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    Re: Lunar trouble, need help
    From: Kent Nordstr�m
    Date: 2008 Jul 5, 13:24 +0200

    Frank wrote: What color light? It's not often mentioned explicitly that this
    factor
    applies only for one specific frequency in the visible spectrum....
    
    Around 5500 �ngstr�m (550 lamda nm).
    
    Frank wrote: Since you're modeling historical methods, you could just input
    the wholerefraction table as printed.
    
    Yes, this approach was considered when I did my modelling. Mybe I should
    re-consider.
    
    Frank wrote:
    May I ask, what is your source material? Are you looking at old navigation
    manuals and textbooks or old logbooks (or similar)? The textbooks tend to
    focus on minor issues (like second-differences, and finding local time from
    star altitudes, and correcting for the oblateness of the Earth) which were
    almost entirely irrelevant in practical navigation.
    
    My sources are navigation textbooks from 1795, 1796, 1842, 1845, 1853, 1873
    and 1896. I have also taken alook into Bowditch 1834.
    What you find in textbooks are good examples which can be used for testing
    and "validation" of your model. That was the very reason for using
    textbooks. It is very rare that you find errors in good texybooks.
    You may have a point that the focus were on "small things", however I don't
    agree with you concerning a exclsuion of correction for earth flatness. One
    of the real challenges with LD's is to get corrections for earth flatness
    correct. But I can certainly understand if navigators in general avoided to
    deal with this correction. It is difficult.
    
    Frank wrote: In fact, lunars with stars and planets were
    nowhere near as common as Sun-Moon lunars. From my experience with logbooks,
    I roughly estimate that around 80% of lunars were Sun-Moon observations.
    
    I think the explaination is simple. It is much easier to find the local time
    using the sun than with any other celestial object. You don't need to
    calculate the long way with Aries, RA etc.
    
    Frank wrote: Watches were not the issue. Plenty of good watches were widely
    available inthe period.
    
    This view is not consistent with advices found in the earlier referencies
    above.
    
    ----- Original Message ----- 
    From: 
    To: 
    Cc: 
    Sent: Tuesday, July 01, 2008 10:16 PM
    Subject: [NavList 5619] Re: Lunar trouble, need help
    
    
    
    Kent, you wrote:
    "The factor 60,35� has been provided to me from the Observatory in Stockholm
    to be used with the true zenith altitudes for altitudes above approx. 10
    degrees. The factor is taken from modern English litterature."
    
    What color light? It's not often mentioned explicitly that this factor
    applies only for one specific frequency in the visible spectrum. That's one
    reason why two people can quote factors differing by an arcsecond and still
    be technically correct. It's also why we shouldn't worry too much about the
    tenths and hundredths of an arcsecond. And it's a big reason why we
    shouldn't shoot lunars when the objects are below about ten degrees: the
    stars and the limbs of the Sun and Moon are stretched out into colorful
    bands at very low altitudes. Incidentally, I use 58" usually.
    
    And:
    "Yes, this is correct. For altitudes below 20 degrees I use the formula
    defined by Smart."
    
    Since you're modeling historical methods, you could just input the whole
    refraction table as printed. Then the software would interpolate between
    values much as a 19th century navigator would have done on paper. This
    approach bypasses all this chatter about various formulae for different
    altitudes. It's also a reasonable approach for a modern analysis. Sometimes
    people doing these calculations obsess over the "Bennett" formula. This is
    because we carry around "baggage" from the calculator era and the early
    years of programming small computers. There's no real advantage to a short
    formula today (except saving a few keystrokes).
    
    And you wrote:
    "So again, what I have tried to achieve is a re-construction of how the LD�s
    were measured and reduced in the old days (by Swedish navigators) and not
    necessarily what will be achieved with todays know-how."
    
    May I ask, what is your source material? Are you looking at old navigation
    manuals and textbooks or old logbooks (or similar)? The textbooks tend to
    focus on minor issues (like second-differences, and finding local time from
    star altitudes, and correcting for the oblateness of the Earth) which were
    almost entirely irrelevant in practical navigation.
    
    And:
    "The first way is what I outlined and this way can be used for any celestial
    body, incl. the sun and provides the local time (MT). The other method was
    to use the sun for generating the local time by finding the sun�s apparent
    time and correct it with the TE. This later method required (requires) less
    calculations and was therefore probably preferred by navigators."
    
    The general method (which you outlined previously) was also preferred by one
    other group: sadistic navigation instructors! Seriously, by the second half
    of the 19th century, very few navigators ever used lunars at sea, but many
    studied them in schools and instructors used the arcane aspects of lunars as
    a means of "spreading the curve" (as we would say today in education) or
    more informally "separating the men from the boys." So an instructor might
    teach this very involved method of getting local time and then put that on
    an exam, just to see who was paying attention. Meanwhile, everyone knew that
    local time was determined, almost without exception, by observations of the
    Sun.
    
    Yet another reason some instructors and theoreticians emphasized the
    possibility of getting local time from the stars is because it seemed "pure"
    in a mathematical sense. If you take a lunar distance observation with a
    star or planet, then surely you should get local time from that same body.
    That sounds good "in theory." In fact, lunars with stars and planets were
    nowhere near as common as Sun-Moon lunars. From my experience with logbooks,
    I roughly estimate that around 80% of lunars were Sun-Moon observations. So
    once again, the common method of finding local time was to measure the Sun's
    altitude. In effect, it turns the sextant into a sundial. It's a simple
    sight and a simple calculation. These sights were almost as common as Noon
    Sun for latitude throughout the period from the late 18th century and into
    the middle of the 20th century.
    
    And you wrote:
    "Also keeping the local time with a watch was used but after what I have
    gathered this was not a common method likely because watches were not good
    enough. But this method, when working, was certainly much easier for the
    navigator than the first method outlined by me."
    
    Watches were not the issue. Plenty of good watches were widely available in
    the period. The real problem with carrying local time on a watch is that you
    have to correct it for the change in longitude since the last time sight. In
    modern terms, it's a running fix problem. It's hard to guess how much time
    since the last sight was considered acceptable historically, but a few hours
    was certainly no problem and even twelve hours does not appear to have
    caused much concern.
    
     -FER
    
    
    
    
    
    
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