NavList:

G.Lapk. Sine the Almanac sunrise time is in L.Mean.T. , the correct U.L. sunrise time at any meridian around the world can be found by applying the latitude in time units to the Almanac (interpolated) figures. The reason is that Mean Time is registered by an artifical sun , orbiting the celestial horizon with unifform acceleration at exactly 15 deg / hr. If checked by the spherics formula for sunrise U.L. at any meridian , a same sunrise time like by the Almanac listing is consistently found in hours, minutes and seconds. Seconds digits are not listed in the Almanac , outcomes are finished to minutes.

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You are attempting to use the sunrise table for a purpose it was not designed for.
You must know the general rule that you can not go beyond the precision of your data but you
somehow attempt to massage the data in the sunrise table to get a greater level of precision than
the level of precision existing
in the original data. The sunrise table in the Nautical Almanac is only approximate and is only to
a precision of plus and minus 30 seconds (only to the nearest whole minute (and only at the
Greenwich meridian) and then for a three day period) and  is used for planning purposes only and
not for actual celestial navigation calculations. It is the main data tabulated in the almanac for
declination and Greenwich Hour Angle  that are actually used for celestial navigation
computations. The most important use of the sunrise  table is so the marine navigator can
set his alarm clock so that he gets out of bed early enough to take a morning round or stars on
ship board during the short twilight period when the stars are still visible and the horizon has also
become visible. It has no such importance for a flight navigator since he can take star sights all
night
long with his bubble sextant so the twilight period is not important to him. Another use of it for a
marine navigator is by looking at the sunrise or sunset table (and the twilight tables) and then at
the derived time entry for Aries he knows the approximate LHA Aries at twilight so can easily
use H.O. 249 volume 1 for selected stars to preplan his shooting schedule.

 A really simple way to show that the sunrise table can’t be used in the manner that you attempt
to use it is to look at the subsequent three day period starting, with July 5th, where it gives the
time of sunrise as 0601, exactly one minute later than the 0600 time given for the period of July 1
though 4 that you used. Ask yourself this question, how did the time of sunrise change by exactly
one whole minute between July 4th and 5th? Did the earth stop rotating for exactly one minute and
then start rotating again?

Basic to your premise is your computation of the time of sunrise at the location that you think the
plane was, at the time of sunrise.  You step  through this computation like this on page 28 of the
2008 article:


“Offset Fix had to be established. In
Noonan's case with the aireraft's 150 mph cruise
speed, this Fix had to be precomputed forthe coordinates
pair (178?47'-W;OOOO9'-N) at 150 mis off
The belonging sunrise time was charted in the
(American) Nautical Almanac (an Air Almanac was
not issued for the year).
Lat 00 deg LMT 0600
July 2,3,4 U.L.H.
Lat 10 deg N LMT 0543
For 00009'-N we find LMT 0600 - 9/600 x 17m =
0559:45 LMT. By adding the West longitude in time
units (I Ih55m08s) it is found that Upper Limb Sunrise
for the Offset Course Shift was at 1754:53 GMT.”


( A navigator would never do the time computations that you did especially he would never use
GAT since the Nautical Almanac in 1937 used GMT for all the tabulations which were for GHA,
not right ascension, and Noonan said himself that:

 “I consider the development the Greenwich hour- angle idea the greatest contribution to the
science
of navigation since Sumner, and have used it exclusively since first published in the Air
Almanac.”  See:

https://sites.google.com/site/fredienoonan/resources/weems/weems-424-425.JPG?attredirects=0

What you are doing here is assuming that the plane was located at 178? 47' west and 0? 09' north
and then calculating the time that the sun would have risen at that location. We only have to look
at
the first part of that computation since the problem there carries through all the rest of your
computations. You looked at the “Sunrise- Sunset” table for July 2, 1937 (you actually must have
looked at a modern Nautical Almanac because there was no such table in the 1937 so Noonan
couldn’t have done the computation that you did, nor would he have wanted to.)  The tabulated
values are
only correct for the middle day of a three day period, which was July 3rd (in the modern almanac
you used. The 1937 almanac was not arranged in three day periods) and you found that sunrise on
the equator was at 0600 and that sunrise at 10? north was at 0543. You then did a straight line
interpolation between these two values to determine the time of sunrise nine NM north of the
equator
at 09' north as 0559:45.

“What is wrong with this picture?”

The most obvious problem is that the data in the table you used is only tabulated to the nearest
minute so no
matter what you do after that with this data it can never be more accurate than the level of the
original data. Based on your tabulated values, the sunrise on the equator (on July 3rd not the 2nd)
was
somewhere between 0559:30 and 0600:30 and the
sunrise at 10? north was somewhere between 0542:30 and 0543:30 with no way to know exactly
where within these ranges. The uncertainty range of plus and
minus 30 seconds in the original tabulated data must be applied to your calculated time so, using
your
method, the time of sunrise at 00? 09' north could have been anywhere between 0559:15 and
0600:15  yet you nail it exactly to
the
second at 0559:45. The “Sunrise- Sunset” table in the Nautical Almanac carries a warning that
when
interpolating for times of sunrise that: “rounding errors may accumulate to about 2 minutes.”
You ignored this warning.

Why is this important?

You may think that I am picking nits, but this 60 seconds of uncertainty in the time causes a 15
NM uncertainty in the derived longitude because the sun is traveling west along the equator at
900
knots, 15 NM per minute. All of your subsequent calculations flow from this calculated time of
sunrise.
At the end of your computations you come up with an error in Noonan’s longitude of just 9 NM
so your
result is swamped by the actual uncertainty in your original calculation of the time of sunrise so
your calculation has
no significance. You also forgot that Itasca was making smoke that blew downwind much further
than the 9 mile error that you claim Noonan made.


Gary LaPook

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G.Lpk. There is no reason to be impressed by anything mathematic since the GHA/LHA listing is arithmetical ; may it be that time sight , or longitude by chronometer do not have , or no longer possess a paragraph in American Practical Navigator , that does not mean that the technique not existed resp. was dispersed among navigators circles , might it be as an emergency measure.

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Well, I would think it pretty amazing that if your sunset method was well known among navigators that no one ever thought to include your sunset method in any of the editions of the American Practical Navigator since 1802 through 2002, two hundred years of publication since it designed to be comprehensive and is the definitive reference navigation text in the U.S.