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    Re: Homemade plotting sheets
    From: Frank Reed
    Date: 2019 Dec 21, 10:58 -0800

    "Saint-Hilaire intercept method"

    Folks seem to go through gymnastics to add this proprietary name and then worry all day about the proper franglish pronunciation. Isn't it enough to call it the "intercept method"? Are we trying to distinguish it from the "Williams-Sonoma intercept method" or the "Lockheed-Martin intercept method"? :)

    It's "the intercept method".

    The singular property of the intercept method which affects plotting is that it depends on azimuth, and that requires a conformal local plotting sheet (that's the "universal plotting sheet" or "UPS" in navigation, very often referred to incorrectly as a "Mercator plot"). A conformal mapping is simply one that preserves shapes: squares on the ground are squares on the plot and circles on the ground are circles on the plot. Therefore such a map also preserves angular relationships, in particular the azimuths that are essential to the intercept method. The most important non-conformal mapping is the easy "rectangular" plot which treats longitude and latitude as x, y coodinates. Plots using the intercept method would require latitude-dependent "protractors" or equivalent "squashed" compass roses in a rectangular plot, which was not an option historically.

    A conformal local plotting sheet (or "UPS") simply scales degrees of latitude to match degrees of longitude. It should cover no more than two or three degrees of latitude in practice. The scaling factor is very simple: cos(lat). How big is a degree of longitude in miles compared to a degree of latitude? It's smaller (in miles, not minutes of arc) by that factor cos(lat). That's all there is to it. Historically, people invented drawing tricks that generated cos(lat) using a protractor and straight edge, like the one in Blewitt's book. In the modern world you can use a calculator, or if you must, you could use a printed table of cosines. A local conformal plotting chart is nothing but a scaled plot where degrees of longitude are reduced relative to degrees of latitude by that factor. If you get to this by scaling up degrees of latitude from degrees of longitude using sec(lat) (=1/cos(lat)), I hope it's clear that this is identical in the end.

    Every navigator should know the scale factor for longitude degrees in your "home" latitude. You don't need it any better than two decimal places. Mine is 0.75. One degree of latitude is 60 nautical miles. One degree of longitude is 75% of that in my latitude, or 45 nautical miles. It's also worth remembering that the factor is 1.00 within five degrees of the equator. Degrees of latitude and longitude are both sixty miles in that band along the equator.

    As I have mentioned a number of times before, you can toss out all this noise about plotting if you use a simple "two-point" system instead of the intercept method. If you calculate two points on each LOP, the line is defined at least as well as it by intercept distance and azimuth (and sometimes better), and since azimuth doesn't enter the picture at all, you don't need conformal plotting sheets.

    Frank Reed

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