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16 Introduction Chap. 1
d
Tangent to surface of Earth
h
r
r
Figure 1–3
Earth
Calculation of distance to horizon.
“see” the transmitting antenna. A formula for the distance to the horizon, d, as a function of
antenna height can be easily obtained by the use of Fig. 1–3. From this figure,
or
d 2 + r 2 = (r + h) 2
d 2 = 2rh + h 2
where r is the radius of the Earth and h is the height of the antenna above the Earth’s surface.
In this application, h 2 is negligible with respect to 2rh. The radius of the Earth is 3,960 statute
miles. However, at LOS radio frequencies the effective Earth radius † 4
is 3 (3,960) miles. Thus,
the distance to the radio horizon is
d = 12h miles
(1–6)
where conversion factors have been used so that h is the antenna height measured in feet
and d is in statute miles. For example, television stations have assigned frequencies above
30 MHz in the VHF or UHF range (see Table 1–2), and the fringe-area coverage of
high-power stations is limited by the LOS radio horizon. For a television station with a
1,000-ft tower, d is 44.7 miles. For a fringe-area viewer who has an antenna height of 30 ft,
d is 7.75 miles. Thus, for these transmitting and receiving heights, the television station
would have fringe-area coverage out to a radius of 44.7 + 7.75 = 52.5 miles around the
transmitting tower.
Example 1–1 LINE OF SIGHT
Plot a graph describing the LOS distance in miles for transmitting antennas with heights from 0 ft
up to 1000 ft. Assume that the receiving antenna is 5 ft above the ground. For the solution, see and
run the MATLAB file Example1_1.m.
† The refractive index of the atmosphere decreases slightly with height, which causes some bending of radio rays.
This effect may be included in LOS calculations by using an effective Earth radius that is four-thirds of the actual radius.