On Distributed Communications Series

VI. Mini-Cost Microwave

V. Relay Station Spacing

Tower Spacing Considerations

Present-day microwave towers, together with attendant real estate alone, cost more, on the average, than the mini-cost microwave repeater being considered.

As a consequence of using less expensive towers and sites, the spacing between relay stations must be reduced. Relatively little information is available on such a tradeoff. Let us start by considering a smooth earth: this is a ball the size of the earth, but without mountains, woods, or similar "bumps." Next, we compute the tower heights to span any desired distance between two points on the smooth earth. Transmission through the variable-density atmosphere of the real earth will lend the illusion of the smooth earth being larger than it is. This value is commonly taken as four-thirds of the earth's diameter. Next, a clearance factor must be taken into account in order to insure that no problems are encountered when the reflected wave bouncing off the earth arrives out of phase with the directly transmitted wave.

Egli describes the spacing of microwave towers and Fresnel clearances required.[1] He recommends the use of a one-sixth Fresnel zone clearance where a unity Fresnel clearance corresponds exactly to the point where the direct and reflected signal components are 180 degrees apart. Figure 8 shows the allowable tower spacing as a function of tower height using these assumptions. Curves are drawn for a smooth earth only, for three separate frequencies, 1, 8, and 13 Gcs. Most points on the earth, of course, will not be so ideal. But, in many areas it will be possible to take advantage of fortuitous high-elevation sites which allow the distance between two antenna towers to be extended.

Although it would appear possible to generate some statistics here, the strongest statement which can be derived from Fig. 8 is that tower height increases approximately as the square of the spacing distance between two towers.

Cost of Tall Towers

The cost of towers also increases very approximately as a square of tower height. Thus, the cost of the towers will increase rapidly with spacing distance.

Figure 9[2] shows the approximate installed cost of insulated AM broadcast station towers, including the cost of the tower foundations, aircraft obstruction lights, and erection costs. Separate curves are shown for self-supporting and guyed towers. From Fig. 9 it is obvious that guyed towers are the cheaper, and that the cost rises sharply as the height is increased. Figure 10[2] shows the approximate installed cost of television broadcast towers, including the cost of the tower, the foundation, FAA lights, and the erection of coaxial and antenna. These curves indicate that costs on the order of $250,000 can be expected for extremely tall towers--on the order of 1500 feet. These curves also suggest that as the tower height is decreased to less than a few hundred feet, costs drop rapidly. We shall return to this subject shortly.

The FCC enforces rigid FAA specifications on lighting and painting of all towers which are deemed by them to interfere with aircraft. Walker considers at length the rigid specifications for marking and lighting antenna towers.[3] These two factors alone--lighting and red-and-white striping--could constitute a heavy annual expense as compared to almost maintenance-free, galvanized, short towers which do not fall under FAA jurisdiction. Therefore, tall towers which require lighting and painting will be avoided. From an examination of Fig. 11,[4] it can be seen that tower lighting and painting will not be required if the antenna is under l70 feet and if sites in the vicinity of airport runways are avoided.

Thus, it is assumed that, in general, all towers will be less than 170 feet high and that red/white painting and lighting will not be required.

Cost of Short Towers

Guyed towers, less than 150 feet tall, are used for TV reception in rural areas, for supporting rotating amateur antenna arrays, for governmental and business radio-telephone, and even in some microwave relay applications. Many companies are listed in the electronics buyers' guides as manufacturing such antenna towers. In Fig. 12 is plotted price versus height for a few representative samples. These costs are the retail prices one pays for a single prefabricated tower and do not include erection cost. They are almost all designed to be erected by amateur radio operators or TV service technicians in a few hours. The life expectancy of these towers is quite adequate; even some of the cheaper towers are post-fabricated dip-galvanized and should not require painting for at least five years.

Figure 12 also includes prices for utility poles. It was originally thought that low-cost utility poles could be used. However, the unknown torsional dimensional stability of the fundamentally hydroscopic, anisotropic medium of wood prevented ready analysis (we didn't know how much the pole would warp when it got wet).

Figure 12, plotted on a logarithmic scale, illustrates that unguyed towers are cheaper than guyed ones; all towers are inexpensive in heights below about 60 feet; cost rises rapidly with height, but a guyed tower of satisfactory quality can be purchased--at retail--for less than $500. As a cost safety margin, this figure will be increased and it will be supposed that all prefabricated sections and parts necessary to erect a sturdy 150-ft tower can be purchased for about $700.

Location of Towers

While seemingly most desirable, mountain-top antenna sites can be extremely expensive, particularly if access roads are not available and must be built. The use of mountain tops will usually entail the purchase of land at the site or purchase of easements. The use of existing government-owned or government-held rights-of-ways along roadways is proposed. Usually public ownership of roadways extends well beyond the paved portion of the road itself. Easements in these areas are granted for power and telephone lines, but generally are non-exclusive to the franchise holders. Such easement space, particularly along undeveloped and rural roads, should prove adequate for locating the antenna sites. Proximity to existing roads will minimize the costs and facilitate the servicing of mini-cost microwave repeater stations. The use of guyed, minimal-height towers along roadways is depicted in Fig. 13.

Some tentative studies at RAND on the availability of roads in the Western desert and mountain regions of the U.S. found that there exist sufficient roadways to make the assumption of use of this type of site tenable. Of course, the mere fact that the government already owns sufficient rights-of-way does not necessarily resolve the site selection problem, so further study is indicated.

Antenna Spacing Determination

We can now combine the curve of our billiard-ball earth (Fig. 8) and the antenna cost curve (Fig. 12) modified by a little "fat"in the cost of the antenna, to obtain a new set of curves. Figure 14-a assumes three values of electronics' costs, $3000 (curve A), $2000 (curve B), and $l000 (curve C), and displays the total cost of antenna plus electronics' cost. For each of these three curves, A, B, and C, a second curve, A', B', and C' is drawn in Fig. 14-b, showing total cost (antenna plus station investment) on a per mile basis. These values are merely the curves A, B, and C divided by the number of miles between repeaters. It can be seen that even with the steeply rising function of antenna cost versus assumed height, the minimum-cost mileages varied from 14.7 to 25 miles, using the billiard-ball earth assumption. The cheaper the relay station electronics, the closer together the towers will be. Hence, optimum spacing between relay stations in this system will probably be on the order of 20 to 25 miles. A spacing of 20 airline miles will be tentatively assumed as the nominal design value.


[1] Egli, J. J., "UHF Radio-Relay System Engineering," Proceedings of the IRE, Vol. 41, January 1953, pp. 115-124.

[2] Due to Walker, op. cit.

[3] Walker, loc. cit.

[4] From Walker, op. cit.


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