U.S. DEPARTMENT OF COMMERCENational Technical Informatimn Service

AD-709 897

MACHINE PLOTTING OF RADIO/RADAR VERTICAL-

PLANE COVERAGE DIAGRAMS

LAMONT V. BLAKE

NAVAL RESEARCH LABORATORYWASHINGTONj D.C.

JUNE 1970

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NRL Repeal 7096

Machine Plotting ofRadio/Radar Vertical-Plane Coverage Diagrams

LAMONT V. BLAKE

Radar Geophysics BranchRadar Division

June 25, 1970

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Naval Research Laboratory* Washington, D.C. 20390

3. RLPORT TtTLE

MACHINE PLOTTING OF RADIO/RADAR VERTICAL-PLANE COVERAGE DIAGRAMS

4. DESCRIPTIVE NOTES ("y'p. ol report end tnP.luaive datet)

An interim report on a continuing NRL Problem.S. AULTHORMS (F,.t nm*.e, mhddte ittitl, lost ha.m,)

Lamont V. Blake

6- REPORT DATE 78. TOTAL NO. OF PAGES (b. NO. OF RrFSJune 25, 1970 54 7

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NRL Problem 53R02-64.201b. PROJECT NO. NRL Report 7098SF-11-141-005-6173

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,,Fortran computer subroutines have been developed for machine plotting of radar or radiovertical-plane coverage diagrams for the case of interference between direct and sea-reflectedwaves. One set of subroutines plots detection or constant-signal-level contours on a range-height-angle chart. A secqnd set plots signal level in decibels as a function of range for atarget at a fixed (low) altitude. The first type of plot is valid for antenna heights that arewithin a few hundred feet of the water and for targets that are at much higher altitudes andnot too close to the horizon. The second type is valid for antenna and target heights that areboth less than a few thousand feet altitude, with no restriction on minimum altitude. Normalatmospheric refraction is taken into account, but scattering and ducting are assumed to be ofnegligible effect. The frequency range considered is from about 100 MHz to 10 GHz. Thefactors taken Into account are frequency, antenna and target heights, antenna beamnwidth, tiltof the beam with respect to the horizon, roughness of the sea (wave height), polarization of theradio waves, and the calculated or assumed free-space range. Sample plots are shown anddiscussed. The plotting techniques employed are briefly described, and listings of the essen-tial Fortran subroutines are given in an appendix.

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RadarRadioDetectionPropagationSignal detection

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CONTENTS

Abstract itProblem Statue itAuthorization it

INTRODUCTION 1

INTERFERENCE OF DIRECT AND REFLECTED WAVES 1

Patter n-Propagation Factor IPath Difference and Divergence Factor 3Surface-Roughness Factor 5Approximate Method for Distant Targets 5Reflection Coefficient of Sea Water 6

THE INTERMEDIATE REGION 9

WLBE PLOTTING 11

Detection- or Constant-Signal-Strength-ContourRange-Height-Angle Plots 11I Signal-Strength-vs-Range Plot for Constant-AltitudeTarget 19

PLOTTING TECHNIQUES 22

ACKNOWLEDGMENTS 23

REFERENCES 24

APPENDIX A - Approximate Equations for Spherical-EarthInterference Calculation 25

APPENDIX B - Listings of Fortran Subroutines 29

)ib

[I.

ABSTRACT

Fortrqn computer stiritutines have been developed for machineplotting of radar or radio vertical-plane coverage diagrams for thecase of interference between direct and sea-reflected waves. One setof subroutines plots detection or constant-signal-level contours on arange-height-angle chart. A second sat plots signal level in decibelsas a function of range for a target at a fixed (low) altitude. The firsttype of plot is valid for antenna heights that are within a few hundredfeet of the water and for targets that are at much higher altitudes andnot too close to the horizon. The second type is valid for antenna andtarget heights that are both less than a few thousand feet altitude, withno restriction on minimum altitude. Normal atmospheric refraction istaken into account, but scattering and ducting axe assumed to be ofnegligible effect. The frequency range considered is from about 100MHz to 10 GHz. The factors taken into account are frequency, antennaand target heights, antenna beamwidth, tilt of the beam with respect tothe horizon, roughness of the sea (wave helght), polarization of theradio waves, and the calculated or assumed free-space range. Sampleplots are shown and discussed. The plotting techniques employed arebriefly described, and listings of the essential Fortran subroutines aregiven in an appendix.

PROBLEM STATUS

This is an interim report on a continuing NRL Problem.

AUTHORIZATION

NRL PROBLEM R02-64Project SF-11-141-005-6173

Manuscript submitted Marnh 16, 1970.

III

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MACHINE PLOTTING OF RADIO/RADARVERTICAL-PLANE COVERAGE DIAGRAMS

INTRODUCTION

When the antenna of a radar or radio station in the VHF to microwave frequencyrange overlooks a reflecting surface, such as the sea, the free-space radiation and re-ception patterns are modified by the presence of a reflected wave, in addition to the wavethat goes by a direct path from the transmitter to the receiver (by way of the target inthe radar case). The modified pattern in the vertical plane is the result of phasor-vectoraddition of the direct and reflected waves; it is an interference pattern, withlalternatemaxima and minima, or lobes and nulls. In optics this phenomenon is known as theLloyd's mirror effect. It is an effect well known to naval radar operators, and the math-ematics of the problem have long been welU understood. In the lobe maxima, the radarecho signal may be increased by as much as 12 dB compared to the free-space signal.In the minima, or nulls, on the other hand, the signal strength may theoretically go tozero.

It is frequently desired to make a plot of the vertical-plane coverage diagram of aradar, taking into account this interference effect, in order to predict regions in whichtargets will and will not be detected. The computations required for such a plot, and theactual plotting, are extremely tedious even though basically straightforward. The obvi-ous present-day solution of this type of problem is the use of digital machine computationand machine plotting. The purpose of this report is to describe a procedure of this typethat has been developed, and to show some typical resulting plots. It is believed that thisprocedure constitutes a valuable tool for the system designer and operational analyst. Itallows detailed plots to be produced in a short time and at moderate cost. These plotsenable the effects of various parameters to be studied visually. To attempt the samething by manual methods would take an inordinately long time and would be prohibitively

* .expensive.

INTERFERENCE OF DIRECT AND REFLECTED WAVES

Pattern-Propagation Factor

The geometry of the interference problem is shown in Fig. 1, with heights greatlyexaggerated relative to range. The mathematikal formulation of the problem that followsis a modification and slight generalization of the one given by Kerr (1), except for Eqs.(24), (25), and (26), which are derived in Appendix A.

It is apparent'that the direct-path wave and the reflected wave traverse differentdistances in going from the antunna to the target; their path difference is

8 - R + R2 - R. (1)

The phase difference'of the two interfering waves due to this path difference is 2b,'/x ra-dians, where x is the radar wavelength. The total phase difference a of the two wayesis this path-length phase difference plus the phase change P that occurs in the reflectionprocess.

2 L. V. BLAKE

TARGET

RR

RADAR 4

T - . FLAT EARTH

REFtECTION CURVE

POINT EARTH

Fig. 1- Geometry of the surface-reflectioninterference problem

If the tivo interfering waves have (at least approximately) the same vector (spatial)

direction, then the, most important factor in their addition is their phasor relationship.The resulting electric-field phasor is

E = idl + - E eZ I (2)

where E