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From: Frank Reed (no email)
Date: Tue Oct 18 2005 - 16:36:50 EDT
SWINGING THE ARC
There are two methods for "swinging the arc". The method that I prefer and
that is really more useful I will call Method 1. The method that a majority of
navigators learned in the second half of the twentieth century I will call
Method 2.
Method 1:
This is the method that you will find described in most older works of
navigation including The American Practical Navigator (Bowditch) through the first
half of the 20th century. You'll also find it in some more recent works such
as John Letcher's Self-Contained Celestial Navigation. The procedure here is
to bring the Sun (other object) down to the horizon and then rotate the
sextant about the line of sight to the object so that the horizon moves back and
forth "behind" the image of the Sun in the horizon glass. The Sun remains more
or less centered in the field of view the entire time. Quoting Bowditch from
1918: "the observer should move the instrument to the right and left of the
vertical, swinging it about the line of sight as an axis, taking care to keep
the object in the middle of the field of view. The object will appear to
describe the arc of a circle, and the lowest point of this arc marks the true
vertical." Letcher in his book has a nice diagram demonstrating that the object
stays in the middle of the field of view throughout the rocking process.
Method 2:
Starting sometime around the middle of the 20th century, navigators began
using a different method for swinging the arc, and many navigation textbooks
repeated it. I believe that this method originally evolved from confusion over
Method 1, but this method does work --up to a point. This method seems to be
described in post-war editions of Bowditch. Though the language is ambiguous,
the diagram is clear. In the diagram illustrating swinging the arc in the
1962 Bowditch, the Sun is moving across the field of view while the horizon
remains level. This is basically what you see when the instrument is rotated
about an axis pointing straight to the horizon.
When you're looking at an object that is, let's say, 35 degrees high in the
sky, both Method 1 and Method 2 will find the vertical, and thus the
shortest, correct distance between the horizon and the object in the sky. They both
work because the sextant is essentially a device that lets you look in two
directions at once. So rotating the instrument about the line of sight to the
object in the sky (Method 1) and rotating the instrument about the line of sight
to the horizon (Method 2) should be symmetrical operations. And that's true.
You can use a sextant upside-down, and it works just fine. But there is in
fact an asymmetry here --it's in the objects we're viewing. While the star or
other celestial object is basically a point in the sky, the horizon is, of
course, an extended object. We're trying to locate a particular point along the
horizon, the point that is directly beneath the star in the sky. Finding
that point on the horizon is the whole point of swinging the arc. By the way,
when the object is very low in the sky, it should be obvious that Method 1 and
Method 2 become identical.
Where's the problem then? The trouble is that, while Method 1 always works,
unfortunately Method 2 will work only when we have already more or less found
the point on the horizon directly beneath the celestial body. If it's
outside the field of view, as it often is at very high altitude, you will have to
find that point by trial and error. Furthermore, when you use Method 2 with
objects at high altitudes, the curvature of the arc becomes harder to see. This
had led many sextant users to the incorrect conclusion that they cannot
accurately measure altitudes above about 70 degrees. Bruce Bauer in his book
concludes from his experience with Method 2 that one should limit observations to
stars in middle altitudes only. And this is simply a mistake. It's an
unfortunate outcome of using this method of swinging the arc.
Since Method 1 came first, always works, and seems no harder to learn than
the more popular Method 2, I highly recommend that students of celestial
navigation stick to this method. Swing the arc by rotating the instrument about
the line of sight to the object in the sky. The Sun or other celestial body
should remain more or less centered in the field of view throughout this
operation. The goal of the operation is to find the point on the horizon where the
image of the Sun just touches the horizon (without dipping below it).
Finally, I would add that swinging the arc is unnecessary when the altitude
is very low, and it's only necessary for basic setup when the altitude is
very high. There is an exception to this and that occurs when the high altitude
object's azimuth is changing very rapidly as it does when it reaches the
meridian. In that case, you're better off facing south or north as the case may
be. This is a separate issue from the question of swinging the arc.
-FER
42.0N 87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars
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