 0 =TT- 00, a = 7T- 00and 0 = 7 - 00, 0 = 7Tr + 0, respectively, and in both cases p = q = 0, giving f (t) = 1. Although these are the directions of maximum scattering, the model that we have used does not reveal any time modulation resulting from the rotation of the plate. This finding is at variance with actual observations on a windmill, and the defect of our model is not hard to see. Because we have assumed the (planar) blades to lie in the plane of rotation and have, in addition, employed a technique for calculating the scattering which is polarization independent, the directions of maximum scattering are the same regardless of the blade position. When the scattering is a maximum, the modulation is then a minimum, and the modulation will become significant only in directions away from the specular and forward lobes. In a practical situation it may be that the receiver cannot lie in a direction of maximum scattering (and we shall explore this case in a moment), but there is one key particular in which any actual windmill blades must differ from our model: they must lie out of their plane of rotation with, in practice, the two blades turned in opposite directions if they are to function as a turbine. They may, in addition, be aerofoil-shaped (non-planar) and/ or coned, but these modifications merely reinforce the effect produced by the twisting 145

of a planar blade about its taxis. If the receiver is in the specular direction for a blade in any given position, the rotation of the blade will now (displace the specular lobe antld it will not be until the blades complete a full revolution that the receiver again picks up the specular lobe. This leads to the concept of a rotating specular lobe or beam, and for a receiver which is appropriately positioned to pick up the maximum return, the signal has the form of a sine pulse repeating every revolution of the blades. We explore this concept further in Section VII. 4. 3., but it is well to note that even for a planar blade rotating in its plane there will be some modulation of the signal if the receiver is somewhat away from the direction of the maximum (specular) scattering. This may be true for all feasible locations of the receiver in a practical situation. For a transmitter which is far away, the direction of incidence on the blade can be assumed to lie in the plane 00 = 7r/2 of the local horizontal (see Figure VII. 3). For any given,P the specular direction is then 0 = 7/ 2, 0 = 7-, but since the windmill is usually much higher than the receiving antenna, it may be that the closest that can be achieved to this direction is 0 = 7/2 +o<, 0 = it- 00, where < is some small angle. Under these conditions, (VII. 15) implies /1 \ 2 \ f (t) W sine c sin o< cos Qtt sine sin < sin stC. (VII. 16) m \ I For a blade of high aspect ratio, L1 > L2, and the time dependence of f (t) is primarily determined by the first factor in (VII. 16). The modulation function now has the form of a sine pulse, and if its width 2 t1 in time is measured by the separation of the first zeros on either side of the maximum, 2t = sin 2 - sin L 2t sin(VII. 17) 2tl fB k sin (V.17) where f is the blade rotation frequency. B 146

Equation (VII. 17) can also be used to predict the spread of the modulation function for scattering in the forward direction. VII. 4.3. Rotating Beam Concept Because of the blades' twist out of their plane of rotation and (possibly) their coning as well, the specularly reflected lobe will sweep out a path through space as the blades rotate, and a stationary receiver so located as to pick up the maximum of the lobe will actually receive a signal only at those times corresponding to a narrow range of the blade rotation angle 0. The angular width A0 of the specularly reflected s beam of a stationary blade as measured between the first zeros of the sine pattern is determined by the narrow dimension L2 of the blade, and from (VII. 14) with 00 = 0 = 7r/2 and 0 = 0 (blade vertical), we have s I (2L2 L2 na = 4 sinn ) ( sn (VII. 18) Since the beam will rotate with the angular frequency Q2 of the blade, the time width 2 to of the observed modulation pulse becomes 2 tO = 27fB - s 0 (VII. 19) c.f. (VII. 17). This will be used later in our analysis of the results observed at Plum Brook. VII. 5. Interference Zone of a Windmill The amplitude modulation of a TV signal received in the presence of a windmill comes about because of the sine type pulses which constitute the scattered field observed at any fixed location. The duration of the pulses depends on the linear dimensions of the blades, their rotation speed, and the angles of observation with respect to 147

the plane of rotation of the blade. The strength of the pulses and, hence, the modulation depth depends on the scattered field strength relative to the ambient level of the direct (primary) field, and as noted above, both m and f (t) are significant in directions close to those of specular and forward scattering. For a receiver so located, the windmill may produce unacceptable levels of video distortion. From the results of the laboratory studies described in Appendix II it was concluded that the distortion would be unacceptable if m > 0.2. All other things being equal, m is a (not necessarily uniformly) decreasing function of distance from the windmill, and the specification m> 0.2 will therefore locate a zone around the windmill within which video distortion can occur. This will be called the windmill interference zone, but it should be emphasized that the situation is not 'black and white'. The distortion decreases with increasing distance and the boundary of the zone is simply the place where the distortion is judged as having passed from unacceptable to tolerable. With this caveat, the boundary of the zone is defined by the threshold 0.2 of the modulation index m. Within the zone distortion will occur only with the passage of the rotating scattered beam through the receiving point, implying that for any given transmitter location the plane of rotation of the blades is such that this can take place. Our calculations of the zone will be carried out under the assumption that for given locations of the transmitter and receiver, the plane of blade rotation is oriented to direct the maximum scattered signal to the receiver. It does not therefore follow that video reception within the zone will be adversely affected at all times: at any given moment, video reception will depend on the orientation of the windmill. The actual shape of the interference -zone is a rather complicated function of the propagation and scattering characteristics, and, in general, can only be determined numerically taking into account the parameters appropriate to the specific situation. We show later an example in which the zone shape has been computed, but for convenience of description most of our calculations have been directed at the radius of an equivalent circular zone around the windmill. Nevertheless, by suitable (albeit drastic) 148

approximation, it is possible to arrive at an analytic specification of the zone, and we shall discuss this case first before going on to a more precise numerical determination later. VII. 5. 1. Simplified Model The simplified model ignores the directional scattering characteristics of the blades and the effect of the earth on the propagation. In effect, therefore, we assume omnidirectional scattering as well as omnidirectional transmitting and receiving antennas, and regard the entire problem as a free space one; but in spite of these assumptions, the model is able to predict the maximum distance from the windmill at which interference can occur, and also provides a valid qualitative picture of the interference. In Figure VIl. 4, T, B and R are respectively the transmitter, windmill blades and receiver all located in the xy plane of a Cartesian coordinate system (x, y, z) whose origin is at B. The transmitter is at a large distance D from the windmill, and the receiver is at a distance d from the windmill in a direction making an angle 0 with the positive x axis. On suppressing the usual time dependence, the direct field at R can be written as T ik(D- d sin ) E (R) c K d (VII.20) D(l - - sin 0) D where K is some constant. The direct field at B is similarly -ikD T e E (B)= K D (VII.21) and if the effective scattering area of the blades is A independent of 0, the scattered field at R is 149

I r B ~ - D -i x Figure VII. 4. Simplified model for interference zone calculations. - ikd EB(R)= - ET(B) d KA e D+ d) Ad D (V. 22) The modulation index is therefore EB(R) E (R) = A (1 — d sin0) Xd D (VI. 23) and since in most practical situations A < < mAD, (VII. 23) can now be solved to give d = - 1 mAD sin ) (VI.24) 150

With m = 0.2, (VII. 24) defines the interference zone around the windmill. The zone is sketched in Figure VI. 5 and is approximately circular of radius A/mX but with the center of the circle displaced a distance A/mXD from the windmill in the direction away from the transmitter. As A increases and/or X decreases, the radius and the center shift both increase. In the limiting case of a transmitter at infinity, the zone is exactly a circle of radius A/mX centered on the windmill. B \ ---- --- -- -- ---- ^ - -- -_ -_ ^T d2^ d1/ x Figure VII. 5. Interference zone based on the simplified model: A A AA dl =-(1 -). d2 =(l(+ d d1 mX mXD d2 mX O+mD m VII. 5.2. Improved Model A large rectangular plate does not scatter isotropically, and as a first improvement to the simplified model discussed above, we now introduce the actual scattering characteristics of the plate. The plate is again assumed to lie in the xz plane of a Cartesian coordinate system and to rotate in the same plane (see Figure VII. 3). To simplify the discussion, the directions of incidence and scattering are taken to be in the (horizontal) xy plane, implying 0 = = 7r/2. In the particular case 0 = 7r/2 representing normal incidence on the blade, the directions of specular and forward scattering are =.7Tr/2 and 0 = 3 7r/2 respectively, and the isotropic scattering model is directly applicable with the parameter A in (V.22) equal to the physical area of the blades. The scattering pattern 151

then consists of two identical sine distributions centered on 0 = 7r/2 and 3 Tr/2, and if we confine attention to just the main lobe of the distribution, the scattering as a function of the angle 0 of reception consists of two lobes centered on the line joining the transmitter to the windmill. This in turn leads to the interference zone shown in Figure VII. 6. y.-. - - - - T X x Figure VII. 6. Interference zone for incidence normal to the plane of blade rotation. The dimensions d1 and d2 are the same as in Figure VII.5 and the widths of the regions as specified, for example, by the 3 dB points, are determined by the electrical dimensions of the blades. A more general case is that in which the transmitter is in a direction 0 $ 7T/2. The specular direction is then 0 = 7r- 0O and as evident from (VII. 14) the effective area of the blades is reduced to A sin 00. The situation is unchanged if instead of displacing the incident direction from 0O = 7r/2 we rotate the plane in which the blades lie; and by observing that the angle between the directions of incidence and reflection is 7r- 200, the effective area of the blades for maximum scattering in a direction 0 152

relative to the x axis is A cos ( 7r/4 - 0/2). The distance d to which the interference zone extends in this direction is therefore d(0) = d cos ( - ) 4 2 (VII. 25) where d1 is as defined before. The zone is a cardioid and is sketched in Figure VII.7. / -d- B F- A- -- - -- d, d, d - - --- - ---..T x Figure VII. 7. The specular ( ) and forward ( ----) scattering portions of the interference zone of a windmill. In addition, however, there is still the forward scattering lobe of Figure VII. 6. Its position is determined only by the direction of incidence and for a transmitter located as shown, the lobe is always centered on the direction BF of Figure VII. 7. The maximum interference distance d2 in the forward direction is achieved when the blades rotate in a plane perpendicular to this, i.e. in the'xz plane, and for rotation in a plane making an angle o< with the xz plane, the forward interference distance df is fn df=d2 cos c. (VII. 26) 153

The total angular width (see Figure VII. 7) of the forward zone is 0 2 (VIL. 27). L2 ~ L2 cos < where L2 is the smaller dimension of the blade, but since our specification of windmill interference is based on the selection of that orientation of windmill which produces maximum interference in any chosen direction, it is sufficient to take c = 0 as regards the forward scattering. We then have df = d2 and in general d2 > d. The complete interference zone is therefore the union of the cardioid produced by specular scattering off the blades and the left hand lobe of Figure VII. 6 attributable to forward scattering. Though our analysis has used only the simplified model in which the propagation effects of the earth are ignored, the inclusion of these effects does not significantly change the shape of the zone. VII. 5.3. Interference Zone Calculation We now present a systematic method for computing the interference zone around a windmill in a fixed location with respect to a TV transmitter. In contrast to the method discussed in the previous section, we now use the expressions in Appendix mI to take into account the effect of a homogeneous spherical earth on the propagation of both the primary (direct) and secondary (scattered) fields. Since the coordinate system used in the analysis of the scattering and modulation function differs somewhat from that in Appendix III, it is necessary to relate the two systems. In the propagation analysis, the origin of coordinates was taken at the center of the earth (see Figure M. 4) with the polar (z) axis aligned along the axis of the windmill tower and the blades rotating in the xz plane. The polar coordinates 9, p defining the locations of the transmitter, receiver and windmill blade center were then identified by the subscripts 1, 2 and 3 respectively. In the present Appendix it proved more convenient to place the origin at the center of rotation of the windmill. The z axis was again vertical and the blades were rotating in the xz plane as before, but relative to our new origin of coordinates, the polar angles specifying the locations of the transmitter and receiver were taken as 00, 1 0 and 9, pS. The two sets of angles are related as follows: 154

00= 01 =02 whereas 0 is related to 1 and 0 to 02 using the transformation relations of Appendix III, for example (111.41). To determine the interference zone the following steps must be performed: (i) Identify TV Channel frequency transmitter coordinates hi, 01 transmitter-windmill great circle distance d31 transmitted power P (in kW) receiver coordinates h2, 02 windmill tower height p blade (geometric) area A. With T, B and R denoting the transmitter, windmill blade and receiver respectively (ii) Use (HI. 68) with = 7r/2 to compute EP(R)j vs d(= d32) for (a) 0 = 7/2, 02 = 7r/2; (b) 0 = 7r/2, 02 = 7r/2. (iii) Use (m. 60) with dS' = A to compute IE (R)| vs d(=d32). (iv) From (iia) and (iii) find the maximum value of d(= d ) for which jE (R) E (R)i = 0.2 (v) From (iib) and (iii) find the maximum value of d(= d2) for which E lE(R) E (R) = 0.2 0 0 155

Based on the isotropic scattering model, the interference zone is then a circle of radius I (d + d ). This is the quantity that has been computed in all our studies of interference at specific windmill sites. To obtain a more realistic estimate of the actual shape of the interference zone, it is necessary to take into account the scattering behavior of the blades. Based on the planar blade model, the following additional steps must be performed: (vi) Compute d(0') = dl cos 2 <', 0 < ' < 7, where ' (= 2- 7r/2) is the angle between the lines joining the windmill to the receiver and the windmill to the transmitter. (vii) Compute d(0') = d2 since — sin O' |, 7r - sin1 Lj< ' <7r where L2 is the (average) smaller dimension of the blades. Steps (vi) and (vii) respectively determine the specular and forward scattering portions of the interference zone, and the complete zone is then the union of the two. Although this should be a closer approximation to the actual interference zone, we caution that it is still only an approximation. In particular, the procedure described has ignored the change in the primary field at the receiver as j' changes. The above also assumes that the receiving antenna is isotropic (or, in practice, has the same gain as regards the primary and secondary fields), and if this is not so the interference zone will be affected. To illustrate, suppose the main beam of the receiving antenna is always directed at the transmitter. If 0" is the angle*between the lines joining the receiver to the transmitter and the receiver to the windmill and if f(0") is the pattern function of the receiving antenna in the plane of observation, with f(0) = 1, (viii) multiply the distance d in steps (iv) through (vii) by f("). This completes the interference zone calculations for a given transmitter location. For a different frequency and/or transmitter location, all relevant steps must be repeated. * For a remote transmitter, 0" 7or- t'. 156

An example of the results obtained based on the isotropic scattering model is as follows: TV Channel frequency: f = 647 MHz h = 300 m, d31 = 79.7 km, P = 1 kW h2 = 10 m, p = 30 m, A = 50 m By referring to Figure VII. 3 and carrying out steps (i) through (v), it is found that d =2.73 km, d2 =4.90km VII. 6. Comparison of Calculated and Observed Results To assess the validity and accuracy of the various models and expressions used in the theoretical analyses, we shall now compare some of the predicted and observed results. All of the experimental data used was obtained during the field tests on the 100 kW wind turbine at Plum Brook (see Appendix VI). Each blade has the following dimensions: length (L1) = 18.3 m (60ft.) width (max) = 1.36 m (4.5 ft.) (min) = 0.46 m (1.5 ft.) (av. =L ) = 0.92m (3.0ft.) 2 The area of a blade is A r 17 m. During the tests at Plum Brook the secondary signal observed at any instant of time was the field scattered specularly off a single windmill blade. In the following we shall therefore use the scattering from one blade only to compute the secondary field at the receiver. VI. 6. 1 Scattering Tests Scattering tests were performed at sites 5 and 6, but since the field scattered by the windmill had to traverse a heavily wooded area to reach the receiver at site 5, we confine attention to the site 6 results alone. The source of the signal used here was 157

TV Channel 24 having frequency f = 533 MHz and wavelength X = 0.56 m. The pattern of the receiving antenna is shown in Figure VI.8. The main beam was directed at the windmill, thereby reducing the signal due to the primary field by 7 dB. Other pertinent parameters are: h =300 m, h2 = 10 m, 2 1 =250~ d31 65.3km; P = kW 2 =155~, d32 0.8km, windmill tower height p = 30 m. The details of the calculations are as follows: Computer outputs: |ET(R)j = -59.68dB IE (R) = -99.34 dB m 0L~~ for 1 = 7r/2, 02 = 7r/2, d32 =0.8 km for 0 = 7r/2, 0 71/2, d32 =0.8 km In the present case JE (R)I = -59.68- 7.00 = -66.68dB and in the direction 01 = 7r/2 IE(R)I = -99.34 + 20log10A = -99. 34 + 20 log1017 = -74.73dB. Hence B E (R) I - = 0.40 E (R) 0 which would be the modulation index for 02 = 7r/2. To convert to 2 = 1550~ multiply by sin 155~ to obtain m = 0.40 sin 155~ = 0.17. 153

The predicted field strength changes above and below the ambiont level are therefore A1 = 20 log10 1.17 = 1.36 dB and A2 =20 log10 0.83 = -1.62dB compared with the observed values (see Figure VI. 5) A = 1.3 dB A2 =-2.2 dB. The agreement is good. VII. 6.2. Operational Tests These were performed at site 14 using TV as the source. Relevant parameters are h1 =300m, 0 = 67.50. d h2 = 10m, 2 = 112.50, d3 Channel 43 (f = 647 MHz, X = 0.46 m) = 79.7 km; P = 1 kW, = 0.47 km. The receiving antenna was pointed with its main beam towards the transmitter thereby reducing the scattered signal from the windmill by about 11.5 dB. The computation of the signal fluctuations is similar to thene described above, and the calculated and observed (see Figure VI. 10) modulations are as follows: Calculated 0.9 dB -1.01 dB 0.11 Observed 0.8 dB -1.0 dB 0.10 m The agreement is excellent. It is also of interest to examine the time duration of the modulation pulses. We can use either of two methods to estimate it. From (VII. 17) with L /X = 39. 8, 159

-00 o< = 5.5~ and fB = 1/3 we obtain 2tl 250 ms. On the other hand, from(VII. 19) with L2/X = 2, 00 = 0 = 67.5~ and fB = 1/3 we find 2t0 517 ms. The two times are rather different, but if we measure the width of the rotating beam between its 3 dB points (which is usual in practice) rather than between its nulls (as was done in VII. 19), the duration 2t0 is halved to become 259 ms, which is in good agreement with the value for 2t. The calculated and observed (see Figure VI. 10) durations of the received modulation pulses are then: Calculated Observed 2t1 250 ms -250 ms The agreement is again excellent. VII.7. Discussion The results we have obtained confirm that for a fixed (distant) TV transmitter, a windmill will interfere with the reception of video signals in its vicinity. The interference is most severe in directions close to those of specular and forward scattering off the moving blades, but as the windmill slews in azimuth, these directions will encompass a complete region about the windmill. On the assumption of a receiving antenna which is omnidirectional, the shape of the interference region has been defined and techniques developed for computing its dimensions. We remark that if it is possible to use a directional antenna to discriminate against the windmill-scattered signals, the level of interference can be markedly reduced. The agreement between the theoretical and observed results indicates that the theoretical model we have assumed is capable of providing a quantitative explanation of the interference phenomenon. As regards the field tests themselves, we have shown that (i) at a given instant of time, only one of the windmill blades is scattering energy to the receiving point; (ii) the windmill produces a sinc-type pulse modulation of the received signal; and 160

(iii) the threshold of modulation for significant (objectionable) interference on Channel 43 is approximately 0.1. In calculations of interference distances performed earlier in this study we set the threshold of modulation at m = 0. 2. This value was chosen based on laboratory simulations using sinusoidal modulation of the signal, and prior to our present knowledge of the actual modulation introduced by a windmill. However, we also took the effective scattering area of the windmill to be A = 50 m, and the interference distance is proportional to A/mr. Since the results now indicate that A should be identified with the area of a single blade (17 m2) and m taken to be 0.1 as judged by the Plum Brook data, our previous calculations of interference distance are too large by 30 percent. 161