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George responded:

> Bill has provided an interesting account of his path to enlightenment, and I
> go along with all he says, except for a little niggle at the end.

"Path to enlightenment?" I openly and freely admit to being student of cel
nav, not a master. I assume you refer to the eighteenth century "Age of
Enlightenment," as opposed to eastern or other religious/cult philosophical
notions. Heck, I would be happy to "Reach nirvana tonight." Or any other
night. 

I'm going with the late, great, Frank (Zappa's) lyrics in "Cosmik Debris" on
the topic of enlightenment/nirvana.

Google: "Frank Zappa Cosmik Debris Lyrics" for the full text.  Your pick of
hits, but I personally look for lyrics where the note taker can correctly
spell words in common usage.  Not that I can ;-)

But I digress.

 > His comment- "The vessel's motion would keep elevation climbing to an
> onboard observer until the rate of climb induced by the vessel cancelled out
> the rate of fall after LAN (to an observer at a fixed position)." shows that
> he has really understood the matter.

Supposedly Albert Einstein was asked what he would do if he was confronted
with the following problem: If the world was going to be destroyed in an
hour, and you might stop it, what would you do?  Einstein reputedly
responded by saying that he would spend the first 55 minutes making sure he
understood the problem, and the last five minutes solving it.

That may well be internet bunk, but I find the principle sound.  No Einstein
here, but I feel a need to understand the problem.
>
> Fuirther on, he wrote- "While I appreciate the Clyde problem you posted both
> for the prose and word pictures, it seemed to me that N 56 during the winter
> solstice would produce a pretty flat curve."  Well, that was its point, of
> course; to test Frank's pet proposal in a demanding (but realistic)
> situation, not just in a benign environment, to check the claims he has made
> for its accuracy.
>
> Bill's alternative situation gives that method a much easier ride, with the
> Sun's maximum altitude up around 73 deg. Then the curve of altitude against
> time would not be nearly so flat as in that Clyde-approach, which makes the
> timing much less imprecise. In Jeremy's recent observations from the
> tropics, the Sun is even higher, and Frank's longitude-around-noon method
> may then be perfectly appropriate.

Regarding "a much easier ride," yes and no. My first thought (testing the
symmetry proposal--trust then verify) was to take a real-world latitude
around which most pleasure sailors operate in during the warmer months, and
is roughly halfway between the extremes of commercial vessels year round.
Also to get a reasonable peak to deal with when considering symmetry.

It did strike me, especially given my "Kant" flat line example that a
nearly-flat curve would not do for my purposes.  I am hardly a
mathematician, let alone a theoretical mathematician, but as I see it a flat
line has no peak, and a line (not a line segment) has no midpoint. (Jump in
here anytime Alex.)  Of course I was speaking east/west, and the concept I
was attempting to digest was the affect of north/south motion on the time of
the peak, so I may be confused (or a victim of Archimedes' Time's Arrow
argument).

As you have noted in the past (and is true of me) I am not a plug & chug
kind of guy. If I can get to and understand the principle, I generally don't
need tons of tables/books. For example, many texts deal with determining
distance off etc. on the run from one object with tables of angles and
special pairs. Once I understood the problem, I could solve it with the law
of sines, the law of cosines, or find the angles of an oblique triangle
given three sides with a $10 pocket calculator.  The equations I can carry
in my head, or on one page of cheat sheet--with the bottom half pertaining
to great-circle solutions and quick methods as posted on NavList. I do need
a backup calculator just in case!
>
> Even so, from 40 North in midsummer, with a Southerly speed of 12 knots,
> Bill concludes-
> "calculated latitude (no instrument or observer error) will only be shifted
> by 0d 00!2 towards north (plot away). Time of peak altitude vs. LAN is late
> by *nominally* 1.5 minutes. That equates to 23 nm, or 0d 29' lon at N 40.
> That's a ton to me, especially as it is a theoretical and does not include
> other potential errors."
>
> I haven't checked the details of Bill's calculation, but at 4 minutes of
> time to a degree (the speed at which the World spins), his deduced
> time-shift of 1.5 minutes would correspond to a longitude shift, if
> uncorrected, of 22.5 minutes of arc, or at 40 deg North, a distance error of
> 17.2 miles. So a bit less than his own figure of 23nm, then; not quite a
> "ton", perhaps, but still a serious matter, not to be taken lightly.

Busted! (I made an error and it was caught.) It is not a "a little niggle,"
it is a gross error/blunder on my part. I got upside down (backwards AKA
bass ackwards) on this).  As to decimal/significant digits, since it was a
*nominal* (Mach-1 eyeball) estimated time I rounded up or down.

Exuses, excuses.  My salt-waters days are two decades behind me.  I sail
primarily on Lake Michigan.  It has a reasonable north/south expanse, but
little in the way of east/west. Being inland it's charts are in statute
miles (thank you Elizabeth I, Queen of England and wealthy land
owners/landlords for the statute mile). As a laid back (sloppy) boat owner I
once knew who was *very* casual about provisioning put it, "Don't worry. You
are surrounded by fresh water, and never more than 50 miles from a hot meal
and cold beer of your choice." I never sailed with him on the big lakes.

Point being, the way I work most of the time I am going from miles to
degrees/minutes.  Given the relatively short distances plane geometry works.
Nautical miles (converted from statute if needed) times the inverse of the
cosine of the average latitude between the waypoints, and bingo, difference
in longitude.

A creature of habit.  In this case I confused arc for nautical miles, and
then converted to arc.  Sloppy on my part.

BTW, if you would like a copy of the spreadsheet/charts of my exercise, or
of my "predicting LAN" math and sketches, I would be happy to distil them
into PDF's and send them to you off list--or post them online (if someone
would refresh my memory as to the NavList online graphics etc. repository).
>
> Bill refers to my words- "But much of this is old ground, which has been
> well-trodden on this list before, and I doubt whether any minds are going to
> be changed."
>
> and asks-
> "References to the "old ground" please. Thread name plus month a help."
>
> To be honest, I would much rather leave it at that, rather than reopen
> further fruitless debate, between the zeal of a prophet who claims to have
> discovered a new way to teach navigation, and the contrary view that
> students should discover navigation via position lines.

Point number 4 of my summary, "Rubber knife." If the "prophet" can help me
reach nirvana, count me in. I cannot consider your example and plot it
unless I do due diligence and dig up your parameters in the archives--or you
spell out the specifics of the "Clyde" test for me. Until I have that
information and the time/inclination to compare a plot at N 56d with date,
time, course and speed to the teachings of a "zeal of a prophet" I am like a
dog with a full bladder between four trees--not a leg to stand on. ;-)

Bill B.


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