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    Re: New compact backup CELNAV system RENAMED Accuracy of Bygrave Slide Rule
    From: Brad Morris
    Date: 2009 Apr 13, 09:56 -0400

    Hi Gary
    
    
    You wrote:
    But let me ask you this, would you enter a narrow unlit channel at
    night based on a celnav fix worked out on H.O.229 that you wouldn't
    enter if you had worked out the same celnav fix using H.O. 249 or your
    MHR-1?  My point is that the flat Bygrave provides the level of
    accuracy needed for practical celnav.
    
    My response:
    
    The Flat Bygrave would clearly provide the level of accuracy for normal
    celestial navigation.
    
    For any method, however, you wouldn't be using celestial navigation for a
    narrow unlit channel, rather coastal piloting would be the choice at that point.
    If it is unlit, you would certainly be taking a chance of wrecking.
    Your comments earlier as to what level of precision is needed at each stage
    of the journey is quite apropos. Celestial navigation not meant for narrow channels,
    in the dark.
    
    There is a bit of a conundrum here.  The amount of work needed to extract a
    value from a set of tables varies little, except if you are using Sumner
    Line of Position or earlier.  There will be some quibbling about the arrangement
    of the tables being "inconvenient" in HO229 or that there is no interpolation
    required of HO249, but at the end of the day, you have spent just a few minutes
    in the tables themselves.  Why not get the maximum resolution that you can?
    
    
    You wrote:
    
    Since you have a MHR-1 I would like it if you could make a trial flat Bygrave
    and test it against your German model and let me know how they compare.
    
    My response:
    
    Being a typical engineer, I took your question literally and not
    in the manner intended.  As such, maybe we can clarify a little bit
    as to what you are after. I wrote that there was some pixilation error, but it was
    insignificant.  That was the engineering answer.  Are you asking for a
    manipulation comparison?  Solve a few problems using the Cylindrical and the Flat
    and see how they stack up in handling?  Or are we after the numerical results?
    
    There may be some cosine error in manipulation.  That is, if the first scale
    is at an angle to the second scale, the numerical result will vary by the cosine
    of that angle.  While no one will expect a serious result when the scales are skewed
    at 45 degrees, it does plainly demonstrate the cosine error.  Place scale B on scale A
    at a 45 degree angle and see how the logarithmic addition (natural number multiplication)
    gives an erroneous result.  But inject a more realistic angle, one that happens through
    imprecise alignment.  The logarithmic addition does not span the correct distance and therefore
    contributes to a numerical answer in the result.  Since the scales are manipulated three
    times, this error can cascade through all of the manipulations.  This misalignment
    CANNOT occur on a cylindrical Bygrave, since the cylinders are concentric and mechanical
    aligned to each other.  How serious is the problem?  I suggest that it depends on the span
    of the calculation on the rule itself.  As the span gets larger, the offset and error in result
    do as well.  For short span calculations, the cosine error may be small enough to be
    ignored.
    
    Please clarify what you would like me to check.  I won't mind it a bit!
    
    Best Regards
    Brad
    
    
    
    
    
    
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