THEORY AND RESULTS 



149 



4.5.3. Theory and Results 



In figure 4.41, although it is known that ray theory does not explain 

 what happens to the radio ray at the point A when the ray is tangent to 

 the top of the duct, because of the apparent ray intersection, it is sufficient 

 to define the first shadow zone as that zone between the two possible paths 

 of the ray tangent to the duct at a point A (this is the ray emitted from the 

 transmitter with an initial angle of ^o with the horizontal). This is possi- 

 ble because it can be readily seen that no radiation will be able to enter the 

 shadow zone, and thus a receiver located in the shadow zone will theoreti- 

 cally receive no signal from the transmitter. The portion of the "split" 

 ray that enters the duct at A will be reflected at point B to point C, where 

 it "splits" again. The distance, d from point A to C projected along the 

 earth's surface will be designated the "length" of the first shadow zone. 

 If the surface duct is homogeneous throughout, the ray will be symmetri- 

 cal about point B and, therefore, 



d, = d. = d/2 = d, 



(4.26) 



where di and dz are the "half-lengths," dhi, of the shadow zone. 



Figure 4.41. Shadow zone occurrence of a curved earth with the transmitter above 



the duct. 



