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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Lat/Lon by "Noon Sun"
From: George Huxtable
Date: 2009 Apr 13, 17:40 +0100
From: George Huxtable
Date: 2009 Apr 13, 17:40 +0100
My heart sank, somewhat, on reading Frank Reed's resending of a four-year-old post, on a familiar topic. That topic was what I referred to recently as his "hobby-horse", which has emerged from the toybox yet again. That original posting presented a completely one-sided view of a proposed method of teaching navigation, without the slightest acknowledgment of any drawbacks. Some of those defects were discussed in detail at the time, and since, but it seems nothing has changed. We have been presented with "the mixture as before". Those that fail to learn from history are destined to relive it. We have had several new members, I'm pleased to see, recently, to whom all this may well be new, and they should be aware that Frank has presented an incomplete picture, painting in only the virtues of his proposal. I will remedy that, for them, by providing yet again some of the warts in the picture. There's nothing new in any of this, and old-hands will sigh, gently, and click on to the next posting. ========================= We need to put it in perspective, though. "Longitude around noon", has been presented in various forms for years, for example by list member Jim Wilson in the journal "Navigation" in 1985. It's sometimes proposed as a form of "emergency navigation", a way that will get-you-home if you know no better. But from his words, "You can cross oceans safely and reliably for years on end using this technique if it suits you to do so", Frank Reed appears to be advocating it as The Way to teach Celestial Navigation to students, and it's this that I regard as dangerous. I have not yet met a graduate of the Frank Reed school of Celestial Navigation, and if I am misjudging Frank's notions, no doubt he will tell me so. If students emerge from such courses with a rounded understanding of position lines and sight reduction, how to read a nautical almanac, how to use the Moon or take a twilight round of star observations, well and good. But if students are led to believe they have learned Celestial Navigation, from the handling of Sun noon sights alone, avoiding any trig., then a generation of navigational incompetents will arise; "one-club golfers" who will quickly become lost at sea, if the Sun doesn't shine for the requisite hour around noon. It would be the dumbing-down of a skill, delivering instant gratification without the necessary groundwork. ========================= Now for a bit of detail about that posting. Accuracy. The claim is made that it will get you "latitude and longitude to about +/-2 miles and +/-5 miles respectively". Certainly, there are many situations where that will indeed be the case, but Frank has been asked about more difficult environments, with a low Sun at noon, at higher latitudes and rough weather conditions affecting the precision of sextant sights, but has not responded by conceding any worsening. If we ask what assumptions have been made about the various uncertainties, in course and speed, and altitude, and how they combine, in such difficult cases, such questions have been evaded. Workload. First, for comparison, lets consider what a navigator using position-lines has to do, to get a precise position by the Sun. That calls for one observation sometime mid-morning, and another in the afternoon, at any-old-time, whenever the Sun happens to shine. He has to correct those altitudes, get Sun positions from his almanac, work two sight-reductions to get azimuth and intercept, draw two position lines, shift one according to his DR, and plot where they cross. Compare that with the task that faces the man who wants to get a "fix around noon". The suggested sequence requires the navigator to be taking and noting timed Sun sights over a period of 40 to 60 minutes, resulting in 5 to 13 observations. To achieve any sort of accuracy, in most conditions the longer time and the greater number will be called for, as I will assume. This must be done at predefined times, irrespective of other urgent jobs arising on board, such as attending to sails. If the Sun fails to shine over that whole period, there's no position-finding that day. He has to estimate his speed over that period, as best he can, and his true course, by correcting the compass. Then get the Northerly component, which to most of us would be simply speed x cos (true course), though Frank explains it otherwise, as he can't bring himself to mention a trig function in this context. Than a small correction, due to Sun's changing declination, must be summed with that speed. Next, for each of 13 observations, he has to multiply that speed by the time interval of the observation from noon, changing sign according to whether it's before or after noon, and sum that with the observed altitude. At this point, we hit a snag. I hear the student ask, "just when is this noon, then?" Well, that's Local Apparent Noon, which is Greenwich noon, corrected for the Equation of Time, and for the longitude. Unfortunately, the longitude is as yet unknown; until the final result is obtained. So how does the poor student follow those instructions? Well, Frank knows, and I know (though the student hasn't been informed) that any old time can be presumed for local apparent noon, at this stage, just for the purpose of correcting the timing of the peak altitude. It can simply be guessed, and the correction worked accordingly (just as long as the peak-altitude of that plot isn't used later, for finding latitude). Having done that, plotted the 13 corrected points, and folded the paper, the centre of symmetry gives the watch time of local apparent noon. After allowing for the Equation of Time, the result, at 15� per hour, will provide his longitude. Now the navigator has to go back to his original uncorrected altitude observations, and interpolate between them to the now-known time of LAT. Then correct as usual for index error, dip, refraction, semidiameter, and allow for declination to get latitude. All familiar stuff. However, compared with the two-position-line option, the proposed procedure can hardly be described as a saving of effort. Almanac. Frank tells us that the job can be done without need of a nautical almanac "you don't need one at all --only a short table of declination and equation of time, possibly graphed as an "analemma" perhaps (he says). He doesn't tell us what precision is available in the use of such a tool, and to what extent his claimed precision of 2 miles in lat, 5 miles in long, would be degraded by it. I would like to know. He doesn't even mention that without a full almanac, both declination and equation of time need to be interpolated between given values for two Greenwich noons, according to the observer's longitude. ================== All the difficulties described above have been ignored or glossed over in Frank's (repeated) posting. These things need to be said. According to previous form, this posting will be followed by an indignant response from Frank Reed, objecting to the denigration of his favourite project. George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. =================================== ----- Original Message ----- From:To: Sent: Sunday, April 12, 2009 11:19 PM Subject: [NavList 7927] Lat/Lon by "Noon Sun" From the archives for June 4, 2005: "Latitude and Longitude by "Noon Sun" From: FrankReedCT---COM Date: 4 Jun 2005 19:54 First things first: I've put the phrase "Noon Sun" in quotes here because the set of sights required for this system goes a little beyond the standard procedure for shooting the Noon Sun for latitude only. This short method of celestial navigation will get you latitude and longitude to about +/-2 miles and +/-5 miles respectively --more than adequate for any conceivable modern practical purpose. You can cross oceans safely and reliably for years on end using this technique if it suits you to do so. Its enormous advantage is simplicity. It's easy to teach, easy to demonstrate, easy to learn, and also easy to re-learn if necessary. I mention this because most people who are learning celestial navigation today will quickly forget it. What's the point of learning something if you can't reconstruct your knowledge of it quickly when and if the need actually arises to use it? It's tough to resurrect an understanding of the tools of standard celestial navigation on short notice, but easy with this lat/lon at noon method. Additionally, this method does not require learning all the details of using a Nautical Almanac (you don't need one at all --only a short table of declination and equation of time, possibly graphed as an "analemma") and it needs no cumbersome sight reduction tables. Here's how it's done: Start 20 or 30 minutes before estimated local noon. Shoot the Sun's altitude with your sextant every five or ten minutes (or more often if you're so inclined) and record the altitudes and times by your watch (true GMT). Continue shooting until 20 or 30 minutes after local noon. [note the difference from a noon latitude sight --we're recording sights leading up to and following noon-- usually these are thrown away] Next you need to correct for your speed towards or away from the Sun. For example, if we're sailing south and the Sun is to the south of us, then each altitude that we have measured will be a little higher as we get closer to the latitude where the Sun is straight up. We need to 'back out' this effect so that the data can be used to get a fix at a specific point and time. This isn't hard. First, we need the fraction of our speed that is in the north-south direction. If I'm sailing SW at 10 knots, then the portion southbound (in the Sun's direction) is about 7.1 knots. You can get this fraction by simple plotting or an easy calculation. Next we need the Sun's speed. The position where the Sun is straight overhead is moving north in spring, stops around June 21, then heads south in fall, bottoming out around December 21 (season names are northern hemisphere biased here). It is sufficient for the purposes of this method to say that the Sun's speed is 1 knot northbound in late winter through mid spring, 1 knot southbound from late summer through mid autumn, and 0 for a month or two around both solstices (it's easy to prepare a monthly table if you want a little more accuracy). Add these speeds up to find out how much you're moving towards or away from the Sun. If you're moving towards the Sun, then for every six minutes away from noon, add 0.1 minutes of arc for every knot of speed to the altitudes before noon and subtract 0.1 minutes of arc for every knot of speed to the altitudes after noon. Reverse the rules if you're moving away from the Sun. Spelled out verbally like this, this speed correction can sound tedious but the concept is really very simple and it's very easy to do. [Incidentally, George Huxtable deserves credit for emphasizing the importance of dealing with this issue (although I don't think he ever spelled out how to do it)] Now graph the altitudes (use proper graph paper here if at all possible): Sun's altitude on the y-axis versus GMT on the x-axis. The size of the graph should be roughly square, maybe 6 inches by 6 inches so that you can clearly see the rise and fall of altitude. For longitude, you will need to determine the axis of symmetry of the parabolic arch of points that you've plotted. There is a simple way to do this: make an eyeball estimate of the center and lightly fold the graph paper in half along this vertical (don't "hard crease" the fold yet). Now hold it up to the light. You can see the data points preceding noon superimposed over the data points following noon which are visible through the paper. Slide the paper back and forth until all of the points, before and after, make the best possible smooth arch (half a parabola). Now crease the paper. Unfold and the crease line will mark the center of symmetry of the measured points with considerable accuracy. Reading down along this crease to the x-axis, you can now read off the GMT of Local Apparent Noon. Reading back up the crease to the data, you can pick off the Sun's maximum noon altitude (which is probably already recorded but if you missed the exact moment of LAN you can get it this way). Next we need two pieces of almanac data: the Sun's declination for this approximate GMT on this date and the Equation of Time for the same date and time. You do NOT need a current Nautical Almanac for this. The exact value of declination and Equation of Time varies in a four-year cycle depending on whether this year is a leap year or the first, second, or third year after. So we don't need an almanac for this. A simple table will do (where to get one? Today, they're very easy to generate on-the-fly... or you could use an old Nautical Almanac... or you could also use an analemma drawn on a sufficiently large scale). Apply the Equation of Time to the GMT of Local Apparent Noon that you found above. You now have the Local Mean Time at LAN, and you already know the Greenwich Mean Time. The difference between those two times is your longitude. Convert this to degrees at the rate of 1 degree of longitude for every four minutes of time difference. Done. We've got our longitude. Now for latitude. Notice that we didn't correct any of our altitudes for index correction or dip or refraction or the Sun's semi-diameter. These corrections are totally unnecessary for the longitude determination. But we need them for latitude. Take the Sun's altitude at the time of LAN (read off the "crease" or actually observed by watching the Sun "hang" at the moment of LAN). Correct it for index correction, dip, refraction and semi-diameter as usual. This gives you the Sun's corrected observed altitude. Subtract from 90 degrees. This "noon zenith distance" tells us how many degrees and minutes we are away from the latitude where the Sun is straight up. The latitude where the Sun is straight is, by definition, the "declination" that we have looked up previously from our tables. So if the Sun is north of us at noon, then we are south of the Sun's declination (latitude) by exactly the number of degrees and minutes in the noon zenith distance. If the Sun is south of us at noon, then we are north of the Sun's declination by the same amount. A simple addition or subtraction yields the required latitude. Done. We've spent about ten minutes making and recording observations of the Sun's altitude over the course of 45 minutes to an hour, and reduced those observations to get our latitude and longitude at noon with about five minutes of paperwork. Not bad! Again, the overwhelming advantage of this "short celestial" is that it can be taught easily, learned quickly, and RE-learned quickly on the spot if necessary. An additional advantage is that it requires an absolute minimum of materials. You need a sextant (metal if at all possible, but plastic will do), a decent, cheap watch or small clock, tables of refraction and dip (one sheet of paper), a four-year revolving almanac of the Sun's declination and equation of time (another sheet or two of paper), and some graph paper and a pencil. You could even print out these (or equivalent) instructions and throw everything in the case with your sextant. As for disadvantages, they really depend on the student and his or her expectations. What is it that we want to do with celestial navigation? Why study any method? And for a thousand students, you will get a thousand answers. The days are gone when celestial navigation was essential and fixed curricula could be dictated for students to either take in their entirety or leave. This field has moved on to the stage of "a la carte" learning. It can be a pain in the neck for instructors accustomed to doing things the same way year after year but it's a real liberation for students and possibly also for more creative teachers and "information publishers". -FER 42.0N 87.7W, or 41.4N 72.1W. www.HistoricalAtlas.com/lunars" --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---