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    Re: Accuracy/precision in plotting tools.
    From: Joel Jacobs
    Date: 2004 Mar 30, 19:12 -0500

    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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