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Herbert,

I enjoyed reading your detailed explanation.

Thank you for writing it,

Joel Jacobs

----- Original Message -----
From: "Herbert Prinz" 
To: 
Sent: Tuesday, March 30, 2004 3:49 PM
Subject: Re: Accuracy/precision in plotting tools.


> Jim Thompson raises a questions that is very pertinent to a list mainly
> concerned with the _history_ of navigation.
>
> Plotting, a short lived and rather cumbersome sight reduction technique of
the
> last century, has not received sufficient attention here, despite the fact
that
> a few aficionados still practice it. Some even go as far as to teach it as
the
> only method of position line navigation, often mistakenly identifying it
with
> the latter. As it is the case with the art of splicing braided line, the
> attraction of plotting, too, is not so much in its utility as in the joy
> obtained from the skillful handling of the tools of bygone eras. Its
popularity
> is connected with the admiration (and the envy) we have for those those
old
> salts who swung their dividers in 12 foot waves without killing some crew
or at
> least poking their eyes. However, there is this unnamed hero who, after
having
> confirmed by plotting that his position was in the navigable zone of a
> hurricane, poked his throat with the dividers and was consequently lost at
sea
> without a trace. (I may have more details on this story on the day after
> tomorrow.)
>
>
> > 1. What are the accuracy and precision that I can expect from a charting
> > tool like a reasonably well made Portland triangle from a reputable
company?
>
> >
> > 2. Are compass roses on small scale Mercator charts not perfect circles?
>
> Dear Jim,
>
> Ad 2. (First things first)
>
> You are probably thinking of the fact that a perfect circle in the real
world
> becomes an egg when projected on a Mercator chart. However, this does not
come
> into play here. A compass rose shows angles, that's all. Whether it is a
piece
> of cardboard in a compass or a stylized diagram in a chart, its shape can
be
> square, octagonal, circular, whatever. It does not matter. What counts is
that
> the graduation is correct. On the other hand, I can see no reason why one
would
> want to draw a compass rose on a chart in any other shape than perfectly
> circular.
>
> In the real world, we measure azimuths by dividing the horizon into 360
equal
> parts, called degrees. Therefore, on a real world compass the graduation
of the
> rose must be uniform all around.
>
> The Mercator projection is orthomorphic (conformal), meaning that it
preserves
> angles at close distances. We know that it does not do this over long
distances.
> Hence the difference between orthodrome and loxodrome. But the distortion
of
> azimuth angles (i.e. the angle between loxodrome and orthodrome) varies
with
> position and distance. So, there is no way to draw a distorted compass
rose on a
> Mercator chart that would show correct great circle azimuths anywhere.
Instead,
> one works with loxodromes, accepting that these are, in fact, bent curves
in
> reality.
>
> Therefore, if you find compass roses on mercator charts that are not
evenly
> graduated, we must assume that this is due to the quality of the paper,
which
> may have stretched with changing humidity more in one dimension than in
the
> other.
>
> The same reasoning holds for universal plotting sheets. You mentioned
using
> practice sheets. I would assume that the high price of the ones sold by
the
> government is partly due to the good quality of the paper on which they
are
> printed. Maybe this is only wishful thinking.
>
> Check the graduation with dividers. But if you use a compass, use the same
> section of the compass for the different quadrants of the rose, and then
vice
> versa. This will tell you immediately whether the rose or the compass is
the
> culprit of any divergence.
>
>
> Ad 1.
>
> To put the question about the practical error in perspective, let us
consider
> the _theoretical_ error that we are committing by using a plotting sheet.
> Remember that the scale of a Mercator projection changes with latitude.
>
> At lat 40 deg, cos(40deg) = .766
> At lat 41 deg, cos(41deg) = .755
>
> The difference is 1.5%, meaning that the difference in scale between these
two
> particular latitudes changes by 1.5 percent per degree. The higher the
latitude,
> the worse this gradual change.
>
> Now, on your plotting sheet, draw a horizontal baseline of 100 mm from the
> center towards east. This corresponds to some 96 nm, or thereabouts,  on a
DMAAC
> VPOSX001 (3 inch per deg lat). If you wanted to represent that same
distance at
> lat 41 within the same plot, you would still use the same 100 mm, wouldn't
you?
> Draw a 100 mm long parallel of latitude at 41 deg, from the center
longitude to
> the east. But the correct length of a line representing the same distance
would
> be 101.5 mm. Draw that, too. Connecting both end points to the center,
compare
> the angles on the rose. What's the difference? Half a degree?
>
> Something to consider before you invest in a set of plotting tools made of
> platinum-iridium alloy.
>
> Best regards
>
> Herbert Prinz

   

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