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Re: Star to Star Distances taken on a Second Hand Sextant
From: Fred Hebard
Date: 2019 Dec 8, 22:15 -0500

It would seem that star-to-star distances are preferred for sextant calibration because of their lack of day-to-day variation.  Thus one could easily compare sets of measurements between days.  It took me a long time to get mean Ho - Hc for position lines down below 0.1’, most of the time.  The standard deviation was a bit larger, maybe 0.1’ to 0.2.

The keys for my improvement were threefold.  First was  accurate assessment of tangency in an artificial horizon.   I improved that by measuring semi-diameter of the sun and comparing the observed value to that in the Nautical Almanac.  Improvement of SD measurement also led to an accurate index error, the second key.  The third key was accurate timing of a sight.  Each second of timing error leads to a 0.25’ deviation in Ho, IIRC.

The suggestions I offered below are an equivalent program of technique improvement for star-to-star distance measurements.  I estimate it would take me several months to achieve proficiency.  Only then could one start calibrating a sextant.  Using stars of appropriate magnitude, as suggested by Peter Monta, would be an an important component.

Sorry for calling you David; he lives in Alabama, not New Zealand.

Fred Hebard

Hi Fred

The arithmetic for finding the standard deviation is readily available on the internet.  I'm quite sure that absolutely anyone who can reduce an observation, can also determine the standard deviation.  In industrial robotics, we cared about a 3 sigma result, to wit, that 997 times out of a thousand, the angle desired would be the angle obtained.

To help you through this, go out and pick out any observation.  The best illustration of the technique is likely a meridian crossing.  The sun hangs there, and it won't strain your neck.  Its a comfortable observation, no?  So take 6 observations in a row, taking care to record each value.  Please check your index error.  Post them up.

We'll go from there!

Owners of vernier sextants need not worry about approaching always from one side.  The only possible lost motion is in the index arm bearing surfaces, which would only occur after substantial use.  The S-N failure curve for a fairly low low load (index arm) on metal bushings will run to the millions before failure.  In consideration that most vernier sextants will never see that level of use, the index arm v arc has very, very little lost motion.  Virtually insignificant for our purposes.

On Sat, Dec 7, 2019, 9:34 PM Fred Hebard <NoReply_Hebard@fer3.com> wrote:
David,

I shared your problems and never felt my observations of star-to-star distances were adequate.  A good place to start might be in perfecting one’s technique for using star sights to measure index error.  Another important piece is that star pairs be vertically or horizontally oriented.  Otherwise, the difficulty of holding the sextant is overwhelming.  Finally, I believe getting one good set of observations on one pair of stars in one night would be a good first objective.

Hopefully David Morris will continue to guide us in data reduction, which is also an important component of the endeavor.

Fred

Fred Hebard

On Dec 6, 2019, at 15:46, David Pike <NoReply_DavidPike@fer3.com> wrote:

Well there was only one thing to do; go out and try it.  Wednesday, Thursday, and Friday we were down in the low light pollution area of Norfolk, so with great fortitude and determination and the temperature down to 2 degrees Centigrade, Mrs P and I drove the car onto Kelling Heath (N52.92789 E1.13489 on Wednesday evening 4th Dec, taking along ‘Navigator’ on a Netbook, and my Hughes Three Circle Mates Sextant No 25410.  First star pair was Deneb at roughly Hs= 48.55 and Az= 286 and Vega at Hc= 27.17 and Az= 299 and a tilt of about 30 off the horizontal.

First thing I found is, with bifocal eyeglasses and only a 2.5x telescope, checking index error against a nice bright star like Vega is nothing like as easy as checking against the sea horizon or a roofline many blocks away in daylight.  All I could say was that index error didn’t seem too far off the sextant’s historic index error of zero.  Next came how to hold the sextant.  I ended up holding it handle side up at a tilt of about 30 degrees to the horizontal.  I found this rather awkward.  No one ever tells you that your carefully attached lanyard will get in the way of just about everything, and to be prepared for an index shade to fall under gravity and leave you wondering where the second star has disappeared to.

After that comes bringing one star onto the other from zero.  Well that might be OK for the ‘Experten’, but for yours truly it explains why I was never any good at ball games.  The ‘wimp’ way to do it is to set the sextant about half a degree lower than what you’re expecting; point at the brightest star though the horizon glass and look for the other star in the mirror.  The half degree was to prove to myself that if, I could only see one star they weren’t, though some sort of fluke, on top of each other.  There turned out to be little chance of that I can assure you.  In fact, I found finding the second star so hard that in the end I unscrewed the telescope and just looked through the hole, even then, I had to cheat a bit at times by keeping both eyes open.

After about 15 minutes practicing like this, I felt confident enough to put the telescope back in and do the job properly.  I found the best method was to rock the sextant ever so slightly like rolling the Sun about the sea horizon and gradually increasing Hs until the reflected star crashed though the index glass star.  I then increased Hs further until the stars separated again.  Going back onto crashing into each other, the best I could manage with the 2.5x scope and my not very special eyesight were values within a couple of minutes of Cdr Bauer’s values.

After all that messing around with Vega and Deneb, Orion and the Twins were becoming nicely visible and with Betelgeuse at roughly Hc= 17.54 Az= 102 and Pollux at Hc=17.42, Az=067, I had two stars horizontal and at a low Hc.  (I’m not sure if this is the worst case or not.  True there’s a fair amount of refraction, but the XP lines are almost parallel at low altitudes, so that might cancel out the refraction effect a bit.)  This was a lot easier.  With handle down I could get greater support from the car roof and steady the telescope with my left hand.  Also, Betelgeuse is a bit more yellow, so I could see which star was which (In my Universe all major stars would be colour coded).  Once again, with my eyes, spectacles, and sextant, all I could say was that my measurement was within a couple of minutes of Baur’s values.  Therefore, my conclusions so far are that for a rough check it does work, but there must be easier ways of checking a sextant, even inland.  However, you need good eyesight, decent magnification, a strong, steady wrist, and most of all you need to be in good practice.

My next job is to work out some 2019 values for the stars used and record my results properly, but I wanted to get something written down while this topic was still hot.  DaveP

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