68 BELL SYSTEM TECHNICAL JOURNAL 



that for both antennas on the ground. The distances between the 

 curves and the straight line labelled " asymptote " give the magnitudes 

 of the factors in equations (32) and {33) by which {4:Trhih2/\d)Eo must 

 be multiplied to give the field strength. 



For transmission over a ground of good conductivity (Q <C 1) with 

 vertical antennas there is a least favorable height for the antennas as 

 indicated by curve 1 of Fig. 13. With both antennas at this height, 

 which is about l.TX^'^ meters for ocean water, the received field is 

 one-half what it would be if both antennas were on the ground. 



Curve 2 for transmission on horizontal polarization over ground of 

 good conductivity (Q <^ 1) shows a steady increase in the received 

 field with increase in antenna height. If curves 1 and 2 were plotted 

 against antenna height in meters for any given ground conditions 

 (Q <C 1), curve 2 for horizontal polarization would not depart appreci- 

 ably from its asymptote until such small antenna heights were reached 

 that curve 1 for vertical polarization would be substantially inde- 

 pendent of antenna height. Hence curves 1 and 4 give a comparison 

 of the received field strength at any height on the two polarizations. 

 At the height for which the field strength is minimum on vertical 

 polarization, the field strength is independent of polarization. For 

 lower antennas vertical polarization gives the greater fields, while for 

 higher antennas horizontal polarization gives the greater fields. The 

 maximum advantage of horizontal polarization over vertical polariza- 

 tion occurs at twice this height and is a factor of two. 



As Q increases curves 1 and 2 merge into curve 3 for transmission 

 over a perfect dielectric. While the shape of the curves for the two 

 polarizations is identical and the received field strength is independent 

 of polarization at the greater antenna heights, the field strength is e^ 

 times as great on vertical polarization as on horizontal polarization 

 with antennas on the ground. 



As an example of the use of the curves for the reflection coefficient 

 the relative advantages of different types of ground for low-angle 

 reception (or transmission) on vertical polarization has been calculated. 

 With vertical antennas both the direct and the reflected components 

 are reduced by the factor cos ^2 so that the right-hand side of equation 

 (21) must be multiplied by cos ^2- The receiving antenna will be 

 assumed to be on the ground.* Figure 14 gives the resulting curves for 

 the indicated ground constants. For very low angles the curves are 

 parallel, indicating that the relative advantages of different types of 

 ground are independent of the angle at these angles. The gain in 



* For higher angles of reception the relative advantages of different types of 

 ground may be made approximately the same by properly adjusting the antenna 

 height. 



