Calculating the Pointing Angle for My Television Antenna

Quote of the Day

If I strive for perfection, I can generally achieve good'nuff. If I strive for good'nuff, I generally achieve firewood.

— Woodworkers Credo. I find this quote holds true for so many things. I used to work for an HP engineer, Warren Pratt, who said similar things about designing printed circuit boards. Basically, you must strive for perfection because things will go wrong that you cannot anticipate. So nothing will be perfect, but you might get something worthwhile.


Figure 1: Television Stations Closest to My Cabin.

Figure 1: Television Stations Closest to My Cabin. (Source)

I spend quite a bit of time at a cabin I have built in northern Minnesota. Technically, I spend most of my time in the garage on the site and I have decided that I need to be able to watch the local television stations in Duluth. These stations are ~75 miles away and I need to determine the bearing along which to point my antenna. This seemed like a good Excel exercise that I can also use as an example for those I tutor at the Hennepin County Library. There are web calculators available that perform this calculation (example), but it is more fun doing it myself.

Once I decided that I needed an antenna, there are two numbers I in order to purchase the correct unit and to point it properly:

  • Distance to the Stations
    Distance determines the type of antenna that I will need.
  • Bearing of the Stations Relative to North
    I will be using a compass to point the antenna and I need an angle from my garage to Duluth.

Equation 1 contains the formulas needed for computing the range and bearing between two points on Earth given their latitudes and longitudes. For more details on these formulas, see this discussion on the haversine formula, which can be derived using spherical trigonometry.

Eq. 1

where

  • θ is the bearing to the antenna from the garage
  • R is the distance to the television antenna.
  • ϕlat is the latitude of the garage
  • ϕlon is the longitude of the garage
  • ψlat is the latitude of the television station antenna
  • ψlon is the longitude of the television station antenna

I implemented the equation in an Excel spreadsheet, which you can download here.  Based on my range calculation, I ended up buying a Yagi-Uda television antenna (Figure 2).

Figure 2: My new television antenna.

Figure 2: My new television antenna.

 
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