46 



ELEMENTARY THEORY OF NONSTANDARD PROPAGATION 



ALTITUDE IN FEET 

 7000 



1 



2 



GROUND BASED DUCT 



v -' 1000 



GROUND BASED DUCT> 



4 



ELEVATED DUCT» 100 ° 



TRANSMITTER HEIGHT-100 

 FREQUENCY- 200 MC 



ELEVATED DUCT> K '°° 



c 



J 



BLIND ZONE DETECTION ZONE 



NORMAL LIMITING~COVERAGi 



RANGE IN NAUTICAL MILES 



Figure 5. Calculated coverage diagram. 



65 GENERAL CHARACTERISTICS 



OF DUCTS 



It is evident that the number of types of M curves 

 that one can construct a priori is almost unlimited. 

 In practice both the types actually occurring and 

 their variability within each type of classification 



are severely limited by meteorological conditions. 



M, as defined by equation (4), is the sum of two 

 parts, the true refractive part (n — 1) and the earth 

 curvature part h/a. At higher elevations the absolute 

 moisture in the atmosphere decreases, and irregular 

 variations of temperature become more and more 

 exceptional so that eventually, at a relatively great 

 height, any M curve approaches the standard curve. 

 An additional limitation comes from the fact that 

 both the temperature and moisture variations in any 

 one climate are subject to definite limitations. An 

 extreme moisture change occurs when there is a 

 boundary separating a nearly or fully saturated 

 warm air mass from a very dry cool air mass. Tem- 

 perature inversions involving differences of more 

 than 10 to 15° C are quite exceptional. As a conse- 

 quence of this both the actual height of the M 

 inversion as well as the difference AM between the 

 maximum of M at the bottom and the minimum at 

 the top of the M inversion are limited. The height of 

 the M inversion layer may be only a few feet if it is 

 close to the ground or sea surface. It frequently is 

 of the order of 50 to 100 ft or even larger. Under 

 particularly favorable conditions in warm climates, 

 elevated M inversions may have heights of several 

 thousand feet. The duct itself can be appreciably 

 thicker than the M inversion layer, as may be seen 

 from the structure of the last two M curves in 

 Figure 1 . 



Again, the decrease AM over the height of the in- 

 version is limited for the same reasons. For low 

 ducts values of the order of AM = 5 to 10 are com- 

 mon. Somewhat larger values will sometimes occur. 

 The maximum value observed is about AM = 40 in 

 high-level inversions at San Diego which originate 

 in the singular climatic conditions found there. 



An important consideration for the detailed mathe- 

 matical treatment of duct propagation is the shape 

 of the knees of the M curve. This, again, depends on 

 the physical nature of the atmospheric stratification. 

 Very often the inflections are so sharp that a succes- 

 sion of two or three straight lines furnishes an excel- 

 lent approximation. These are known as bilinear and 

 trilinear ducts and are of very common occurrence, 

 especially with elevated ducts and a large class of 

 ground-based ducts. On the other hand, there are 

 also ground-based ducts in which the corners are 

 extremely well rounded. 



It follows from the restrictions on the numerical 

 values of M that there are severe limitations on the 

 angle a for which duct effects can occur. Thus AM = 



