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Math Help - Distortion and Curvature

  1. #1
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    Distortion and Curvature

    I am trying to work out a formula for use on sails for boats. This is a complex art and is usually done at great expense by use of a CAD package to make life simple.

    What i am looking for is a little hard to explain, so i will simplify as much as possible.

    2 pieces of cloth are to be joined together. They are both square pieces with the same length sides. they will be joined square end to square end.

    On the lower piece of cloth, a curve is drawn. This is an arc with apex touching the centre of this top side of the cloth. This curve is cut out to give 3 square sides and one bulging side.

    This curve is then laid over the top piece of unaltered cloth and stuck in such a way that the curve is attached parallel to the straight edge of the top piec of cloth.

    This forces shape into the 2 pieces that are now one.

    I would like to know if there is a way of working out the relationship between the flat curve and the 3D outcome.

    I say this because if a curve is drawn that is 10% of the distance across that panel, in 3D it will become a much greater depth of curve (perhaps something like 30% depth of the distance between edges of the cloth.

    Cheers
    Chris
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  2. #2
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    Quote Originally Posted by ctgould1 View Post
    What i am looking for is a little hard to explain, so i will simplify as much as possible.
    I'm sorry but I really don't understand your explanations... could you provide a sketch of what the pieces look like? (simply made with mspaint for instance)
    As far as I understand, you have one square, and another square that you have cut so that it looks like a half-square + a half-disc, is that it? And then you glue them together, but I don't get how...
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  3. #3
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    does this help?

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  4. #4
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    Quote Originally Posted by ctgould1 View Post
    I think I finally get it (from ), but the problem is that the shape you get may depend on properties of the fabric. Indeed, in order to stick the curved side to the straight side "exactly" (i.e. edge to edge, without gap or bubble/fold), the sheets have to be perpendicular to each other... The reason why they aren't so is because the seam (or rather the tape) is not just along a line but has a one-centimeter width, say, hence the rigidity of the fabric prevents it from making a 90 angle. I think you'll have to stick to CAD or trial-and-error technique...
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  5. #5
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    hmm, you can get the seams to be at 90 degrees , thats the easy bit. It just gives a distortion when laid flat but a 3D form when held up
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  6. #6
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    Quote Originally Posted by ctgould1 View Post
    hmm, you can get the seams to be at 90 degrees , thats the easy bit. It just gives a distortion when laid flat but a 3D form when held up
    Fine. Then I don't know what it is that you wanted to know: the 3D form is made of the curved piece (which is flat), perpendicular to the other straight one (which is shaped like a portion of cylinder) along the curve. After stretching/folding the fabric, other shapes are possible but uneasily computable.
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