Bowl Making

[EIEIO]

DWSudekum posted a bowl last week with the following dimensions: the original board is 14 mm thick (T=0.551"); the walls are 3/8" thick (W=0.375"); the blade size was not provided, so assume #9 blade thickness for the kerf (K=0.018"). Blade angle was reported at 34.2 degrees.

I interpreted this to mean that the distance between cut lines on the surface of the board was 3/8" (not the wall thickness, which would be 0.375 * cos(34.2) - .018 = 0.292").

The trig for a 3/8" wall looks like this:
sin(blade angle) = (W+K)/T = (.375+.018)/.551. angle = 45.5 degrees.

If we want a measured wall thickness of 3/8", distance between cut lines on the pattern would be (.375+.018)/cos(45.5)=0.561".

Does this look about right? Is there a posted app note on making these calculations, or are they usually done trial and error?

(corrected 2/26/13 AM)

[Rapid Roger]

Don't get so excited about measurements, that is why God created sand paper! 
Does it really matter how thick the walls are? 

Rog

[EIEIO]

Don't get so excited about measurements, that is why God created sand paper! 
Does it really matter how thick the walls are? 

"Wall thickness" matters if you are making the calculation of the angle to set the blade.

 - If Wall Thickness means the distance between the lines on the pattern, then a 14mm (0.551") thick board with 3/8" between pattern likes gives an angle of arctan(0.375/0.551) = 34.2 degrees. Measured thickness of the wall is then 0.375*cos(34.2) - Kerf(0.018 for #9) = 0.292".

 - if Wall W means the actual thickness that would be measured with a caliper after the cut is made on a board with Thickness T and cut with a blade with Kerf K, then sin(angle) = (W+K)/T. For the values W=0.375, K=0.018 (#9 blade), T=0.551", angle = arcsin((0.375+0.018)/0.551) = 45.5 degrees. The distance between pattern lines would be (.375+.018)/cos(45.5) = 0.56".

Most angle cuts I've seen are reported to the tenth of a degree. The difference between 34.2 degrees and 45.5 degrees is a big difference.   

[Merlin]

Come on who of us here are mathematicians.
I wood assume most of us would be more of the trail and error type.
 Most bowls I have done have a blade angle of 2 - 3 degrees on a 3/4 inch piece of wood.

***Merlin***

[mrsn]

http://scrollmania.com/ is a website that has some calcuations and stuff on bowl making and might have what you are looking for.

I do have a question, and I don't mean to be rude, but why are you so concerned about getting your wall thickness exactly 3/8. I am not sure I understand why you are need to be so exact, like roger said that is why we have sand paper. Also, I always sand out my drill marks and smooth out stuff anyway.

I have made dozens of bowls using the math
inverstangent (wall/thickness) = angle needed

[Rapid Roger]

OK. Now I understand what you are trying to do but, you don't have to carry the measurements out to decimal points.
I drew a chart out on paper using the actual dimensions of the wood (thickness.....1/4, 1/2, and 3/4") and several angles (10 degrees, 15, 20, 25, 30 and so fourth) and it works for me.
I also would recommend a book by Carole Rothman called "Wooden Bowls from the Scroll Saw". It is available from Fox Chapel Publishing for $19.95 and is the most informative book that I know of. Not only does she show you howto make the most beautiful wooden bowls, there is a chart on the last page to tell you how to calculate the angles for various thicknesses of wood. Yes she does use decimals in the chart but, that is really a lot more than is necessary.
As far as the blade kerf. goes, I can't get real excited about that either.
As far as the thickness of the walls in the finished bowl goes, I repeat, It doesn't matter because there is so much sanding that needs to be done that you couldn't possibly maintain a  given thickness any way. In fact, I would guess that wall thickness varies in circumference and top to bottom in a given bowl regardless of who made it.

Rog

[EIEIO]

I would let this drop except that I was asked the question, so here goes.

I'm a retired engineer and design is part of the package for us. It's not that exactly 3/8" is important, it's  more a matter of designing the job to give an expected result. The arctan calculation you mention is right if you call the distance between lines on the flat pattern "wall thickness": tan(a)=P/T. But when the angles are this big (30 degrees or so) then the actual thickness of the wall is a lot less than the distance between lines on the pattern. In the original bowl, the 3/8" (0.375") between lines on the pattern results in a wall thickness of about 0.29" and an angle of 34.2 degrees. For a bowl that holds oranges, the difference is not important - either one will hold oranges. But for an engineering design that expected 3/8" thickness, that's a difference of  23%. It might matter if you were trying to make use of that dimension, say to make a slot in a handle for the bowl. If your slot was .375" but the wall is 0.29" then your handle would fall off. If the math were used, you're still free to lay out the pattern at 3/8", and you'd expect 0.29" when you were done.  

I'm not suggesting that anyone has to use trig to make a bowl if they don't want to - beautiful work is done here every day without it (but note that the arctan equation above is the same trig). If someone did want to use it, I was asking about the math behind the design. It was not meant to insult or challenge anyone, only for my own information.  

That said, I surrender.

[EIEIO]

Roger - thanks for the reference.

[mrsn]

EIEIO-
Thanks for clarifying why you want the additional accuracy. It makes more sense now, although personally I'll stick to my method and not try anything "extra".

[Scroll Down]

I thought I was doing good when I figured out how to use this  http://www.scrollmania.com/AngleCalc.html

I gotta.go lay down, I'm dizzy now

Measure with a.Micrometer
Mark it with a crayon
Cut it with an axe
Sand to fit

[EIEIO]

I made a simple bowl to see what the laughs were about. It's a 6x6 piece of 3/4" pine with 1/2" rings cut at a 34 degree angle. Square with rounded corners. Nothing fancy - just trying the process. It's pretty clear to me now that the wall thickness has as much to do with sanding and shaping with the grinder as with the original cut.