Chapter 14 

 DIFFRACTION OF RADIO WAVES OVER HILLS 



Experience has shown that frequencies in the 

 VHF (very high frequency) range and higher 

 are propagated over hills and behind obstacles more 

 easily than has been commonly expected. Hills or 

 other obstacles in the transmission path cast shadows 

 which may make a radio system unworkable when 

 either antenna is located close to the obstacle, but 

 recent experiments, notably the work of Jansky and 

 Bailey, 334 have shown that hills and mountains can 

 cause constructive interference as well as destructive 

 interference. In other words, with proper antenna 

 siting, the field intensity beyond the line of sight -may 

 be higher than is expected for the same distance over 

 plane earth. This improvement in field intensity may 

 be 5 to 10 db or more. 



One attempt to develop a theory for radio trans- 

 mission over hills is based on the computed field 

 intensity over the solid triangle shown in Figure 1. 



P(0,Y,Z) 



Z AXIS IS PERPENDICULAR TO 

 THE PLANE OF THE PAPER 



Figure 1. Analysis of field intensity over a solid triangle. 



It was reasoned that a good approximation to the 

 field over any profile might be obtained from a 

 knowledge of (1) the field over a perfectly smooth 

 earth, (2) the field over the solid triangle that 

 encloses the actual profile, and (3) the field over a 

 knife edge equal in height to the highest point in 

 the profile. The theory of propagation over a perfectly 

 smooth earth is well known; it is the basis of all the 

 published theoretical curves on radio propagation. 

 The. corresponding expressions for the field intensity 



"By K. Bullington, Bell Telephone Laboratories. 



over a solid triangle and over a knife edge are indi- 

 cated in a paper by Schelleng, Burrows, and Ferrell, 447 

 but some effort is needed to place these expressions 

 in a convenient form for computation. 



The method of obtaining an expression for the 

 field over a solid triangle is indicated in Figure 1, 

 and the same analysis applies to each of the ideal 

 profiles shown in Figure 2. The field intensity at any 



T 



H 



I L 



Figure 2. Analysis of field intensity over various tri- 

 angular profiles. 



point P in the vertical plane through the apex of the 

 triangle is assumed to be the sum of a direct ray and 

 a ray reflected from the ground which is equivalent 

 to a ray from an image antenna. In a similar manner 

 the field at point P is propagated to the receiving 

 antenna by means of a direct ray and a ground 

 reflected ray. By integrating over the plane above 

 the apex of the triangle (that is, from y = H to 

 y = co and from z = — co to z = co) an expression 

 for the total received field is obtained. The complete 

 expression is not as complicated as the expression 

 for propagation over a smooth sphere, but two simple 

 approximations will be sufficient for the present 

 discussion. When the height of the hill H = and 

 when the ground reflection coefficient is — 1, the 

 complete expression reduces, as it should, to the well- 

 known formula for VHF propagation over plane earth. 



E = 2E sin 



2Thihz 

 X (xi + x 2 ) ' 



(1) 



When the height of the triangle H is greater than 

 three to five times the average height of the. antennas 

 and when the reflection coefficient is ■ — 1, the com- 

 plete expression reduces to 



E = 4E S sin 



2tt/Mi . 2irHh 2 



~hXi 



sin 



Xxt 



(2) 



110 



