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Andrew Corl wrote:
" I have followed the recent posting regarding the subject of determining
position from two intersecting circles.  As strange as it may seem this is
what I always thought celestial navigators did.  Shoot three objects and get
a position on the map and know where they were and then figure out where to
go from there.  Little did I know what I was getting myself into."

and Bill Noyce answered:
" Well, yes, in principle.  But the math for doing that directly is more
complicated than necessary.  Thus, the most commonly-used method for
reducing sights by hand is to start from an assumed position, and calculate
what the altitude would have been from that position, as well as an azimuth.
Comparing with the measured altitude tells you how far you are from the
assumed position, and the azimuth tells you in which direction (and how to
draw the line-of-position)"

An American called Martin Creamer has sailed a yacht around the globe
without using any navigational instruments. As to when: best clue is my
memory that the story appeared in the first issue of the magazine 'Ocean
Navigator'. Seventies? He sealed up sextant and timepieces and all the rest
and stowed them up under the bow ( yes I know - not necessarily the part of
the boat that gets pounded the least!). Just in case.

More than anything else I think it was a mental challenge in slow motion. He
spent months thinking about what he saw as his biggest problem: getting
around Cape Horn. The specific problem was how narrow the strait is, and the
imprecise nature of alternative methods of navigation used. Too far north
and he risked the traditional hazard of running into the southern tip of
South America: the complex mess of islands with perverse currents and tides
swirling around them, the whole swept with catatonic winds, often with very
deep water right up to the shore. Too far south and not only might the
weather get even worse but the risk of meeting icebergs became exponentially
greater. Not that far away is the most northern peninsula of Antarctica.

(As an aside, at least one of its South American neighbours lays claim to
it. To bolster what they see as their case for sovereignty, they flew down a
heavily pregnant woman to give birth there, thus producing the first-born
citizen of that land. Then mother and new-born were flown home again.)

How did Creamer do it? The solution for that specific problem was simple:
shoot for the middle, avoiding all land. It worked out fine. I seem to
remember that a number of navigational techniques were used during this
circumnavigation and perhaps this is the point - that nav is not about one
technique or machine or tradition or necessarily any particular other.
Rather it is potentially about all of them. The funny thing is that Creamer,
who proved this in the most convincing way, had a technical background.

One helpful method he used belongs to celestial navigation. Without any
instrument. If a zenith body can be found and identified then the boat's
position is known. Imagine a line running from the centre of the earth
through the boat and extending outward all the way to the celestial sphere,
where it meets a body (eg; star). That unique point on the celestial sphere
is defined via its declination and hour angle. They in turn have equivalents
on the earthly sphere, known as latitude and longitude. The result, where
that line from the star meets the earth, is not a position line, but a
unique point. A fix. The advantage of using stars for this is that they do
not wander around the sky. Over a lifetime there is generally minimal change
in position. Of course judging when a star is indeed at the zenith is
something of an acquired skill. I've found the best way is to lie flat on
the deck and try to become mentally still with the stars while boat and body
slosh about underneath.

With practice and familiarity with the sky, position can be monitored by
observing how stars approach and retreat from the zenith; their relative
position. Eventually the changing position on earth becomes readable through
observation and knowledge of the heavens. There is nothing new about this.
Polynesians have used similar techniques, and others, to sail great double
hulled canoes all over the vast Pacific, colonizing most of it before
Europeans came.

But this specific method is never going to become very popular. It is too
difficult (especially, when using a sextant, determining azimuth near the
zenith) and there will not always be a convenient star at the zenith. The
popular method we are familiar with is a kind of variation. A body at the
zenith is not required; any convenient body will do. Let's say it is
observed to the north, at x degrees of altitude. Another observer could
measure the identical altitude of the same body at the same moment, but for
her the body lies to the south. They are both located along a circle with a
radius of (90-x) degrees. Any number of observers located along this circle
see the same body at the same altitude at the same time, with differing
azimuths. A small portion of this circle near the observer is the position
line, or LOP. That is the drawback: instead of a unique position all we have
determined is that we are somewhere along this circle. To locate a unique
position (we actually get two when combining two circles) we need to observe
at least one other body, derive another LOP, and take their intersection.

What if there isn't another body? People have sailed quite gaily around
oceans using only the sun. An earlier LOP from say, a morning sight can be
'run forward' to intersect with a later one in the afternoon. This is quite
legitimate, although accuracy depends on how well the course and speed; the
DR plot, has been maintained between the two sights.

Since this is the case, instead of moving a tiny portion of a position
circle, can the whole circle be run forward? This is where we came in. That
is the question that has been under discussion here, thanks in part to Mr
Zevering who has a few ideas all of his own on the subject.

   

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