58 



FACTORS INFLUENCING TRANSMISSION 



thumb for the applicability of the reflection formulas 

 is that the A'ertical height of the irregularities should 

 not exceed X/16i^, where X is the wavelength andi/- 

 the grazing angle in radians. Suppose, for instance, 

 that the wavelength is 1 meter and the grazing angle, 

 1 degree. The limit of tolerance is then 56/16 = 3.5 

 meters. Hence, on this wavelength one may expect 

 specular reflection o\'er sea in most cases. For 

 X = 10 cm, on the other hand, the limit is only 35 cm, 

 and for X = 3 cm it is 11 cm. For larger grazing 

 angles, the limit of tolerance will be correspondmgly 

 smaller. 



*^ DIFFRACTION (GENERAL SURVEY) 

 *^ ' Definition 



The term diffraction -wall be understood to apply 

 to those modifications of the field produced by 

 material bodies outside the transmitter that cannot 

 be described Ijy the ray methods of geometrical 

 optics. 



With this limitation of the term diffraction, there 

 are three main topics to be considered: 



1. Diffraction by the earth's curvature. 



2. Diffraction by irregular features of the terrain, 

 such as hills, houses, etc. 



3. Diffraction by objects, primarily metallic 

 (targets) in two-way transmission (radar echoes). 

 Also scattering by raindrops. 



4.3.2 



Diffraction by Earth's Curvatvire 



The diffraction field in this case is the field appear- 

 ing below the line (jf sight determined by use of the 

 equivalent \'alue of the earth's radius ka. The case 

 of an idealized earth with smooth surface and given 

 electrical properties can be treated mathematically, 

 and the field obtained is often designated as the 

 standard field (see Chapter 5). If one moves away 

 from the transmitter hcjrizontally, at a fixed height 

 above the earth, the field strength decreases expo- 

 nentially with distance once the line of sight is 

 passed. Similarly the field strength decreases expo- 

 nentially with height al30\'e the ground on going 

 vertically downwards from the line of sight. In 

 many instances, the variation in the field strength, 

 in the diffraction region is independent of the electric 

 properties of the ground. The main exception occurs 



in a comparatively shallow layer near the ground. 

 Only for the important case of propagation over sea 

 water and for frequencies below 100 megacycles 

 does this layer become high enough to cover an 

 appreciable part of the whole diffraction region. 



4.3.3 Diffraction by Terrain 



The problem of diffraction by terrain features 

 requires special treatment. Frequently a field of 

 apprecialile magnitude is found behind hills, houses, 

 etc. Diffraction is also important when there is a 

 sudden change in ground properties, as for instance 

 in a transition from land to sea. In this case the 

 shore line acts as a diffracting edge. Only a limited 

 number of cases lend themselves to evaluation by 

 simple formulas. The cases are those which can be 

 treated by the Fresnel-ICirchhoff method of optics 

 which leads to a somewhat intricate but straight- 

 forward mathematical formula for the diffracted 

 field strength. In spite of its apparent limitations, 

 the Fresnel-Kirchhoff foi'mula is often applicable 

 to short-wave propagation problems. It is treated 

 in Chapter 8. 



4.3.4 



Diffraction by Targets 



This problem can be dealt with theoretically by 

 methods similar to those used in computing diffrac- 



FiGURE 19. Reflecting pattern of an airplane. 



tion by terrain features, the main difference being 

 that the angle of scattering is nearly 180 degrees 

 instead of approximately degrees. 



In the case of target diffraction, theory is less 



