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    Re: Swinging the Arc
    From: Frank Reed
    Date: 2012 Aug 18, 14:50 -0700

    No offense to anyone who's just discovered this graphic on Wikipedia, but it's really, really OLD! ;) Well, ok, it's old in Internet terms. That graphic was first published waaaay back in April of 2007, two months before the first iPhone appeared on the market... I had a pet pterodactyl back in those days.

    I have mentioned this graphic a couple of times on NavList and I also mention in to most of my students because it perpetuates the inferior method for "swinging the arc". This inferior method became the standard one and the only one that most navigators had ever heard of sometime in the latter half of the twentieth century. If you swing the arc by rocking the sextant about the axis to the horizon and making the Sun flit back and forth across the field of view, as shown in that animated GIF file (another sign of the late Jurassic), then YOU ARE USING AN INFERIOR METHOD. Right about here, you should be thinking, "Now wait just a minute... I have used that method for swinging the arc for years and it..." So let me interrupt that thought by saying that the method shown for swinging the arc does work, and it works fine when the object is below 45 degrees high. And it works passably well up to about 60 degrees. Beyond that it's no good. Of course altitudes above 60 degrees are only a small fraction of the sky (less than 15% of the sky is above that altitude), so you could get by for years without noticing any problems and perhaps concluding that high altitude sights are intrinsically worse. Indeed some of you remember that Bruce Bauer's "Sextant Handbook" (is that the title?) specifically suggests avoiding high altitudes because it's so hard to swing the arc for high objects. He, and most navigators who learned how to use sextants in the past fifty years, did not know that there is another way to swing the arc --another way that works better and works in all cases.

    The preferred method for swinging the arc is to rock the sextant about an axis that passes through the celestial object. That can be hard to visualize, but the result in the sextant's field of view is easy to describe. As the sextant is rotated about the axis to the object, the object remains nearly centered in the field of view (exactly centered in principle) while the horizon passes by beneath it. The horizon falls away as the sextant is tipped to the left. It comes back up to touch or pass the object when the sextant is vertical. And it falls away again when the sextant is tipped to the right. In fact, you can roll the sextant all the way from horizontal on the left side through vertical and over to horizontal on the right side keeping the Sun or other celestial object centered at all times. During this 180 degree circuit, if you notice that the Sun clips across the horizon, you can easily find the vertical azimuth halfway between the two crossings. You don't need such an exaggerated swing (from horizontal on the left to horizontal on the right) in practice, of course. Ten or twenty degrees of rocking is usually enough.

    For Bill B.: I cannot imagine what you're doing wrong that makes this seem difficult. Are you sure you're doing it as described above?

    You'll note that Byron Franklin re-discovered this preferred method of swinging the arc. Since he studied modern late twentieth century navigation, he does not recognize this as "swinging the arc" and sees it as some new technique. But any navigator in an earlier era would probably have seen this as nothing more than the standard method of swinging the arc. There are few modern texts that properly describe this preferred method. One that did get it right, with a nice diagram, too, back in 1970s was John Letcher's "Self-Contained Celestial Navigation with H.O. 208" (a book that I would recommend today to any navigator and which is still widely available on used book sites like abebooks.com).

    Finally, why do I call it the "preferred" method? You might think that you should learn both methods. But the commonly-taught method has no advantages --except that it has been repeated in so many sources. The preferred method works for all altitudes. You don't need the common method ever. It won't do any harm at low altitudes; you simply don't need it.

    All of this assumes incidentally that the line of sight is "collimated". That is the line of sight of the eye or the axis of the telescope is parallel to the plane that is perpendicular to both of the mirrors (parallel to the frame in a standard sextant). That's no problem in most modern sextants, but it does create interesting issues for the "Bris sextant". How do you ensure that your line of sight is collimated AND make sure that you are properly swinging the arc for a vertical altitude? You need to consider two different type of rotation. Just something to think about... Or better yet, something to experiment with...


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