NavList:

   

Reply

A few days ago, in reply to one of my posts, George H wrote
"A series of sights, taken around noon, will indeed be quite "symmetrical",
as long as the vessel's North-South component of speed stays constant. It's
simply a parabolic curve. Not symmetrical about Local Apparent Noon,
however, but about some moment, displaced from noon by an amount which
depends on that speed component. Allowing for that time-offset presents one
problem, but not the biggest one."

Hi George, I'm sorry I confused you with my use of the word 'symmetrical'.
What I was saying is that the altitudes are no longer symmetrical in the
sense required by the usual "equal altitudes" method of determining
longitude around noon. That's the problem that arises due to the motion of
the vessel and the slowly changing declination of the Sun. Of course, it's
easy to deal with that.
[Incidentally: you noted that the curve, when shifted is "simply a parabolic
curve". Of course. No matter what's happening, the curve must be parabolic
according to the laws of mathematics: any continuous curve can be
approximated to some level of accuracy by a parabolic curve around a maximum
or a minimum.]

I wrote earlier,
"But these issues can be corrected without a whole lot of trouble and you
will then have a longitude, too. The longitude would not be as accurate as
the latitude but not too bad either. It depends on the details (as Bill
noted in another post)."

And George H replied:
"Frank is minimising the difficulties here, which we have been into in some
detail on the list before."

George, you're exaggerating the difficulties. It's not that tough to deal
with those small difficulties, and no, George, it's not blasphemy or heresy
to say so either :-).

And you wrote:
"The trouble is that the altitude is changing so slowly, near noon, that the
procedure is inaccurate, unless the observation is extended over a long
period either side of noon, to determine the moment of symmetry. And that's
the biggest problem. I agree with Jeremy's assessment of such a method of
obtaining longitude as "horribly impractical"."

Nah. That's an exaggeration.

Let's suppose in a typical case we start twenty minutes before noon, take
four Sun altitudes over the course of ten minutes. Then around noon we take
four more sights over the course of ten minutes. Finally starting about ten
minutes after noon, we take four more sights over ten minutes. So that's a
time period of forty minutes. And notice that there's really no significant
distinction among the individual sights. I've grouped them into three sets
just for the explanation. Is "forty minutes" (total) what you mean by a
"long period on either side of noon"? If so, how is that horribly
impractical? After we have the sights, each consisting of an altitude and a
Greenwich time, we correct for the motion of the vessel and changing
declination, which is quite easy and we plot them out on graph paper. Then
we fold our graph paper in half (so that we can see through it if we hold it
up to a light) and we line up the sights so that all of them, before noon,
near noon, and after noon, all lie on one nice half of a parabola. Unfold
the paper and the crease gives the actual time of LAN. Read off the best
estimate of altitude there and process that as a normal noon Sun sight for
latitude [important note: this is the ONLY altitude that has to be corrected
for index error, dip, refraction, and semi-diameter --the others can be used
raw]. Read off the GMT corresponding to the crease, correct that GMT with
the equation of time to get Greenwich Apparent Time, and then find the
difference between 1200 and that GAT and convert to longitude at the rate of
15 degrees per hour of difference (if GAT is earlier than 1200, then the
longitude is east, else west). In typical cases, the accuracy of the
latitude is about five times better than the accuracy (in miles) of the
longitude. So if I can get my latitude to 1 n.m. accuracy and my longitude
to 5 n.m. accuracy without buying, carrying, or learning any real sight
reduction tables, is that impractical?? Of course, some students of
navigation will prefer the more elaborate approaches involving tables and
LOPs. Nothing wrong with their preferences.

And you wrote:
"Indeed, the observation that Jeremy was detailing, with a Sun that's very
near the zenith, gives the best chance of making such a assessment of
longitude, because then the altitude change is much sharper, close to noon,
that it as around a noon with a lower Sun."

That's true. While you may need to take bracketing sights covering forty
minutes in typical situations, in those cases where the Sun is near the
zenith, the time period can be greatly reduced. Generally, the results would
be about the same in terms of accuracy when the Sun's azimuth shifts by ten
degrees from the beginning to the end of the sight-taking period.

And you wrote:
"It isn't easy for the navigator to find the best direction to face with his
sextant, with such a high Sun, but that's another matter."

If the navigator knows that there are TWO ways to swing the arc, then this,
too, is no problem.

 -FER



--~--~---------~--~----~------------~-------~--~----~
Navigation List archive: www.fer3.com/arc
To post, email NavList@fer3.com
To , email NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---

   

Reply