1082-3-Q Copy THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL ENGINEERING Radiation Laboratory 1082-3-Q - RL-2025 DOPPLER RADIATION STUDY Quarterly Report No. 3 1 January 1968 - 1 April 1968 By Chiao-Min Chu, Joseph E. Ferris and Andrew M. Lugg April 1968 Contract No. N62269-67-C-0545 Contract With: The U. S. Naval Air Development Center Johnsville, Warminster, PA. 18974 Administered through: OFFICE OF RESEARCH ADMINISTRATION. ANN ARBOR

THE UNIVERSITY OF MICHIGAN 1082-3-Q TABLE OF CONTENTS Peg ABSTRACT i I INTRODUCTION 1 II EXPERIMENTAL EFFORT 3 III THEORETICAL STUDY 5 3.1 Spal Distribution of peularly Reflected Radiation 5 3.2 Temporal Variation of Radiation Speularly Refleted from a Plane Ground 13 3.3 Effect of fpecularly Reflecting Clouds 23 3.4 Reflection from a Diffuse Ground 27 3.5 Effect of Refractive Properties of Atmosphere 36 IV TRIPS 44 REFERENCES 45

THE UNIVERSITY OF MICHIGAN 1082-3-Q ABSTRACT In this, the Third Quarterly Report on "Doppler Radiation Study", some results of the theoretical investigation and details of the experimental efforts are reported. Much of the experimental work is directed toward preparing the equipment which will be used during the forthcoming fly-by tests. The radar tracking, data collection and communication equipment has been checked out and is ready for the scheduled test. In the theoretical study, the numerical calculation of the spatial and temporal variation of the reflected radiation from a perfectly conducting ground, based on the scheme suggested in the last quarterly report, has been carried out. Further, some simplifications in presentation of the numerical results by using nomographs are introduced. The reflected radiation due to a diffusely reflecting ground is determined numerically and in an approxaimate but closed form; and finally the effect of some meteorogical conditions, such as cloud reflection, and the variation of the refractive indeix of the atmosphere are also, considered. ii

THE UNIVERSITY OF MICHIGAN 1082-3-Q I INTRODUCTION This is the Third Quarterly Report on Contract N62269-67-C-0545, "Doppler Radiation Sudy". It covers the period 1 January to 1 April 1968. The primary objective of this project is to characterize the radiation from airborne doppler navigational radar systems, and to determine the probabilityof detecting this radiation. The task is being carried out in the following phases: 1) Experimental measurement of the radiation patterns of several antennas that are currently being used in doppler navigatioal systems. 2) Based on the measure radiation pattern, the distribution of radiation in space and the effects due to ground reflection, airplane maneuvering, and meteorological conditions are investigated. 3) The theoretical results in (2) are to be checked out against results obtained from the flight test. 4) From the theoretical and experimental:results, estimates of the probability of detecting the radiation at different ranges will be made. During the present research period, the following has been accomplished: 1) The data collection, radar tracking, and communication equipment that is to be used in a fly-by test scheduled for April, 1968, have been checked out and are ready for operation. 2) Numerical computation of the radiation reflected by a perfectly conducting ground from an AN/APN-153 doppler antenna has been carried out, the results being presented in a compact, normalized form. Several nomographs are developed in conjunction with the computed data to facilitate the estimation of spatial and temporal variation of the reflected radiation for differing aircraft trajectories. The use of the computed data and monographs is illustrated and explained by means of examples. 1

THE UNIVERSITY OF MICHIGAN 1082-3-Q 3) Formulations and schemes for the calculation of radiationreflected from a diffusely reflecting ground are presented. Anticipating that narrow beams will be used in future doppler systems, an approximate formulation of the computation, in which the beam is assumed Gaussian, is also carried out. 4) An initial investigation of the effect of meteorological conditions on the propagation of radiation is outlined. The effect of a specularly reflecting overcast layer and the effect of a linearly varying refractive index of atmosphere with height, are considered. Some of the results a the above investigations were included in the Memorandum 01082-508-M. For a coherent, integrated discussion of the problem, some of these results are also included in this report. In the next research period, more numerical calculations involving a diffusely reflecting ground using finer increments of integration will be carried out to determine the effect of the fine structure of the measured radiation pattern. Numerical methods for investigating the effect of various meteorological conditions and maneuvering will also be developed, and the numerical results will be compared with the data obtained from the fly-by tests. 2

THE UNIVERSITY OF MICHIGAN 1082-3-Q II EXPERIMENTAL EFFORT Much of the experimental effort during this period has been concentrated towards readying the radar site for the fly-by tests which are to be conducted in the early part of April. Preparation of the radar site has involved readying the following equipment: 1) Communication equipment, 2) Radar tracking equipment, 3) Data collection equipment, The transmitter and receiver of the communication equipment have been checked out and are operating satisfactorily. Durirg the fly-by tests a frequency of 248. 3 MHz is to be employed for voice communication between the ground and air. The communication link will be required to maintain contact with the air - craft and as an aid in directing the aircraft's course. The communication equipment is compatible with the ARC-27. Its nomenclature is a GR-217 radio transmitter capable of transmitting 100 watts of RF power. The radar system which will be employed during the fly-by tests is a NIKE missile system. The NIKE system consists of three radars; a missile tracking radar (X-band), target tracking radar (X-band), and a search radar (S-band). The missile tracking radar will be employed to track the aircraft during the flyby tests. The target tracking radar will be slaved with the missile tracking radar, such that, during tracking, it will follow and point in the same direction as the missile tracking radar. Rather than using the receiver normally associated with the target tracking radar, a K -band horn antenna will be employed with a target tracking pedestal. In this configuration the horn will point toward the aircraft during the tests. Data collected by the K -band antenna will be transferredthrough a transmission cable to a laboratory receiver (a Micro-Tel Wide Range WR - 250 3

THE UNIVERSITY OF MICHIGAN 1082-3-Q Receiver). In addition to the Wide Range Receiver, a small amplifier will be required at the output to further amplify the received signal from the doppler navigation system. The amplified signal is required for the data recording system. The S-band search radar will yield information of other aircraft in the area. In the data recording system, we are employing two sub-systems. The first consists of an analog data system, the 4-channel Sanborn Recorder, and the second is a multi-channel digital system. The two sub-systems will be connected in parallel so that analog and digital data may be collected simultaneously. The following information is to be recorded during testing: the doppwlr navigation signal strength and the x, y, and z coordinates of the aircraft (from the missile tracking radar) during the fly-by tests. In addition to the above data, we have the capability of collecting sin 0 and sin information (from the target tracking radar) when making specular reflection measurements. During the initial phase of the fly-by tests, data will be collected from the doppler system by pointing the tracking radar antenna with the K -band receiving u system at the aircraft and by collecting the relative signal strength as a function of aircraft position. This data will be compared with predicted signal levels to confirm the feasibility of detecting the aircraft. During the second phase of the fly-by tests, efforts will be made to determine the probability of aircraft detection on the basis of specular reflections. These specular reflections will be assumed to occur as a result of the signals that may be reflected from the earth toward the radar or possibly specular reflections that are reflected from the earth up to the sky and re-reflected from clouds or other atmospheric phenomena. 4

THE UNIVERSITY OF MICHIGAN 1082-3-Q III THEORETICAL STUDY 3.1 Spatial Distribution ot Specularly Reflected Radiation The calculation of the component of radiation specularly reflected from the ground (assumed to be smooth, and perfectly conducting), by using geometrical optics, has been formulated and reported previously in Chu et al, (1968). In this quarter, the pertinent numerical calculation based on the measured radiation pattern of AN/APN-153 doppler antenna were carried out. Nomographs, reducing the actual geometrical distances between the at enna and the observer into a set of normalized coordinates are constructed. When these nomographs are used in conjunction with one set of calculated, reflected radiation data an estimation of the reflected radiation at different points of observation and under various flight trajectories of the vehicle carrying the doppler radar, can be found. As reported previously, for an antenna at T (xa, y z a) and an observer at B (xh, Y, h), as illustrated in Fig. 3-1, the calculation of the reflected radiation can be more conveniently carried out by introducing the normalized coordinates defined below: z -h a (3.1) Z +h a x-x X = 2 = - ' --- tan cos0 (3.2) z! + ' and y-y 2 Y =... = -- tan0sin0. (3.3) z 1+9 a 5

1082-3-Q T(xa^Ya Za A Z A Direct Signal B(x: \~ Reflected Signal - Mrouna z=u I - I -- I - I - - Ima I - I - I-,s^ I ~' I s I JJ I j I / I~ i~u~g FI.31 EMTY O ELCE A h i 6

THE UNIVERSITY OF MICHIGAN 1082-3-Q The normalized coordinates can be expressed in terms of the values (x - x ), (y - y ), z and h. A nomograph has been constructed te link these two coordiate systems. It is given in Fig. 3-2. Fig. 3-2 is a nomograph which relates the actual position of an observer (x, y, h) to the normalized position vector (X, Y,?). Here the initial aircraft position is (x = xa, y = ya, z = z). An example, x = 5000 ft., y = 10,000 ft., z = 20, 000 ft, h = 5000 ft. is given in Fig. 3-2 to illustrate the way the nomograph is to be used. The procedure for finding X, Y. and 9 from the nomograph is as follows: 1) On the left hand axis mark (x - x ) or (y - ya) and on the center axis a a mark z. Where the lines joining these points intersect line A, mark off X or Y. 2) On the right hand axis mark h. Where the line joining a on the center axis and h intersects line B, read off. Now, in terms of the normalized coordinates the intensity of the ground reflected radiation from an antenna with radiation pattern f (0, (), power Pt and gain Gt is given by P G f2(6) Pr MY,) 2 2 2 2 ' (3.4) z (- T ) sec 2 If we take the power level of the reflected radiation at any height of observation from the direction of maximum radiation as 0 db, then, the reflected radiation due to rays in any direction (0, 0) is given by db (8, ) = db (9, ) + 20 log sec 0M -20 log see (3.5) 7

1082-3-Q z (x 10,000 ft. ) a 0 5 -10 - 10 - 0 X.5 -10 -(OV-1 Example: If 2 x = 5000ft. y = 10,000 ft. a= 20,000 ft. h = 5000 ft. h = 5000 ft. Then from constructions: X = 0.25 Y = 0.5 e =0.6 h(x 1 (x-xa, y-a) (x 10,000 ft. ) )00 ft. ) FIG. 3-2: NOMOGRAPH RELATING (x, y, h, z ) to (X,Y, ). a' 8

THE UNIVERSITY OF MICHIGAN 1082-3-Q where db (0, 0) is the measured radiation pattern and (0M, 0 ) is the direction of maximum radiation. Numerically, for each 0, 0, we may calculate db (0,0 ), while for each 0, 0, E, we may compute a set of X and Y. It was suggested previously that contour plots for constant db in the X-Y-plane can be plottedfor each. However, an inspection of Eq. (3.2) and (3.3) reveals that for each 0, 0, the dependence of X, Y on e is simple. Thus, it is seen that one set of computation, relating db to the normalized coordinates X and Y for e = 1 is all that is required. For any other value of X, the same graph of the computational results may be used if we change the scale of X and Y. This change of scale is given by X(e) = 1 X( = 1) (3.5) and 2 Y(9) = 1+- X(= 1). (3.6) The transformation can be easily accomplished by the nomograph given in Fig. 3-3. Figure 3-3 may be used in eactly the same was as the nomographs introduced above. For example suppose h/z =. 1, e = 0.817. If we desire the position on a the X(9 = 1), Y ( =- 1) scales for X = 1, Y = 0.4, we mark off 1 unit on the left hand scale and draw a line through this point and the point 9 = 0.817 on the e scale. Where this constructed line meets the right hand scale, X (9 = 1) is read off. In this case X (9 = 1) = 0.908. Similarly when Y = 0.4; Y( = 1) =. 363. In Figs. 3-4 and 3-5, a contour plot of db in the X-Y-plane for e = 1 is given. This one set of curves, as suggested above may be used for all values of e by changing of the scales of X and Y. 9

X, Y 1082-3-Q 3 - 0 2- 0 -1 0.25 0.5 0.75 / YX(=l) Y( = 1) 1- / R-2 0 -3 FIG. 3-3: NOMOGRAPH RELATING XsY, Y TO X(~ = 1), Y(I = 1). 10

0.5 20 db Down 0 (20) 0 00 I3 -1.0 1.0 20 db Down -0.5 FIG. 3-4: SPECULARLY REFLECTED POWER FOR FEED NO. * AT S = 1. (20)

(20) 20 db Down rN3 -1.0 1.0 O 00 (30 zlS O2 (20) 10 db Down -- 20db Down FIG. 3-5: SPECULARLYREFLECTED POWER FOR FEED NO. 2 AT = = 1.

THE UNIVERSITY OF MICHIGAN 1082-3-Q For completeness, it is seen that given x, y, h and xa, ya, Za, the ground reflection observed can be directly estimated by using the contour plots in Figs. 3-4 and 3-5. From Eqs. (3. 1), (3.2) arid (3.3), we have: x-x = X( = l)Fz +hl (3.7) a a y-Ya = Y(( =l) Za (3.8) These relations may be used to obtain the values of X ( = ), Y ( = 1) directly for estimating the reflected radiation from Figs. 3-4 and 3-5. The necessary nomograph is given by Fig. 3-6. It is to be noted that for the calculation of the specularly reflected radiation the use of Fig. 3-6 in conjunction with Fig. 3-4 and/or Fig. 3-5 will yield the required information. However, it is seen later in this report that, when using these computed results to estimate the temporal variation the reflected radiation, and when the case of a diffusely reflecting ground, is considered then X () and Y(9) are the more convenient normalizations. 3.2 Temporal Variation of Radiation Specularly Reflected from a Plane Ground From the basic equation for the power level of the reflected radiation observed at any point, sec M M db (0, ) = db (0,0) + 20 log sec r o se 0 and the graph of the variation of db with X and Y (Figs. 3-4 and 3-5), the temr poral variation of the reflected radiation due to a pulsed source and a moving vehicle can be computed. The basic scheme for such a computation has been given in the previous report (Chu et al 1968). During this research period, this scheme has been applied to the AN/APN-153 antenna system for level flight of the vehicle. 13

1082-3-Q (x 10,000 ft. ) 7 6 5 *1 -2 X(Q = 1) Y(C = 1) (x-xa) (y-ya) -3 3.4 (z^+ h) a 2 1 5 6 -7 (x 10,000 ft. ) FIG. 3-6: NOMOGRAPH RELATING (x-x ), (y-y), (z +h) TO X(9 =1), Y(= 1). a a 14

THE UNIVERSITY OF MICHIGAN 1082-3-Q Basically, the temporal variation of the intensity of the reflected radiation is due to the following: 1) The modulation of the source, 2) The time delay depending on the time taken for the wave to propagate between the source and the observer. This delay, as mentioned in Chu et al, (1968), is given by R a 2 2 2 2' (9 T = t - t = R /X2 y2+ ( 2 )2' 3) The change of 0 and 0 which result from the aircraft motion. As illustrated in Chu et al, (1968), for a moving vehicle with trajectory described by x (t), y a(to), za (t) and with radiating, time varying pulsed power, P(t) the intensity of radiation observed by a fixed observer is formally given by f2 P(t + r (to)) Gt f(6 (to),0 (to)) sec2 oM 0 0 t 0 0 M r 4 Lz (to)+y (to)+ (- ) sec 0(t) This formula indicates that the temporal variation of the intensity of the reflected radiation may be separated into two parts, the part P (to + r (t) ) Gt depending on the form of the modulation of the antenna signal, and the term ) = f ((t), 0(t )) sec M M(t) =...... -- -...... — 23.11) 4 r^ [X(t + Y2 (to) + ( + see (t L- (t0) 0% For an aircraft flying at a fixed height, the variation of M with X, Y expressed in db relative to the maximum power level observable at that height may be plotted. 15

THE UNIVERSITY OF MICHIGAN 1082-3-Q Thus, knlwi t the, t wriatot of M (to) [se in ter a db(to)] with t am be calculated directly. o To illustrate this variation, we shall cosdr two cases f6rletWl fiof the airplane. For these caes za, and hence C are constant with reset to a fixed observer. The airplane is assumed to be moving with uniform velocity. Por convenience, the normalized time soale Vt s 0.o (3.12) 0 Z a is also introduoed. o:r the first case, the airplane is taken to be flying parallel to the x-axis. The projections of airplane trajectory observer on the ground are Illustrated in Fig. 3-7. For this case, the normalized coordinate Y is not changed during flight. Furthermore, if we take to = 0 at the moment when the airplane is nearest to the observer (point A in Fig. 3-7), we find that X(t) - (3.13) a Curves of db (t) against t for E = 1, Feed No. 1, and several valus of ro o Y are given in Fig. 3-8. It is seen from the Fig. 3-8 that when the aircraft pses overhead, the peaks are not symmetrical and are well below the maximum power level. The reoeived power in this ase derives from the 'fine structure". When the distanoe of closest approaohlts YN = 0.15, the received power goes through maxima at 8 =0.38 and at 8 = -0.4. At the former normalized time the O o power reoeived derives from the mainiobe and at S 4 -0.4 it derives from a sidelobe. As the dl it.oft atretapproach Increases the maxima decrease (see curve for YN 0.5). The reoeiver, uder this conldition ispicking up radated power from the "edges" of the manlobe!sanddildel bes. 16

1082-3-Q Airplane Nearest to Observer A | N 0 Observer Airplane Trajectory FIG. 3-7: GEOMETRY FOR AIRCRAFT FLYING AT A CONSTANT HEIGHT AND WITH Y(5) = CONSTANT. 17

1082-3-Q -.1.1 o YN 0.15 N YN=0.15 N N= 0.3 N Y=0. 5 YN=0 N Power Level (db Below Maximum) FIG. 3-8: RECEIVED POWER AGAINST NORMALIZED TIME FOR X = 0, e = 1 AND VARIOUS VALUES OF YN. 18

THE UNIVERSITY OF MICHIGAN 10e-3-Q Alo, It a-lal be M ott at oter hIt (g 1 tlhse ourve" may also bwe ued In oejtloo.o with 1 aofSrplh givb tia g. 3-3 or Fig. 3-6. The rw1ltl i time scale ohae it directly proportioal to chugl in thm X oale givAo in the nomograph. The procewe for finding the time oale ito follows: us Fig. 3-3 or Fig. 3-6 to find the chare in the X scale for the new height. This soale thou beoomes the ow 8 *oasle. The plot of power level i db below mldnao is now givre lurt So for t requred fixed Bhelht. For the eoood llhutrativo ca"e, let us coonder an airplane flying with oircular path, as llumtrted by the ground projection in Fi. 3-9. tf again, we choose to 0 when the airplane Is closest to the observation point (.e. a. point A in Fig. 3-9) we have at to 0, X(o) = 0 Y(o) ' YO If the radiu of circling s P (R/s ) then for any to, we have, X(t) -(p - Y).in (-) and S Y(to) p(P-Yo() Y t0) " p (0 — YO)coas ) * Numerical rolt* for p 1, ad Yo 0.1 aipresented in Fig. 3-10. The time of the propaaton for these cae can be also calculated. For the first case, (t) ~iX(t)2 + y+(- )2 T(t ) ' (3.14) 19

1082-3-Q Airplane Trajectory FIG. 3-9: GEOMETRY FOR AIRCRAFT CIRCLING WITH CONSTANT RADIUS R. 20

1082-3-Q 0 1 2 3 4 5 6 7 10 20 30 Sidelobe Mainlobe Note: Power received from feed No. 1 by an observer at (X = 0.9, Y = O, 9 = 1) for an aircraft circling about (X = 0, Y = 0) at a constant distance p = 1. Power Level (db Below Maximum) FIG. 3-10: RECEIVED POWER AGAINST NORMALIZED TIME FOR AN AIRCRAFT CIRCLING (Q = 1). 21

THE UNIVERSITY OF MICHIGAN 1082-3-Q Therefore, t+ '(t, V / S2 2 2 2 S s V S + +Y( (3.15) z o c o 1'' a a For the second case, Za 2 2 2 22 T (to) -^p-Y) asin2S + P -(p-Y )cosS +( )2 (3.16) Therefore, latV VA 2 2_ 2 2' Sm- S + -'y(p-Y )+p -2p(p-Y)cos +( (3.17) a o' o o y. ( 3.1 7 For normal aircraft flight, V, of course, is much less than c, so that the normalized S may be approximately taken as So. For a closer estimate, we see that the AN/APN-153 antenna is pulsed, withpulse duration approximately equal to a few microseconds. Thus for the duration of a 2 pulse, S is much smaller than Y, Y, or 1, and can be neglected from the second terms in the expression for S (Eq. (3.15) and Eq. (3.17)). This implies that as far as the average power is concerned, we may neglect the change of time delay due to the motion of the airplane * In other words the curves given by Fig. 3-3 and may be interpreted as illustrating the temporal variation of reflected radiation from a CW transmitter due to airplane motion. As a first approximation, for a pulsed transmitter, the intensity of the reflected radiation observed can be taken as the product of the two time functions, P (to) and M(to). In addition there will be a slight, and approximately constant shift of time scale given by Eq. (3.9) and (3. 11). This approximation should be good for the duration that the reflected radiation is detectable by an observer. Thus, it is a reasonable approximation to apply when calculating radated power. It is, of course, not valid when the frequency spectrum of the ifleted iifCtl&'tis aTider investigation. 22

THE UNIVERSITY OF MICHIGAN 1082-3-Q 3.3 Etoca To obtain a estiate o te effect of overcast on the doppler radiatio observed at any point, we consider here a pessimistic case: that the cloud layer pecularly reflects the radiation which reaches it. If the ground is also specularly reflecting, then the radiation observed at any point must consist of a sequence of rays representing the direct radiation, radiation reflected oe from the ground, the radiation reflected from ground and bouncing back from the cloud, etc. Analytical expressions for these rays were given in the previous Radiation Laboratory Memorandum 01082-508-M. For the calculation of the power level of these multpl reflected rays, it is seen that the calculated dat for the case of a specularly reflecting ground can be employed directing. In Fig. 3-11, the cloud layer is assumed to be of height s. Two rays are sketched: 1) The ray received by the observation point otter a single reflection from the ground and 2) The ray received after reflection once from the ground and once from the cloud. By the method of images, it is easy to see that the total radiation observed at any point may be considered as being due to an infinite set of sources (actually, sources and images) located at heights given by z + 2nz c n = 0, 1, 2,3..., and their respective images * the previous discussion the calculation of direct radiation and ground reflection due to sources at any height are formulated, Hence the tsl radiation observed at any point can be obtained by summing up all the reflected components. For example, for an antenna and observation point configuration described by the normalized coordinates X, Y and ~, the evaluation of the Theoretically, there is another set of image sources located at heights 2nz - z, n - 1, 2, 3... corresponding to rays reflected first from the cloud. However, for most normal operation of the radar, these components may be neglected because the beams are directed downwards. 23

1082-3-Q Image for once Reflected Ray from Cloud 1 \ z +z C a Specular Reflecting Overcast z =z C (Xa' Ya' Za) (x,y,h) z =0 z a FIG. 3-11: GEOMETRY FOR SITUATION IN WHICH THERE IS SPECULAR REFLECTION FROM CLOUDS. 24

THE UNIVERSITY OF MICHIGAN 1082-3-Q radiation from the various images can be obtained for the same X, Y by changing. For a source at height z + 2 n z, the value of e is given a c n by N (1+ 2n + E (3.18) + 1 2n (3.8) In order to present an estimate of the power levels of the various orders of reflected rays the following case has been considered X = 0.5 y 0 h Y = 0 = 0.817 or = 0.1 z a and z c 2. Z a In Fig. 3-12, the relative power levels of the direct and the reflected radiation are plotted against n. For the case of the curve marked "direct radiation", n 0 corresponds to the directed radiation, and any order n corresponds to rays reflected n times from ground and cloud. For the case of the curve marked "ground reflected radiation", each order n corresponds to rays reflected (n + 1) times from ground and n times from the cloud. The decrease in the power level with the multiplicity of reflection is to be expected* In practical cases, of course, the cloud and ground are not perfect reflectors, This fact may be accounted for by assuming a reflection coefficient r for the g *It should be noted that for some configurations (e.g., the observer "in line" with one of the multiple reflected rays which derives from the mainlobe) that the largest receiver power may occur for n # 0. These particular cases are at present being studied. 25

1082- 3-Q 0 I 2 3 4 5 n r-4 (1) Q) Q .q Q.) p. F.4 -0 pq P-4 o Q Q) > pq.r-4 V;G r —4 (1) 9 10, 20 - 'Direct' Radiation x x x n 'Ground Reflected' Radiation P —4 0) Q) 4 k Q 0 P4 0).0.4 4) P -4 —) C.) (1) -i "Z P-4 0 la) pq;8 x 20 - x x x x FIG. 3-12: RELATIVE POWER LEVEL FOR VARIOUS MODES OF REFLECTION. 26

THE UNIVERSITY OF MICHIGAN 102-3-Q W- a r bw - elmemd. t, t pwr.l at ehrdr at the "k~t " -1 bo dbtlit y tdw r Wm a )ot "reLat y r" asld be modfted by tho bet (I F rig e "Moteyd uy" shonld b modfod by tb fator f" (r I )u+1. Fwr lmd le vatlu r r e g. f6 It isalnobrlou that whesloslatul g the effect of olods, only a few of the reflected waves need to be eoaired. I ls to be oated that the m-ltlple rflected ay do aut remh the poit of oberrtkiN at the ame time. The time delay for eaeh order o the "direct ay" is give by t 2+Y2+ (3,19) 11+ while the time delay for each order of reflected rays is. ~^X2+Y +. (3.20) For the givea aenOple: X - 0.5 Y 0 ~ 0.817 and _2 S.2 the time delay for tho vlous orders o reflected rays is given in Fig. 3-13. 3.4 R to from a round The rflected radiation due to a completely difft ed ground observed at any point can be oomputed by Integrating the power radiated from each part of the 27

1082-3-Q 15 -10 - x X 'Direct' Rays.. ct z a 5 - Kx 0 I -t 2 3 4 5 x 15 -10 - x x x 'Ground Reflected' Rays ct z a 5 - / FIG. 3-13: TIME DELAYS FOR VARIOUS MODES OF REFLECTION. 0 - 28

THE UNIVERSITY OF MICHIGAN 1082-3-Q ground. Referring to Fig. 3-14, it is seen that the power density of the direct radiation reaching the ground at a direction (0, () from the antenna is, P G f2(0 0) Sd = 2 2 (3.21) 2 2 4wr z sec 0 a For any signal radiated from the antenna t, the direct radiation will reach a part of ground as indicated by AA in Fig. 3-14 at a time t z sec 0 t t + a (3.22) d o c From the geometry we have: 2 2 AA -z2 tan 9 sec20 A0 A0 a The power reflected by this elementary surface is P G f2 (, 0) SdcosAA - Sa 0 A * 0 (3.23) d 4 7 By the law of diffused reflection, this reflected power is uniformly distributed in the upper hemispherical region above A A, and would be observed at a point xh, Yh, h at atime t given by z a 2 2 1- 2' t = t d X-tan0cos0) +(Y-tan0sin0)2+ -+). (3.24) The observed power density reflected from this elementary area is, therefore, Ptt f2(. ) t 0 A O A ( 1) ra X- costans 2n./2..25 29

1082-3-Q I A(xa, Ya, zaa y 0 x FIG. 3-14: GEOMETRY FOR DIFFUSE SCATTERING. 30

THE UNIVERSITY OF MICHIGAN 1082-3-Q Due to the coordinate dependence of the time delay, a detailed analysis of the spatial and temporal variation of a pulsed signal from transmitter is extremely complicated. As a first approximation, based on a similar argument ( but less coninvingy, perhaps) to that given in Section 3. 2 we may investigate the power density of the reflected radiation observed at any point from a CW source, and use this result as the first order correction for the diffusely reflected power density from a moving, pulsed transmitter. For a CW transmitter, the observed power density at any point may be obtained by integrating Eq. (3. 25). The result is given by, PG 0' 702rr PtGt = S(xhYhh) = - L2 = 0 d r 2 'h 2 j.r J a 2 f2(0, ) sine(.L+) + ~* T5 L.(3.26) (X - tan cos 0) + (Y - tan slin)+ () 1 If we write PtGt S (xh y h) = S(X, Yo ) (3.27) 47nZ a a set of universal curves for SN may be calculated for the radiation pattern of the transmitter, and may be referred to as the "pattern functions" of each antenna. Numerical calculations for the pattern functions of the antenna pattern of AN/APN153 are currently being programmed and will be discussed in detail in the next report. In our Memorandum 01082-508-M, we have considered the scattering from a model of rough surface which is not completely diffused, nor a Lambert surface 31

THE UNIVERSITY OF MICHIGAN 1082-3-Q in the conventional sense. In that model, the surface is assumed to be composed of isotropic scatters that reflect radiation uniformly in all directions. For this model, it was shown that the power observed at any point, due to a CW source, and after scattering from the ground is given by PtGt dI do i =2' d (4 7 z )2 0 = = a _ f(9.) tan+(.4). (3.28) X-tan cos 0)2 + (Y - tan 0 sin 0)2 +( ) Therefore the pattern function for this model is given by N e= de d0 2 - (O.'-,- ~.. -,-tan 0....(3.29) *X-tanO0cos0)2 +(Y-tan0sin0)2 + ( < ). J The comparison of results derived from this "isotropic" model of the surface and the Lambert surface would of course yield some indication of the effect of the reflection properties of the surface on the intensity of the observed radiation. Numerical results for the radiation reflected by the "isotropic" model of diffused surface for the antenna AN/APN-153 have been discussed in detail in the Memorandum 01082-508-M. Further results are given in Figs. 3-15 and 3-16. To find the isotropically scattered power without resorting to a computer, an expression for the antenna pattern function must be assumed. In the progress 32

Normalized Power Density I \ r\ I I I I \ I \ I I I I I I I'\ I \ I I I \ /. 3 \ \.3 \ / / O 06 I / / / /.2 / / / = 0.817 / = 0.5 j/ 00 = 0. 333 -9 -1. -.5 0 Y FIG. 3-15: RECEIVED POWER FROM FEED NO. 1 AFTER ISOTROPIC SCATTERING FOR X = 0.4 AND VARIOUS VALUES OF ~.

Normalized Power Density.5 / / / / / / I "Oo. —., p / / / / / / / / / / / / \ \ \\/ ==0.817 V / o0 l\3 I 2 / / /.2 / / = = 0.33 e =0 -1.0 -.5 0.5 1.0 X FIG. 3-16: RECEIVED POWER FROM FEED NO. VARIOUS VALUES OF ~. 1 AFTER ISOTROPIC SCATTERING FOR Y = 0 AND

THE UNIVERSITY OF MICHIGAN 1082-3-Q report, 1082-2-Q by Chu et al (1968) the Gaussian beam was introduced. For this case, Eq. (3.26) has the following form: P. G -^ re 39 -S(xh Yh' h) = - t 2 4r hrz a = -9 - v 0 a a 2 ~[(a a)2+ (b~2] 2 2 e sec (9-a)sec sec da dd. 2 -2 2 tan n( -a)+ se C tan g+ 1 X I+ Y2+( 1+e ) + tan' -a)+ se c tain O- 21-2X2 a aa (3.30) where '1 a tan (6a - a) cos a - sec a tan 3 sin a and 2 A tan(0a -) sin a + sece tan cos0 The integral, Eq. (3. 30), cannot be evaluated easily by hald unless some stronger restrictions are placed on the shape of the beam. If the beam is assumed thin, i. e., that a and b are large, then it is possible to assume that the exponential term dominates. Finally, we find that 2 4 rz SN(XY ) PtGt ) Sr(h' Yh h) sec 9 a =a a + Y +( + )+ tan -2tan Xcos+ Ysin (3.31) (3.31) 35

THE UNIVERSITY OF MICHIGAN 1082-3-Q Figures 3-17 and 3-18 show the power received at fixed observation points in the direction of flight and in a direction perpendicular to the direction of flight. The corresponding curves obtained by numerical calculation are presented for comparison. This type of approximate solution will, it is expected, be much better fit to the actual solution for narrower beams than that of the AN/APN-153. Until we obtain the results for the power scattered by a diffuse ground, we will reserve making detailed comparison of these various curves. 3. 5 Effect of Refractive Properties of Atmosphere In the previous calculations of the radiation from a doppler radar system, the atmosphere is assumed to have the properties of free space. In practice, of course, the atmosphere has properties which vary with meteorological conditions and, in general it is stratified. Some dominant effects of meteorological conditions on the wave propagation considered in radar problems are: 1) The attenuation and scattering of radiation by precipitations and fog. Under these conditions there s an attenuation in the doppler signal whih is returned to the antenna as well as in that seen by an observer. The scattering by precipitations and fog usually causes a change in the radiation spectrum. As far as the power level of radiation is concerned, the actual power returned to the aircraft or received by the observer must be multiplied by an appropriate attenuation function. 2) The stratification of the atmosphere, i. e., the variation of the refractive index of the atmosphere with height. Thus stratification of the atmosphere, causes the rays to be curved, and at times focussed with the result that a net chage of the spatial distribution of the direct and ground reflected radiation occurs. Under extreme conditions, the gradient of the index refraction may cause the radiation to be guided along ducts and to be propagated over large distances without attenuation. 36

Normalized Power Density 1.0 0.8 — Experimental Results / 0.4 / Approximate Sol / of Integral for / / Gaussian Beamwith 0 = 21~ N ea 0= 1 20 0/ 0.2 N b '-pb 0 ^ N Ole -1. -.5 0.5 1. FIG. 3-17: NORMALIZED POWER DENSITY AFTER ISOTROPIC SCATTER FOR FEED NO. 1, Y = 0, = = 0. 817 AGAINS X r X

Normalized Power Density.8.6 I' I'\ CO I (Q6 / / /.mental Results / / / / -Approximate Sol of Integral for Gaussian Beam with 0 =21~, 0 =1.2~ a b. - - -1. -.5 0.5 1. Y FIG. 3-18: NORMALIZED POWER DENSITY AFTER ISOTROPIC SCATTERING FOR FEED NO. 1, X = 0.4, 9 = 0.817.

THE UNIVERSITY OF MICHIGAN 1082-3-Q A theoretical investigation of the effects of stratification primarily with application to doppler radiation has been started in this research period. Some mathematical deductions and approaches are outlined below. It is well known that the refractive index of the atmosphere changes with height, due to changes of air density, pressure, temperature, etc. with height. For the standard atmosphere, the rate of change of atmospheric index of re-6 fraction, n, with height is about -. 039 x 10 per meter (see NDRCreport (1946)). Over desserts and water a non-standard atmosphere is to be expected. The function n (z), the refractive Index profile, which describes the variation of refractive index with height must be used to characterize the atmosphere under such conditions. Further it is known that a discontinuity, or sudden change in the slope of n (z), in general, causes some form of trapping or ducting effect. Given an index profile n (z), the differential equations for wave propagation may be written down. However an analytical solution for these equations, for arbitrary n (z), are in general intractable. For high frequency propagation, the geometrical optics approaeh, or ray theory is adequate. For an account on the ray equation, and the amplitude variation along the ray in a stratified media, see Jones (1962). According to the ray theory, the field variation in the medium is approximately of the form: i- L P e c where P is the power density associated with the field, and W L is the phase c variation. The phase function L satisfies the Eikonal equation 39

THE UNIVERSITY OF MICHIGAN 1082-3-Q VL * VL = n2 (3.32) and the power density satisfies the power conservation relation V [PVL] = 0. (3.33) The radiation in a general media is primarily propagated along rays which are everywhere perpendicular to the surface of constant phase (or L). For a stratified media, differential equation may be derived from Eq.(3. 32) and(3. 33)to describe the ray path and the variation of L: dx c1 d Cl (3.34) 12 22 n (z) - c1 - c2 d = c2 (3.35) dz I2 2 2' 2 (z) -C1 - C2 and 2 dL n (z) ( =. - (3.36) d z 2 n (z)- c1- c2 where c1, c2 are constant along a ray. To investigate the effect of the stratification of atmosphere on the doppler radiation, we shall for convenience represent the function n (z) by several broken straight lines, and investigate the change of ray path, power density, and the possibility of trapping for several slopes of n (z). 40

THE UNIVERSITY OF MICHIGAN 1082-3-Q We shall first consider the direct radiation, assuming that the antenna is at (z, ya z ), and in an atmosphere characterized by a a8 n(z) = n(z ) + P(z-z ) (3.37) a a where p is the slope of n(z). Consider a ray starting from the antenna in a direction (0, 0). If the atmosphere is uniform, the ray follows a straight line path as indicated in Fig. 3-19 (path I). Now is the atmosphere is stratified then from Eq. (3.37) we see that for this ray: c = n(z ) sine cos0 (3.38) C2 = n(z )sinesin. (3.39) a Equations (337) through(3a 39) yield an expressionfor tf(z) which when substituted into Eqs. (3. 34) and (3.35) give the following solutions for the raf path: x-x n(z ) sine h 1 In(z )+ P(z-z ) -1 fCos0) a coshn co sin C) j j. Y- Y a os0 For p < 0,,, the ray is curved toward the source, (path II in Fig. 3-19). On the other hand, for p > 0, the ray is curved upwards, (path III in Fig. 3-19). This latter case is extremely undesirable in the operation of the doppler radar. In the first place, for some value of p and 0, the ray may be curved upwards without striking the ground, thus, causing a decrease or loss of the doppler signal. For a ray propagating from the antenna, the value of n(z) decreases as the ray approaches the ground, provided p > 0. From Eq. (3. 36) we find that the ray will not reach the ground unless n(o) > n(za ) sine a 41

1082-3-Q III I FIG. 3-19: RAY PATHS FOR A NON-CONSTANT REFRACTIVE INDEX. INDEX. 42

THE UNIVERSITY OF MICHIGAN 1082-3-Q 0 Now the major portion of radiation is concentrated at 0 - 20. Thus, if the vehicle is in a region at which the refraction index is over four times that near the ground the ray will never reach the ground. Furthermore for this case (p > 0), the reflected radiation is always traveling further, as evident from a comparison of rays II and III in Fig. 3-19. Numerical schemes for investigating how the profile gradient effects the detectability of doppler radiation will be continued in the next research period. Extension of the anlyis above, by considering n(s) to be composed of two or three straight line segments of differing slopes, will give an indication of the possibility of ducts forming. 43

THE UNIVERSITY OF MICHIGAN 1082-3-Q IV TRIPS Mr. Joseph E. Ferris visited the Canadian-Marconi organization in Montreal, Quebec, during the early part of March to discuss the systems being developed and produced by this organization. During this visit Mr. Haberl of Canadian-Marconi spent considerable time explaining and providing the visitor with information about systems being developed and the operation of Canadian - Marconi systems. Also during this visit pattern data for typical doppler systems was obtained. During the discussions it was learned that Canadian-Marconi does not make three-dimensional plots of their radiation patterns. However, they make an effort to obtain the two principal plane cuts and to evaluate the sidelobe levels and general pattern characteristics of their antenna on the basis of them. Their system operation is similar to that of the General Precision Laboratories (GPL) visited earlier by Mr. Ferris. Mr. Haberl expressed an interest in obtaining copies of our reports if they are available at the end of the contract. He felt it may be helpful to them in their future planning of the development of doppler systems. 44

THE UNIVERSITY OF MI CHIGAN 1082-3-Q REFERENCES Atwood, S. S. (1946), "Radio Wave Propagation Experiments,"t Summary, Technical Report of the Committee on Propagation, NDRC, Washington, D.C., II. Chu, C-M, J.E. Ferris and A. M. Iiagg(15 January 1968), Dw rt Radiation Study, The University of Michigan Radiation Laboratory Report No. 01082-2-Q. Jones, D. S. (1962), "High-Frequency Refraction and Diffraction in General Media," Phil. Trans..Roa Soc, 255, Series A, Londone Lugg, Andrew M. (1968), "Corrections to 1082-2-Q and a Outline of Work Completed Between January 15 through February 15 through Februy 15, 1968, The University of Michigan Radiation Laboratory Memorandum No. 01082-508-M. 45

UNCLASSIFIED <~ ttr ilna ifir:fatinn bectirity t-iassiticati onI I i DOCUMENT CONTROL DATA - R & D /cuf..tv classliication of tItle. hnodv of abstract find iidefxling annotation nuNtS be entered when tho overall report Is classified) 1. ORIGINATING ACTIVITY (Corporate autlhor) 20. REPORT SECURITY CLASSIFICATION The University of Michigan Radiation Laboratory, Dept. of UNCLASSIFIED Electrical Engineering, 201 Catherine Street, 2b. GROUP Ann Arbor, Michigan 48108 3. REPORT TITLE DOPPLER RADIATION STUDY 4. DESCRIPTIVE NOTES (Type of report and Inclusive dates) Quarterly Report No. 3 1 January 1968 - 1 April 1968 5. AUTHOR(S) (First name, middle irltial, last name) Chiao-Min Chu, Joseph E. Ferris and Andrew M. Lugg 6. REPORT DATE 7~. TOTAL NO. OF PAGES 7b. NO. OF REFS April 1968 45 1 4 8a. CONTRACT OR GRANT NO. O9. ORIGINATOR'S REPORT NUMBER(S) N62269-67-C-0545 b. PROJECT NO. 1082-3-Q c. r!h. OTHER REPORT NO(S) (Any other numbers that may he assitnce this report) d. 10. DISTRIBUTION STATEMENT I Requests for this document should be directed to NADC, Johnsville, Warminster, PA. 18974 _.-. II. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY U. S. Naval Air Development Center Johnsville, Warminster, PA 18974 - -- II A*qTRad-T I I J. A U I n A X I In this, the Third Quarterly Report on "Doppler Radiation Study', some results of the theoretical investigation and details of the experimental efforts are reported. Much of the experimental work is directed toward preparing the equipment which will be used during the forthcoming fly-by tests. The radar tracking, data collection and communication equipment has been checked out and is ready for the scheduled test. In the theoretical study, the numerical calculation of the spatial and temporal variation of the reflected radiation from a perfectly conducting ground, based on the scheme suggested in the last quarterly report, has been carried out. Further, some simplifications in presentation of the numerical results by using nomographs are introduced. The reflected radiation due to a diffusely reflecting ground is determined numerically and in an approximate but closed form; and finally the effect of some meteorogical conditions, such as cloud reflection, and the variation of the refractive index of the atmosphere are also considered. I r pLU 7 F 4L1u U A SI AF UL L I NOV 6514 73 UNCLASSIFIED St-cuurilN, C Iass if ticiitirc~n

UNCLASSIFIED Security Classification 14. LINK A L IN K 3 LINK C KEY WORDS | -.W RO L E W T ROLE J WT R OLE WT -.... i DOPPLER NAVIGATIONAL SYSTEMS AIRBORNE RADAR RADIATION PATTERNS GEOMETRICAL OPTICS U IR Ij L. L L. L L I a J I.__ _.J J / UNCLASSIFIED S ot- lrirtv t ('Iiri,.S i i t lol m