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    Re: Manufacture new Bygraves?
    From: Gary LaPook
    Date: 2009 Jul 09, 20:06 -0700
    Thomas Kleemann wrote:

    "How so? By prolonging the scale down to values below the original
    0° 20'? Twelve turns for 19 minutes of arc?"
    
    Yes, it takes 12 more turns to extend the cotan scale down 19' because each turn equals a change of log (cotan) of .1. The log cotan of 20' is about 2.2 and the log cotan of 1' 30" is about 3.4 a change of twelve .1 changes of log cotan requiring 12 turns.
    
    To see this for yourself look no further than your slide rule. An easy place to start to see the relationship between the change in log cotan (or log tan since they are the same) and the turns on the Bygrave is to look at the mark for 45º which lines up with the end of the log scale on your slide rule. Now look at the .9 on the log scale, a change of .1, and look at the value on the tan scale, 38º 27'. Move down one more .1 change on the log scale to .8 and you find 32º25' on the tan scale. If you go all the way to the left end of the log scale, a change of ten .1 units, you find 5º42' on the tan scale. Now look at the same point on the ST scale and you find 34' which is down 20 units of .1 log tan from 45º. Look at .2 on the log scale, down 18 units from 45º, and you find 54' on ST scale.
    
    Now download the cotan scale I uploaded at :
    
    http://www.fer3.com/arc/img/107501.f2-lapook1.pdf
    
    print it out and then draw a vertical line through the 45º mark and you will see that it cuts through the same values and you will find the 5º42' down 10 lines from the 45 mark, .1 change of log tan (cotan) for each line or turn. My scale only goes down 18 turns (lines) from 45º and you will find that it ends at 54' just like the example on the ST scale on your slide rule.
    
    Then download the cosine scale from:
    
    http://www.fer3.com/arc/img/107501.f2-lapook2.pdf
    
    and make the same comparison with the cosine scale on your slide rule and you will find the same relationship.
    
    gl
    
    
    
    
    




    Thomas Kleemann wrote:
    my text woven in below...
    
    glapook---.net schrieb:
      
    You're close to the original Bygave which has a cotan scale 8.8 meters
    long. But you would have to adjust your spacing slightly because there
    can only be 44 turns between 20' and 89º40' since each turn must equal
    a change in log cotan of .1. The log cotan of 89º 40' is about  -2.2
    and the log cotan of 20' is about 2.2, a range of 4.4 making  44
    changes of .1 which is the reason for the 44 turns on the original
    Bygrave. 
        
    
    I did't get that.
    Do you mean, there is some restrictin in the spacing - that one turn on 
    the scale has to have a certain interval (0.1) covered?
    
    I thought I'm free to choose whatever diameter I like and that the 
    scales length divided by the circumference gives the approximate number 
    of turns. Why 44, then?
    
    Or do you just talk about the original dimensions?
    
      
    Its tube is 2.5 inches in diameter 
        
    
    Well, 2 inches was just an example...
    I took it, because anything between 40 and 50mm diameter handles well, 
    haptically.
    
      
    times Pi makes the
    circumfance of 7.85 inches times 44 turns equals 345.58 inches or 8.77
    meters. If you adjust the spacing but keep the pitch unchanged and
    make 56 turns it would cover a range of 1'30 to 89º 40' and so
    eliminate the problem of sun sights near the equinoxes.
    
        
    
    How so? By prolonging the scale down to values below the original
    0° 20'? Twelve turns for 19 minutes of arc?
    
    Regards,
    	Thomas.
    
    
    
    
    
      


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