RAY THEORY 357 



Bauer, Mason, and Wilson [28] obtained an equation for accurately 

 estimating radar target heights in a specific exponential atmosphere. 

 Beckmann [29] presented a i)robability estimate of the height errors with- 

 out meteorological measurements. 



The purpose of the study is to investigate the correlation between 

 available meteorological ])arameters and height errors for targets of 

 interest in terminal air traffic control and to develop height error correc- 

 tion procedures using these parameters. 



8.4.2. Refractive Index 



The radio refractive index, n, of a propagation medium is the ratio of 

 the free space velocity of light, c, to the velocity in the medium, v, (i.e., 

 n = c/v). Since the propagation velocity of the atmosphere is only 

 slightly less than the free space velocity, it is often convenient to use the 

 scaled up difference between the refractive index and unity. This ciuan- 

 tity is the refractivity. 



The refractivity is obtained from (1.20). Normally, the equation for 

 N is dominated by the first term so that the refractivity can be approxi- 

 mated by an exponential function of height as shown in section 3.8. 



8.4.3. Ray Theory 



If the refractive index is assumed to satisfy (for a spherically strati- 

 fied atmosphere) 



I > - 7- («-^«) 



then, for frequencies greater than 100 kc/s, the path of a radio ray is 

 determined by Snell's law for polar coordinates (3.1) of chapter 3 (see 

 fig. 8.27) and the bending angle, r, is determined from (3.2). The dis- 

 tance, d, along the surface of the earth is obtained from (3.62). 



The length of the path is called the geometric range and is obtained by 



R = I CSC dr, (8.30) 



and the apparent or radio range is found by 



Re = I n CSC e dr = R -\- N X 10"^ esc d dr. (8.31) 



