DIFFRACTION' OF RADIO \\AVKS BY A l'ARAHOI,IC CVIJXDKH 13!) 



The amplitude of the wave striking the ridge at Q is AG/l\/2. The 

 \/2 comes from the horizontal sidewise spi'oading of the wa\^e in going 

 from / to 2(. If we were dealing with the energy instead of the amplitude, 

 the factor would he 2 instead of \/2. When this wave is assumed to be 

 plane and traveling in the PQ direction, similar reasoning shows that 

 the amplitude of the disturbance at the receiver »S is A(f/C-\/^. 



If, instead of two ridges at P and Q, as shown in Fig. 3.1, there are N 

 ridges between the transmitter at T and the recei\'er at .S, the amplitude 

 of the radio wave at *S is AG^ /C\/N + 1. The distance between T and S 

 is approximately (A'" + 1)^, and the free space amplitude at S is A/ 

 (N -\- l)C. Hence 



Actual Amplitude at S _ ^n/i^ i iV'- d ^\ 



Free Space Amplitude at S 



The actual field at S is therefore 



20 N logio (1/G) - 10 logio (N + 1) (3.2) 



db below the free space field. 



As an example, let us assume a distance of 280 miles between the 

 transmitter and receiver, and a distance of 40 miles betw^een successiA-e 

 ridges. This gives N — 6. For a wavelength of 10 meters and a radius 

 of curvature of 100 meters for the diffracting ridges, the formulas of 

 Section 2 show that the ridges behave like half-planes and that G ^ 

 0.227. Equation (3.2) then says that, for a distance of 280 miles and a 

 wavelength of 10 meters the actual field should be about 69 db below 

 the free space field. Although this is in fair agreement with the ex- 

 perimental results, calculations for other distances indicate that the 

 field strengths predicted by (3.2) tend to be smaller than the ones 

 observed. 



When the work is carried through for X = 1 meter and a distance of 

 280 miles, (3.2) says that the field is 120 db below free space. The ob- 

 served fields are 70 ± 15 db below^ the free space value. 



These figures suggest that the roughness of the earth's surface might 

 possibly account for transmission far beyond the horizon for wavelengths 

 of the order of 10 meters. For wavelengths of the order of 1 meter either 

 the approximations leading to (3.2) break dow^n or some other explana- 

 tion is required. 



4. SERIES FOR THE ELECTROMAGNETIC FIELD 



Here we set down series for the electromagnetic field when a plane 

 w'ave strikes a perfectly conducting parabolic cylinder. Since Epstein's 



