NavList:

Around local noon, there's a period I call the "hang time" during which the altitude of the Sun does not measurably change. With a parablic approximation of the noon curve, which is accurate under the majority of cases, the hang time in minutes is given with good accuracy by:
   hangT = 11 × √(s) × √(tan Lat - tan Dec),
where s is the sensitivity of your sights in minutes of arc (might as well assume s=1 for a first estimate), and, of course, Lat and Dec are the observer's latitude and the declination of the body reaching the meridian, respectively. In the case of a Noon Sun sight, the dec is the declination of the Sun which is limited within the range -23.45° to +23.45°. If in addition we limit the Latitude to less than 50° or 60°, then there's an even easier approximation for the hang time:
   hangT = 1.5 × √s × √ZD₀,
where ZD₀ is the Sun's zenith distance at local noon in degrees. The nice thing about this easy approximation is that you can do it in your head, and it's plain how the duration depends on the observation sensitivity and the noon zenith distance.

Example: Suppose we stick with a sensitivity of 1.0 minutes of arc. And suppose the Dec is -15°, as it will be in two days. For a latitude of +40°, the nearly exact version above gives a hang time of 11.6 minutes while the quick approximation gives 11.1 minutes. And sure enough, if you check, in that latitude on Saturday for over 11 minutes around local noon, the altitude of the Sun is within one minute of arc of its peak "noon" value.

The reason we need to know this, of course, is so that we don't treat the apparent event of local noon as an event with a precisely defined time. Noon lasts a while!

Frank Reed

PS: Of course, in the equations above, you can move "s" inside the other square root. I like them separated like this to emphasize their independent significance. The Lat and Dec (and ZD at noon) depend on our geographic and temporal circumstances. By contrast the sensitivity depends on our sextants, our skills, and our willingness to accept some uncertainty in our sights. Both of these factors enter the hang time equation as a factor under a square factor.