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Converting electrical degrees to height in meters or feet

Here is one of those things that can often be a head scratcher for the uninitiated:

The FCC data base gives antenna height in electrical degrees when what you really want to know is how tall is that tower.  Never fear, to figure all this out, requires math.  Pretty simple math at that, too.  I prefer to do these calculations in metric, it is easier and the final product can be converted to feet, if that is desired.

First of all, radio waves travel at the speed of light, known as “c” in many scientific circles.  Therefore, a quick lookup shows the speed of light is 299,792,458 meters per second (m/s).  That is in a vacuum, in a steel tower, there is a velocity factor, most often calculated as 95%, so we have to reduce speed of light in a vacuum to the speed of RF in a steel tower.

299,792,458 m/s × .95 = 284,802,835 m/s (speed of a radio wave in a steel tower)

Frequencies for AM radio are often given in KHz, which is 1000 cycles per second.  For example, 1,370 KHz × 1000 = 1,370,000 Hz (or c/s)

Therefore:

284,802,835 m/s ÷ 1,370,000 c/s = 207 meters per cycle.  Therefore the wavelength is 207 meters.

There are 360 degrees per cycle, therefore:

207 meters ÷ 360° = 0.575 meters per degree

If the height of the tower is 90°, then 90° × 0.575 m/° = 51.57 meters.  Add to that the height of the base insulator (if there is one) and the concrete tower base and that is the total tower height.

To convert meters to feet, multiply by 3.2808399.

In the United States, that tower would be 169.78 feet tall.

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