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CONSTRUCTING BONGO DRUM SHELLS
(or...How to calculate the bevels of the staves for conical shells)
------------------------------------------------------------------------

For a simple cylindrical shell, the formula is just:
	
	a = 180/n

	where:
	n = number of sides
	a = bevel angle of stave

Since there are two bevels for each side (twice as many angles)

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For a conical shell, you can simply cut the items in a jig, like:
                     
    +------+                 
    |      |
    |      |         || 
    |      |         || 
    |      |         || blade
    |      |         || 
    |      |         || 
    |      |
    |      | <<<<<<<<<<<<
    |      |  <<<<<<<<<<<<
    |      |   <<<<<<<<<<<<
    |      |    <<< wood <<<
    |      |     <<<<<<<<<<<< 
    |      |      <<<<<<<<<<<<
    |      |       <<<<<<<<<<<<
    |      |
    |      |       determines angle of conical taper
    |      |         |    |
    |      |         v    |
    |      |              v
    |      +---------+ for
    |                | first 
    |                | cut
    |                +----+ for
    |          beveled -> | second 
    |             edge -> | cut
    |                     +----+
    |                          |
    |                          |
    |                          |
    +--------------------------+


And calculate the bevel angle similarly as:

    a = 180/n

The difference between the first and second cut is whatever was cut off.  The
bevel of the edge (for the second cut) should account for being butted up
against the first cut.  Might want to draw a line down the center to make sure
the angles cut with both are the same.

Slight correction of cut may be needed.


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ROUGH GRAPHIC OF STAVE (ANGLES a, b NOT TO SCALE)
------------------------------------------------------------------------

          top          top pressed against edge

                                  .  a  .
                                   .    .
                                    .   .
       ---------             ---------  .
      / .     . \           /  .      \ .
     / .       . \         /  .        \.
     -------------        --------------



         front                   side
                                  
    +-------------+                +---+
     |           |.               |   |.
     |           |.               |   |.
     |           |.               |   |.
     |           |.               |   |.
      |         | .              |   | .
      |         | .              |   | .
      |         | .              |   | .
      |         | .              |   | .
       |       |  .             |   |  .
       |       |  .             |   |  .
       |       |  .             |   |  .
       |       |  .             |   |  .
        |     |   .            |   |   .
        |     |   .            |   |   .
        |     |   .            |   |   .
        |     |   .            |   |   .
         +---+    .           +---+    .
                b                    b'

Angles b and b'are the same, since the top and bottom polygons will be in some
proportion, and all linear properties of them scaled up at the same proportion.

If you are curious of what the angle is, looking straight down at the top of
the stave, it is:

    tan(a') = tan(180/n) / cos(b)

To check the widths of the stave, let the following be known variables:

    width_top_outside    (width at top of stave, outside of the drum)
    width_bottom_outside (width at bottom of stave outside of the drum) 
    thickness            (thickness of stave) 

then:

    width_bottom_inside  = width_bottom_outside - thickness * tan(a')
    width_top_inside     = width_top_outside - thickness * tan(a')

Note that the top and bottom of the stave will be leveled to angle b as well,
so that it sits flat.


If you want to estimate the diameter of the drum, you can use:

    diameter = width * n / 3.14

Or alternately:

    width = diameter * 3.14 / n

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Copyleft Kevin Seifert 2008