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    Re: The Sun does not stop for anyone
    From: Frank Reed
    Date: 2016 Dec 30, 10:48 -0800

    Bob Goethe, you wrote:
    "For those who object to calling a universal plotting sheet a Mercator projection, what TYPE of conformal projection is it?"

    It is a locally conformal, small area plot. The reason it doesn't get its own nifty name is because it covers all of the global projections that you mentioned: the Lambert conformal conic, the standard Mercator, the UTM (Universal Transverse Mercator, which is a distinct projection very different from the standard Mercator), and so on. It also covers a great many other projections which are not globally conformal but are locally conformal within some region. For example, you can use a "universal plotting sheet" (or a "small area conformal plotting sheet) in a region within a few degrees of the center, or point of tangency, of a gnomonic (great circle) chart. That's not much use in practice. But one that does matter is a standard "perspective" projection. This is what you get in nearly all modern global visualization software, like Google Earth. When you have that "bird's eye view" of the globe, any region near the center of the view (except right at the poles) can be represented very well by a small area conformal plot. The only property that matters here is longitude-scaling. That's all you need for a small area! It's not a Mercator projection. In practical terms, when you "zoom in" on a region a few hundred miles across in Google Earth, you are getting a locally conformal (longitude-scaled) view. Features on the map are geometrically similar (preserving all angles, not just 90 degree angles, by the way) to features on the real surface of the Earth. If I have six buoys arranged in a perfect hexagon one mile across and a mile east of those I have three buoys arranged in a perfect equilateral triangle, then when plotted on a longitude-scaled plotting sheet, I will have buoy markers in a small perfect hexagon and a small perfect equilateral triangle. This is what is mean by conformality. This is what we get from longitude-scaling by the factor cos(lat). This is not a Mercator projection.

    You added:
    "I am beginning to wonder if the universal plotting sheet perhaps represents an 'unnamed conformal projection, resembling a Mercator more than any other.' "

    No. It does not resemble any specific projection. It "resembles" them all. A small area plotting sheet is not a Mercator chart. It is simply ignorant to refer to it as a Mercator chart. Of course, the origins of this particular entropy --this erroneous attachment of the name Mercator to a simple longitude-scaled plot-- are lost somewhere in the middle of the 20th century, perhaps during the Second World War. The fact that the error turns up, either directly or indirectly in vague phrases like "basically Mercator" (why not "kinda Mercator" or "sorta Mercator") in the Holy Scriptures of Bowditch leads some to call for jihad against the blasphemers (ha ha ha). Thou shalt not question the Holy Bowditch! :) And yet we all know that modern editions of Bowditch have many errors and many lazy descriptions and poorly-written sections. Right?? We all know this, don't we? Bowditch is not a textbook. It's not even a very good reference work. It is, at best, a collection of encyclopedia articles, some of which are good and many of which are quite mediocre, and of course it remains a nice compendium of printed mathematical and navigational tables, though such things are largely obsolete. 

    By the way, I think it is also the case that the instructions for hand-drawing an actual Mercator projection, included in many books on navigation, usually borrowed from a source like Bowditch, are a major source of confusion on this issue. You don't need those drawing instructions for anything. A standard plotting sheet is not drawn using those instructions.

    Frank Reed
    ReedNavigation.com
    Conanicut Island USA

       
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