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Alex

There is an old joke in West Lafayette/Purdue University.  When there is
someone online at a grocery store with a full cart in the "Express,
12-items-or-less" lane, the quip is, "Are they humanities majors who
can't count, or engineering (math) majors who can't read?

As you have stated, you are a professional mathematician devoted to truth.

You also maintain you have read the 2007 thread "Coastal Plotting
Sheets." To quote you, "I looked at it. They are talking of a different
problem. Finding a position of the ship from BEARINGS. You need TWO
bearings to find your position...."

Yes, the words "compass" and "two points" are used, but you have taken
them totally out of context in your assessment. (Please see below.)

You don't want jokes or innuendos, you want truth. My impression of the
truth is this thread was almost totally devoted to the use of 3-arm
protractors/station pointers and possible perils.

Following are excerpts from the thread for readers who choose the
'Readers Digest" version of the posts. (I encourage you to peruse the
entire thread.)



Yes, to fix by horizontal sextant angles you need to have three marks on
shore, and in the right sort of geometrical alignment to give a good cut
between the circles, as against only two marks for compass bearings. But
in terms of the precision of the result, there's really no contest.

If you try to determine an offshore position in relation to coastal
features or landmarks, magnetic compass bearings don't establish a
bearing to better than a degree or two, even in calmish conditions. If
you are plotting 2 or 3  bearings, that error applies to each. If you
want to find the angle between  two landmarks, the error in the
difference is somewhat greater.--George Huxtable

Given a known angle between two known objects viewed from the boat, it
is possible to construct a circular LOP for the boat through the two
objects. This is then repeated for another pair of objects to get
another circular LOP. Where these circles cut is the boat's position.
Because you save the geometric effort of drawing the circles when using
a station pointer or similar, you get no indication of the angle of cut
between the two circles, hence the potential danger.

In the extreme case, if all three fixed objects lie on a position circle
which also crosses the boat's position, the 'plotted' position circles
will lay over each other, and the boat will get the same ambiguous
horizontal angles wherever it lies on the joint position circle - a
major danger. The general advice to avoid these dangers is to ensure
that the middle object used for the fixes is the one nearest to the
boat. In that case there is no way the boat can be on a circular LOP
which includes all three objects. Even so, that set up does not ensure a
decent angle of cut.--Michael Bradley

Presumably this technique would be useful if a compass was not available
but horizontal angles between shore objects could be measured, with a
sextant for example, although the distance inland of the middle object
was unknown. Then the danger you warn of would be relevant.--Peter Fogg



Bill B















On 4/4/2012 11:33 PM, Alexandre E Eremenko wrote:
>> Answering my own question, I *finally* found the discussion of 3-arm
>> protractors/station pointers in the archives under "Coastal Plotting
>> Sheets."  The discussion ran from March 17, 2007 through April 1, 2007.
>
> I looked at it. They are talking of a different problem.
> Finding a position of the ship from BEARINGS.
> You need TWO bearings to find your position if the bearings are exact.
> Using three bearings is just for checking the error in bearings.
> The size of the triangle you obtain more or less tells you what was
> the accuracy of your bearings.
>
> Bearing is taken with some kind of compass. The accuracy of a compass is
> usually
> something like 1/2 degree. Well, perhaps 1/4 degree with some very
> advanced compass.
>
> The 1' station pointer is not needed for this. Ordinary protractor
> will suffice.
>
> The 1' station ponter is used with a SEXTANT, not a compass.
> And the position is found from two HORIZONTAL ANGLES, not bearings.
> You need THREE objects on the shore, 2 is not enough as with bearings.

   

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