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    Re: Manufacture new Bygraves?
    From: Hanno Ix
    Date: 2009 Jul 5, 20:46 -0700


    This is, no doubt, very fine work and beautiful to behold!

    However, am I right in the conclusion that it will not regularly give you an error of less than 5 sm? Or even less than 10 sm?

    I suppose you did perform tests. Can you tell us what the results were? What were the error mechanisms due to limited acc/res of the scales, and due to mechanical reasons?

    What were the navigational situations of the smallest and of the biggest errors?

    You have indeed raised the general interest in this instrument.


    --- On Sat, 7/4/09, Gary LaPook <glapook@pacbell.net> wrote:

    From: Gary LaPook <glapook@pacbell.net>
    Subject: [NavList 8949] Re: Manufacture new Bygraves?
    To: NavList@fer3.com
    Date: Saturday, July 4, 2009, 1:59 PM

    I need to correct the links to the scales for the flat Bygrave, also usable for making a cylindrical Bygrave. The links I had provided were for earlier versions of the scales and the final version corrected some minor issues , using ' instead of " for minutes. So you should download the following pdf files instead:



    I believe the original Bygrave was made with a printed scale glued to the tubes much like the Otis King slide rules. My method of making a working model uses the same method except the scale is held on by the clear plastic adhesive protector sheet. This sheet also protects the scales.

    You can make adjustments with your printer to get the scales to print out to the correct size to fit around the tube you are using. For the base tube I used a 1-1/2 inch sink drain pipe (I think it is called a "tail piece")  12 inches long, about four bucks at any Home Depot or Do-It Center. Print out the tan/cotan scale and cut it about in half to allow some overlap. Wrap it around the tube, twisting it slightly to get the spirals to line up. After doing this the first time you may you may have to make a slight change to the printer controls to get it to the exact right size, cut and try.

    You will need to buy a package of ten "Scotch Self-Sealing Pouches" for about thirteen bucks. These consist of two pieces of plastic one of wich is coated with adhesive, covered with a protective sheet. Cut one of the sticky sheets to overlap the tan/cotan scale. Carefully wrap that scale around the tube and, starting near where the scale overlaps (to hold the joint together), carefully wrap the sticky sheet around it with the overlap at the top and bottom holding everything on to the tube. You might have to start over if it gets stuck in the wrong position but you can, sometimes, peal the plastic back up if necessary to reposition.

    Now comes the trickiest part, making the cosine/secant scale. This is made with two of the sticky sheets with the scale sandwiched between. Cut the plastic sheet as before but make a large overlap on the bottom so that it will extend below the cursor tube so that you will be able to move it with the cursor all the way down to the zero mark on the cosine scale. When you print out the cosine scale, and try it on for size around the tan scale, make sure you allow a little bit for the plastic sheet that will be underneath the cosine scale. Now place one of the sticky sheets, sticky side out,  and the cosine scale around the tube and and carefully line up the scale. Wrap it tightly enough so that friction will hold it in place and not too tight so that it can be rotated.  But, before you do this, consider the overlap of the plastic sheet already set on top of the cotan scale. You want the overlap on the plastic sheet under the cosine scale to be positioned so that it will not hang up on the slight ridge of the the underlying overlap. If you don't allow for this the two overlaps will act like a ratchet or a set of pawls and prevent your rotating the cosine scale in both directions. The next step is to place the second sticky sheet over the cosine scale which is relatively easy to do.

    The third step, and the easiest, is to form a clear plastic tube to carry the cursor. I drew a line on a piece of paper and copied it onto a plastic transparency sheet using my ink jet printer. On earlier versions I just drew the two indexes with a marker, their alignment is not critical. Form this into a tube to wrap around the cosine scale and use tape to hold its shape or a piece of one of the sticky sheets. The length of this tube must be slightly more than the height of the cosine scale since it must be able to reach from the zero mark on the cosine scale to extend past the top of that scale so that it points onto the cotan scale.

    There are some frustrating points in this process and the flat version is much easier to make but the cylindrical version is easier to use.


    Gary LaPook wrote:

    Here are some pictures of the Bygrave replica I am using. The first 
    picture, 2891, shows the co-tan scale. When printed the scale only had
    tick marks every 10 minutes and I added some 5 minute marks near each
    end of the scale. I used the periodicity of the scale to figure out
    where to place these tick marks. For example, to place the mark for 89º
    15' I took its tan, 76.39, divided by 10, 7.639, and took the arc tan
    of that giving me 82º 32'. I used the mark for that value (visually
    interpolating) and with the use of a t-square I placed the mark for 89º
    15' directly above it. I also hand labeled a number of tick marks to make
    it easier to find the value I was looking for.
    Picture 8292 shows the scale along side of the 12 inch drain pipe that I
    mounted the scale on.
    Pictures 8297 and 98 shows all three components, the tube with the
    co-tan scale mounted and covered in clear plastic sheet; the cosine
    scale sealed between two sheets of plastic formed into a tube and the
    sheet of plastic formed into a tube and marked as the cursor.



    Gary LaPook wrote:
    I have had great success with printing the scales of the flat Bygrave 
    and wrapping them around a tube and sealing them in place with clear
    adhesive plastic sheets.

    Here are some pictures of one example:


    Links to the scales:





    I picture of one made by Geoffrey Kolb:


    Try it.


    Hanno Ix wrote:

    I agree. Bygraves could be build.

    However, there are some cumbersome questions, the most obvious being,
    How to generate a drum-shaped scales with the required accuracy and
    resolution. Remember, we will have to maintain sub-millimeter acc/res
    over many turns, with "many" meaning perhaps 20 to 50. This should be
    possible, but is still not easy.

    If someone could generate the mechanical construction and quality
    assurance methods for this challenge we could talk about manufacturing
    more seriously. Her are my ideas:

    Personally, I am thinking of an ink-jet head printing on a turning
    drum where the printing is synchronised with a digital encoder on the
    drum' s axis. The process control could be handled by one of the
    relatively simple contollers on the market.

    Another approach would be to replace the ink-jet printing with an
    engraving system.
    With the first I personally have experience, with the second none

    However, more problems lurk. What are the limits for excentricity of
    the drums when in use? How about friction? How to stabilize the thing
    when under the influence of temparature changes, humidity, sun's UV,
    spray salt water, etc, etc.

    So, you can see that the conceptual simplicity of the Byraves is
    offset by many practical obstacles.

    Compare this, for instance, with the Ageton method (H.O. 211)! Only 12
    pages of a table, a sheet of paper and a pencil is virtually all you
    need to get a generally higher res/acc than with a practical Bygrave.

    Yes, you will also need the skill and concentration to exercise the HO
    211 calculations under virtually any condition at sea - particularly
    when you are a submarine commander at war. Well, I guess, in this case
    a Bygrave, well designed under a government contract, does make sense!

    --- On *Fri, 7/3/09, Greg Rudzinski /<gregrudzinski@yahoo.com>/* wrote:

    From: Greg Rudzinski <gregrudzinski@yahoo.com>
    Subject: [NavList 8924] Re: Manufacture new Bygraves?
    To: "NavList" <NavList@fer3.com>
    Date: Friday, July 3, 2009, 9:40 AM

    There must be a combination of PVC tubing that fits on itself snugly.
    If the white PVC were engraved with black and red scale markings as a
    regular plastic slide rule is then I think you would have something.

    On Jul 3, 12:18 am, <engin...@clear.net.nz
    </mc/compose?to=engin...@clear.net.nz>> wrote:
    > A few years ago, when I and a couple of friends wanted each to
    own a gear hobbing machine, we cooperated. One made the casting
    patterns and saw them through the local foundry, another did the
    heavy machining and I did the small parts like feedscrews and
    their nuts. It occurs to me that several handy people could
    combine their skills to produce replica Bygraves slide rules.
    There will surely be someone who knows where to access tubing in
    which each size nests snuggly in the next largest size, someone
    else will know how to produce hard-wearing replica scales, another
    may be prepared to turn the bobbins at each end and I would
    volunteer to do small bits of metalwork. The results do not have
    to make profits, though a little would be nice. Since there seem
    to be very few surviving Bygraves calculators, one could at least
    have the satisfaction of owning a replica. The starting point of
    course would have to be accurate, dimensioned drawings of an
    original, preferably following the metric system, so the
    manufacturing consortium would not have to be confined to the USA.
    > Any offers/takers?

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