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    Wires, back sights and collimation
    From: Alexandre Eremenko
    Date: 2004 Nov 24, 13:12 -0500

    Dear Fred,
    
    1. Now I think I understand what Hadley writes
    about wires. He worries about parallelism of
    the line of sight to the plane of the quadrant.
    The lack of parallelism can arise from
    a) collimation error and
    b) if the objects touch away from the middle line
    of the field of view.
    Hadley assumes that collimation is perfect and
    the distance of each wire from the central line
    (the line parallel to the plane of the arc, and passing
    through the optical axis) is 1 and 3/8 degrees.
    Then, if the objects touch on one of the wires,
    the error in minutes is
    -2 tan(A/2),
    where A is the measured angle.
    
    Chauvenet, on p. 113 of volume II gives the precise formula,
    as well as the following approximate one:
    error=-i^2 sin(1') tan(A/2),
    where the error is in minutes, and i is the distance of a wire
    from the center line in minutes.
    
    In my sextant, this distance i (half of the distance between
    the wires) is approx 1 degree,
    something
    in between of what Headley recommends and the 30' distance
    "of the best sextant telescopes" according to Chauvenet.
    
    Now both Hadley and Chauvenet recommend to have the
    objects touching as close as possible to the central line,
    and it is clear that the wires help to do this.
    (The total field of view of my telescope is about 6 degrees).
    
    But Headley goes even further. He suggests making several
    (more than two) parallel wires, over the field of view,
    and than applying a special correction, depending on
    the place where the objects touch.
    
    From my experience there is at least one reason why one would want
    to touch the objects away from the central line. The reason
    is the following. I found that under certain conditions
    my horizon glass
    reflects very
    well by its FRONT (unsilvered surface). So that its transparent
    part of it works like a "full view mirror". I find this feature
    very useful, especially in taking the distances.
    This requires a touch near the LEFT wire, rather than in
    the middle. Now I am waiting for good weather to test
    Hadley's formula in this situation:-)
    
    2. Inspecting the formula, we see that there is indeed a big
    problem with measuring distances close to 180 degrees,
    when the tan(A/2) blows up.
    
    This is the mathematical explanation of why
    
    a) the quadrant with back sight feature cannot be
    used as a dipmeter, and
    
    b) why everyone experienced the problems with finding
    the index correction for back sights with Wollaston method.
    (See my previous messages on this subject. I can conclude
    from his paper that Wollaston did not actually experiment
    with a quadrant, just speculating on the basis of
    "thought experiments":-)
    
    Same difficulties should occur with "periscope method"
    by Blith as described by George, and with George's
    self-made periscope attachment.
    
    This also explains why the other method of finding the index
    correction for back sights described by George is superior
    to the Wollaston method.
    I recall: this other methodi involves
    a measurement of an angle close to 90 degrees
    (which can be taken by BOTH fore sight and back sight).
    First you determine the index correction for the fore sight.
    Then you measure some angle close to 90 degrees by a fore sight.
    And then you measure the same angle by the back sight,
    to determine the back sight index correction.
    
    It seems clear that this method can hardly be practiced
    in sea. (Indeed, the only appropriate objects would
    be two stars at approx 90 degrees distance, the Moon
    is not appropriate because the angle should not change while
    you switch from the fore to back observation). I think
    this is the
    reason why back sights were
    abandonned by the mariners. I can add that all sorts of
    collimation errors (including the non-parallelism described
    above) will interfere with the index correction performed
    with this "90-degree method".
    
    It seems extremelly interesting to me, how the dipmeter
    designers overcame this difficulty. Unfortunately the picture
    in the Shufeldt paper (as it was transmitted by fax) does
    not permit me to determine the details of its construction.
    and Shufeldt
    himself does not say anything about this.
    
    Alex.
    
    
    

       
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