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One of the advantages of making the cosine scale tube and the cursor 
tube out of plastic sheets is that these sheets are so thin that this 
eliminates the parallax problem reading the scales.

gl



Gary LaPook wrote:
> 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:
>
> http://www.fer3.com/arc/img/107501.f2-lapook1.pdf
>
> http://www.fer3.com/arc/img/107501.f2-lapook2.pdf
>
> 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.
>
> gl
>
>
> 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 89� 
>> 15' I took its tan,  76.39, divided by 10, 7.639, and took the arc tan 
>> of that giving me 82� 32'. I used the mark for that value (visually 
>> interpolating) and with the use of a t-square I placed the mark for 89� 
>> 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.
>>
>>
>>
>>
>> gl
>>
>>
>>
>>
>> gl
>>
>>   
>>
>>
>>
>>
>> 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:
>>>
>>> http://www.fer3.com/arc/m2.aspx?i=106329&y=200809
>>>
>>> Links to the scales:
>>>
>>> http://www.fer3.com/arc/img/107473.lapook2.pdf
>>>
>>> http://www.fer3.com/arc/img/107473.lapook1.pdf
>>>
>>> http://www.fer3.com/arc/img/108719.revised%20form%206-18-09.pdf
>>>
>>> http://www.fer3.com/arc/img/107419.bygrave-manual.pdf
>>>
>>> I picture of one made by Geoffrey Kolb:
>>>
>>> http://www.pisces-press.com/graphics/Bygrave.jpg
>>>
>>>
>>>
>>> Try it.
>>>
>>> gl
>>>
>>>
>>>
>>> Hanno Ix wrote:
>>>   
>>>> Hello:
>>>>
>>>> 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 
>>>> whatsoever.
>>>>
>>>> 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 //* wrote:
>>>>
>>>>
>>>>     From: Greg Rudzinski 
>>>>     Subject: [NavList 8924] Re: Manufacture new Bygraves?
>>>>     To: "NavList" 
>>>>     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, >>>     > 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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>


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