RADIO PROPAGATION 



67 



to be inversely proportional to the square of the distance. The devi- 

 ation of the attenuation curve from the straight line E/2Eo = 1/x 

 shows the degree of this approximation for antennas on the ground. 

 If this is satisfactory then equation (27) applies.* An evaluation of 

 the parameters in equation (27) for the greatest antenna height allows 

 a determination of whether equations (28) and (30) apply. If R is 

 within the range where it is a linear function of ^2, that is if the curves 

 for 1 — K vs sin ^2 (Figs. 5, 7, 9 and 11) are straight lines for this 

 value of ^2, and if sin AThihi/Xd is approximately equal to 4:Thih2l\d, 

 then equations (28) and (30) apply. If also Q is very different from 

 unity then either equation (32) or equation (33) applies. 



An evaluation of the parameters in equation (27) for the lowest 

 height will allow a determination of whether equation (21) applies. 

 If the second term within the brackets is small compared with the 

 first term, equation (21) applies. 



0.05 



0.1 0.2 0.3 0.5 1.0 2 3 4 5 10 



RELATIVE ANTENNA HEIGHT (Kh) 



Fig. 13 — Variation of received field strength with antenna height. 



The variations of the received field strength with antenna height 

 for the four cases of especial interest given by equations (32) and {33) 

 are plotted in Fig. 13. The ordinate gives the ratio of the field strength 

 at the height corresponding to the abscissa to that for zero height. If 

 both antennas are off the ground the product of the ratios corre- 

 sponding to the antenna heights gives the ratio of the field strength to 



* As the antennas are removed from the earth's surface the error introduced 

 because of this deviation is less. 



