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Math Mavens & Geometry Wizards Needed . . . .

Started by TexasTimbers, May 29, 2007, 10:18:59 AM

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TexasTimbers

I have selected the wood for my stave snare drum shell I want to build. I decided on a stave shell because the process to buils a multi-ply flate grain shell is more than I want to tackle. The math would be alot easier for sure, but the process would be more involved than a stave shell.

However, the math on a stave shell is way over my head. I don't even know how to guess at it. The drawing below gives a rough idea of what i am talking about. The staves will 6" long; you can't see that dimension this is an above view. The thickness I would like to have around a 1/2" starting thickness. The sides where they meet will remain at the starting thickness, but once the staves are all joined (biscuit or splined) the shell will have to be processed down to a 14" circle by hand. Unless I can talk Burlkraft into putting it on his lathe after it is built and turning it down for me.  ;D It has to be real close to 14" and real close to perfectly round in order to take a round drum head.

So that's what I gotta do. I need to figure out how many staves (I think somewhere between 12 and 20 would be optimum) I need, at what angles, that will just fit inside an imaginary 14" circle (or be a hair larger) that I need. Well, that's not what *I* gotta do; it what I gotta find someone to do for me. That's not asking too much is it ???

This is a real rough drawing but it should give you an idea of what I have to do to build the shell.

The oil is all in Texas, but the dipsticks are in D.C.

Radar67

Your cut angle for 16 pieces would be 22.5°. To get your lengths, find the circumfrence of 14" and divide by 16. That will give you the long points of your cuts. Should be roughly 2.75 inches each.

Stew
"A man's time is the most valuable gift he can give another." TOM

If he can cling to his Blackberry, I can cling to my guns... Me

This will kill you, that will kill you, heck...life will kill you, but you got to live it!

"The man who can comprehend the why, can create the how." SFC J

TexasTimbers

Okay now tell me how you did that Math Maestro!

And did you figure it so the staves will "fill up" the imaginary circle and not so any of the circle would be outside the staves?
The oil is all in Texas, but the dipsticks are in D.C.

Radar67

To start with, I divided 360 (the number of degrees in a circle) by 16 (the number of pieces) to get the 22.5°. Then I went to Calc Menu to figure the circumference of a 14 inch diameter circle, which came out to 43.98. I divided that by 16 (the number of pieces) to come up with 2.74875. I rounded that up to 2.75.

This measurement should get the points of the staves to just a hair over 14 inches. You can extend the length of the staves to get the flat parts out to 14 inches and the angles will not change. If you extend the length, also consider making the stave thicker to keep the inside dimension where you want it.

I learned to do this when my interest in segmented bowls peaked.

Stew
"A man's time is the most valuable gift he can give another." TOM

If he can cling to his Blackberry, I can cling to my guns... Me

This will kill you, that will kill you, heck...life will kill you, but you got to live it!

"The man who can comprehend the why, can create the how." SFC J

TexasTimbers

Man that was very helpful. I can tweak the numbers fom here and get what I want. When you say length I know you mean width.

Many thanks. You've made the hardest part easy for me! :)
The oil is all in Texas, but the dipsticks are in D.C.

beenthere

Quote from: kevjay on May 29, 2007, 11:26:52 AM
.............When you say length I know you mean width.
.................

Original message:
QuoteThe staves will 6" long.

And that is what you meant too ??    ;D ;D ;D
south central Wisconsin
It may be that my sole purpose in life is simply to serve as a warning to others

TexasTimbers

yes when I said "6" long" I meant "6" long" because I was giving length info. When Stew said
Quote from: Radar67 on May 29, 2007, 11:18:51 AMYou can extend the length of the staves . . . .
he meant width of the staves. I knew what he meant.

Let me know if I can clear up anything else for you.
The oil is all in Texas, but the dipsticks are in D.C.

Radar67

I'll clear it up even better...I said length in place of width because you usually think of the length of something between long points.  ;)

Stew
"A man's time is the most valuable gift he can give another." TOM

If he can cling to his Blackberry, I can cling to my guns... Me

This will kill you, that will kill you, heck...life will kill you, but you got to live it!

"The man who can comprehend the why, can create the how." SFC J

TexasTimbers

True, and the long points are not between the angled sides which you can see but from bottom to top (which can't be see in my top view drawing).

It probably looks that way in the drawing so I can see how bt thought he nailed me on a faux pas. That's usually pretty easy to do with me so I don't see the sport in it really. ;D
The oil is all in Texas, but the dipsticks are in D.C.

Don P

You got the total angle of the joint by dividing 360* by 16 = 22.5*. that could be a square edge meeting a 22.5* or bisect the 22.5* angle to 11.25*  ;)

Larry

To turn the project into child play you might want to consider doing a bird's mouth joint.  Lot of places are selling the router bits anymore and include instructions.  First one off the top of my head from Lee Valley.

http://www.leevalley.com/wood/page.aspx?c=2&cat=1,46168,46174,45160&p=45160

No experience using the router bits but I have made quite a few cylinders and one boat mast on the shaper with home grown tooling. 
Larry, making useful and beautiful things out of the most environmental friendly material on the planet.

We need to insure our customers understand the importance of our craft.

TexasTimbers

I like the possibilities presented by that bit. I was not familiar with it. I don't know that it would offer a stronger joint than a full length spline joint though. It would be one less step though, if not two or three counting having to make the splines as well.
The oil is all in Texas, but the dipsticks are in D.C.

Gary_C

Don P is right. the angle on each side of that board will be 11.25 degrees.

Also the width of each piece needs to be 2.7713 to get the minimum diameter at 14 inches at the center of each board. Then in order to get it round you would need to take off  0.1414 at each of the corners to make it round. If you start with 0.500 thick boards you will have just 0.3586 thickness remaining at your joints.

All that is assuming you assemble it perfectly.   ;D
Never take life seriously. Nobody gets out alive anyway.

TexasTimbers

Perfect assembly huh. Well I have a better chance at that than figuring out the math. ;D Thanks for the exactness. I will fudge a little on the thickness just in case I have to take off a little extra for any um, imperfect boards. ;)
The oil is all in Texas, but the dipsticks are in D.C.

metalspinner

Discovery Channel's "How It's Made" had a segment on this type of drum.  It was a fun episode to watch.

As Stew alluded, segmented turner's use this type of figuring all the time.  The following book has plenty of formulas and charts to help determine the angles and thicknesses neccesary for this type of construction.

http://www.amazon.com/Segmented-Wood-Turning-Step-Step/dp/0941936864
I do what the little voices in my wife's head tell me to do.

TexasTimbers

man I cannot believe I missed that show. I would not have thunk they would do a show on stave drums I did not know they were that ubiquitous. they are certainly more attainable for a DIYer I guess that is the reason.
The oil is all in Texas, but the dipsticks are in D.C.

Tom


TexasTimbers

Um, I mean, I did not know they were so . . . . . . common. ;D
The oil is all in Texas, but the dipsticks are in D.C.

metalspinner

Kevjay,
The drum they made on "How It's Made " was a bongo type drum.  But it was made with stave construction.

I know what you mean about missing out on that show.  There is a segment on metalspinning that I missed twice. >:(  I watch that show every day trying to catch that episode, but always miss out.
I do what the little voices in my wife's head tell me to do.

Furby


jokers

Quote from: Radar67 on May 29, 2007, 01:50:33 PM
I'll clear it up even better...I said length in place of width because you usually think of the length of something between long points.  ;)

Stew
.......and the length of those staves would relate to what`s known as arc length.

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