1)11 I KACTION OK KADIO WAVES <>\KK MILLS 



II 



1>.[X, + X 2 ) 



Figure 3. Shadow-loss factor S. 



The factor S is the shadow loss shown in Figure 3 

 as a function of 



2 3 45*78910 20 



DISTANCE FROM TRANSMITTER IN MILES 



Figure 4. Theoretical and experimental results in meas- 

 uring field intensity of horizontally polarized waves. 

 Frequency 116 mc. 



u = H ■ 



2x\Xz 



\X (xi + xi) ' 



The other symbols in the above expressions have 

 the following meanings: 



E = field intensity in microvolts per meter, 

 Kn = free snn.ee field intensitv in mierovnll 



E = free 



per meter 



_ 3 V5P X 10 6 



space field intensity in microvolts 



■r mptpr 



Xl + Xi 



P = radiated power in watts, 



X = wavelength in meters, 

 H = height of the obstruction in meters, 

 h\,li2 = antenna heights in meters, 

 X\,x% = distances as shown in Figure 1 in meters. 



The approximate expression given in equation (2) 

 indicates that the field intensity for points well 

 beyond the line of sight may be greater than the 

 field over a plane earth which is given in equation (1) . 

 The sine terms in equation (2) indicate interference 

 patterns beyond the line of sight which seem to 

 offer an explanation for the experimental fact that 

 behind hills raising the antenna may cause a loss, 

 or lowering the antenna may result in a gain, in 

 signal intensity. 



A comparison between theory and experiment is 

 shown in Figure 4. These data, which were taken 

 from the previously mentioned NDRC report pre- 

 pared by Jansky and Bailey, show measured values 

 at 116 mc for horizontally polarized waves propa- 

 gated over the profile shown in the bottom of the 



drawing. The open circles show the field intensity 

 in decibels below the free space value when both 

 antennas are 29 ft in height, and the dots give 

 similar data for 19-ft antennas. The two dashed 

 lines running from upper left to lower right are the 

 computed values for smooth earth for 29-ft and 19-ft 

 antennas, respectively. The solid line with the inter- 

 ference fringes is obtained from equation (2) for the 

 case of 29-ft antennas. The correlation between 

 theory and experiment is not complete, but at least 

 the theory may be a step in the right direction. 

 Similar theoretical and experimental results are 

 obtained with vertical polarization. 



Thus far the only type of profile considered has 

 been one with a single prominent hill, and it is 

 natural to ask what happens over profiles containing 

 several hills. There are less experimental data avail- 

 able on this point than for propagation over a single 

 hill, and consequently the remainder of this discus- 

 sion is more speculative than the preceding part. 



An ideal profile consisting of two hills of equal 

 height is shown in Figure 5. The complete mathe- 

 matical solution for this case is difficult, but an 

 approximation can be obtained in the following 

 manner. The field at any point P midway between 

 the two hills can be obtained by means of the expres- 

 sion for the diffraction over a single hill. The field at 

 this point is then propagated over the second hill to 

 the receiver. The total received field is obtained by 

 mechanical integration, that is, by adding the effect 

 (magnitude and phase) of many evenly spaced points 

 in the vertical plane midway between the two hills. 



