MODIFIED EFFECTIVE EARTH'S RADIUS 59 



which upon substitution from (3.33) and (3.31) gives 



do.ft = V2/i(4/3) a, (3.36) 



or, more familiarly, 



do,h = V2kah . (3.37) 



A very convenient working formula is derived from (3.37) hy k = 4/3, 

 a = 3960 miles and using units of miles for the ground distance to the radio 

 horizon, do,h, and feet for the antenna height, h: 



do.h = V2h miles (3.38) 



This is the familiar expression often used in radio propagation engineer- 

 ing for the distance to the radio horizon. 



3.7. Modified Effective Earth's Radius Model 



The effective earth's radius model, although very useful for engineering 

 practice, is not a very good representation of actual atmospheric A^ struc- 

 ture. For example, the data on figure 3.3 represent the average of 

 individual radiosonde observations over a 5-yr period at several locations 

 chosen to represent the extremes of refractive index profile conditions 

 within the United States. The Miami, Fla., profile is typical of warm, 

 humid sea-level stations that tend to have maximum refraction effects 

 while the Portland, Me., profile is associated with nearly minimum sea- 

 level refraction conditions. Although Ely, Nev., has a much smaller 

 surface A'^ value than either Miami or Portland, it is significant that when 

 its A'^ profile is plotted in terms of altitude above sea level, it falls within 

 the limits of the maximum and minimum sea level profiles. It is to take 

 advantage of this simplification, that altitude above sea level rather than 

 height above ground is frequently used throughout this monograph. The 

 A'' distribution for the 4/3 earth atmosphere is also shown on figure 3.3. 

 It is quite evident that the 4/3 earth distribution has about the correct 

 slope in the first kilometer above the earth's surface but decreases much 

 too rapidly above that height. It is also seen, by noting that figure 3.3 is 

 plotted on semi-logarithmic paper, that the observed refractivity distri- 

 bution is more nearly an exponential function of height than a linear 

 function of height as assumed by the 4/3 earth atmosphere. One might 

 expect the refractivity to decrease exponentially with height since the 

 first term of the refractivity equation (1.20) involving P/T, comprises at 

 least 70 percent of the total and is proportional to air density, a well- 

 known exponential function of height. 



