Gary:
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.
Regards
--- 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@navlist.net 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:
http://www.navlist.net/img/107501.f2-lapook1.pdf
http://www.navlist.net/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 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.
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.navlist.net/m2.aspx?i=106329&y=200809
Links to the scales:
http://www.navlist.net/img/107473.lapook2.pdf
http://www.navlist.net/img/107473.lapook1.pdf
http://www.navlist.net/img/108719.revised%20form%206-18-09.pdf
http://www.navlist.net/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 /<gregrudzinski@yahoo.com>/* wrote:
From: Greg Rudzinski <gregrudzinski@yahoo.com> Subject: [NavList 8924] Re: Manufacture new Bygraves? To: "NavList" <NavList@navlist.net> 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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