UL TRA -SHOR T-WA VE PROP A GA TION 



257 



represented by ri, and by reflection at G, as represented by ri, the 

 distance between transmitter and receiver being represented by d. 

 For the practical case where hi and h^ are small compared with d 

 the reflected wave impinges upon the ground at nearly grazing in- 

 cidence, so that a negative reflection coefficient the magnitude of 

 which is unity ^ for ordinary ground (not water) is obtained. This 



Fig. 3. 



results in the field at B being the difference between two vectors of 

 approximately equal magnitude and differing in phase by an amount 

 corresponding to the difference in path lengths, r^ and ri. For the 

 case under consideration, 



rs - ri = Ihxhild, (1) 



and the angle between the vectors is 



2ir{ri - ri)l\ = ^Thih^/Xd. (2) 



^ The magnitude is more e xactly 1 — 2e{hi -f hijld-^e — 1 for vertical polarization 

 and 1 — 2(/ji + h2)/d'\e — 1 for horizontal polarization, making the corresponding 

 values for the received fields. 



/!+• 



Khi + h^yx' 



and 





(e - \)^T^%i%2^ 



(O) 



{b) 



respectively, instead of as in equation (3). When the lower of the two antennas is 

 more than a couple of wave-lengths off the ground, the radicals are substantially 

 unity. For the case under consideration it would be more accurate to refer to ex- 

 pression (a) as the theoretical formula but lack of knowledge of the magnitude of 

 the dielectric constant and antenna heights that apply would introduce unnecessary 

 uncertainty if the results were referred to this formula. It might be remarked that 

 neglecting the presence of buildings and referring all heights to the local street level 

 the radical represents an increase of 7-12 db for vertical polarization in the cases 

 under consideration. 



