The Geodetic Distance

Consider the effect of signal refraction on a propagating radio signal, as depicted in the diagram below. If there were no refraction then the signal would simply travel in a straight line and strike the earth at the horizon. This path is called the geodetic line. The geodetic can never be observed in the real world. The distance to the horizon based on zero refraction (K=1) could be geometrically calculated considering the earth to be a sphere. The lines tangent to the geometric sphere, taken in conjunction with the radius, would allow calculation of the true geodetic distance to the horizon from an antenna.

In practice, however, the refractive index of dry air is roughly 6/5 (K=6/5) and a surveyor, using an optical instrument (a "transit") to determine the distance between two points, must reduce the observed measurement by this factor. Assuming the K=6/5 yields the Visual Line-of-Sight distance to the horizon. This is, "how far can I see?"

The most typical refractive index for RF design is K=4/3. This is the refractive index of water and there is water vapor (to varying degrees) in the atmosphere. Of course, refraction is the result of the varying density in the atmosphere. The air closer to the ground is (generally) more dense than that at higher elevations. The result of this variance in density is that the distance traveled by an RF signal (the Refracted Ray, shown above and to the right) is greater than the geodetic line (the "Visual Line-of-Sight". RF can "see" slightly beyond the visible horizon.

How far can it "see"? If you were at an elevation such that the geodetic line to the horizon were exactly 10 miles then (using the refractive index of dry air, K=6/5) you would see the horizon 12 miles away (6/5*10=12). Using K=4/3 (typical for RF design) the "Radio Line-of-Sight" (also called the "Radar Line-of-Sight") would be 13.3 miles away (4/3*10=13.33).

Occasionally a reference is made to "K=Infinity". This is referred to as the "flat earth" scenario where there is no geodetic line; a wave continues to propagate forever without striking the earth's horizon. This is the scenario that exists when considering the communication path from an earth-based radio to an orbiting radio. The propagation that's of interest is "up" and not "horizontal". Hence, by setting K=Infinity calculations can be performed on "slant range" links. This is also the case when the roof-mounted antenna on a 20-story building is transmitting down to the roof of the 2-story building a few miles away. The Connect802 Antenna Designer takes these factors into consideration.