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    Re: FW: Plexiglass horizon
    From: Jared Sherman
    Date: 2003 Jul 15, 05:40 -0400

     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.
     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, 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.
     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.) 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! 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 

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