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formula for determining angle between two known dimensions

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  • formula for determining angle between two known dimensions

    Math not being my strong suit, could anyone either point out where I can find the formula or tell me what it is please. I am turning down a piece of material to make a solid spacer for a suspension part and it would be certainly faster to set the angle once than to trial and error it. Thanks, Jim

  • #2
    Originally posted by jmm03 View Post
    Math not being my strong suit, could anyone either point out where I can find the formula or tell me what it is please. I am turning down a piece of material to make a solid spacer for a suspension part and it would be certainly faster to set the angle once than to trial and error it. Thanks, Jim
    Plenty of people here that can help you, but I think you may need to provide more information. Can you give, as best you can, a thorough description of the spacer you are making? Please include all the dimensions you currently have to work with, as that's what best describes a part.

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    • #3
      I’m ok with math/numbers but never had or studied trig or geometry. For the most part I can get by with available online calculators.

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      • #4
        I think he may be making a tapered cylinder and wants to know the half angle to set the compound.

        If D1 is the diameter of the large end and D2 the diameter of the small end and these two diameters are separated by a length 'L', then the included half angle is arctangent [(D1-D2) / (2*L) ]
        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
          Thanks guys, if I am reading mklotz's formula correctly do I need to consult the trig table in machinery's handbook to obtain the angle in degree's? (his description of what I am doing is correct) Jim

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          • #6
            Originally posted by jmm03 View Post
            Thanks guys, if I am reading mklotz's formula correctly do I need to consult the trig table in machinery's handbook to obtain the angle in degree's? (his description of what I am doing is correct) Jim
            Any machinist worth the name should have a scientific calculator in his toolbox and know how to use it.
            Regards, Marv

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

            Location: LA, CA, USA

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            • #7
              Originally posted by jmm03 View Post
              Thanks guys, if I am reading mklotz's formula correctly do I need to consult the trig table in machinery's handbook to obtain the angle in degree's? (his description of what I am doing is correct) Jim
              You could do it with trig tables, but as Marv K. notes this is a few seconds with a cheap scientific calculator. If you have a smartphone, you already have the calculator or can have one in a few seconds. Amazing world we live in these days.

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              • #8
                Draw a picture with known dimensions
                rest is easy, ish
                mark

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                • #9
                  Originally posted by jmm03 View Post
                  Thanks guys, if I am reading mklotz's formula correctly do I need to consult the trig table in machinery's handbook to obtain the angle in degree's? (his description of what I am doing is correct) Jim
                  mklotz's formula is correct, and yes, you will find the angle in the trig tables. Doing the calculation electronically you would return the arctan function of the number in the formula. To find the angle in the trig tables look in the Sine column. The Machinerys Handbook I have gives an example where the large diameter is 1.5" the small diameter is 1.0" and the distance is 5"
                  1.5- 1.0=.5
                  .5/ (2x5) = 0.0500
                  on a calculator: arctan .05 = 2.8624 degrees or 2 degrees 51 minutes 44.66 seconds
                  Looking down the sine column in the handbook 0.05001 is sine for 2 degrees 52 minutes

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                  • #10
                    If the specified length is the axial length, you need to use the tangent. If the specified length is the slope length (i.e., along the taper), use the sine tables.
                    For small angles, sine and tangent are almost but not quite the same figure, since the hypotenuse and the adjacent side of the triangle are almost the same length.

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                    • #11
                      Or just paste this into Google search box (with D1,D2, & L replaced with actual dimensions):
                      57.29 * arctangent [(D1-D2) / (2*L) ]

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                      • #12
                        Originally posted by Mike Burch View Post
                        If the specified length is the axial length, you need to use the tangent. If the specified length is the slope length (i.e., along the taper), use the sine tables.
                        For small angles, sine and tangent are almost but not quite the same figure, since the hypotenuse and the adjacent side of the triangle are almost the same length.
                        Yes. Thanks for the clarification.

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                        • #13
                          Originally posted by jmm03 View Post
                          Thanks guys, if I am reading mklotz's formula correctly do I need to consult the trig table in machinery's handbook to obtain the angle in degree's? (his description of what I am doing is correct) Jim
                          Not only can you easily download a full scientific calculator with trig functions for your phone but assuming you typed your post on a Windows operating system then you have a full scientific calculator included. Just bring up the calculator and up in the top left corner click on the three lines (Win 10) and all your options for calculating will appear as a list box.

                          Chilliwack BC, Canada

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                          • #14
                            Originally posted by BCRider View Post

                            Not only can you easily download a full scientific calculator with trig functions for your phone but assuming you typed your post on a Windows operating system then you have a full scientific calculator included. Just bring up the calculator and up in the top left corner click on the three lines (Win 10) and all your options for calculating will appear as a list box.
                            And, if you're really clever, you'll go here and download and install this excellent emulator of HP's HP35S...

                            https://www.educalc.net/2336231.page

                            It has some things that most of those built-in calculators don't have...

                            Switchable between RPN and algebraic mode (although I can't imagine why anyone would use the latter)

                            Is fully PROGRAMMABLE (just like the one HP sells)

                            The onscreen window looks just like the real calculator, so, using the emulator, will get you in shape for using the real thing, should you buy one (~$60).

                            Highly recommended!

                            Regards, Marv

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

                            Location: LA, CA, USA

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                            • #15
                              Originally posted by tom_d View Post

                              mklotz's formula is correct, and yes, you will find the angle in the trig tables. Doing the calculation electronically you would return the arctan function of the number in the formula. To find the angle in the trig tables look in the Sine column. The Machinerys Handbook I have gives an example where the large diameter is 1.5" the small diameter is 1.0" and the distance is 5"
                              1.5- 1.0=.5
                              .5/ (2x5) = 0.0500
                              on a calculator: arctan .05 = 2.8624 degrees or 2 degrees 51 minutes 44.66 seconds
                              Looking down the sine column in the handbook 0.05001 is sine for 2 degrees 52 minutes
                              "Doing the calculation electronically you would return the arctan function of the number in the formula"

                              Right!! Many ways to skin a ca.... JR


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