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    On lunars generally
    From: Frank Reed
    Date: 2009 Jul 6, 19:50 -0700

    Douglas Denny, you wrote:
    "I note you are an afficionado of 'Lunars' and you have on more than one 
    occasion I note, made a very strong reaction to any challenge to their 
    validity in navigation."
    Yes, it's fair to call me an "afficionado" of lunars. You're incorrect to say 
    that I oppose any challenges to their "validity in navigation". For example, 
    I do not anywhere suggest that navigators should have continued using them 
    longer than they did in the 19th century, BUT THEY DID USE THEM for 75 years 
    after the first true chronometer was completed and tested. The expression 
    "Longitude by lunar" is found throughout many logbooks from late 18th and 
    early 19th century vessels. Even in the latter half of the 19th century, 
    there was a rapidly-declining, but still active group of navigators, who 
    insisted on using lunars at sea to verify their chronometer longitudes. That 
    usage (after 1850), however, is interesting because it is so exceptional, not 
    because it represented common practice.
    [an aside: so that there is no confusion, I have also suggested an entirely 
    different use for lunars today: you can get a position fix in both latitude 
    and longitude from two lunar sights without a visible horizon. But this is 
    mostly for amusement since vessels at sea are no longer navigated by 
    celestial except in extraordinary circumstances (some sailing races, a few 
    rare emergencies, instances of personal challenge).]
    And you wrote:
    "I can cite a number of references made from various sources, contemporaneous 
    and modern, to how useless they are in practical navigation terms."
    And no doubt your resources would be secondary sources like the one you posted 
    previously which erroneously claimed that it took an hour to do the math for 
    a lunars sight. As for "contemporaneous" sources, one potential error that 
    may well trip you up is to treat sources from decades after lunars were 
    commonly used at sea as if they are describing current practice. If you cite, 
    for example, a source from 1895, that's much too late. But I agree that you 
    can EASILY find sources from the latter half of the 20th century repeating a 
    long list of myths about these sights (impossible to use, four hours of 
    terrible math, loved only by astronomers, immediately obsolete after 
    Harrison's chronometer, and so on). This standardized history had been handed 
    down from one author to another for decades.
    And you wrote:
    "As far as I am concerned, my understanding is they were promoted, developed 
    and made into a _just_ practical method by the astronomers because there was 
    nothing else possible - until the chronometer - that is all.  They remain an 
    astronomical and navigational curiosity.  It took a genius English carpenter 
    to remove them from their undeserved place of astronomical and maritime 
    prominence.  Some astronomers have never got over it I guess."
    There's some truth to that. The astronomical community could only see what 
    they understood themselves, and they did not devote as much attention as they 
    perhaps should have to "clockwork" solutions. Of course, we have the 
    advantage of hindsight here. As for lunars, they were made practical at a 
    time when there was only ONE functioning chronometer in the world. They were 
    actively employed by real navigators at sea for 75 years after they were 
    first practically introduced, and they were also used in land exploration and 
    mapping for another 50 years after that. The idea that lunars were dropped as 
    soon as Harrison demonstrated his chronometer H4 is incorrect.
    And you wrote:
    "My opinion is Lunars are inherently flawed because of the very thing which 
    has been discussed here under star distances - practical measurement to 
    sufficient accuracy  under 'normal' conditions of bouncing around in the 
    Lunars were what they were: a medium-accuracy method for determining 
    longitude. A lot of folks operate under the assumption that if lunars weren't 
    exactly equivalent to a chronometer in practical terms, then they would have 
    been useless. But this theory is over-turned by the real evidence we have 
    today. I've personally slogged through around a hundred logbooks from this 
    period of time looking for evidence of how navigation was actually done (as 
    opposed to how we imagine it may have been done based on armchair 
    speculation). And as I've noted in many posts over the past few years, lunars 
    were never the primary means of determining longitude. The logbooks I've 
    examined were primarily from American merchant vessels, and there is abundant 
    evidence in them of lunars being used on long-distance voyages through about 
    1850. That period can be divided in two, very roughly, at about 1835. In the 
    period up to 1835, dead reckoning was the principal means of determining 
    longitude (chronometers were relatively rare on American merchant vessels 
    before this turning point). After 1835 (I emphasize, very roughly), the 
    longitude was determined primarily by chronometers. And all through this 
    period, from at least the 1790s through 1850, lunars were widely used as a 
    check on the primary means of determining longitude. Lunar distances are not 
    available every day, and lunars taken using the Sun as the other body around 
    First Quarter and Last Quarter were popular for a variety of reasons. So for 
    several days, every two weeks, lunar observations were made and compared with 
    the primary longitude. If they disagreed substantially (and this depended on 
    the individual) then the navigator would worry about it in his logbook. 
    You also wrote:
    "That is ignoring the difficult calculations - which they _are_ to most people 
    excepting scientists like yourself. I accept in modern times the calculations 
    which were formidable to pre-calculator sailors can be done more easily, but 
    the fact remains they are impractical for sailors at sea - even now."
    That's just not true. Clearing lunars was no more difficult than an ordinary 
    time sight (which every navigator worked every day), and in fact there is a 
    considerable similarity geometrically in the bulk of the calculation. Many 
    commentators on lunars in later decades (AFTER they had fallen out of common 
    use at sea) mistakenly claimed that it must have been the "difficult math" 
    that kept mariners from using lunars. This claim is belied by the logbooks. 
    Lunars were actively used when there was a reason to use them. The 
    calculations took longer than anything else a navigator might choose to do, 
    but that amounted to no more than twenty minutes of work. And using some 
    short tables, the work could take as little as ten minutes. The calculations 
    were NOT unusually difficult.
    I should add that my mathematical and scientific background does give me some 
    advantage in being able to re-derive and reverse-engineer the various methods 
    that were used for clearing lunars. But let's be clear here: this ain't 
    rocket science. There's nothing more difficult than standard spherical 
    trigonometry and some very basic calculus (not to clear the sights, but to 
    derive the clearing methods).
    And you wrote:
    "They were never really accurate enough to make practical use a full reality, 
    and the fact the chronometer spelt their death knell almost as soon as they 
    were invented was because of the convenience, practical use and consistent 
    results more accurate than 'lunars'. "
    See above. Lunars were WIDELY used at sea through about 1850, but they were 
    not used in the same fashion as chronometers.
    And you wrote:
    "If 'Lunars' were an easy, practical and sufficiently accurate method - it 
    would have carried on into the twentieth century as saiors are notoriously 
    slow to change methods. It did not. It was ditched immediately the cost of a 
    chronometer could be bourne by the shipping companies."
    Yes, that's mostly correct. Lunars were no longer used much after 1850, and 
    that's because chronometers had become cheap and reliable. It was easier to 
    buy two chronometers than to pay for the high-quality sextant required for 
    lunar observations. And by the way, I've mentioned the dates 1835 and 1850 
    above. Those dates are based on the American merchant fleets. For British 
    mariners, subtract roughly 25 years from each. So in the Royal Navy, you can 
    assume that lunars were over and done with by about 1825 --but note that this 
    is still SIXTY years after Harrison's H4 was considered successful.
    For an entertaining example of the use of lunars in the early period, you 
    might enjoy the story of young Basil Hall put in command of a captured 
    American topsail schooner, the Erin, back in 1807. This vessel was suspected 
    of breaking the British blockade of Napoleonic France and was taken to 
    Bermuda for processing. Along the way, Hall became uncertain of his longitude 
    and he shot some lunars to test his longitude. To his dismay, the lunars 
    indicated that the small, fast vessel he was commanding had overshot Bermuda 
    and against his "seat-of-the-pants" instincts, he trusted his lunars and 
    turned back to the west. Sure enough, Bermuda was sighted at dawn.
    Here's the full story:
    I think you'll like it.
    And you suggested:
    "and it is unlikely to change until and unless you have hard evidence to show 
    it is not so - such as going out onto a small boat in force 3"
    Such an experiment might well prove that lunars cannot be done at all in a 
    small boat in force 3 winds. But so what? Lunars were widely used at sea 
    through about 1850, and they were widely used in land exploration for decades 
    after that. And in addition, I should say that there are around a dozen 
    current NavList members who have done lunars, for their amusement or for 
    historical understanding, in real practical conditions. That is, it's not 
    just me.
    And you wrote:
    "using your sextant about fifty times doing 'Lunars' then with an analysis 
    of the results .... as Gordon did with the 1964 report I sent in.
    Then I might take more interest in your hearsay statements about accuracy of lunars and star distances."
    Labeling my analyses as "hearsay statements" speaks volumes about you but says nothing about me. 
    I have shot hundreds and hundreds of lunars for my own entertainment (such as 
    it is), but experiments like this are only marginally relevant to a practice 
    that is purely historical. If you want to understand how and when lunars were 
    used (and when they were not used), how accurate they were (or were not), how 
    difficult they were (or were not), then you need to go to the hard data, the 
    extant logbooks from the era, as I have done.
    And you wrote:
    "Finally; I note you have completely ignored the main aspect of my submissions 
    about star distances and sextant observational accuracy - namely the 
    resolving power of the eye itself."
    Not so. I have been discussing this for years and years. The normal resolution 
    (for standard resolving tasks) of the human eye is around 1 minute of arc, 
    somewhat better under excellent conditions. Do you recognize now that when 
    you look through a telescope (a GOOD telescope) that angles on the sky are 
    magnified? And therefore if the eye can normally see details of one minute of 
    arc without magnification then using a 3x or a 7x telescope, the observer can 
    see details of 0.33 and 0.14 minutes of arc respectively? I should emphasize 
    that the standard deviation for my lunar observations with a 7x telescope is 
    about 0.25 minutes of arc which implies that there are other sources of error 
    in addition to the limiting resolution of the eye-telescope system.
    And you wrote:
    "curiously, very close to the ultimate practical accuracy of a single 
    observation with a sextant. This I have noted with practical observations I 
    have made myself, in discussion about  accuracy to friends who use sextants, 
    (including one master mariner who used them 'for real') and is confirmed in 
    the 1964 report by Gordon."
    It appears to me that you are confusing a couple of things here. The 
    resolution of what we can see through the telescope of a sextant (which 
    depends on the resolution of the eye and the magnification of the telescope) 
    is not the same thing as the final effective accuracy of a celestial 
    navigation sight. Standard LOP sights are strongly influenced by 
    uncertainties in the horizon and those uncertainties appear to be the 
    limiting factor in standard cel nav sights. When you do sights which do not 
    involve the horizon, such as lunars, that particular uncertainty is removed. 
    Adding magnification to sights which have intrinsic variability on the order 
    of 0.5-1.0 minute of arc (like standard LOPs off a sea horizon) does not 
    offer significant improvement, as is well-known. But when you add 
    magnification to sights which do not involve the horizon, there is 
    significant improvement in direct proportion to the magnification as long as 
    the optics of the telescope are reasonably good.
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