Radio Propagation Over Spherical Earth

HE electrical disturbance at the surface of the earth due to a vertical dipole has been calculated by G. N. W a t s o n 1 and others. The results for the case of a perfectly conducting spherical earth with transmitter and receiver both situated on the surface m a y be reduced to the form: R = 30(2T) h '*III ^ e - f i n ^ ^ m a 5/6 ^ X /°Vsin 6 7 P» where p,, and /3,, are constants whose values have been calculated as follows: Pi = 0.8083 n 1 2 3 4 5 6 1.000 3.188 4.74 6.047 7.236 8.336 Pn/Pl Pn-l2ir/a0.00376 0.01199 0.0178 0.0227 0.0272 0.0313 * Published in I. R. E. Proc., M a y , 1935. Presented before U. R. S. I. meeting, W a s h i n g t o n , D. C., April 26, 1935. 1 G. N. W a t s o n , " T h e Diffraction of Electric W a v e s by the E a r t h , " Proc. Roy. Soc. (London) A95, 83-99, October 7, 1918. 477 478 BELL SYSTEM TECHNICAL JOURNAL and II is the effective height of the transmitting antenna in kilometers, I is the transmitting antenna current in amperes, X is the wave-length in kilometers, a is the radius of the earth in kilometers (= 6370), d is the distance between transmitter and receiver in kilometers, 0 is the angle at the center of the earth subtended by radii to transmitter and receiver (= d/a), and E is the received field strength in volts per kilometer. p,, and /3n were evaluated for n = 1, 2 and 3 by H. M. Macdonald, 2 while the remaining values have been calculated by the present author. For distances for which this solution would be used (i.e., where the effect of the ionized region of the upper atmosphere may be neglected) sin 0 very nearly 3 equals 0 so t h a t the above formula reduces to the following: 30(2ir) 5l3HI y-, g-M^^x