NavList:

David P: Yes, that's a great question. How can we assess the calibration of our sextants at home?

I have for many years advocated using lunars for sextant calibration. They're an excellent choice, and it's the best modern excuse for shooting lunars. It's simple with some calculating tool (like my well-known lunars web app here). Just shoot some lunar angles in the range you need, and see how they compare with what they should be. Repeat a few times and average. It's just that simple.

But let's consider some other options, too. Suppose you have a good liquid (Mercury metal?) artificial horizon. You could shoot meridian altitudes of stars during a single night and get a pretty good sextant calibration that way, too. We'll need altitudes of bright stars, and the standard navigation stars will work well enough. Suppose I'm doing this tonight. I can run a simulation and select stars in advance with meridian altitudes ranging from 5° to 60° which, doubled by the mirror horizon, will yield sextant angles from 10° to 120°.

Here's a list of true meridian altitudes and times for stars observed tonight from the latitude of Mystic Seaport Museum (41.362° N):

• Kaus Australis 14.264° 20:19
• Nunki 22.371° 20:50
• Altair 57.573° 21:45
• Enif 58.627° 23:38
• Fomalhaut 19.148° 00:52
• (N) Dubhe 11.983° 00:58
• Diphda 30.789° 02:37
• (N) Alioth 7.192° 02:47
• (N) Kochab 25.420° 04:42
• (N) Polaris 41.999° 04:55
• Menkar 52.826° 04:56

The stars marked "(N)" are on the north side of the meridian (three below the NCP... Polaris above). This set of meridian altitudes would yield a calibration table with values (double the altitudes) at 14, 24, 25, 29, 38, 45, 51, 62, ... 106, 115, 117°. There's a big gap from 62 to 106°. Use some non-nav stars? Shoot some lunars? Maybe some star-star distances? Try some non-meridian altitudes? Or you could just wait a few months and fill in that gap with the stars of Orion when they reach the meridian before dawn...

Suppose you're not at that location. If your latitude is exactly one degree further north, then the true altitudes on the south side of the meridian will be lower by exactly one degree, and the altitudes on the north side higher by exactly one degree. We can always pre-calculate the true altitude on the side of the meridian away from the pole by getting the meridian altitude of the celestial equator (dec 0°). That is exactly 90°-latitude. Then we add the (signed) declination onto that. Example: if my latitude is 35.000°N, and I observe the planet Saturn at meridian passage tonight and its declination is -7.408°, then the altitude of the celestial equator on the meridian is 55.000°, and the true altitude of Saturn is 47.592°. Observed with an artificial horizon, this should provide a calibration test for an angle of 95°. For meridian altitudes on the same side as the celestial pole (north side in the northern hemisphere), it's easier to take the star's "polar distance", 90°-dec, and add or subtract that from your latitude (which is also the true altitude of the celestial pole). Example: if my latitude is 35.000°N, what would be the altitude of Kochab when high above the true pole and also when passing below the pole? The dec of Kochab varies slowly, but for this coming week we can use 74.057°. That's a polar distance of 15.943°. Add/subtract that from the lat, and we find that the meridian altitude can be either 50.943° above the pole or 19.057° below the pole (both in one night in late January).

A difference in longitude would change the timing. The listed times would be near enough to the local mean (daylight!) time in a different longitude, but we only need these times for planning. The observation is made at maximum altitude, which is an observable event (meaning we don't really need to know the time in advance). And when working on land, we can also arrange to observe close to the east or west side of a north-south aligned building which lets us "see" the meridian.

A different date would also change the timing. If there are clouds for a few days, then the meridian passage times will be earlier by about four minutes per day, every day. And note that it would be smart to try these observations on at least four separate days and then average. The variation from one day to another will encourage (or reduce) your confidence in the new calibration. If the numbers are bouncing around by a minute of arc from one day to the next (they really shouldn't!), then the calibration you're creating probably can't be trusted to a tenth of a minute of arc even with averaging. But if you use a good high-powered scope and apply a few standard tricks for quality sights (like "always clockwise" micrometer rotation), then you should expect results that are stable to just a couple of tenths of a minute of arc.

The altitudes above are "true" altitudes (or at least they're supposed to be... not guaranteed!). We observe refracted altitudes and have to correct for refraction as usual. Note that the refraction should be adjusted for non-standard atmospheric conditions since we're trying for maximum accuracy.

Why meridian altitudes for calibration and not other altitudes? First, of course, they change rather slowly near meridian passage. That's convenient. The timing matters very little for meridian altitudes, assuming we observe for maximum altitude (or minimum "below the pole"). Also the sextant can easily be preset to the correct altitude.

We can greatly enhance the whole observation process by mounting the sextant on a tripod, which is easier for altitudes (easier than for lunars or star-star distances) since the sextant is held vertically.

Frank Reed