# Calculating Bevel



## RockerBug17 (Jul 19, 2010)

Hello. I am building a stave drum (same method used for making barrels) and want to double check my math. The drum will be 24 staves, each 2 inches wide. I came up with a bevel of 7.5 degrees. I need my finished product to have an outside diameter of 13.75 inches but don't quite understand how the calculated bevel takes diameter into account?

This is my first time making a drum and I've got a limited quantity of wood to use (Eastern Red Cedar I processed into boards). I want to make sure I've got my math perfect before I proceed with cutting.

Here are the directions I've been using.

Thank you.


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## TomC (Oct 27, 2008)

Go to Charles Neil web site. Look at the vedio for making a bucket. It will cover all you questions such as angle to cut and width of staves.
Tom


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## Gene Howe (Feb 28, 2009)

It's a lot of work, but I'd make a mock up of pine or poplar, first.


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## amckenzie4 (Apr 29, 2010)

Ok, there are two different pieces here. I had to read the page through a few times, but I think I've got it right now. Before I start, though, a warning: please don't trust my math. Check it yourself. I'm good with concepts, but I constantly hit the wrong keys on calculators.

1) Finding the bevel angle. The bevel angle has nothing to do with the diameter, although it seems like it should. The bevel angle is purely a function of the number of staves: the combined angles of all the joints must always add up to 360 degrees in order to have a complete circle. So, broken down: Bevel of board 1 + Bevel of board 2 = 360 degrees / number of boards. Since the bevel on each board is the same, you can reduce that to 2 x bevel = 360 / number of boards, or bevel = 360 divided by the number of boards divided by two. In your case, that's:

Bevel = 360 / 24 / 2 = 7.5 degrees, as you thought.

The thing is, that holds true no matter how wide the staves are. If the staves are 1" wide, 2" wide, or a mile wide, the bevel will be the same. The width of the staves is what changes how big the circle is (see footnote 1). That brings us to part 2:

2) Finding the board width. The formula they give is the diameter times pi (3.14159, approximately), divided by the number of boards, with a fudge factor for putting the thing on the lathe. This is just the standard formula for finding the circumference of a circle (C = 2 * pi * radius), with additions to chop it up into segments. You know the diameter, so you can just plug it in:

Width = (3.14159 * 13.75) / #boards = 43.19/#boards (more or less).

You want 24 boards, so Width = 43.19/24 = 1.8. Then round up to the nearest eighth (1/8, converted to a decimal number, is .125): each board should be 1.875 inches wide at the outside.

Footnote: If you're having trouble with the idea that the bevel doesn't affect the circumference, try it with easier shapes: a triangle and a square. A square is easy: all the angles are always 90 degrees, no matter how big it is. For a triangle, it doesn't matter what any given angle is, as long as the angles of all three sides always add up to 90 degrees, and each angle has to be greater than 0 degrees. If you want a REALLY FLAT triangle, they could be 88, 1, and 1. Again, what changes the size is how long the sides are, not how big or small the angles are.


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## TomC (Oct 27, 2008)

Footnote: If you're having trouble with the idea that the bevel doesn't affect the circumference, try it with easier shapes: a triangle and a square. A square is easy: all the angles are always 90 degrees, no matter how big it is. For a triangle, it doesn't matter what any given angle is, as long as the angles of all three sides always add up to 90 degrees, and each angle has to be greater than 0 degrees. If you want a REALLY FLAT triangle, they could be 88, 1, and 1. Again, what changes the size is how long the sides are, not how big or small the angles are.[/quote]

I believe the 3 angles in a triangle have to add up to 180 degrees.
Agree with everything else.


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## rrbrown (Feb 15, 2009)

TomC said:


> Footnote: If you're having trouble with the idea that the bevel doesn't affect the circumference, try it with easier shapes: a triangle and a square. A square is easy: all the angles are always 90 degrees, no matter how big it is. For a triangle, it doesn't matter what any given angle is, as long as the angles of all three sides always add up to 90 degrees, and each angle has to be greater than 0 degrees. If you want a REALLY FLAT triangle, they could be 88, 1, and 1. Again, what changes the size is how long the sides are, not how big or small the angles are.


I believe the 3 angles in a triangle have to add up to 180 degrees.
Agree with everything else.[/quote]

I second that.


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## Willie T (Feb 1, 2009)

Don't ya just hate it when that happens?


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## TomC (Oct 27, 2008)

I guess I started this so I will take the step to stop it. The number of degrees in a triangle has nothing to do with the question asked. If we want to talk more on this lets start a new post. I apologize for getting this thread off track. Sorry
Tom


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## TexasTimbers (Oct 17, 2006)

For a 14" shell (13.875 finished) you need 20 (not 24) staves 2.2" wide, each with a bevel of 9.0 °.




.


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## TomC (Oct 27, 2008)

TexasTimbers said:


> For a 14" shell (13.875 finished) you need 20 (not 24) staves 2.2" wide, each with a bevel of 9.0 °.
> 
> 
> You can make a 14" shell using 20, 24, 32 or whatever. The variable is the angle and width of the staves. One advantage of using 24 is this angle can be cut on a router table with an easy to find router bit. Just make sure when routing you don't decrease the width of the outside of the stave. Again Charles Neil has a great online vedio (free) that covers this.
> ...


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## amckenzie4 (Apr 29, 2010)

TomC said:


> Footnote: If you're having trouble with the idea that the bevel doesn't affect the circumference, try it with easier shapes: a triangle and a square. A square is easy: all the angles are always 90 degrees, no matter how big it is. For a triangle, it doesn't matter what any given angle is, as long as the angles of all three sides always add up to 90 degrees, and each angle has to be greater than 0 degrees. If you want a REALLY FLAT triangle, they could be 88, 1, and 1. Again, what changes the size is how long the sides are, not how big or small the angles are.


I believe the 3 angles in a triangle have to add up to 180 degrees.
Agree with everything else.[/QUOTE]


Well, yes. I told you not to trust my numbers! (Or something like that!)


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## TexasTimbers (Oct 17, 2006)

TomC said:


> You can make a 14" shell using 20, 24, 32 or whatever. The variable is the angle and width of the staves.
> .


I'm aware of that (took for granted it would be obvious from my answer). But I was answering it from the perspective of a drummer more so than a woodworker. Ask any experienced drummer and he'll say the fewer staves the better for tonal quality. And the fewer glue lines the better. So really a 24 stave shell has no advantages over a 20 - from a drummers perspective.


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## RockerBug17 (Jul 19, 2010)

TexasTimbers said:


> I'm aware of that (took for granted it would be obvious from my answer). But I was answering it from the perspective of a drummer more so than a woodworker. Ask any experienced drummer and he'll say the fewer staves the better for tonal quality. And the fewer glue lines the better. So really a 24 stave shell has no advantages over a 20 - from a drummers perspective.


Actually, I am doing all this to put drummer ears to the test!

WARNING! MUSIC JARGON AHEAD.

This all came about when my grandmother removed a cedar poll from here yard. Of course being a drummer I had to hit it! That later escalated into "Gee, I wonder what a cedar snare drum would sound like?" So, I was able to get enough wood out of the poll to make a 24 stave drum.

I've also always been skeptical of guitarist and drummers, in particular, and the CLAIMED influence specific woods have on their overall sound. I for one think an electric guitar's wood is irrelevant in the sound because of it's restricted resonance. I apply the same theory to conventional plywood drums. With all the glue and mounted hardware restricting the drum shell from resonating how can a $1000 set of maple drums and a $300 basswood set be that different? They both are so restricted from resonating that the drum head selection plays more of a roll (PUN!) in overall sound than the actual shell.

So, I decided to put it to the test. My cedar drum is just out of pure curiosity but my next shells will not be. I plan to make stave snare shells of maple, birch and mahogany, all equal in weight, thickness, diameter and depth. I have even gone as far as making my own free-floating tensioning system so that the drum heads will not change in pitch! I feel this will give the clearest idea of what each wood sounds like.

And, like all good things, I am going to put it on YouTube! Sound samples of all three drums to be polled by drummers. Once I collect enough data I'll reveal it to the masses.

Or at least, that's the plan at the moment!:yes:


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## TexasTimbers (Oct 17, 2006)

You can be "skeptical" all you want, just remember you can bend the laws of physics sometimes but you can never break them. Cedar will never give the tonal qualities of say Birch, Mahogany, or Maple no matter the type of shell construction you use. We're talking drums here not guitar bodies - there's a huge difference you can't lump them together. 

Stave construction has ~ 0.01% the glue surface of ply construction, but I would wager the farm you'll never get the power and projection out of a cedar stave shell that you would a Maple ply shell. Because the characteristics inherent in the wood do matter that much regardless of your doubts about it.

You aren't going to reinvent the wheel, but tinker all you want, that's best way to learn and even make new discoveries on occasion. Go for it.


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## amckenzie4 (Apr 29, 2010)

Should be interesting! Different woods definitely have different densities, which could affect tone, but I'm not aware of a truly scientific test of it. Certainly all the musicians I know say it makes a difference, but it'll be interesting to hear the tests.


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## RockerBug17 (Jul 19, 2010)

amckenzie4 said:


> Should be interesting! Different woods definitely have different densities, which could affect tone, but I'm not aware of a truly scientific test of it. Certainly all the musicians I know say it makes a difference, but it'll be interesting to hear the tests.


This is more in line with what I meant. I'm not trying to make a cedar drum sound like X wood.

What I'm trying to do is test the psychoacoustics of drums. Or, in layman's terms, I don't think a lot of drummers could accurately identify DRUM X, Y or Z based solely on sound. That's why I'm going to such length to make the drum shell the only factor in this test.


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## dvalery20 (Jan 27, 2011)

I will have to disagree with that, though your right, most drummers probably couldn't tell, but if you play an oak drum compared to a maple drum, you'll find that the oak drum sounds louder... Not because your hitting it harder but because of how oak affects the actual sound wave, it sounds bright, aggressive and obnoxious as to where maple has a warm but pronounced tone, not bright and not muffled, I'd be more interested in finding the Hz range on what different kinds of woods would create. Let me know how your progress goes with this though, I am interested.
Also it's kind of late, I'm kind of tired so I might have read your comment wrong, so sorry for my rant if it isn't coherent with your comment, haha


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