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    Re: Bowditch tables and sexant parallax
    From: Bill B
    Date: 2005 Apr 28, 14:12 -0500

    > Bill you wrote:
    > "My Astra IIIB has an aprrox. vertical distance of 2.25" between the  center
    > of the horizon mirror and the index mirror.  Using a plane right  triangle,
    > and knowing the distance to the object, I should be able to  calculate a
    > useable correction for parallax.  For 100 yards approx. 0d  2' 9", for 0.1 nm
    > approx. 0d 1' 4", for .5 nm approx. 13".
    >
    > Distance  must be known to calculate the above, and distance is what we want
    > to solve  for using the tables. Is it reasonable to hold the sextant
    > horizontally,  align the sides of the object between the horizon glass and
    > mirror, and use  that angle (off the arc so, add to sextant measurment)
    > plus/minus IC to  correct to the actual angle?"
    
    > Frank responded.
    > If I've understood you right,  yes.
    
    Frank
    
    I believe we are on the same page.  While my example had to do with Bowditch
    tables, they are usually not that precise, so a poor choice to use as an
    example. A simple use of determining parallax error would be finding the
    height of an object on a chart (water tower, Michigan City smoke stack and
    cooling tower etc. whose height is not given) when I know its position and
    my position, so I can calculate height for later use as a nav aid.  (Some
    heights may be available on aviation charts?)
    
    > Frank added
    > I've been thinking along similar lines for a "laboratory" test of  arc
    > errors. The parallax within the instrument (because of that 2.25" distance
    > between
    > the line of sight through the horizon glass and the index mirror that  you're
    > describing) is something that we can calculate exactly and correct for.  For
    > example, I could do an index correction by looking at a an index card across
    > the room. If the top and bottom of the card are aligned (assuming that's the
    > same as the distance between the line of sight through the horizon glass and
    > the  index mirror), then my sextant should reading should be identical to the
    > I.C.  based on objects observed at great distance (the standard method for
    > checking  index correction). For other angles, I am guessing that the parallax
    > goes
    > as  d*cos(h) where h is the angle read off the sextant and d is that distance
    > (2.25"  in your case).
    
    Very clever idea. I had roughed out parallax correction for points nearby
    using the vertical distance between the horizon and index mirror points
    which would intersect the line of sight from the index mirror above the
    horizon mirror center, and tangent of that distance divided the distance to
    the object from the horizon mirror. I see now that the vertical distance
    will vary as line of sight from the index mirror varies.  So I really need
    to solve an oblique triangle first. Let H be the point where the central
    axis of the scope pierces the horizon mirror, I be the point on the index
    mirror on the axis and O be a point on the object viewed.  Let angle OHI be
    known, length of line segment HI (side o) be known, and length of line
    segment OH (side i) be known.  Using the law of cosines solve for line
    segment OI (side h).  With that known, use the law of sines to solve for
    angle O.  Construct a line perpendicular to OH (side h) from point H.  Now I
    have a right triangle with angle O and segment OH (side i) known, and can
    solve for the height of the your "index card." But I would wager you already
    know that.
    
    For measuring error along the arc, we add a movable point, B.  If line
    segments OH and OI remain constant, and distance of point B from point I
    equals the length line segment we establish for segment OI previously, then
    we should be able to apply the parallax error and IC to angles measured with
    the sextant to the true angle of OHB to determine error arong the arc.
    I have a nagging suspicion with a front-silvered index mirror the length of
    HI will vary with angle set on the sextant.
    
    I have thought about "projecting" angle scales on a wall from point I
    through  point B, but run out of intellectual horsepower (making the huge
    leap of faith that has not happened paragraphs before).  If I change the
    length of segment IB won't the parallax error change?
    
    Which leads to yet another question.  How the heck do I correct for parallax
    error for two points at varying distance? I could observe both and pick them
    off the sextant, but how do I combine them into a meaningful value?
    
    Try coastal piloting as an example.  If I were trying to use three objects
    for a three-arm protractor fix, my position was roughly .5 nm off the center
    object, 3 nm from the left object, and 1 nm from the right object, how do I
    determine a parallax correction for each angle?  It seems the error could
    approach 0.3', and a three-arm protractor is precise to 0.1'.
    
    A potentially greater error might occur in measuring the angle on the bow,
    using a distant object and the forestay.  I place my eye on the lubberline,
    put the forestay in the horizon glass and object in the mirror.  34 ft
    craft. so approx. 21' parallax error in the forestay value.
    
    Any thoughts?
    
    Bill
    
    
    

       
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