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Thread: Why is Math Lying to Me?

  1. #1

    Why is Math Lying to Me?

    I'm trying to recreate a light fixture that I saw in a restaurant a few weeks ago (see attached image). It is a round light made from vertical slats of wood. Each slat has an angle cut along the length so that when all the angles are brought together it completes the circle. I'm looking at making a 24" diameter light with slats around 1.5" wide. My math tells me that I will need 50 pieces at 1.5" with with a 3.6 degree angle on each side.

    Here's my math:
    Number of pieces: 24" circle has a circumference of 75.375", divide that by 50 to get 1.5"
    Angle: 360/50=7.2 degrees/2=3.6 degrees

    I cut all the pieces for a mock up tonight to check the math and it just flat out didn't work. I tried to do the assembly the same way I would a four sided box, by laying down a length of tape and laying each piece on the tape. After I had done had added all 50 pieces, I tried to roll it all up and found that I had way too may pieces and I wasn't able to actually complete the roll before pieces started falling off. I tried painters tape at first and then duct tape, neither was sticky enough. Either way, I know that something is wrong. If the math is right then something else is the problem. Tape to stretchy? Pieces not snuggly butting up to one another? ? ? ?

    I also used this website to confirm my math: http://www.woodturnersresource.com/e...alc/index.html
    IMG_4220.jpg

  2. #2
    Join Date
    Sep 2013
    Location
    El Dorado Hills, CA, USA
    Posts
    205
    How did you set your 3.6 degree angle to cut? One of the digital readouts on the table saw blade?

  3. #3
    With that many pieces any small deviation from the desired width and angle will add up and cause problems. If the angles add up to 360 you will have a faceted cylinder, if your widths are 1.5" the cylinder will be about 24" diameter. Work on precision in the milling process. A powerfeed or featherboards may be helpful. An accurate protractor will help, but the rollup will tell the real story.

    Clear packing tape works well for miterfolds. Make sure the pieces are free of dust and set precisely edge to edge with their ends cut square and butted against a straightedge. Burnish the tape onto the outside of the segments with a wood block and do a test. Adjust the angles if necessary and repeat. Alternatively you could glue up the segments in a semicircular cradle and then fit and glue the halves together.
    Last edited by Kevin Jenness; 07-25-2021 at 1:44 AM.

  4. #4
    Join Date
    Feb 2003
    Location
    McKean, PA
    Posts
    13,675
    Your math isn't lying to you, your precision is off. The length of each segment should be 1.507 inches long. However, if you make an error of 0.01 inches on all 50 pieces your circumference is off by half an inch, which won't work. You will need to cut your pieces slightly wide and trim them by hand until you get a near perfect fit to complete your circle or, just trim one or two pieces more than the others to make your circle go together albeit not a perfect circle. A good hand plane can trim off 0.001" at a time. Each piece doesn't have to be perfect, but the sum of the errors has to be awfully close to zero. No one will notice the slight differences in the width of each piece. This doesn't account for angle errors! A tenth of a degree times 100 angles is a 10 degree error.
    Lee Schierer
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  5. #5
    My process to cutting the pieces was to rip the plywood to length and then used a digital caliper to place a fence on my miter saw and used it as the stop to cut each piece the same. I used a magnetic digital angle finder to set the angle on the table saw and a scrap piece to set the fence in the right place so that I was getting the angle but not taking off any of the width.

    In hind sight I should have ripped the pieces to width first, cut the angle in them and then taken them to the miter saw and cut to length.

  6. #6
    Keep in mind that magnetic digital angle indicators like a wixey will in no way have the resolution for something like this. They will have nearly .5 degrees +/- possible error which as stated will crush you with that many segments. Extreme precision or leaving one single segment for final fit if possible will be critical.
    Sometimes I just want to look at pretty pictures,... Thats when I go to the Turners Forum

  7. #7
    I assume that you have tried gluing two halves then lay on flat surface and then sand both sides to fit, with that amount of cutting, even the saw and blade must be perfect, I don't understand way to meany pices, but I am just learning segmented woodturning.

  8. #8
    Join Date
    Jan 2010
    Location
    Tampa Bay, FL
    Posts
    2,739
    Can you just build a quick shooting board or donkey's ear to fine tune the slats until it's correct? You'd have to nail the angle on it, but once done, everything should come out the same.
    - When God closes a door, he opens a window. Our heating bill is outrageous & six raccoons got in last night. Please God, this has to stop!
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