NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Index error
From: Bill Morris
Date: 2008 Jun 4, 22:50 -0700
From: Bill Morris
Date: 2008 Jun 4, 22:50 -0700
I have been following in a desultory way the current discussion between George Huxtable and Frank Reed about errors in lunars. My interest is perhaps more in the instruments of navigation than in its practice. I did once do a lunar about thirty years ago, under the tutelage of a retired surveyor who spent his holidays as �fifth mate for navigation� aboard a South Pacific islands steamer. We used seven figure log tables, so you will understand that I was not necessarily keen to repeat the experience. In a previous posting about sextant calibration, I gave the re-setting error of my ex-USSR SNO-T sextant as about 4 seconds, its micrometer error as about 2 seconds and its backlash error as up to 12 seconds. On the occasions when I have directed a sextant at the sky rather than at an autocollimator instrument, I have noticed that my determination of index error is seldom the same twice running. At first I put all of it down to my inexperience and shaky right arm, but I have quite a lot of experience with making and using optical instruments and am a careful observer. George�s requests for �Error budgets� led me to try to find out what sort of spread of results I(and possibly others) might expect when finding the index error of their sextants. I made three sets of thirty careful observations for each method: using a sharply defined land horizon about 6 km away; using the sun�s limbs; and using a 2nd magnitude star. To make things easier and to avoid fatigue, I clamped the sextant atop a theodolite sextant so I could make each observation a leisurely one. I also glued a simple but effective paper vernier over the micrometer index to reduce to some extent a tendency to bias the results in a more or less favourable direction when estimating tenths. Here are my results for the standard deviations: Method S.D. 95% range Horizon, reflected image up to direct image 0.142 0.56 Horizon, direct image up to reflected image 0.157 0.62 Sun�s limbs 0.155 0.61 Star 0.174 0.68 For those who might think that statistics is a new form of contact adhesive, I should point out that the standard deviation is a measure of the dispersion of the results about the mean value; and 1.96 standard deviations each way will �capture� 19 out of 20 or 95% of results. 1 S.D. each way will include about 64% of results. So, my sextant-eye-brain system will give an index error of more than 0.3 minutes away from the best estimate, the mean, one time in twenty. About 45% of the time it will be more than about a minute and a half away from the mean. Physicists are supposed to be good at error estimation and my education was in the biological sciences, so I leave the rest to George and others... Bill Morris --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---