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    Re: Follow-up to Jared's post, Re: levels
    From: Brooke Clarke
    Date: 2003 Jul 15, 10:42 -0700

    A surveyor's hand level, when used with the bubble on the top has a sensivity of about 1 degree for the bubble to travel end to end, which is about 1/2" or a sensivity of about 4 arc minutes per millimeter.  If the level is turned up side down the bubble wants to go to either end indicating that the level vial is bent.

    Some surveying instruments, like the K&E 76 0000 alidade, Zeiss Ni 2 level, and many others,  have an optical system consisting of suspended prisms that automatically level the line of sight.  I would think it would be possible to design a sextant that would only require that that the instrument was held within say 1 degree of level and the rest of the leveling would be automatic.

    Have Fun,

    Brooke Clarke

    Marvin Sebourn wrote:
    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, jared.sherman---.net writes:

    Jared - I placed a couple of comments on the operation and construction of spirit levels within your interesting post.

    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 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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