A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2021 Sep 27, 10:12 -0700
If you see "side error" in your sextant, it is not a source of error in any real sextant observation (with one very minor exception). There is no reason to reduce side offset (so-called "side error") except for your own amusement or personal convenience.
Wait, one very minor exception?? The exception is the case of a Sun-Sun index correction test (or any angle measured that's smaller than a few degrees). It does not affect the actual index correction value in any way, but it does slightly change the measured Sun SD, which can provide a useful sanity check (as Tony mentioned earlier today). A better sanity check, regardless, is consistency from one trial to the next. In the case of the measured SD, you're observing an angle of about half a degree. A side offset of 5 minutes of arc --which is big and obvious-- will yield an error in the measured SD of about 1 minute of arc (but remember, you don't need the measured SD, and the index correction that results is unaffected). So what about larger angles? For small-ish angles up to about 10°, the resulting "side error" is inversely proportional to the observed angle itself. So if the side error from a 5' side offset is 1' for angle of 0.5°, then it's 0.1' for an angle of 5° and completely negligible for any larger angles. In the more general case, the potential "side error" is inversely proportional to the tangent of the observed angle which fall off even faster than simple inverse proportionality.
But wait again... if you're a perfectionist, and you shoot lunars, would it matter? No. Since the "side error" resulting from a normal side offset (5', as above, is what I mean by "normal" side offset) is inversely proportional to the tangent of the observed angle, the small error is less than 0.1' for angles above 5°, less than two seconds of arc, for any observed angle greater than about 25° and less than half a second of arc for any angle greater than about 45°. These are completely unmeasurable, negligible differences --even for lunars.