# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: [9955]time of meridian passage accuracy
From: Antoine Cou�tte
Date: 2009 Sep 27, 05:37 -0700

```Dear Jim and George,

Thank you George for so kindly providing me with Jim's paper.

Thank you Jim and Congratulations for your Navigation paper. It is one of the
Best and most Comprehensive I have seen dealing with a "graphs only"
approach. I will now on keep it on file as a quite precious addition to my
Naval Academy Navigation course and to the Book by M. Mortimer Rogoff you
made a reference to. Longitude error quite high sensitivity to observation
errors is also very clearly mentioned as it was in Mortimer Rogoff's Book.

I still need to dig out in further depth the (other) graphical method
mentionned to me a few days ago with a referenced http link on this NavList
site and which was published recently (this summer I think).

The interest of graphical methods is to avoid computations. They also show
that LAN's can be much more extended than the restrictions I was earlier
taught with limitations to zenit distances less than 20?.

It could be noticed that in the method you published, which is based on the
differentiation of the well known/fundamental Height formula, such
differentiation is first order. IN LAN's first order is generally well
sufficient to deal with the majority of practical purposes, but it does have
definite limitations if and when you tackle observations closer and closer to
zenit.

"Computation only" methods using first order terms have a limitation because
of the presence of significant UNEVEN ORDER TERMS in the higher order
development of hights vs time when we deal with cases with either changing
Body declination or N/S observer speed component.

For this very reason, and as a cherry on the cake, if we consider LAN methods
based exclusively based on Computations alone (no graphs), Douglas Denny and
George are BOTH right on what seems an apparently Contradictary and
irreductible statement/argument between them, with Douglass stating "The
Height curve IS skewed" and George stating with equal force "the Height curve
is NOT skewed, only displaced left or right". If you consider cases
sufficiently close from LAN time and to an accuracy of 0.1 arc minute for
example, then the Height curve is NOT skewed as George points out, ... but if
you deal with examples of heights sufficiently far away from Culmination
time, then ODD terms will eventually come to play in some significant manner
and the height curve when referenced to elapsed time IS definitely skewed.

Peace be with you all !   :-))

I would still guess that ALL first order methods - including the graphical
ones such as yours Jim - might share the same practical use limitations for
near zenit culminations with high N/S Obervers speeds and or significant
changes in declination. It might be worth verifying this with examples. I
should have between 10 and 15 past examples of LAN with cumlminations above
85?. We could check results with your graphical method Jim.

Now, for most practical purposes, and assuming that you want your LAN's
results as accurate as achievable (which we all aim at), I would offer the

1) - Try getting an as wider "heights span" as possible in order to improve
Longitude accuracy. "Heights span" here means the difference between
culmination height and you lowest observed height in your set of height
shots. A One arcminute observation error on observed heights has less
relative effect on longitude accuracy if you have a full 8 to 10 degree
height span than if you have only a 3 degree height span.

2) - Whenever achievable, prefer culminations closer to zenit. With low
culminations heights, the "heights vs time" curve becomes more "flat" and it
heights, the "heights span" criteria adressed in 1) herabove requires longer
observations time spans, therefore increasing both the constraint duration
for a constant bottom speed, and the effect of speed knowledge uncertainties.

3 ) - Shoot as high LAN's as possible, then ? Not quite, because of at least 2 reasons :

3.1) - Sextant swinging will become more difficult and possibly more inaccurate close to zenit, and

3.2) in the cases with high N/S speeds and/or high declination speeds close to
zenit, even if primary consequence is to move "sideways" (i.e advance or
delay) the "heights vs time" curve, such curve may eventually become
significantly skewed. Ignoring such skewness (right term ?) may result into
appreciable errors mostly on Longitudes determination. Accuracies on
Longitudes remain a "weak point" of LAN's methods since most often the
observed span of azimuths necessarily remains quite narrow around the
horizon.

Have a Great day, ALL of you !

Antoine

Antoine M. "Kermit" Cou?tte

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