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    Re: Scales used on Bygrave
    From: Wolfgang Hasper
    Date: 2010 Feb 19, 21:31 +0100

    I'll try a quick translation of page 166 / �80.
    You may judge if it can compete with google's...
    I will try to keep it as literal as possible, so 
    everyone can follow the original text if they want
    
    BEGIN
    
    [end of �79] The altitude slide rule manufactured by 
    Dennert Pape has proven useful and was introduced to 
    navy and air force.
    
    �80. The position-fix altitude slide rule
    
    The position-fix altitude slide rule is based on the 
    following considerations: The basic celestial triangle 
    of pole-zenith-star (fig. 105) is divided in two 
    rectangular spherical triangles by drawing a 
    perpendicular from the star S to the meridian, the 
    base point of which shall be A. Denoting the side PA 
    of the triangle PSA "90-x" and the side ZA of the 
    triangle "90-y" one can derive the following group of 
    formulae to calculate altitude and azimuth from these 
    two triangles.
    
    cotan x = cotan delta *cos t 
    cotan Az=cotan t*cos y/cos x
    cotan h=cotan y/cos Az
    
    In doing so x is to be taken greater than 90� if the 
    hour angle t is greater than 90�. y equals 90�-phi+x 
    if phi [latitude] and delta are of same name. If of 
    contrary names, y=90�-phi-x The azimuth Az on the 
    northern hemishere counts from the South Point, on the 
    southern hemisphere from the North Point and is to be 
    assumed in the same quadrant as y, thus greater 90� if 
    y is greater than 90�.
    These formulae consist of the trigonometric functions 
    cotangent and cosine only. This allows to build the 
    slide rule with only two sliding scales, with which 
    all three formulae can be solved. To achieve the 
    required precision (1 minute of arc) the two scales, 
    divided with log cos and log cotan respectively, are 
    fitted in a spiralling manner on two concentric 
    cylinders. Thus they can, naturally, be very much 
    longer than on on a linear arrangement, without making 
    the slide rule bulky. The log cotan scale fitted to 
    the inner cylinder would unwound be about 7 metres 
    long, the log cos scale unwound from the outer 
    cylinder would be about 4 metres long. The scales 
    cannot, however, be set next to each other to make a 
    reading as on a conventional slide rule. A pair of 
    cursors, fixed to a small outer ring [here the 
    description does in my eyes fail] compensates for 
    that. It resembles the hair line of an ordinary slide 
    rule. Setting of the zero mark on the log cos scale is 
    simplified by a fixed zero-stop for the cursor-pair.- 
    the scales do not only show markings from 0-90� but 
    also the respective complements, thus cumbersome 
    side-calculations can be omitted, if one only follows 
    the sign-rules as given above.
    The use of the slide rule in detail unfolds from the 
    instructions for use printed on the device.
    
    END
    
    Well, google would have been a lot faster!
    
    Wolfgang
    
    Am Freitag, 19. Februar 2010 01:35 schrieb Gary LaPook:
    > A while ago we had an ongoing discussion of what
    > scales were actually used on the Bygrave and the
    > German version, the HR1. Wolfgang just posted an
    > excerpt of a book in German which supplies
    > additional information on this issue. I am attaching
    > pages 166 and 167 of this book. Even without
    > speaking German I think it is clearly stated on page
    > 167 that the inner scale is a log cotangent scale
    > and the other scale is a log cosine scale. Also page
    > 166 states the formulas that are actually solved
    > with these slide rules which identify the scales as
    > a cotangent scale and a cosine scale.
    > ----------------------------------------------------
    >-------------- Some of you may be interested in the
    > linked pages of "Lehrbuch der Navigation"
    > Bremen 1943, volume II
    > They show different aircraft sextants and describe
    > their use and properties. (in German...)
    >
    > Most intersting is the last paragraph on mechanical
    > calculation devices for the celestial triangle,
    > including HR1.
    > It reads:
    > "The altitude slide rule manufactured by Dennert &
    > Pape has proven useful and was introduced to navy
    > and air force."
    > Another hint that MHR1 is not likely to mean
    > "marine" HR
    >
    > Wolfgang
    >
    > Pdf documents, zip compressed are linked ~ 5MB
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    > Linked File:
    > http://www.fer3.com/arc/imgx/f1-Lehb_d_Navigation.zi
    >p
    >
    >
    >
    > ----------------------------------------------------
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    > gl
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    > Linked File:
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    >df
    
    
    

       
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