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    Re: Emergency Navigation
    From: Alexandre Eremenko
    Date: 2012 Jul 14, 04:09 -0400

    > Brad and Lu,
    > I also think that these simple methods are not as simple if you try to
    > implement them in real life.
    > a) Taking the altitude of Polaris.
    > For this you need to divide a circle, say to 1 degree accuracy.
    > Can you do this without instruments? I cannot. I need at least a divider,
    > and even then this is a highly non-trivial task.
    > Alternatively, you can make an instrument of straight sticks (kind of
    > cross staff). Then the same problem arises: to measure the length
    > of these sticks. Dividing a ruler is no simpler task than dividing
    > a circle.
    > All this is BEFORE you "use trigonometry". But how exactly you use
    > trigonometry without a calculator/tables? You compute a table of sines
    > and or tangents? With Ptolemy method, or using a Taylor series?
    > It is true, you will need the tangent of only one angle when measuring
    > Polaris altitude with a cross staff, but the problem of making a ruler
    > remains.
    > I already mentioned on this list a Russian captain Golovnin who spent 10
    > years in captivity in Japan in the early XIX century. He taught the
    > Japanese
    > some modern navigation, and
    > his mate computed tables of trig functions for the Japanese.
    > I wonder how many modern captains or mates are capable of doing this:-)
    > b) Using Sun. Certainly the method is not practical on a ship.
    > To find the noon altitude of the Sun with a gnomon (vertical tick),
    > you need a flat horizontal ground, a plumb line to install your stick,
    > then you probably have to observe for several days to find the noon
    > altitude on a certain day.
    > Declination does not seem to be such a big problem in principle:
    > you can compute it approximately from the dates of the solstices
    > and the angle between the equator end ecliptic.
    > (Assuming that Sun rotates on a circle not an ellipse, as the ancients
    > did). If you can make trigonometric tables, then you probably can
    > do this as well.
    > With any of these methods, determination of latitude, say to 1-2 degrees
    > will take many days and only possible from land.
    > By the way, all this is described with some details in Jules Verne novel
    > Mysterious Island. According to Jules Verne, Cyrus Smith used his height
    > (which he knew precisely) as a unit of length. But the details how he
    > divided this unit into smaller units are omitted:-)
    > Jules Verne apparently did not understand that to measure an angle
    > you can use arbitrary unit of length, and its relation to feet or
    > inches is irrelevant. The main difficulty is in dividing this unit
    > with sufficient accuracy.
    > Alex.
    >> Brad:
    >> I must respectfully disagree.   If I plant a stick in the ground
    >> and are
    >> willing to measure its shadow for a full year (or at least from one
    >> solstice to the other), I can indeed deduce my latitude.   If I
    >> want to
    >> do it in less time (say in just a day or in a week) I must have a
    >> declination table  and an idea of what date it is.   While the
    >> latter
    >> was not necessarily forbidden by the statement of the problem, the
    >> former
    >> certainly is.
    >> I had originally wondered if I could have applied the Rule of Twelfths
    >> to
    >> approximating the sun's declination for any particular date, but it
    >> turns
    >> out that the curve of the sun's declination is NOT a sine wave (nice
    >> explanation in Wikipedi
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=119938

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