NavList:

 

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I think you misunderstand my post George.  I indeed know the difference between LAN and maximum altitude, but that is just not the way it is taught in the USN and USMM; which was my point.  The whole issue arose from the QMOW manual that instructed the navigator to arrive on station 10 minutes prior to calculated LAN.  This practice is to allow ample time to observe the sun to rise and then "hang" to take the sight.  This sight, as you graph displays, shows errors, especially on ships traveling at speed north or south.  I have looked in my 4 editions of Bowditch, and except for a single sentence with the caveat about errors caused by N/S velocity in the 1984 edition, they all say the same thing about observing LAN.  Wait until the sun hangs and then go about the reduction.  Since this is the reference of choice in the US, this is what American navigators do at sea, even though it can introduce errors.  In this case, the speed and simplicity of the reduction trumps any errors in latitude.

 

The real issue is how we solve the problem since ships now routinely travel at 20+ knots and the 2-3 nm error in latitude can be an issue.  (I am deliberately skipping the idea of Longitude at noon as it is not practiced on US merchant ships at sea.) 

 

As you mention, you can shoot at maximum altitude and either do an ex-meridian or use your formula.  This is fine and dandy, but adds work to the simple noon reduction, especially a tabular ex-meridian reduction and I don't see using tables for your formula.  Ex meridians also fall apart when the vessel is too close to the GP of the sun.  If, as Henry asked, you have not had a fix since the previous day, you may have a good idea about time, but not Longitude.  In this case, you would DR your track and keep an eye out for maximum altitude and go from there.  Here is a good chance for George's formula to work its magic, if you had it on hand.  You would still have to do two iterations to get an accurate latitude entry however. 

 

You can also shoot the sun directly at calculated LAN.  This is good if you know time and longitude accurately.  Errors in either input will result in errors in latitude.  This is fine if the errors are expected from inaccurate time and longitude to be less than the error you can foresee due to shooting at maximum altitude instead of LAN.  This is probably the best "modern" solution as you are probably using Celnav as a check on electronic navigation so you can be fairly certain of both time and longitude.  While this will require a second estimate calculation of LAN, it maintains a simple reduction process.  As an interesting aside, this is how I was taught to shoot transits of other bodies.  I now shoot all transits (including the sun) at the time I calculated, not by maximum altitude.  Since I converted to this method, my errors in latitude have decreased significantly. 

 

Henry spoke of the universal LOP method for all observations.  In other words: "Why not do away with the noon sight altogether?"  I have a hard time arguing against this idea these days.  Since the whole traditional reason for the noon sight was to get a reasonably accurate latitude having only rough ideas about your longitude and time, while maintaining a very simple reduction form; why do we persist in its use?  In today's era of modern tables, navigation calculators, and computers, the use of LAN, instead of creating a simple LOP as we would for any other sunline, is not efficient.  This is especially true in light of the errors occurring due to modern ship speeds using the traditional techniques.  Since reduction speed and accuracy are the measures, rather than simplicity of calculation, we can certainly do our work better and faster with a standard LOP rather than LAN.  This is especially true when we can't readily observe when transit actually happens (high speed at higher latitudes).  I can certainly do a fully manual HO 229 reduction without a calculator faster than an ex-meridian, and if I use a calculator or computer faster still.

 

Still I don't see enough people either agreeing with my assessment of the whole observation to abandon the tradition noon sight; or going to the mathematical trouble of correcting the sight when observed at maximum altitude to shift the paradigm.  We have enough trouble convincing people that longitude can sometimes be obtained with reasonable accuracy at noon.

 

These days at the academies, celnav is rapidly losing importance in the curriculums, so that in short order, professional navigators will have only a basic knowledge of the sextant and the standard LOP and any more detail will have to come from extracurricular studies.  I am afraid that the LAN observation will soon go the way of the time sight.

 

Jeremy