REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 643 



lations are identical with the calculations for elevation steering; the ele- 

 vation angle 62 is related to the azimuth angle 5 and the beamwidth angle 

 a by 



A calculated curve of received power versus azimuth angle is shown in 

 Fig. 1 1 for the Crawford Hill-Round Hill circuit together with the re- 

 ported experimental data. The agreement is considered good. 



THE VALUE OF FACTOR M IN EQUATION (12) 



An average value for the factor M can be obtained from propagation 

 data. Using equation (12), the ratio of received powers corresponding to 

 free space and beyond-horizon transmission is 



D n- ^ 0.750' f 2 + f) 



Pr (tree space) _ \ 6 J , . 



Pr (beyond-horizon) 



MKaj 



© 



This ratio was found experimentally to be 5 X lO*' (67 db) for the circuit 

 between St. Anthony and Gander in Newfoundland. For this circuit, 

 a = 0.081, 6 = 0.0164, X = 0.6. Substituting these values in (22) we 

 obtain, 



ilf = 3 X 10"'* (23) 



Substituting this value for M in (12) leads to the following equation for 

 a beyond-horizon tropospheric circuit. 



p^ = P^X 10-'" -' 



a" 



(24) 



Equations (6) and (23) give 



b'K'N = 1.5 X 10"'' (25) 



Although values of the layer dimension, b, the change in gradient, Ki , 

 and the number of layers per unit volume, N, are not known, it is interest- 

 ing to calculate A^ from (25) assuming reasonable values for b and A'l . 

 Assuming A'l = 4 X 10"*", which is half the value of K', the average 

 gradient of the dielectric constant in the troposphere, and b = 1,000 

 (1 km) we find A^ = 10"^ or 10 layers per cubic kilometer. 



