# John F. Hughes - Personal - BoatsFinding the Sun's Azimuth, by Brute Force (under construction)

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## What information do I need?

To find the sun's azimuth, you need
• The date.
• The time in Greenwich, England.
• The Nautical Almanac or some other ephemeris.
• A calculator that can compute trig functions (if you don't have the Nautical Almanac)

### Two routes to the same result

• If you have the Nautical Almanac, follow the procedure for "sight reduction" given there; you can either use the one that has you play with a calculator (which is what I'll describe below) or the one that has you use the tables. The only problem is that this procedure has you start with an "observed altitude", and eventually produces a direction and a distance as its answer. Where do you get the "observed altitude" for the sun? It turns out not to matter! Since you're probably doing this in the morning or evening, use "10 degrees," or any other small number that's easy to work with, as your observed altitude, and when you're done, the "direction" produced by the computation will be the azimuth of the sun, and the "distance" can be ignored.
• If you merely have something that tells you the "geographical position" of the sun -- its "GHA" and declination -- start from there and follow the procedure below:

#### The brute force computation, using a calculator (with an example)

You'll need your latitude, which we'll call "lat", and your longitude, which we'll call "long".

But if your latitude is north, we'll write it as a positive number, and if it's south, we'll write it as a negative number. As examples: 24 N becomes +24. 13 degrees 30 minutes south becomes -(13 degrees 30 minutes). We'll also convert your position, in degrees and minutes, into one involving decimal degrees. We do this by taking the "minutes" part, dividing by 60, and adding it to the "degrees" part. (If you're getting your position from the loran of GPS, you can probably read decimal degrees from the display anyhow, and can ignore this step.)

Example: 12 deg 41 min N. First take 41 and divide by 60 to get .6833; add this to 12 degrees to get 12.6833 deg N; because it is North, the end result is lat = +12.6833.

Another example: 21 deg 11 min S. Divide 11 by 60 to get .1833; add to 21 to get 21.1833 deg S. Because it is South, the sign is "-" and the end result is lat = -21.1833.

Now we'll do a similar thing for longitude. West longitude is positive, and east longitude is counted negative. For example, 15 deg 22 min W gives "long = 15.3666", but 165 deg 48 min E gives "long = -165.8".

You'll also need the sun's declination and "GHA". These are tabulated in various books, including the Nautical Almanac, the Air Almanac, and some other ephemerides.

First determine the date in Greenwich, England.

Then find Greenwich Mean Time. You'll need to either get this from your GPS, or compute it from a local time signal.

#### Now, the computation

You'll need lat, dec, and diff to do this computation.
• Enter diff in your calculator. Press "cos".
• Press +/-.
• Press *.
• enter lat. Press "sin."
• press =
• press +
• enter dec
• press "sin"
• press =
• press /
• enter diff
• press sin
• press =
• press /
• enter lat
• press cos
• press =
• press "inv"
• press "cos"
• write down the result, and call it Z.

The value Z needs a little interpretation, unfortunately. It's not the azimuth, in general. First of all, it will always be between -90 deg and 90 deg, while the azimuth will be between -180 and 180 (or, by adding 360 to those values less than zero, between 0 and 360). Follow these rules:

• If your latitude is less than the sun's declination, .... you have to wait for me to finish writing this page...

# A lower-budget computation, for sunrise and sunset only

If you want to find the sun's azimuth at sunrise or sunset, which is know as the sun's "amplitude", and getting it right within just a degree or two will suffice, you can use this Excel spreadsheet . Of course, if you want to know how the spreadsheet works, you can read a somewhat lengthy document that explains the computation in detail. Go back to boats page.