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Too much discussion of the finer points of theoretical mathematics, 
statistics, and the proper costuming of angels dancing on the head of a pin 
gives me a headache, I readily concede.

Which leads me to wonder if the admirable attempts to refine position relative 
to a triangle are simply the result of approaching the problem the wrong 
way--mathematically trying to solve a "simple" graphic problem.

I was taught that when one is trying to print or publish data (charts, plots, 
graphs, any kind of data presented graphically) that one should take care to 
properly represent the full extent of the data. That usually means starting 
an axis at a 0,0 point, rather than some "convenient" point higher up a 
scale, so the entire range can be seen and appreciated. And, in the case of 
mapping a function which has an inherent RANGE rather than a fixed value, one 
should try to represent the full range rather than the fixed value 
itself--which inevitably will be incorrect.

For sextant navigation, or anything similar, this means that if you know your 
sextant sight may have cumulative errors of say, +-4 minutes (including all 
errors in the observation) that you MUST plot your LOP as a line being 8 
minutes wide--the full range of +-4 minutes, not simply the observed number.

Depending on the chart scale being used this may simply mean "use a crayon" 
instead of using the sharpest pencil in the boat. Or a "lumber pencil" which 
has a wide lead.

The end result will be that your triangle may not be a triangle at all--but 
the area where the lines intersect will also generate a "smudge of position" 
which includes a prominent display of the error amount that you must account 
for.

To a professional navigator, I know that must sound like blasphemy, since 
using the finest line and then generating a "circle of error" is the usual 
technique. But the simple graphic artist's technique of using the proper 
width pen stroke should, I think, generate substantially the same information 
with no extra math being required at all.

A circle of error may still be needed to accomodate other factors, but at 
least the inherent error RANGE in each sighting is immediately visible when a 
simple wide stroke is drawn.

   

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