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From: Marvin Sebourn (no email)
Date: Tue Jul 15 2003 - 09:56:13 EDT
Sorry if this is a duplicate, believe I sent to Jared instead of Nav-L.
In a message dated 7/15/2003 4:42:17 AM Central Standard Time,
writes:
Jared - I placed a couple of comments on the operation and construction of
spirit levels within your interesting post.
> Gentlemen...
> I'm afraid Bruce Stark's attraction to the black plexi and RIchard Pisko's
> mention of levels that are accurate within 20 seconds of tilt crawled under my
> brain and forced me to do some long thinking. Bear with me, this is either
> madness or fiendish elegance.<G>
>
> I realized first that I had no idea of how a spirit level (a simple tube
> with a bubble in it) works. Only one internet source mentioned accuracy of their
> level, in that case a circular design used for leveling silicon wafer
> fabrication equipment to 30 seconds of accuracy with no price mentioned. I assume
> that means "terribly dear".
>
> I suspect the readable accuracy of a spirit level tube is enmeshed in the
> flatness of the tube walls,
I believe that for a spirit level to function, the interior, upper,
fluid-holding bore of the level cannot be perfectly straight along its length. If it
were, when the device was moved off level, then all the fluid would move to the
lowest point in the tube, and the bubble go to the high end. This of course
disregards the properties of the liquid and the gas, but if the bore were
perfectly straight, and the tube was moved from level, why would the bubble
stabilize at a particular spot along the tube length?
I believe that the bore of the tube has to be slightly convex when viewed
from above the tube. This would afford a mechanism whereby the effects of gravity
on the fluid would equalize on both sides of the bubble, and the bubble
stabilize at a position along the length of the tube according to the tilt of the
level.
The more sensitive a spirit level is designed to be, would dictate a
lessening convexity of the tube over its length. Imagining a perfectly circular spirit
level tube as seen from the side (like an "O"), then it becomes obvious that
the larger the diameter of the circle, the smaller angular displacement the
circle must be displaced to accomplish a movement of the bubble a certain
distance on its circumferance. (The sensitivity of machinist spirit levels is often
measured or rated in XX second accuracy per grad (graduation), or so many
thousandths (or ten-thousandths) of an inch out of level per foot. The more
accurate levels have cross-vials to assure the main vial is placed in line with the
vertical). IF the surface tension of the liquid can be disregarded (and surely
in very accurate levels, low surface tension is highly desirable) and other
effects disregarded also, then the degree of convexity of the vial could be
determined by its sensitivity, that is, how far the bubble moved for a specified
angular displacement. Thinking again of a large circular tube aids me in
visualising this.
I admit the above is conjectural, and a sor-of thought experiment. (What is
the term used earlier here for that)?
the surface tension of the liquid (less being better), the density of the
gas bubble (less
> being better?) compared to the fluid, and the length of the tube and
> bubble, with a long tube and long bubble being more accurate for the same reasons
> that a "longer" base would make a ssiphon level more accurate. But without any
> certainty about this, I decided to pass up thinking about using 12" long
> glass chemistry tubing for spirit levels and did some rough calculations about a
> siphon level.
I have seen no visible tube length greater than roughly 3 or 4 inches, in
transits or machinist's levels. A longer vial would give greater range but would
introduce other effects: bulkiness, thermal sensitivity, difficulty of
achieving and maintaining an accurate tube shape over a long length, etc. In
positioning heavy machinery, rough leveling is done with a less sensitive level that
more easily shows the effects of gross preliminary adjustments toward making a
piece of machinery level (or sometimes off-level, as needed to allow for
thermal expansion). The base-length of machinist's levels does increase as
sensitivity increases. I think that Starrett's Precision Machinist Level is 12" long,
at least. It is stated to have 10 second accuracy.
Thanks again, Jared, for your thought-provoking post. I read it only
considering how spirit levels worked, and now I must return to the rest of your work!
Best to you & all,
Marvin
Marvin Sebourn
>
> That's the kind where you take a "U" of clear tubing, fil it with liquid,
> hold up the two ends and sight across them. As the water seeks its own level,
> the water line in each end will be at equal heights and sighting across them
> gives a level line between the two columns of water.
>
> So...for an accuracy of 20 seconds, 13 degree, I wanted a measurement that
> could be read easily with the eye and picked a convenient millimeter as being
> sufficiently precise, or crude, as you would have it. If you took a mark one
> millimeter wide to be 1/3 of a degree, you would need a circle with a
> circumference of 360x3, or 1180 millimeters, to simply mark the 1/3 degree intervals
> so you could sight across them and line two of them up equally. That would
> be a circle with approximately a 7.5" radius, i.e. 15" diameter.
>
> Now, if I haven't made too many wrong assumptions yet, that would indicate
> that taking a siphon level "around" the bottom half of a 15" diameter circle
> (held vertically) would allow one to sight across the middle of the circle,
> and assuming your eye could even up the two ends of the water column within
> that one millimeter of being even...You would have established a level line
> accurate to 20 seconds.
>
> I wrestled with how to apply this to a black plexi plate and think it can be
> translated somewhat simply and accurately.
> Suppose that we take a bar of 1" thick plexi, selected arbitrarily because
> we're already working with plexi and the flatness and eveness of the sides of
> the bar should be fairly good from the manufacturing process. (By all means,
> use Jacobsen blocks if you have them.<G>) Cut two 1" long pieces from the
> bar, keeping "this side up" the same for both of them in order to keep them even
> in case they are not perfectly made. You now have something like two 1"
> cubes of plexi. Glue the two cubes along the edge on top of a black plexiglass
> sheet, 15" apart from each other's centers. Use plexi cement so they weld
> properly.
>
> You know have a black plexi sheet with two "dice" glued on top of it, next
> to one edge. Now, drill a convenient 1/4" wide hole down the niddle of each
> cube, all the way through the plexi sheet. use a drill press to make it nicely
> vertical, although exactness will not cause great problems. Insert a 2" long
> piece of 1/4" wide glass tubing in each hole, so that it extends below the
> plexi, and above the cube, mainly above the cube.
>
> Connect the two bits of tubing with some hose (poly, rubber, whatever)
> beneath the plexi. Slowly fill the tubing with alcohol, perhaps with a bit of
> bright food coloring in it, until it is just level with the tops of the two
> cubes, or perhaps several millimeters above them. Stop. Connect the tops of the
> two tubes with another bit of tubing--they must be connected so the air can
> move and teh fluid can find its own level in the two columns.
>
> You should now have a siphon level with a 15" base, capable of resolving 20
> seconds or better of "level". Adding a scale to the columns, or choosing the
> fluid/plexi colors so as to increase contrast, all are icing on the cake.
>
> Construct a second such level along another side of the plexi, and you've
> now got a lack plexi sheet 15" square with two highly accurate levels fixed
> into it. Add screw legs below to adjust it, and I suspect you've got a
> fiendishly elegant artificial horizon.
>
> Problems, caveats, finessing: At 15", the plexi will have to be a bit
> thicker in order to avoid sagging. You may chose to brace it from below (i.e. by
> adding Sintra or other lighter weight rigid plastic) or use thicker plexi, and
> add plexi "beams" below it to stiffen it. And you could, of course, literally
> carve channels into the bottom of the plexi so no tubing was needed beneath
> it and the liquid was captive between two plexi sheets, in a channel.
>
> My numbers are rough and the accuracy and size you chose ill be your own
> compromise, but I think it should scale marvelously.
>
> If "spirit levels" can be accurately made by simply taking a 12" long glass
> tube, filling it mainly with spirits, and marking the distance from the ends
> (and a longer bubble being better, so you'd want to get an air bubble that
> nearly came to the ends?) then of course it could be even simpler.
>
> I confess, my mind is churned to butter from trying to figure out how spirit
> levels REALLY work, somehow we never learned the physics of them in school.
> Perhaps one of you could be so kind as to explain this to me.
>
> Bruce and company...if you're feeling really ambitious and you DO build one
> of these, and it DOES work...I'll expect you to send one to me as well!<G>
> And if you go into business making them, I'll expect a partnership, I could use
> a new job.
>
> If my thinking on all this is hopelessly wrong, or highly accurate
> commercial levels really can be found inexpensively...Well, it was good exercise
> anyway.<G>
>
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