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    Re: Thin triangle: where is your fix?
    From: Frank Reed
    Date: 2025 Dec 5, 08:33 -0800

    Lars Bergman, you wrote:
    "Assuming your graph's origin is at lat=long=0 and using the procedure described in the Nautical Almanac (2024), I will estimate the offsets to be 11.1 n.m. north and 20.5 n.m. east."

    Yes! That looks good to me. :) It's near the middle of the short side of the triangle.

    Some background on this:
    For many years, most of us have known about methods for finding the proper fix. from multiple sights. The mathematical procedure, especially as detailed in the Nautical Almanac itself, has been available to us all since the late 1980s. But it's a bit of a black box. What's going on in there? And do I really need to do all that math to get the fix? Many of us have also learn about drawing the "symmedian" lines in a triangle, and we have understood that the crossing point of the symmedians in the triangle produced by three sights is identical to the same "black box" math. But drawing lines like that is a lot of work, and not many navigators will bother with it...

    For some years, on and off, when I have some free time, I have been "brainstorming" ideas for shorter rules. I've been looking for tricks, both analytical and geometrical, that could allow a navigator with an interest in accuracy but without much patience for the black box math to determine that proper "fix" location. And it turns out that there are, in fact, some fun tools available, which are either completely unknown to the larger navigation community or (more likely?) known only a small handful of people.

    Some navigators, I have found, have a prepared "antibody" reaction to anything new. A common complaint is 'why would I need some fancy trick... as long as I am in the right ocean...' etc. The response to this, that I think is worth emphasizing, is to ask how many digits they keep when they apply altitude corrections in a celestial sight analysis. I might say:

    "Do you work only to the nearest minute of arc or two minutes? Then maybe you don't need any new tools. But do you normally include altitude corrections to the nearest tenth of a minute of arc to "do it right"? Then in that case, you want this new trick! If you get to the end of working up a three-star fix working to tenths of a minute (tenths of a mile) at every step, and then just put a dot on the plot where it "looks nice" in the triangle, then you're throwing away half your work."

    [well, something like that... inertia is difficult here]

    More detail later today.

    Frank Reed
    Clockwork Mapping / ReedNavigation.com
    Conanicut Island USA

       
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