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    Re: New compact backup CELNAV system RENAMED Accuracy of Bygrave Slide Rule
    From: Brad Morris
    Date: 2009 Apr 11, 16:48 -0700

    Hi Gary
    
    The MHR-1 has the instructions printed on the rule itself, so they are right 
    where you need them.  Naturally, they are in German.  I fiddled around and 
    came up with this translation (using online word by word translation.
    
    Begin Translation
    
    Special case: with azimuth between 85 degrees and 90 degrees, the calculation 
    is repeated with the permutation of latitude and declination. Instead of 
    latitude in the second step, use declination and calculate b=90 ? 
    declination.  In the third step, Azimuth is the helper angle that is used 
    only for the calculation the altitude.  Don?t use the slide rule when the 
    hour angle and declination is between 0? and 20?, as well as when the hour 
    angle is close to 90.
    
    End translation.  
    
    Azimuth => helper angle, but not a valid Azimuth at that point. I think you 
    are supposed to get the azimuth by running the calculation TWICE.  In the 
    first instance, you get the azimuth close to 90.  In the second instance, you 
    solve for altitude.
    
    -------------
    
    The MHR-1 also permits the use of hour angles beyond 6 hours or 90 degrees.  
    So, if you were beyond the arctic or antarctic circle and wanted to calculate 
    the alitude of the sun as it runs around the sky in 24 hours without setting, 
    you can do so.  I have done just that.  It took a bit of thought to see how 
    the MHR-1 was to be manipulated, but it does clearly word (and compares well 
    with calculator comparison).  In addition to the black numbers printed by the 
    lines, there are also red numbers that extend the scales to 180 degrees.
    
    -------------
    
    In answer to your querry regarding the Flat Bygrave compared to the 
    Cylindrical Bygrave, we have only to look to the printing process, assuming 
    that you did follow the equations.  The modern person, like you or I, will 
    print our scales directly on a one to one basis.  That is, the print size is 
    the final size.  We will be subject to the resolution of the printer.  300 
    DPI (dots per inch) will look just fine but you may wish to jump to the 
    highest resolution possible.  No matter which resolution you obtain, this 
    will force the ticks on the Flat Bygrave to one line of pixels or another, as 
    a function of the printer resolution.
    
    For the cylindrical Bygrave, I will have to resort to a bit of speculation.  I 
    wasn't around when the original English Bygraves were made and I certainly 
    wasn't in Nazi Germany for the MHR-1 construction.  However, the general 
    principal is to make one huge master and photo reduce it down.  This 
    principal was used to great advantage.  The creator spends alot of time with 
    a massive scale, measuring off and marking lines where they are to be.  Then 
    the image is reduced for production.  You essentially have infinite 
    resolution, since each line is individually created, one at a time.  Any 
    small errors in tick creation are masked when the photo reduction occurs.
    
    The benefit of the directly printed scale is the speed at which it is 
    initially created and the lack of creation errors (assuming those equations 
    are right).  The draw back is the pixelation.  
    
    The benefit of the photo reduction method is the infinite resolution for the 
    tick marks.  Slow as molasses in creation though.
    
    I strongly feel that there will be little if any affect on the resultant 
    reductions.  The Bygrave does not depend on precise alignment of the tick 
    marks, merely the closest one, by eye.  
    
    Best Regards
    Brad
    
    
    
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