NavList:
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Re: Real accuracy of the method of lunar distances
From: Trevor Kenchington
Date: 2003 Dec 31, 17:44 +0000
From: Trevor Kenchington
Date: 2003 Dec 31, 17:44 +0000
Jan, You wrote: > But let us consider that lunars were recommended for checking GROSS errors of D.R. after many days of sailing - they never could be used for verifying the position from one day to another. And facing the real possibility of such gross errors, how the navigator was to recognize a lunar observation to be at the limit of the 99% error and therefore unusable comparing it with his very vaguely known D.R. position? Before answering that directly, I should perhaps point out that I advanced just one (hopefully plausible) reason why the distribution of errors in lunars should be somewhat leptokurtic. I did not intend that to be the only reason. Your attempt to estimate how great the error might be in two or three cases in every thousand really stretches your assumption of Normal errors. Without real-world data (based on many thousands of lunars, each separately worked up) to show the probability density function of the error term in the outer limits of its tails, I would not take such estimates very seriously at all. As to gross errors in DR and the navigator's ability to identify outliers amongst lunar estimates: I think Frank's evidence from whaling log books has already given you one answer: In at least some cases, it seems to have been the practice to take two lunars a couple of days apart. That way, they would have been worked up separately and a careless error in one would not have been automatically repeated in the second. If the first one confirmed the navigator's DR, then the second lunar might not be needed. If the DR was highly suspect, then two lunars that roughly agreed would have given grounds to call it a celestial fix and start a new DR reckoning. If the DR and the first two lunars were all very different, then do a third lunar on another day and see what that indicated. We should remember that, before the days of GPS linked to an electronic chart, navigation wasn't about knowing exactly where you are. (And whatever the textbooks and land-based courses say today, it shouldn't be about that now either.) It was (and should still be) more a matter of having a general idea of where you are and then conducting your vessel so that she would be safe even if you are not where you think you are. In the context of lunars: It is entirely possible to navigate your way around the ocean with no means of estimating longitude at all, save for DR. After all, the Norse operated a regular trade route from Norway to Greenland and back (without touching land in between) on that basis starting nearly a thousand years ago. The Portuguese opened the way to ElMina, then the Cape and ultimately India without being able to estimate longitude. And, of course, Columbus and everyone who followed him for nearly 300 years managed crossing the Atlantic without lunars or chronometers. Of course accident rates were much higher (and hence the prizes were offered for a solution to longitude estimation) but I suspect that the real cost was in lost time. Without a firm indication of longitude, a navigator had to pick a safe landfall (such as high land rising out of deep water), even if that meant sailing a dog-leg course. Then he had to stand off the land until he could approach it in clear weather and daylight. Lunars allowed a bolder approach to the land and yet a lower risk of accident. The combination of one chronometer with occasional lunars gave increased confidence in estimates of longitude and hence still bolder approaches with still lower risks. Multiple chronometers not only saved the work of doing any lunars but also gave sufficient confidence for ships to head straight to their ports of destination. [I doubt that it was any accident that steamers started the practice of carrying multiple chronometers (if, in fact, they did). Time was money for a steamer, in a way that it was not for a sailing ship outside of the packet trades. Greater navigational certainty paid off in hard cash and so justified the cost of the instruments. Of course, it is also true that chronometers were a lesser percentage of the higher capital cost of a steamer, while the lower accident risk they offered was more important with a more valuable ship and typically one carrying more valuable cargoes.] Seen in that context, I suspect that a navigator would be very glad of the information that a lunar could provide, even though it was imprecise and he might have to resort to working up two or three in order to identify any outliers. Think of yourself in mid-ocean, unsure of your reckoning, though with the ability to determine your latitude and that of a safe landfall. Would you rather feel your way towards land, shortening sail every night but still worrying through the hours of darkness until dawn revealed a clear horizon, lengthening the voyage as the water went foul and the food ran out? Or would you welcome a lunar that, for all its potential imprecision, told you that you were safe to carry a press of sail for the next few days, before feeling your way in through the last 100 miles or so to your landfall (by which time you might be in soundings or might speak a ship outward bound which could give you your longitude? The skilled navigator had many sources of positional information and, I suggest, lunars were valuable as part of that complex, even though they could not substitute for all of the rest -- in the way that too many people suppose that GPS can. Trevor Kenchington -- Trevor J. Kenchington PhD Gadus@iStar.ca Gadus Associates, Office(902) 889-9250 R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251 Nova Scotia B0J 2L0, CANADA Home (902) 889-3555 Science Serving the Fisheries http://home.istar.ca/~gadus