ANALYSIS OF ANGLE-OFARRIVAL MEASUREMENTS 



207 



angie-of-arrival studies through next year. Eecords 

 made to date are now being studied in detail, and a 

 report will probably be written covering this work. 



13.2 METEOROLOGICAL ANALYSIS OF 

 ANGLE-OF-ARRIVAL MEASUREMENTS" 



^^"■^ Purpose 



Recent experiments on propagation in the X band 

 conducted by Bell Telephone Laboratories [BTL] 

 have indicated that the angle of arrival of microwaves 

 may be considerably at variance with that computed 

 on the basis of rectilinear propagation. Deviations as 

 large as 0.-16 degree from true bearing'^ were measured 

 during the summer season over a 34-mile path, partly 

 over land and piartly over water. The deviations found 

 experimentally exceed considerably the tolerances spec- 

 ified on angle of elevation, azimuth, and height deter- 

 mination in present military characteristics on fire- 

 control radar equipment. 



An analysis of propagation from the meteorological 

 point of view has been undertaken to determine 

 whether deviations from rectilinear propagation can 

 be explained by, and predicted from, meteorological 

 data and whether observed extreme deviations can be 

 realized from plausible meteorological stratification. 

 The Bell Laboratories' experimental angle-of-arrival 

 measurements made during the summer of 194-t have 

 been compared with deviations evaluated from mete- 

 orological data obtained concuri'ently by the Signal 

 Corps though not coordinated at tJie time with tliese 

 exjoeriments. The current paper is intended to report 

 the results of this study and the procedure utilized in 

 the analysis and, in turn, to establish a framework 

 for interpreting further propagation experiments of 

 this type. 



13.2.2 Theory 



The equations of propagation can be written in a 

 form such that the angle of departure of the radiation 

 at the transmitter (the direction of the normal to the 

 wave front) and the angle of arrival at the receiver 

 can be written as functions of the meteorological 

 stratification and the constants of the installation (dis- 

 tance between and heights of transmitter and re- 

 ceiver). The solution of the equations of motion is 



••By George D. Lukes, Signal Corps Ground Signal Agency. 



"The term "true bearing" as used in this paper refers to the 

 vertical angle between the horizontal and a line perpendicular 

 to the wave front at the receiving point. 



gi\cu below by the use of an electromagnetic wave 

 velocity profile obeying a radial power law. The re- 

 lation of the exponent m in this power law to the 

 excess modified refractive index M is then deduced. 

 The power vi in the velocity profile equation is as- 

 signed the definition of "meteorological stratification 

 parameter," since it determines the change of modi- 

 fied index of refraction with height. 



Figure 4. Geometry of a ray in tlie atmosphere. 

 From Figure 4, 



de 



dr ds 



(1) 



?■ tan /? b 

 Introduce the electromagnetic wave velocity profile 



(2) 

 (3) 

 (4) 



(5) 

 (6) 

 (7) 



(8) 



ds dfi 



Now 

 where 



h 1 — m 



r=b + h, 



