A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Celestial Navigation without a sextant.
From: Frank Reed
Date: 2008 Mar 10, 21:12 -0400
From: Frank Reed
Date: 2008 Mar 10, 21:12 -0400
George, you wrote: "What does Greg base his "6 minutes of arc" figure on, when it must include the uncertainties in refraction for the Sun, as seen on the horizon? How well does he know what that refraction will be, and how much it might vary from the "book" value of 34 arc-minutes?" Strikes me as a 'not unreasonable' value. There is an awful lot of variability within the variability. What I mean by that is that under certain very common circumstances, e.g. at sea in temperate climates, the day-to-day variability in the refraction at the horizon is relatively small (a few minutes of arc), but under other circumstances, which might be common for some observers, e.g. near the coast in cold weather, the day-to-day variability in refraction could be much larger (tens of minutes of arc). You quoted Meeus, " ... According to Schaefer and Liller, the refraction at the horizon fluctuates by 0.3 degrees around a mean value normally, and in some cases apparently much more" And quoted Bowditch, "Generally, the error in tabulated refraction should not exceed two or three minutes, even at the horizon" ...which you called 'absurd'. The Bowditch statement is weak because it doesn't provide any ranges. The refraction tables, when properly corrected for temperature and pressure, can in fact be counted on as exact for all practical navigation down to THREE degrees altitude. Although some navigation manuals still recommend avoiding sights below ten degrees altitude, this is over-cautious. Meanwhile, claiming "two or three minutes" variability at the horizon seems to be in conflict with the other source which suggests 18 minutes variability in normal cases (incidentally, Greg's "6 minutes" is close to the geometric mean of these other claims, for whatever that's worth
). So who's right? I think they're both right under certain conditions. As I noted above, I think this is due to the great difference between the temperature profile of the atmosphere on a large landmass (or near the coast), especially in winter, and the temperature profile at sea. Extreme temperature inversions are common near a continental coastline but rare at sea. You can look at real data on this from daily weather balloons. Pick an island location like Bermuda, and you'll see much less variability than at a coastal or inland location. By the way, there are sometimes temperature inversions even at sea. Calm weather especially is associated with them. It's worth knowing that the same conditions which would lead to anomalous low altitude refraction at sea will also often lead to "sea fog". Finally then, what range in variability of the refraction should a navigator (or a celestial navigation enthusiast) use? I would recommend these: 1) Trust the tables for altitudes of 3 degrees or above, but be sure to correct for temperature and pressure. There's no reason to worry about anomalous refraction above these altitudes. You DO have to be concerned about anomalous dip, however, as a separate issue, no matter what the object's altitude. 2) Ignore tenths of a minute of arc in the refraction below 1 degree altitude (so you can ignore the "improved" refraction tables published in the Nautical Almanac starting in 2004 --they result from a relatively trivial change in the atmospheric temperature profile). 3) Where temperature inversions and other low-level variability are likely to be small (a good distance from large landmasses, not becalmed, no sea fog), expect less than six minutes variability in refraction even at the horizon, probably less than three minutes. Also, under these same conditions, anomalous dip is likely to be small. 4) If there is any reason to believe there is an unusual temperature profile in the lower atmosphere (particularly close to shore in cold weather, especially in the early morning), be aware that the refraction can easily vary by 20 or even 30 minutes of arc. Incidentally, I base these conclusions, in part, on a large number of refraction integrations that I ran back in 2005 (I think) when Marcel got me interested in the production of refraction tables. It's quite straight-forward to take an observed temperature profile and generate a refraction table just for those special conditions. Of course, navigators at sea do not generally have access to current atmospheric temperature profiles. Some naval navigators might have been able to observe the real temperature profile (by launching balloons or even aircraft), but the computing power to generate refraction tables "on the fly" probably arrived too late for naval celestial navigation. And again, it's totally unnecessary for altitudes above three degrees, so the value of such tables is limited in any case. -FER --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavListfirstname.lastname@example.org -~----------~----~----~----~------~----~------~--~---