640 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



in the table. This is a characteristic feature of beyond-the-horizon prop- 

 agation. In free space, doubling the antenna dimensions would result 

 in a r2-db increase in output power. 



Large antennas and high power transmitters are costly, and a proper 

 balance between their costs requires careful studies which are outside 

 the scope of this paper. In general, it is not believed worth while from 

 power considerations to increase the antenna size much beyond the di- 

 mensions that correspond to a pattern angle, a, equal to angle d. 



Another factor to be considered, however, is the effect of antenna size 

 on delay distortion in bej'ond-the-horizon circuits. From simple path 

 length considerations, one concludes that the delay distortion decreases 

 when the beamwidths of the antennas are made smaller. Therefore, delay 

 distortion requirements may dictate antenna sizes that are not justified 

 by power considerations alone. 



SEASONAL DEPENDENCE 



Both the effective earth radius. Re , and the magnitude of the discon- 

 tinuities in gradient, Ki , are related to the season of the year. During 

 the summer when the water vapor content of the air is high, the effective 

 radius and the discontinuities in gradient are larger than in winter. Sub- 

 stituting a/Re for 6 and assigning summer and winter values for Re and 

 Ki , (12) may be used to calculate the ratio of the power received in 

 summer and in winter. 



Pr (Summer) 

 P« (Winter) 



(21) 



For example, if we assume Kis = 2Kiw and Res =1.2 Rew , then Prs/ 

 Prw = 11-9 (10.75 db). A seasonal variation has been observed.^ ^ 



DEPENDENCE OF RECEIVED POWER ON ANTENNA ORIENTATION 



The variation of received power with orientation of the antennas at 

 the terminals of a be\'ond-the-horizon circuit differs considerably from 

 that observed under line-of-sight conditions. Consider, for example. Fig. 

 10 which shows the beams of the transmitting and receiving antennas 

 elevated simultaneously. The variation of received power can be calcu- 

 lated from (13). As an example, consider the 188-mile circuit between 



