NavList:

You folks just need a bigger boat. You're gonna get a bigger boat, right? Last summer in calm weather and gentle seas north of Cape Cod, my sights were within a mile (-ish) aboard the 100-foot-loong, 300-ton whaleship that we borrowed for the day... Here's a nice video released today by Taylo Sahl, one of the voyagers on my sailing leg. You can briefly see me taking sights with my "old quadrant," to borrow a phrase from Mr. Bligh, at about 6:06 in the video (screen cap attached).

I tell my classes that the theoretical limit of celestial navigation altitude sights with a sea horizon (not lunars, and not artificial horizon sights) is about 0.5' thanks to the variability of refraction. That's it. Can't expect better than that. Of course one can expect worse as conditions slide down that slope from perfect weather and calm seas on a large vessel to cloudy skies and rolling swells on a small boat. And that's why there's never any real consensus on this question of the "average" expected accuracy of celestial navigation. You can't average over all conditions on all vessels in any meaningful way. 

Frank Reed

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