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I know many people don't like doing complicated math, so I figured I'd share two formulas I made. One is for calculating how big of a tube you need in order to be able to put 3 smaller cylinders into it, and the other is for calculating the angle of a cone and other values about that cone based on the shape used to form it (a circle with a wedge removed).


I made 2 spreadsheets so that it's simple to enter the values and get the results.

For the 3-Cylinder Cluster spreadsheet, simply type the outside diameter (OD) of a cylinder into cell A2, and cell B2 will display the inner diameter (ID) of the smallest possible tube that 3 of the cylinders can be crammed into. Alternatively, you can enter the radius or circumference of a cylinder into A2, and B2 will show the necessary radius or circumference, respectively, of the tube into which you put the 3 cylinders.


For the Cone Formulas spreadsheet, enter the angle (in radians) of a slice removed from your starting circle into cell A3, and the radius of your starting circle into cell B3. In the visual diagram, A3=x and B3=r. Cell A7 will display the angle of half of the cone's peak (in radians), which is unaffected by the radius of the starting circle. In the visual diagram, this is ß. Cell B7 will display the circumference of the cone's base, which is c in the diagram. Cell C7 will display the radius of the cone's base (which is fairly easily calculated from its circumference, B7), which is a in the diagram. Cell D7 will display the vertical height of the cone, or h in the diagram. The length of the cone's horizontal slope is the same as the starting circle's radius, B3, or r in the diagram.

Degrees seem to be a more familiar and easier-to-visualize unit for most of us (myself included), so I made two conversion calculators. To convert radians to degrees, simply type the number of radians into cell M4, and cell N4 will display however many degrees the radians are equal to. To convert degrees to radians (for example, to change an angle measurement of the slice so that it can be inputted into A3), just type the number of degrees into cell M6, and cell N6 will display the equal number of radians.


In the zip folder I included 2 diagrams to help visualize these formulas. For those who don't always have internet access, I figured having these files could be useful. For those who have more reliable internet, but maybe don't have a lot of hard drive space, you can just delete the images and instead follow the imgur links provided in the spreadsheets.


Here's the link to download the files: http://www.amateurpyro.com/forums/files/file/112-cone-and-3-cylinder-cluster-equations/


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