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  • Need some quick math help

    What is the method ( if there is one) for figuring the radius of the circle below when all I have is the chord length (red line # 2 = 177inches) and the radius segment ( blue line #1 = 12 inches).

    (The blue line segment is on the radius even if my image shows it a little off.)

    My guess annd check method using some graph paper gets me 336 inches, but I'd like to be a little more confident.
    thanks
    Mark


  • #2
    Using the CSEG program available on my page, we have:

    CIRCULAR SEGMENT CALCULATIONS

    Input whatever data you know; press return if not known.
    You must enter two data items to obtain a solution.

    Radius of segment [0] ?
    Segment included angle [0 deg] ?
    Chord of segment [0] ? 177
    Height of segment (sagitta) [0] ? 12

    Radius = 332.3438
    Angle = 30.8873 deg
    Chord = 177.0000
    Height (sagitta) = 12.0000
    Arc Length = 179.1616
    Area = 1421.1932
    Regards, Marv

    Home Shop Freeware - Tools for People Who Build Things
    http://www.myvirtualnetwork.com/mklotz

    Location: LA, CA, USA

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    • #3
      According to my CAD program, r = 332.3+", but there must be a formula....
      ----------
      Try to make a living, not a killing. -- Utah Phillips
      Don't believe everything you know. -- Bumper sticker
      Everybody is ignorant, only on different subjects. -- Will Rogers
      There are lots of people who mistake their imagination for their memory. - Josh Billings
      Law of Logical Argument - Anything is possible if you don't know what you are talking about.
      Don't own anything you have to feed or paint. - Hood River Blackie

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      • #4
        The formula is:

        radius=(4.*height*height+chord*chord)/(8.*height);

        where:

        height = sagitta = 12 for this case
        chord = 177 for this case

        The derivation of this formula is left as an exercise for the student :-)
        
        Regards, Marv

        Home Shop Freeware - Tools for People Who Build Things
        http://www.myvirtualnetwork.com/mklotz

        Location: LA, CA, USA

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        • #5
          Here's a handy page of circle math:

          http://www.1728.com/circpart.htm

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          • #6
            Radius of Arc

            Let R= the radius your looking for
            C=straight distance between the ends of the arc
            h= height at the center of the arc

            The radius is given by:
            R=(C^2/ (8*h))+(h/2)

            I believe this is what you want.
            Chuck

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            • #7
              Thanks!

              Exactly what I needed.
              Mark

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