A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Checking a sextant calibration.
From: George Huxtable
Date: 2003 Oct 5, 11:55 +0100
From: George Huxtable
Date: 2003 Oct 5, 11:55 +0100
This relates to Jared Sherman's recent mailing with the complex thread name- .Re: [NAV-L] CEKCTAH SNO-T [Re: lack of manufacturer's non-adjustable error info...] In reply to a question from Courtney Thomas, as follows- "Once those sights were taken, how would you suggest then differentiating instrument error from observer error ?" Jared replied- > I don't know that you can differentiate the two readily. Let's suppose >the instrument is made with +-20" of error throughout the arc, like >Celestaire's new Chinese models are. Take your sights, reduce them by the >means of your choice. let's suppose that position comes up 1-1/2 miles off >from reality. > Now run a couple of the sight reductions again, using an observation that >is +20" off, and then -20" off. > You may find that the +-20" change reflects in a 2 mile change in your >position...If it brackets reality by that much in either direction, you >might assume that the "instrument+observer" has less of an overall error >than 20". But if your reading, regardless of the +-20", is still five >miles away from reality, then you can assume the greater error is coming >from something you are doing--not from the instrument's arc error. > I know that's still vague, ... ================= Remarks from George- Well, to me, it's vague indeed. I really can't see what Jared is proposing to do. When he says " You may find that the +-20" change reflects in a 2 mile change in your position...", why should that be so? Perhaps he is crossing two altitude observations of bodies at different azimuths to obtain a fix, then comparing his result, North and West coordinates, with the given coordinates of his trig point. But a much simpler and more accurate process would be to take the position of the trig point in lat and long, and simply work out the altitude of a single observed body from that spot, and compare that with its (corrected) altitude observed by the sextant. In that case a 20" change in observed altitude will result in a 20" discrepancy, no more, no less. That's the best that can be done. Nor do I understand the next sentence- "If it brackets reality by that much in either direction, you might assume that the "instrument+observer" has less of an overall error than 20". I don't follow the logic here. Perhaps I am being dim. I wonder if Jared can offer an example. To discern a sextant error of 20", the errors in measuring the altitude of the body, and in predicting that altitude, must when combined be significantly less than 20". That's a rather tall order. Do any of us claim to be able to meet it? Here is a list of some errors in that chain. ================ 1. Nautical almanac predictions are given to the nearest 0.1 minutes, but on page 261 (para 24) it's stated that the maximum error for Sun GHA may reach 0.25'. Maybe more accurate predictions from computer calculations or tables, aimed at astronomers or surveyors, can be used. 2. Sight reduction tables have limited accuracy, which can be avoided by using computers or calculators with many digits. 3. Refraction due to the shades can occur and needs to be checked for each shade. 4. The inherent resolution of the human eye is of the order of 1 minute, but may be somewhat better for those with particularly sharp eyesight. This effect can be improved if a high-magnification telescope is fitted to the sextant, but often only a mag of 2.5 or 3 is available. 5. The effects of irradiation (which inflates the boundary of a bright object as seen in the eye) are rather unpredictable, and variable between observers, but can reach a significant fraction of a minute. 6. Refraction in the view of the object in the sky can vary in an unpredictable way from the predicted value, as can be seen sometimes in the squashed appearance of a lowish Sun. It can be limited by restricting observations to bodies well up in the sky, but not when checking a sextant, when a wide range of altitudes has to be covered. Refraction can be corrected to some extent for changes in sea-level temperature and pressure, but this is only partially effective. 7. A still day must be chosen so that the horizon as seen is the same as the mean sea level, rather than a collection of wave-tops. Similarly, the observation should be made from the shoreline or from a vessel in quiet surroundings with no heave. And to achieve sufficient accuracy, height-of-eye needs to be known to a few inches. 8. The tabulated dip includes a correction for refraction of light at is skims past the horizon and travels close to the sea surface to reach the observer's eye. This is highly dependent on the temperature of air layers within a few feet of the surface and can vary considerably (anomalous dip). Variations from the tabulated dip by 1 arc-minute are common, and 2 or 3 minute errors, though unusual, are not rare. In mirage conditions, dip errors of many minutes can occur. Refraction correction tables don't help here. Anomalous dip is one of the most intractable problems in accurate sextant observation, because it isn't apparent when it's happening. 9. There's only a certain precision with which even the most skilled observer can read a sextant's micrometer (and there are two readings involved, because the index error must be subtracted). And his readings can be perturbed by tilt error, particularly. ==================== I may have left some out, but with as many possible errors as I've listed, how many of us could put his hand on his heart and declare that he could detect a sextant error of, say, 20" from altitude measurements? If anyone seriously wishes to pursue the best possible accuracy for a sextant calibration, I suggest an on-land programmme of measuring angles between suitable pairs of stars, choosing stars that are rather high in the sky. It's a demanding job calling for much skill, rather like measuring lunar distances (only harder). I wouldn't like to take it on. The calculation is similar to that of a lunar, but simpler because it's only for the two refractions, there being no parallax. ==================== With modern sextants designed the way they are, it seems unlikely that even a drop to the floor is likely to degrade the precision of its scale-division noticeably, without the damage being sufficient as to cause the index arm to bind somewhere on the arc. The most likely thing to suffer, in my view, is collimation error due to the telescope becoming misaligned. Any mirror derangements can normally be adjusted out. I have seen many pious exhortations in textbooks about never using a sextant unless it has a recent calibration certificate. This must have provided plenty of business for Kew laboratory (NPL) and others. I wonder how many list members have managed to check on their sextants and discover any real reproducible scale error? I refer to reputable modern makes: not Pakistani backyard jobs, nor antiques with hand-divided scales. My bet is that not one has discovered any such errors. Let's be realistic about all this: Sextants were designed to measure lunar distances, a measurement that demands (but seldom obtains) 30 times the accuracy of a normal altitude sight. That degree of accuracy is no longer needed, except for the "lunartics" among us. Except for such lunar observations, if your sextant can give you position lines within 3 or 4 arc-minutes, that's as good as a small-boat sailor normally needs. And as much as a small boat sailor can usually expect, with the motion of a small craft in a turbulent sea. So should a small-craft navigator be worried if his sextant has no calibration certificate from its maker? I doubt it. It's almost certainly good enough for his needs. He should relax and enjoy using it - but always keep his eyes open for signs of any serious discrepancy, as applies to any instrument, new or old. George. ================================================================ contact George Huxtable by email at george---.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================