II M>\\li:VI'\I.S OK l>ROPA<;\TIOI\ 



197 



point in space. Though it is not, easy to state the re- 

 sult in general terms for any position, it is possible to 

 evaluate the change in field strengl h near the surface 

 i In 'low 60 m altitude for 600 me and somewhat higher 

 tor lower frequencies) and well within the diffraction 

 region, for moderate changes in /,-. Here the decibel 

 attenuation below that for the free space field is de- 

 creased approximately in the ratio fcf. If, for in- 

 stance, k changes from % to 8, the original decibel 

 attenuation is to be divided by 3.3. To state the mat- 

 ter another way, the range at which a given field 

 strength is found will be increased approximately in 

 the ratio A - f . This has an important bearing on the 

 problem of propagation for communication purposes 

 in this region. 



It has been shown above that a linear variation of 

 refractive index can be converted into a change of 

 earth's curvature. The reverse process is equally 

 feasible: to eliminate the earth's curvature by using 

 a modified refractive index curve. This is a general 

 procedure which involves no assumption about the 

 variation of refractive index with height. From the 

 equations in Section 17.1.6 it is seen that the effects 

 of the earth's curvature are equivalent to those of a 

 refractive index increasing linearly with height at the 

 rate of 1/a. Hence one effectively flattens the earth, 

 thus eliminating the curvature effect, by adding to 

 the refractive index the term h/a. In other words, 

 the angles between a ray and the horizontal over a 

 curved earth are the same as the angles between a 

 ray and the horizontal over a flat earth when the re- 

 fractive index n has been replaced by n + h/a. In 

 practice, the quantity M defined by equation (7) is 

 used. If M increases steadily with height, which is the 

 case for the standard atmosphere, the rays appear 

 curved upwards on a fiat earth diagram, which is 

 illustrated in Figure 13. 



TRANSMITTER, 



NTERrERENCC REGION 



VML 



Figure 13. Raj r s in a plane earth diagram. 



Summarizing, it is seen that three types of graphi- 

 cal representations of a coverage diagram may be 

 used. (These are illustrated in Figure 14 for the 

 lowest lobe.) 



1. The true geometrical representation. With 



TRUE EARTH 

 RADIUS a 



EQUIVALENT EARTH 



radius ka 



FLAT EARTH 



k = oo 



Figure 14. Shape of lobes as affected by method of 

 representation. 



standard refractive conditions the lobes appear bent 

 downwards. Refractive index n decreases with height. 



2. The equivalent earth radius representation. 

 Earth's radius changed to ka (normally k=%). For 

 standard refractive conditions the lobes appear 

 straight. Equivalent refractive index n' is inde- 

 pendent of height since the equivalent atmosphere is 

 homogeneous. 



3. The fiat earth representation. The earth's sur- 

 face and other surfaces of constant height have been 

 flattened out. For standard refractive conditions 

 the lobes appear bent upwards. Excess modified 

 index M increases with height. 



The quantities n, n', and M for these three cases 

 are illustrated in the left-hand series of diagrams 

 in Figure 15. 



17.1.7 



The Horizon — Diffraction 



From simple geometrical considerations it can be 



