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 database gives antenna height in electrical degrees when what you really want to know is how tall is that tower.  Never fear, figuring 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 the 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.

If the CRTC has any sense….

They’ll run away screaming “NOOOOOOOO!” to this notion:

Canada’s plan “B” might include iBiquity.

(as reported by Inside Radio)

Let’s just hope that this is more of iBiquity’s wishful thinking, which is often presented as actual important news being based in fact.  By iBiquity.

Why does the CRTC need a plan B anyway?  Is it not enough that Eureka 147 failed mainly due to a lack of public interest?  If it was something that was commercially viable, wouldn’t it have taken off on its own?  Now they are thinking of ruining the FM broadcast band, which, in my experience in Canada, is working perfectly fine.

Who says “digital” is better?  If anything, what has been discovered in this country is when it comes to HD radio, digital is worse.  Thus far, HD radio has the following going for it:

  • Proprietary system with expensive licensing fees
  • Complicated infrastructure
  • Insufficient building penetration
  • Poor performance in mobile reception environments
  • Lack of original programming
  • Adjacent channel interference
  • Poor receiver sales
  • Lack of general interest and/or knowledge by the public

All of these things have been well documented.  If you work for the Canadian Radio-Television and Telecommunication Commission (CRTC) and are thinking about this, contact me.  I’ll even invite you down for a drive around and you can experience HD radio, in all its glory, firsthand.