A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Lunar distance measurement in ideal conditions: attainable accuracy.
From: Alexandre Eremenko
Date: 2013 Jan 7, 00:27 -0500
From: Alexandre Eremenko
Date: 2013 Jan 7, 00:27 -0500
Bill, Could you tell us the dates of your observations? the spreadsheets only say January 2013. Alex. > Recent posts have questioned vehemently (2 Jan 13 per Frank Reed) or > mildly (31 Dec 12 Alex Eremenko) whether it is or was possible to achieve > particular degrees of accuracy and consistency with lunar distance > observations. My own interest is in the instruments of navigation rather > than the many uses to which they can be put. In 2011 I took up the > challenge of the late George Huxtable to see how instruments perform in > the real world at sea. I regarded recent statements as a challenge to see > what can be achieved for lunar distance measurements in the best of > conditions using the best of sextants. I say nothing about the quality of > the observer except that I have spent a lot of amateur time peering > through optical measuring instruments of various types, my vision can be > corrected to 6/5 (it isn’t at present, as optometrists in New Zealand > charge like wounded bulls for new lenses) and, as a copper-bottomed > brass-bound , dyed-in-the-wool sceptic I do my very best not to > “tweak” observations despite feeling tempted at times. > > The sextant used was a 1978 Russian SNO-T sextant whose non-correctable > errors in the range of angles measured were under 3 seconds, so I ignored > them. As Frank Reed had sung the praises of a x7 telescope, I assumed he > had used a prismatic monocular, so I did too for my first series, a > vintage Beck Kassel 6 x 30 borrowed from a 1953 C Plath sextant. For my > second and third series I used the Keplerian (“inverting”) telescope > supplied with the instrument. The mirrors and shades are in perfect > condition and, as I overhauled the instrument myself, I am confident that > it is in as good a mechanical condition as possible. While backlash is > well within the 6 seconds allowable by the specification, I consistently > turn the micrometer drum in the direction of increasing the reading, both > when estimating index error and when making observations. To minimise > digit preference bias, I glued a paper vernier reading to 0.1 arcmin to > the index. > > Even quite large telescope collimation errors are of little importance in > modern navigation, but when taking lunar distances one is trying to > squeeze the last bit of accuracy out of the results and the angles > measured are often large, when collimation error is most important. For > example, if the telescope is mis-aligned by half a degree, the error at > 105 degrees is about 20 seconds. The easiest way to check collimation is > to use an engineer’s square to see that the face of the objective lens > mount is square to the face of the sextant frame. You should not assume > that it is safe to transfer a telescope from one sextant to another > without checking this. There are several other, more-or-less sensitive > ways of doing it. I had to place shims between the Beck Kassel mounting > bracket and the body of the monocular to correct a large error, and by the > time my patience had run out there was still a small collimation error > remaining. > > If the estimate of index error is wrong, then it is possible to have > series of observations tightly clustered about a mean that is wrong. The > results will have a small standard deviation (a measure of central > tendency, or distribution of the results about the mean), implying good > consistency of measurements, but the figure of interest, the mean, may be > wildly wrong. For this reason, it is worth while taking great care with > the index error. Though several people, Greg Rudzinsky most recently (6 > Jan 13), have stated a preference for a particular method of estimation, > when a few years ago I compared 30 observations each using the horizon, > the sun and two stars, I could detect no statistically significant > difference of the methods in my hands. On this occasion, I used the ridge > of a barn on the horizon 6 km away. It is easier on the neck. For these > and subsequent observations I clamped the instrument on top of a > theodolite tripod. It makes a big difference to the ease of observations, > especially in a 20 km/h wind gusting to 40 km/h. Incidentally, collimation > error does not apply to index error estimations, as the reading is made at > zero. > > In the spread sheet file “Lunar 1”, Cell B25 gives the mean of 20 > index error estimations and, for what it is worth, cell B26 gives their > standard deviation. > Before making the lunar distance observation, I first achieved coincidence > by holding the sextant in my hands. I used no shades and proceeded from > the moon to the brighter object, the sun, using the sun’s glare as a > guide to when I was approaching coincidence, at which point I put a dark > shade in place. I then mounted the sextant on the tripod again and > adjusted the index shades so that when the images overlapped, the moon was > visible through the sun. I found it easier to determine contact of the > limbs by bringing them apart. To minimise the effects of collimation and > other optical errors, it is important to keep the objects as close to the > centre of the field of view as possible. > I used Frank Reed’s lunar calculator to determine what the result should > have been for the position and conditions, and the differences between the > calculated and observed results are given in column H > > Cells J13 and J14 give the means and standard deviation (SD) for ten > observations with the monocular, while cells J23 and J24 give the results > using the inverting telescope. The latter seems to give the better results > and we do not need to do a Student’s t-test to see that there is a > significant difference in the means of the errors. For a first attempt, > these are not poor results. > As the following day was also fine, I did another set of observations, > this time checking the index error using the same telescope, the > inverting, that was to be used for the observations. These are shown in > the file “Lunar 2”. Cell C25 gives the mean of 20 IE observations. The > dispersion of results about the mean was somewhat closer than before. Cell > G30 shows the mean error of 25 lunar distance observations, 0.032 arcmin > or about 2 seconds, while the standard deviation in cell G31 tells us that > about two thirds of the errors fall within the range of +11 seconds to -7 > seconds. > > Thus, by taking care with adjustment of a high quality sextant and > averaging many results, it does indeed seem possible to achieve high > accuracy on land with the instrument steadied on a tripod. The errors are > likely to be much greater on land with a hand-held instrument and still > more so at sea. The file “Cape St Diego” gives results of observations > by the astronomer Richard Green aboard the Endeavour in January 1769. We > can see that three sets of three observations were made and that readings > were to the closest 30 seconds. Jesse Ramsden’s first dividing engine > had been completed only two years previously, not to his satisfaction, and > his second engine, which revolutionised precision angular measurement, did > not become operational until about seven years later. It is likely that > Green used a Hadley’s quadrant, probably of 15 inches radius, divided by > hand with a vernier reading to half a minute. > > To put these observations in context, the astronomer William Wales later > wrote:”…the longitude…is near a degree too great; which is not at > all surprising, if we consider, that although the air was extremely clear > when these observations were made, yet the sea ran so high that it filled > the quarter deck three times while they were observing and the motion of > the ship was so great that Captain Cook did not attempt to observe.” My > own errors using a metal sextant of 8 inches radius with a vernier reading > to 30 seconds, made some time between 1790 and 1810, are shown at the > bottom of file “Lunar 2”. The sextant was steadied on a tripod, no one > was playing a fire hose on my legs and the ground was not rocking and > shaking, yet my errors are of the same order as those of Green. > > Bill Morris > Pukenui > New Zealand > ---------------------------------------------------------------- > NavList message boards and member settings: www.fer3.com/NavList > Members may optionally receive posts by email. > To cancel email delivery, send a message to NoMail[at]fer3.com > ---------------------------------------------------------------- > > > > Attached File: http://fer3.com/arc/img/121731.lunar-1.xlsx > > Attached File: http://fer3.com/arc/img/121731.lunar-2.xlsx > > Attached File: http://fer3.com/arc/img/121731.cape-st--diego.jpg > > > View and reply to this message: http://fer3.com/arc/m2.aspx?i=121731 > > >