PROPAGATION OF RADIO WAVES 



0.039 X 10-« units per meter (3) 



_1_ ^ _ rfn _ 



p dh 



and p, therefore, is equal to 25.5 X 10" meters, which 

 is approximatelj'' four times the radius of the earth 

 (p = 4a). As a result the distance to the radio horizon 

 is some 15 per cent greater than the geometrical line- 

 of -sight distance from the transmitter to the horizon. 

 This curvature of the rays by the atmosphere is 

 called refraction. 



Figure 2. Curvature of lays in the standard atmos- 

 phere. 



For the purpose of calculating waxe propagation, 

 only relative curvature of the earth and the rays is 

 of interest. We can be compensated for the effects 

 of refraction by replacing the actual earth with a 

 radius a by an equivalent earth with a radius ka 

 and replacing the actual atmosphere (in which the 

 index of refraction n decreases with height) by a 

 homogeneous atmosphere (constant n) in which the 

 rays are straight lines. Since \/a is the curvature 

 of the earth and 1/p the curvature of the rays, we 

 may set their difference equal to l/ka, the curvature 

 of the equivalent earth. Thus 



and 



k 



(4) 



l-(«/p) 



1 



Since p = 4a, k = 4/3, and ka, the radius of the 

 equivalent earth, equals 8.49 X 10^ meters. See 

 Figures 4 and 5 in Chapter 4. 



Not infrequently the lower atmosphere is stratified 

 in horizontal layers in which the variations with 

 height of the temperature and moisture content 

 are nonstandard. Of particular interest is a sharp 

 rise m temperature with increasing height (tempera- 

 ture inversion), or a sharp decrease m water vapor 

 content, or a combination of the two. If these varia- 

 tions from the standard distribution are sufficiently 

 great, horizontal radio ducts may be formed in the 

 atmosphere. In this event an appreciable fraction 

 of the wave energy (only that fraction mov-ing in the 

 nearly horizontal direction) may be constrained to 

 propagate along the duct to distances far beyond 

 the horizon and the field strength may be large 

 compared vnt\\ tlmt obtainable under standard 

 conditions. This phenomenon produces a marked 

 bending of the wave paths or rays and is known as 

 super-refraction. To take fullest advantage of this 

 phenomenon the antennas should be located in the 

 duct. 



Ducts are of various types: 



1. Overland. These are surface ducts formed at 

 night by the radiation cooling of the earth. 



2. Oversea. In the trade-mnd belt there appears 

 to be a continuous duct of the order of 50 ft thick 

 starting at sea level. 



3. Land to sea. Warm dry air flowing from land 

 out over cooler water often .vields surface ducts 

 100 or more feet thick. 



4. Elevated. Caused by subsidence of large air 

 masses, these ducts may be found at elevations of 

 perhaps 1,000 to 5,000 ft and may vary in thickness 

 from a few feet to 1,000 ft. They are common in 

 Southern California and certain areas in the Pacific. 



Depending upon the strength and the thickness 

 of the duct, there is a limiting frequency below 

 \\hich the duct cannot trap the wave energy. 

 Though trapping does at times occur at 200 mc, 

 it is more likely to occur at the higher frequencies 

 such as 3,000 mc. 



Abilitj' to calculate performance under standard 

 conditions is necessary if performance under non- 

 standard conditions is to be evaluated. 



1.2.5 Propagation in Nonstandard 

 Atmospheres 



Though this subject is beyond the scope of this 

 volume it is desirable to present a brief discussion 

 of the salient features. 



1.2.6 



Radio Gain 



The basic problem to be solved is that of com- 

 puting the radio gain of a transmitting-receiving 

 system. 



The radio gain of a tran.smitting-receiving system 



