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    Swinging the arc: two methods, one preferred
    From: Frank Reed
    Date: 2011 Jan 4, 20:22 -0800

    Greg Rudzinski, regarding your Jupiter sights, you wrote:
    "I did use Byron's vertical sextant technique of rocking the body from horizon to horizon through the dark back ground of the sea then splitting the difference to get the mid point."

    Note that what you are describing here is essentially the original (and preferred) method of "swinging the arc".

    Sometime in the middle of the 20th century, probably involving the big changes of navigation education during the Second World War, navigators started swinging the arc by rocking the instrument about the axis of the telescope that points to the horizon. This makes the Sun or star shoot from side to side across the field of view and, while it does make an arc, it's not much of an arc and especially for high altitude objects it can be hard to say whether that arc is really hitting the horizon at its low point. This is definitely the most widely taught method of rocking the sextant, and it's not literally wrong, of course. It works very well for low altitudes.

    The original method for swinging the arc is described with some cumbersome words in most older books on navigation going at least as far back as Maskelyne in the 18th century. It involves rocking the sextant by rotating it about an axis pointing to the body in the sky, and necessarily that means that the observer has to rotate from side to side while the instrument is being rocked. By doing so, the Sun or star remains centered in the field of view while the horizon shifts up and down beneath it (that's what you see looking through the instrument). If you're having trouble picturing this, try holding a sextant horizontally, face up, with it set to the approximate altitude of the Sun. Point the direct "horizon" view through the instrument to a point in the sky left of the Sun at about the angle from the Sun that you have pre-set. Scan about until you see the Sun (reflected image, properly shaded! don't point the horizon side at the Sun). Get the Sun reasonably close to the field of view. The horizon side should show nothing but sky. Now slowly rotate the instrument down to a vertical orientation keeping the Sun centered in the field of view. Then continue rotating until the sextant is horizontal again but face down on the other side. This is an exaggerated 180-degree sweep through the motion of the original method of swinging the arc. In practice, you would normally only sweep through a small fraction, say 30 degrees, of this motion. When you use this method of swinging the arc, if you start with an altitude that is a bit too large, the Sun will cut the horizon on one side descending, then pass a low point in the middle where its image is partly superimposed over the sea (and that low point naturally is vertical position), and then the Sun will cut the horizon again rising on the other side. The vertical orientation is, of course, in the direction halfway between the two azimuths where the Sun crossed the horizon during the rocking motion.

    The mid/late-20th century method of rocking the arc is the one described in nearly all modern textbooks, and if you see animations, they almost always show the horizon remaining fixed with the Sun swinging back and forth across the field of view (there's an animation just like this on the Wikipedia "Sextant" article). There are some exceptions. For example, in John Letcher's "Self-contained Celestial Navigation with H.O. 208" there's a very fine diagram illustrating the original (correct) method where the Sun stays centered in the field of view for the whole operation (Letcher's book is filled with interesting little gems and I always recommend it. It's still available from used book dealers. John Letcher is yet another former physicist who found great pleasure in celestial navigation. Yes, we are a pox on the subject, aren't we?).

    A number of people, including, so it would seem, Byron Franklin, have re-discovered the original method of swinging the arc at some point in the past few decades and done their best to recommend its virtues. I'm in the same boat. Unfortunately, navigators tend to be "mildly confident" in the veracity of those things which they learned at their first navigation instructor's knee, and there's tremendous resistance against doing things the "right way". How, after all, could it be wrong if so many navigators have used it successfully for so many decades?? And that's the thing, it's not "wrong" --it's just less effective and definitely worse, to the point of being useless, for higher altitudes. BOTH methods of swinging the arc work very well for low altitudes, and both work well enough for middle altitudes (though the original method has a real advantage here), but ONLY the original method works at all altitudes, including those times when the Sun or star are very high in the sky. The original method is universal --there are no cases where it fails-- and it's no more difficult to learn than the more popular late-20th century method of swinging the arc.


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