I 'L TJti -SHOR T- ]VA I 'E TRA NS MISSION PHENOMENA 



221 



LEVEl 



Fig. 22 — Geometry of airplane reception, 

 where, 



£o = the free space field at distance of 1 mile 

 K = amplitude change at reflection 

 6 = phase change at reflection 



{K and d are functions of the angle of incidence and the ground 



constants) 

 (;.2 — n) = the path length difference between direct and re- 

 flected ravs. 



(r2 - ri) = 



2H1H2 2AB tan2 $ 



D 



D 



(2) 



provided Ih and Ih are small in comparison with D. 



Ill and H2 are the heights of transmitter and receiver above the 

 plane tangent to the earth at the point of reflection. 



The height of the tangent plane above the earth's surface is 



Ai = i? 



and, 



1 + 



l+TT, 



4: 



= ^ (app.) 



(3) 



A2 = 



B^ 

 2R 



R is the radius of the earth, which, due to atmospheric refraction, is 

 taken to be 5260 miles,^ an increase of 33 per cent over the actual 

 radius. {Hi + Ai) is always 280 feet, the height of the transmitting 

 antenna above the reflecting surface, which, in the case at hand, is 

 about 100 feet above sea level. 



(7/2 + A2) is constant for any flight at constant altitude. 



For any value of A, H, and hence tan * may be calculated and 

 plotted as in Fig. 23. In this figure B is also plotted, for a flight at 

 8000 feet, against tan *. The total distance D is obtained by adding 



8 Schelleng, Burrows, and Ferrell paper, this issue of Bell Sys. Tech. Jour. 



