RADIO PROPAGATION FUNDAMENTALS 603 



Refraction 



The dielectric constant of the atmosphere normally decreases grad- 

 ually with increasing altitude. The result is that the velocity of trans- 

 mission increases with the height above the ground and, on the average, 

 the radio energy is bent or refracted toward the earth. As long as the 

 change in dielectric constant is linear with height, the net effect of re- 

 fraction is the same as if the radio waves continued to travel in a straight 

 line but over an earth whose modified radius is: 



a 



ka = — 



1 , « ^ (7) 



"^ 2 dh 



where 



a = true radius of earth 



— = rate of change of dielectric constant with height 



CLil 



Under certain atmospheric conditions the dielectric constant may in- 

 crease (0 < /v < 1) over a reasonable height, thereby causing the radio 

 waves in this region to bend away from the earth. This is the cause of 

 the inverse bending type of fading mentioned in the preceding section. 

 It is sometimes called substandard refraction. Since the earth's radius 

 is about 2.1 X 10^ feet, a decrease in dielectric constant of only 2.4 X 

 10"^ per foot of height results in a value of A- = ^, which is commonly 

 assumed to be a good average value. ^ When the dielectric constant de- 

 creases about four times as rapidly (or by about 10~^ per foot of height), 

 the value of A- = oo . Under such a condition, as far as radio propagation 

 is concerned, the earth can then be considered flat, since any ray that 

 «ta,rts parallel to the earth will remain parallel. 



When the dielectric constant decreases more rapidly than 10~'^ per 

 foot of height, radio waves that are radiated parallel to, or at an angle 

 above the earth's surface, may be bent downward sufficiently to be re- 

 flected from the earth. After reflection the ray is again bent toward the 

 earth, and the path of a typical ray is similar to the path of a bouncing 

 tennis ball. The radio energy appears to be trapped in a duct or wave- 

 guide between the earth and the maximum height of the radio path. This 

 phenomenon is variously known as trapping, duct transmission, anoma- 

 lous propagation, or guided propagation.'"- " It will be noted that in 

 this case the path of a typical guided wave is similar in form to the path 

 of sky waves, which are lower-frequency waves trapped between the 



