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    Re: Compass Check
    From: Bill Lionheart
    Date: 2016 Mar 21, 22:07 +0000

    Dear Bob
    1) Correcting a compass with the sun. Its strange that I never learnt
    this in a navigation class but it is clearly why binnacle compasses
    have a spike in the middle to cast a shadow. I have an old Sestrel
    compass with a much bigger and better spike.
    2)  I had assumed that you just use it to check the compass whenever
    the sun casts a nice shadow and you happen to note the time and have a
    chance to  calculate the azimuth (eg when you are doing a sun sight).
    Of course it is now much easier as to calculate azimuth with a
    computer or phone app.  If you are sailing with the sun not shadowed
    by the sails  you can sheet in to increase the angle of heal on the
    same course and see the healing error too (assuming you can still see
    the shadow when it heals!)
    3) One sunny day with no sails up i decided to check what happens if I
    motor slowly in a circle (well it was a polygon as I used the auto
    pilot). What happens is of course that the shadow of the sun stays in
    the same place on the compass card (at least when it catches up). In
    practice with some deviation it moves depending on the heading. If you
    calculate the azimuth of the sun and know the local variation you can
    correct the compass from this, just making a table.
    4) When you make a deviation table the deviation should be represented
    as the first 5 terms of a Fourier series D = A0 + A1 Cos T + B1 Sin T
    + A2 Cos 2T + B2 Sin 2T where T is the magnetic ships heading. If you
    do it quick enough that the change in azimuth is too small to measure
    (you can only read my steering compass to 5 degrees anyway) then this
    only affects A0 which is effectively the lubber line error, that the
    compass itself is not aligned with the ship's head. The other
    components are associated with soft iron A2 and B2  and permanent
    magnets A1 and B1.  I am not sure where to suggest one reads about
    this (Fourier series stuff)  but I read it in a very old Admiralty
    Manual of Navigation in our department library! I think perhaps it was
    first described by Lord Kelvin. I am aboard my boat at the moment so
    its not easy to check sources!  I think in old navigation books the
    coefficients are labelled A to E.   As I understand it a compass
    corrector removes the A1 B1 error by putting small magnets in the base
    of the compass and the A2 and B2 with the big soft iron balls you see
    on big steel ships. [sorry this is all from memory].
    Hope that helps or is off interest
    On 21 March 2016 at 21:23, Bob Goethe  wrote:
    >>>Even if you don't know the azimuth you have the Fourier coefficients for
    >>> compass correction except  the constant term. Much easier than transits and
    >>> pelorus.<<
    > Bill, I am unfamiliar with this.  I have always been into transits and
    > peloruses.  You intrigue me.  Could you unpack what you are talking about
    > here just a bit?  Or if there is a discussion of this elsewhere in NavList,
    > just mention that and I will dig a bit deeper.  But sometimes searching for
    > something - which may or may not exist - can be like trying to look up a
    > word in the dictionary when you don't know how it is spelled.
    > Thanks,
    > Bob
    > View and reply to this message
    Professor of Applied Mathematics

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