NavList:

Hi Bill, you wrote:
"I can only surmise you worked refraction backwards, from Hc to Ho using
an Ho to Hc table or formula. As discussed in star-to-star measurements,
this may come very close for higher altitudes, but IMHO does not pass
the "...seat of the pants practical and mathematically elegant" test for
a sun near the horizon."

Ah, thanks, Bill! Good catch. I thought it through "backwards" just as you suggest. Instead, I should have looked for that observed altitude where the refraction correction is exactly equal to the observed altitude. And that happens right around 28.5' of arc altitude for a star. Ah, but we really want the Sun's center at zero degrees corrected altitude, and, as you note, the lower limb is refracted significantly more than the center. This is accounted for in the usual tables in the front of the Nautical Almanac. So it looks like the altitude would be just about 15' of arc. If the altitude of the Sun's Lower Limb AFTER subtracting dip is 15' (near enough to 1 SD) insteaad of the the 18' (-34+16) which I gave previously, then the corrected altitude of the Sun's center is nearly 0° 00.0'. The T/P correction can easily amount to a couple of minutes of arc, too, but the main factor that is usually ignored is just dip. The difference between 25' (at 100 feet height of eye) and 15' (right at the top of the waves) is certainly observable. In tropical latitudes, the difference in azimuth from that difference in altitude is small and not significant for navigation. Nothing to worry about. Hence the various recommended "rules" for this would not matter EXCEPT in higher latitudes --anywhere above 45° latitude an error of altitude of some number of minutes yields an equal or larger error in azimuth.

Of course, if I had considered the modern case more fully, my previous suggestion that you could just measure the actual altitude as a means of bypassing the amplitude tables and the ambiguity of their related rules is no longer relevant. The Sun's true and apparent altitudes and therefore its azimuth are known almost exactly because the vessel's position is EXACTLY known at any given instant. Any altitude (low enough so that you don't have to worry about the problems of observing higher azimuths which Henry Halboth mentioned) is just as good as any other. Given lat, lon, UT (and possibly temperature and pressure if they're extreme), the apparent azimuth of the Sun or any other celestial body is a known quantity and can be immediately compared with observation. The old "amplitude" procedure has only historical interest (always fun for NavList). Just to reiterate, getting azimuths by the Sun is not obsolete. But the old rules are no longer needed.

Bill, you concluded:
"it strikes me that Prof. Saemundsson's Hc to Ho refraction formula would more appropriate than working backwards from the NA, Bennett et al tables or formulas."

I would say it's the same thing. You're just using the tables in reverse (or by iteration, if you prefer). Saemundsson's formula is no more and no less than a computationally quicker way of doing that at the expense of having a separate table or bit of software to worry about. It's JUST a fit to the tables, like Bennett's similar formula. The tables themselves are derived by numerical integrations based on standard atmosphere models.

-FER
PS: You started your message by saying, "It is not my wish to become the next "Noonan sunset" B.S. guy". Quit impossible, Bill! As for the aforementioned "artist", I scared him off. He explained that I am not a very nice person, and he no longer wished to be part of NavList. He asked to be removed, and I granted his wish --permanently.
...I'll thank the gods that he's gone. You can thank me. ;) Crackpots like him can be a huge nuisance in online groups. I have been contributing in online communities on an almost daily basis since 1991, considerably more than half of my adult life. I've seen a number of online forums crushed or severely degraded when a crackpot or two (or three or ten...) decide that they have found a comfortable place to peddle their nonsense. He's gone, and good riddance.

----------------------------------------------------------------
NavList message boards and member settings: www.fer3.com/NavList
Members may optionally receive posts by email.
To cancel email delivery, send a message to NoMail[at]fer3.com
----------------------------------------------------------------