NavList:

Well put, Brad!

People forget to put celestial in a historic and technological perspective.  In the glory days of celestial (first half of 20th century), mariners on big, stable ships with topnotch German sextants could get very good shots.   But there's still uncertainty.  Least bit of mist and a question of where the horizon is.  Least bit of haze and question of where the limb of the Sun or Moon are.  Least bit of roll by the vessel and the horizon is bouncing around.  And so forth.  But I'll bet Columbus would have given anything to know his position to within 10 miles of where it really was. 

Now we've got GPS which can give our position to 50 ft (and even less with WAAS) and people somehow want to see similar accuracy from celestial (or even accuracy to 0.1 nm), not understanding how impossible that is with a sextant making celestial observations.

If one goes back and looks at the way navigation was taught 50, even 20 years ago, there was a sharp separation between coastal and offshore navigation.   The goal of offshore navigation was to put you within 10 miles or so of your desired landfall when you came "on-soundings"   From that point onward you looked for coastal features, took bearings on them, took RDF bearings, measured horizontal and vertical angles, etc, to pinpoint your position using these shoreside features.

If you want your position to 50 ft, get a GPS.  If you want a backup to your GPS and/or simply want to enjoy the pleasures of celestial, do celestial.   But don't expect it to compete with GPS for accuracy.

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From: Brad Morris <bradley.r.morris@gmail.com>
To: NavList@fer3.com
Sent: Thursday, November 1, 2012 7:32 AM
Subject: [NavList] Re: Thoughts on Celestial.

I consider this to be entirely amusing!  Are you really worried that you are inside or outside a cocked hat?

Celestial was designed for deep water ocean crossings.  So plus or minus 10 miles is good for fix.  Draw two longitude lines, one at +10 the other at -10. Do the same for latitude.  Look at the size of that box compared to your cocked hat.  It should be enormous!

If you have eliminated systemic errors, and we are only concerned with measurement errors on the order of 1 to 2 arc minutes, then the cocked hat is small compared to the large box.

Yes, you do have to select the numerical answer.  Yes, you wish to get the "correct" answer on your examination.  But as a practical matter, it matters little.

You are somewhere in that box.  Want to get closer?  Get a theodolite and a tripod.  Want to do that in the ocean?  Get a GPS.

Tempest in a teapot. 

Respectfully
Brad Morris

On Nov 1, 2012 9:40 AM, "David Fleming" <d.l.fleming.1@gmail.com> wrote:

We can categorize errors as random or systematic. Random errors have equal probability of being positive or negative. If the standard deviation of the random error distribution exceeds the precision (size of smallest division on the scale) of the measurement then by averaging a series of measurements on a single body when can minimize the random error down to the level of the precision of the instrument. By plotting altitude versus time we can spot potential mistakes ie outliers not part of a random distribution. Such measurements are mistakes and should not be included in averaging.

Systematic errors will still remain.

For systematic errors we may or may not know what they depend on. If we are worried about sun heating the sextant causing a shift in our readings, absent measuring the sextant temperature and having a model for the error as a function of temperature we will be unable to deal with such errors. In the case of heating it is not connected azimuth so it tells us nothing about being inside or outside of the cocked hat.

For something like index error(which we should have eliminated down to the precision of our measurement) but if we made a mistake in that factor then that error affects all measurements the same. Likewise, anomalous refraction ( in Dip) will affect all measurements the same and the placing of a fix at points inside or outside the cocked hat based on azimuths is a sensible procedure.

Sextant calibration measurements as was common with older instruments are systematic but must be applied to each measurement. They vary with altitude rather than being constant for all azimuths.

Dave Fleming
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