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Math Help - 3D Trig - Two 45 Deg Elbow At Differing Hts

  1. #1
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    3D Trig - Two 45 Deg Elbow At Differing Hts

    I have attached two images showing my problem.

    I have two pipes, each with a 45 Deg elbow.
    >The pipes are at different heights (H).
    > The Pipes do not slope.
    >The height of the pipes is known and the angle between the pipes is known.
    >The elbows can be positioned anywhere along the pipe centre lines.
    >The elbows can also be swivelled 360 deg around the pipe centre lines.

    Q) From my attached images, how do I calculate distances 'L' and 'W'?
    Attached Thumbnails Attached Thumbnails 3D Trig - Two 45 Deg Elbow At Differing Hts-3d-trig-view-1.jpg   3D Trig - Two 45 Deg Elbow At Differing Hts-3d-trig-view-2.jpg  
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  2. #2
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    Quote Originally Posted by Hugh_Compton View Post
    I have attached two images showing my problem.

    I have two pipes, each with a 45 Deg elbow.
    >The pipes are at different heights (H).
    > The Pipes do not slope.
    >The height of the pipes is known and the angle between the pipes is known.
    >The elbows can be positioned anywhere along the pipe centre lines.
    >The elbows can also be swivelled 360 deg around the pipe centre lines.

    Q) From my attached images, how do I calculate distances 'L' and 'W'?
    The drawing states "non level changing pipe" but you state "the pipes do not slope" -- that implies level.

    More specific data is required: a point in the centerline of the Pipe1 with a vector of the centerline of Pipe2, and point in the centerline of the Pipe2 with a vector of the centerline of Pipe2.

    If appears that either pipe may be cut at any point. If you specific an exact terminal point for either pipe, then the solution has a restricted value.

    If you supply the coordinates (x,y,z) for the end of the pipe that is not be be cut and a vector for that pipe,
    and you supply coordinates for a point in the centerline of the pipe is is allow to be cut and also give a vector for the centerline,
    then a solution can be given.

    In the placement of pipes in a treatment plant, these types of problems are routinely solved.

    Can you supply additional information?
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  3. #3
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    3D Trig

    Hi Aiden

    Thanks for having a look at the problem.

    Each individual pipe (Pipe 1 and Pipe 2) do not change level. This means the start point and end point of each pipe has the same level. The two pipes are at different heights - this is shown as 'H' on the second image.

    The vectors for the pipes are 'Free' vectors since I don't know the termination points. The vectors can be determined from the known Angle between the pipes. I'm not sure how to work out the vectors.

    Both pipes will need to be cut and there is only one value for L & W that will enable a straight piece of pipe to be added between the elbows. I can't tell you either L or W as I don't know how to work them out

    I design commercial water features and this is a very common problem for me. I usually work it out by trial and error but this takes me time. I would like a formula / procedure to work out 'L' and 'W' so that I can put it into a .Net routine which will position the elbows in my CAD system. If it can be solved on here then I'll be happy to post the solution on my website: http://www.3DCADMax.com
    Last edited by Hugh_Compton; May 26th 2009 at 02:22 AM.
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