NavList:

There are a couple of easy ways to predict the time of LAN (Local Apparent Noon). If you have an almanac app or something like the USNO web app, you can test for it by finding the time when the Sun reaches its maximum altitude by binary search ("a little up... no, too high... a little down... etc"). Testing by altitude is not very sensitive so it's usually more effective to test for the time when the azimuth of the Sun is 180.0° (or 0.0° if you are south of the Sun). With a different tool, it may be easier to search for the time when the Sun's GHA is identical to the observer's longitude. Any of these will find noon.

Yesterday I tried a different approach for beginners in celestial navigation. Although there are plenty of apps for this sort of thing, I was looking for an "easy entry" approach. The simplest I could come up with is based on the times of sunrise and sunset, which are available from many sources. For example, I can say to my phone (even without walking over and picking up), "OK Google... what time was sunrise today?" and it answers with a time, precise to the nearest minute. Yesterday it answered "6:38a.m." Then I asked for sunset, and it told me "5:22p.m." At that point it's easy to see that we need a time halfway from sunrise to sunset. It's not hard to see that 6:38 is 5 hours and 22 minutes before 12:00 and 5:22 is 5 hours and 22 minutes after 12:00, so... uh-oh. Turns out yesterday was one of the two days in the year when local apparent noon occurred exactly at 12:00 "o'clock" here. Foiled again by zone time! But on any days other than those two, this can be a nice way to explain when local noon happens. 

A better example: Jumping ahead two months, on April 18 this year, sunrise will occur at my location at 6:01a.m. (5h59m before 12:00), and sunset will occur at 7:29p.m. The total time from sunrise to sunset is 13h28m. Divide that by two, and I get 6h44m. So I add that onto 6:01 and and get 12:45. Double-checking... I could average: 06:01 added to 19:29 is 25:30... divide that by two, and I get 12:45. Yes, that's halfway between sunrise and sunset, 6h44m on either side. Thus on April 18, local noon occurs here at 12:45p.m. There will occasionally be one minute differences due to changing declination, but this method if easy to understand and easy to teach. Everybody gets the idea that "high noon" is halfway between sunrise and sunset. If nothing else, this trick provides a sanity check, too, on the more formal methods (azimuth or GHA tests, as above). And finally, it's a lazy method, which is sometimes nice to have. :) 

Frank Reed