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    Re: Accuracy/precision in plotting tools.
    From: Herbert Prinz
    Date: 2004 Mar 30, 15:49 -0500

    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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