ANALYSIS OF ANGLE-OK-ARRIVAL MEASUREMENTS 



209 



RCVR 



XMTR 



492' 



353' 



RCVR 



XMTR 



HORIZONTAL PLANE 



RCVR 



> EARTH 

 SINGLE DIRECT PATH 



Figure 6. Types of vertical variation in ray paths. 



refractive index between receiver and transmitter 

 must be in range — 2.4 to -|-3.4 M units. Tliese 

 limits liold for an approximately linear variation of 

 index between receiver and transmitter. 



Radiation along paths of type C, which penetrates 

 the layer below the receiver height (see Figure 6B), 

 arrives at the receiver at an angle a < ; therefore, M 

 will of necessity increase l\y more than 2.4 units from 

 receiver to transmitter. We consider three stratifica- 

 tions producing paths of this category. 



1. The so-called "standard" atmosphere utilized 

 for the purposes of representing "normal" propagation 

 by rectilinear rays on an earth distorted to a radius 

 4/3 that of the true earth. The increase of M is at a 

 rate of 3.6 units per 100 ft. 



2. Adiabatic equilibrium for an unsaturated at- 

 mospheric layer, representing the condition of a com- 

 pletely stirred or mixed stratum of air. The increase 

 of M is 4.0 units per 100 ft. 



3. Rectilinear propagation on a true earth. For this 

 condition there is no variation of electromagnetic 



velocity with height, and M increases by 4.76 units 

 per 100 ft, ec^ual to the rate of curvature of the earth. 

 The computed deviations of the angles a and /? at 

 the recei^'er and transmitter, respectively, are given in 

 Tal)le 2. It will be noted that the condition of recti- 

 linear propagation on a true earth produces an angle 



Table 2 



Type of 

 atmospheric 

 stratification 



"Standard" 

 atmosphere 



Adiabatic 

 equilibrium 



Rectilinear 



propagation on 

 a true earth 



Deviation 

 Of at /3 at of a and /3 



receiver transmitter from true 

 (degrees) (degrees) bearing m 



- 0.069 - 0.194 + 0.042 2.44 



- 0.0S3 - 0.20S + 0.02S 0.16 



0.111 



0.236 











a = — 0.11°, which is the true bearing from receiver 

 to transmitter. From the data of Table 1 it follows 

 that a "standard" atmosphere and an atmosphere 

 vertically mixed so as to be in adiabatic equilibrium 

 both provide a variation of modified refractive index 

 with height of a magnitude such that the angle of 

 arrival measured at the Beer's Hill receiver under 

 these conditions is within 0.04° of true geometric 

 bearing. In view of the fact that the instrumental ac- 

 curacy of the Beer's Hill antenna system is ±0.04°, 

 it follows further that the differences among these 

 three meteorological stratifications will not be evident 

 in the measurements. 



Consider now a case in which the radiation path 

 penetrates the layer above the transmitter. The oc- 

 currence of an angle of arrival at the Beer's Hill re- 

 ceiver in excess of 0.336° above true bearing will re- 

 quire a path of propagation rising to some level above 

 the New York City transmitter. The variation of M 

 with height within the layer immediately above the 

 transmitter will be critical in determining the magni- 

 tude of the signal received and its angle of arrival. 

 The analysis following is limited to one particular 

 case of this category producing an extreme deviation 

 from true bearing in the angle of arrival. 



For the paths shown in Figure 6C, the M distribu- 

 tion between 353 and 492 ft above mean sea level is 

 that computed from the observed meteorological data 

 on the 400-ft tower at 0800 on Jiily 7, 1944. Using 

 only this portion of the actual sounding, the variation 

 of modified index of refraction in the layer immedi- 

 ately above the transmitter has been computed as a 



