604 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



earth and the ionosphere. However, there is httle or no similarity be- 

 tween the virtual heights, the critical frequencies, or the causes of re- 

 fraction in the two cases. 



Duct transmission is important because it can cause long distance 

 interference with another station operating on the same frequency; 

 however, it does not occur often enough nor can its occurrence be pre- 

 dicted with enough accuracy to make it useful for radio services requir- 

 ing high reliability. 



Diffraction Over a Smooth Spherical Earth and Ridges 



Radio waves are also transmitted around the earth by the phenomenon 

 of diffraction. Diffraction is a fundamental property of wave motion, 

 and in optics it is the correction to apply to geometrical optics (ray 

 theory) to obtain the more accurate wave optics. In other words, all 

 shadows are somewhat "fuzzy" on the edges and the transition from 

 "light" to "dark" areas is gradual, rather than infinitely sharp. Our 

 common experience is that light travels in straight lines and that shad- 

 ows are sharp, but this is only because the diffraction effects for these 

 very short wavelengths are too small to be noticed without the aid of 

 special laboratory equipment. The order of magnitude of the diffraction 

 at radio frequencies may be obtained by recalling that a 1 ,000-mc radio 

 wave has about the same wavelength as a 1,000-cycle sound wave in 

 air, so that these two types of waves may be expected to bend around 

 absorbing obstacles with approximately equal facility. 



The effect of diffraction around the earth's curvature is to make possi- 

 ble transmission beyond the line-of -sight. The magnitude of the loss 

 caused by the obstruction increases as either the distance or the fre- 

 quency is increased and it depends to some extent on the antenna 

 height. ^^ The loss resulting from the curvature of the earth is indicated 

 by Fig. 5 as long as neither antenna is higher than the limiting value 

 shown at the top of the chart. This loss is in addition to the transmission 

 loss over plane earth obtained from Fig. 2. 



When either antenna is as much as twice as high as the limiting value 

 shown on Fig. 5, this method of correcting for the curvature of the earth 

 indicates a loss that is too great by about 2 db, with the error increasing 

 as the antenna height increases. An alternate method of determining the 

 effect of the earth's curvature is given by Fig. 6. The latter method is 

 approximately correct for any antenna height, but it is theoretically 

 limited in distance to points at or beyond the line-of-sight, assuming 

 that the curved earth is the only obstruction. Fig. 6 gives the loss rela- 

 tive to free-space transmission (and hence is used with Fig. 1) as a func- 



