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    Re: New compact backup CELNAV system
    From: Gary LaPook
    Date: 2009 Feb 26, 00:21 -0800

    I decided to work a sample problem, latitude 30� north; declination 30� 
    north; hour angle 30�.
    .
    K&E solution using sine-cosine formulas: Hc 64.1�, Az 82.5�.
    
    Flat Bygrave solution: Hc 64� 04', Az 82� 25'.
    
    Cylindrical Bygrave: Hc 64� 05',Az 82� 23'.
    
    H.O. 229: Hc 64� 05.7', Az 82.4�
    
    Take your pick.
    
    Even the K&E came within 0.3' of  the H.O. 229 Hc and the Az was within 
    0.1�!
    
    The cylindrical Bygrave within 0.7' and the flat Bygrave within 1.7' on 
    the Hc and both had spot on Azs.
    
    You can check the computation of the Bygrave by using a digital 
    calculator and Bygrave's formulas.
    
    Using the above test values and the Bygrave form:
    
    Tan W = tan dec / cos H.
    tan 30�/ cos 30� = .66666
    W= inv tan .66666
    W = 33.69006� = 33� 41' 24.2"
    
    X= co-lat + W
    X = 60� + 33.69007�
    X = 93.69006�
    Y = 180� - X
    Y = 180�- 93.69007�
    Y = 86.30993� = 86� 18' 35.7"
    
    Tan az = cos W / Cos Y * tan H
    Tan az = cos 33.69006�/cos 86.30993�  * tan 30�
    Tan Az = 7.46410
    Az= inv tan 7.46410
    Az = 82.36925 = 82� 22' 09.3"
    
    Tan Hc = cos az * tan Y
    Tan Hc = cos 82.36925� * tan 86.30993�
    Tan Hc = 2.05895
    Hc = inv tan 2.05895
    Hc = 64.09492� = 64� 05' 41.7"
    
    Using the flat Bygrave the values were:
    W = 33� 40'
    X = 93� 40'
    Y = 86� 20'
    Az = 82� 25'
    Hc = 64� 04'
    
    gl
    
    
    
    
    
    Gary LaPook wrote:
    > Nothing in this world is perfect. You guys have identified a problem 
    > that does not arise in practice with this model of the Bygrave. To the 
    > level of accuracy expected from this device, the scale distortion 
    > produced errors that you guys are concerned about just don't occur. The 
    > errors you are concerned about "fall into the noise" of the two minute 
    > expected accuracy. I have made 12 of these and worked more than a 
    > hundred sample problems and checked the results against the results from 
    > a digital calculator and all the results agreed within two minutes of 
    > arc. Two minute accuracy is sufficient for practical off shore 
    > navigation and is certainly good enough for a "backup" system. Even my 
    > ten inch long Keuffel & Esser 4080-3 slide rule can produce calculated 
    > altitudes that are accurate enough for off shore navigation but not at 
    > all places on the scales as they become bunched near the ends. What 
    > makes this flat version of the Bygrave very good for celestial 
    > navigation is that the cotangent scale is not ten inches long it is 
    > 351.5 inches long, 29.3 feet, 8.9 meters! Having logarithmic scales this 
    > long allows for much greater accuracy than from a ten inch long slide 
    > rule and they consistently produce results agreeing within two minutes 
    > and often are in exact agreement.
    >
    > Many of the buildings you stand in, many of the airplanes that you fly 
    > in and most of the bridges that you drive across today were designed 
    > with the use of slide rules so they have for many years provided 
    > calculations that we still rely upon for our daily safety.
    >
    > So make one and give it a try, just don't expect agreement within 
    > one-tenth of a minute and you will see the usefulness of this for a 
    > backup celnav system. As it says on the side of the medicine bottle, 
    > "safe when used as directed."
    >
    > gl
    >
    >
    > Brad Morris wrote:
    >   
    >> This problem does not exist on a �real� Bygrave because the cylinders 
    >> are stiff and remain concentric with each other. I do recognize the 
    >> difficulty in getting the scales mounted and keeping them referenced 
    >> to each other when going through the zig-zag pattern of solution.
    >>
    >> I think that local distortions of the one scale to the other will 
    >> clearly result in errors. Slide rules in general work when the one 
    >> logarithmic scale is referenced to another logarithmic scale. 
    >> Distorting one or the other cannot be permitted. NSG21 is absolutely 
    >> correct.
    >>
    >> I remember being the last class to take slide rule instruction in High 
    >> School. When you use a slide rule today, most people think of it as 
    >> black magic and have no idea how it works. Further, the electronic 
    >> calculator leads young engineers to give me as many decimal places as 
    >> their calculator does, without judgment as to the meaning of those 
    >> digits. Empty resolution without addition to accuracy.
    >>
    >> Best Regards
    >>
    >> Brad
    >>
    >> *From:* NavList@fer3.com [mailto:NavList@fer3.com] *On 
    >> Behalf Of *Gary LaPook
    >> *Sent:* Wednesday, February 25, 2009 4:39 PM
    >> *To:* NavList@fer3.com
    >> *Subject:* [NavList 7430] Re: New compact backup CELNAV system
    >>
    >> I haven't seen the problem you mentioned. I sealed the Cotangent scale 
    >> in normal plastic protection sheets (about one buck each at Fryes) 
    >> used for protecting documents which are quite rigid. I will experiment 
    >> with bending the scale and working a sample problem and get back to you.
    >>
    >> gl
    >>
    >> --- On *Wed, 2/25/09, nsg21---.com //* wrote:
    >>
    >> From: nsg21---.com 
    >> Subject: [NavList 7427] Re: New compact backup CELNAV system
    >> To: NavList@fer3.com
    >> Date: Wednesday, February 25, 2009, 9:47 AM
    >>
    >> I would like to share some experience in using this (transparency over printed)
    >>
    >> style of the slide rule. The surface it is placed for calculation MUST
    >>  BE
    >>
    >> ABSOLUTELY flat. Even small warping of the surface (such as normally found on
    >>
    >> small plastic tables) leads to big errors in calculations.
    >>
    >>   
    >>
    >>   
    >>
    >>   
    >>
    >> From: glapook---NET
    >>
    >> Date: Tues, Feb 24 2009 12:06 pm
    >>
    >>     
    >>> There are often posts on the Navlist regarding using celestial as a backup
    >>>       
    >> to
    >>
    >>     
    >>> GPS and finding a simple way to do this. I think I have found a method
    >>>       
    >> that
    >>
    >>     
    >>> is simple, self contained, takes up little space, needs no almanac or
    >>>       
    >> sight
    >>
    >>     
    >>> reduction tables 
    >>>       
    >> ...
    >>
    >>   
    >>
    >>   
    >>
    >>   >
    >>   
    >>
    >>   
    >>
    >>   
    >>
    >>
    >>     
    >
    >
    > >
    >
    >   
    
    
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