bowl making question

[newfie]

i want to make little bowls for my daughters school project.i'm planning on using 1/2" thick material and the ring i want them 1/4" thick so it doen't look to bulky. the bottom is about 1-1/2" wide the top is about 2-1/4" wide and the height is about 2-1/2" high.my question is what degree angle would you use to get this? i attached a pic of a tin one i have its the same size of the measurements of what i'm looking for.   

[luckypup]

I don't have a quick answer for you - but...   If you were to draw a side profile with those dimensions a simple protractor would probably give you the required angle.

Hope this helps,

ray

[TheCamMan]

what size blade are you going to use?

[EIEIO]

You calculate the angle by the inverse tan of (ring thickness/board thickness) = inverse tan(0.25 ring/0.50 board) = inverse tan(0.5) = 26.6 degrees.

So set your saw for 27 degrees. You'll need the base plus 4 rings to get to 2.5" tall. Remember to sand the inside before gluing on the bottom.

You might also consider using a 2x4 for your blank (1.5" thick), make 2 rings, then resaw the base to a reasonable thickness like .25" to match the rings. In that case, the angle would be inverse tan(.25/1.5) = 9.5 degrees (bump it up to 10 degrees).

Another way is to use the 2x4 and set the angle where you like (say 10 degrees). Cut the center and one ring. The center will drop into the ring just a little (depends on blade thickness, but it will be small - maybe 1/8"). Then pull the center out and resaw 1/4" or 3/8" off the bottom (your saw is already set at the right angle to resaw off the bottom slice of that piece). Then glue and drop the 1/4" slice back into the ring, lined up just like it was cut. It makes a pretty slick cup, but is only 1.5" tall. If you need a longer drill than you've got on hand (to get through the 2x4), you can cut a 3" length of welding rod to use as a drill bit. It makes a long, thin bit that usually is good enough to drill a 2x4.

   

[newfie]

what size blade are you going to use?

either a #3 or #5

[newfie]

You calculate the angle by the inverse tan of (ring thickness/board thickness) = inverse tan(0.25 ring/0.50 board) = inverse tan(0.5) = 26.6 degrees.

So set your saw for 27 degrees. You'll need the base plus 4 rings to get to 2.5" tall. Remember to sand the inside before gluing on the bottom.

You might also consider using a 2x4 for your blank (1.5" thick), make 2 rings, then resaw the base to a reasonable thickness like .25" to match the rings. In that case, the angle would be inverse tan(.25/1.5) = 9.5 degrees (bump it up to 10 degrees).

Another way is to use the 2x4 and set the angle where you like (say 10 degrees). Cut the center and one ring. The center will drop into the ring just a little (depends on blade thickness, but it will be small - maybe 1/8"). Then pull the center out and resaw 1/4" or 3/8" off the bottom (your saw is already set at the right angle to resaw off the bottom slice of that piece). Then glue and drop the 1/4" slice back into the ring, lined up just like it was cut. It makes a pretty slick cup, but is only 1.5" tall. If you need a longer drill than you've got on hand (to get through the 2x4), you can cut a 3" length of welding rod to use as a drill bit. It makes a long, thin bit that usually is good enough to drill a 2x4.

   

thanks Ray not sure if I undestands it compleatly but see what happens.

[EIEIO]

There's another thing tho - if cutting from one flat piece, like we make stacked bowls, if you make the base 1.5" diameter, rings 1/4" thick, and you stack the base and 4 rings to get to 2.5" tall, then the top diameter will be 1.5 + 4*.25*2 = 3.5" - wider than the 2.25" you're looking for.

To get the top to be 2.25", you need an angle of inverse tan(.375/2.5) = 8.5 degrees. That angle requires the rings to be cut to match the original equation - ring thickness = tan(8.5) * board thickness = 0.150 * 0.5 = 0.075" (5/64 inch). This is a very thin wall - too thin to cut and sand.

The way around this, if you still want to keep the 1.5" base and the 2.25" top, is to increase the board thickness (for a 2x4, thickness = 1.5" rather than 0.5").  Then the equation looks like ring thickness = tan(8.5) * 1.5 = 0.224" (7/32). Stack 2 rings to get 3" tall and the top will be 1.5 + 2*.224*2 =  2.4". Trim it to 2.5" tall and you'll have 2.25" top diameter.

If you can use extra wood - meaning the rings are not all cut from a single blank - then you can use the .5" thick blank, the 8.5 degree cut, make the rings .224" thick, and it should come close to your dimensions. Get 2 blanks 2.5x2.5x1/2" thick. On the 1st blank, Mark and Cut the 1st (top) ring with 2.25" OD and 7/32" thick at 8.5 degree angle. Move that top ring to the 2nd blank and use it to mark the outline of the 2nd ring (just hold it there and run your pencil around its inside and outside).Cut the 2nd ring, then put it on top of the center cutout from the 1st blank and mark the outline of the 3rd ring. Keep doing that, alternating from 1st blank to 2nd blank, until you have 4 rings, then use the lowest ring to mark the base.

I'll try to make a pattern tomorrow AM.

Sorry if this is confusing - you're trying to balance several dimensions and it gets tricky if you also try to make the concentric rings cut from a single piece of wood.

[spirithorse]

I was just going to say the same thing, Ray,
You beat me to it! 

Just kidding, great explanation of how you derived
the angle.
God Bless! Spirithorse

[BilltheDiver]

Ray, you obviously payed attention in math class!  Over my head, but very good explanations.

[EIEIO]

Todd - I apologize for the ramblings last night. It was after midnight and I wandered a bit.

I attached a PDF pattern to make the cup just the way you requested - 2.5" tall, 2.25" top, 1.50" bottom, 1/4" thick rings. But to get this shape you cannot cut it as concentric rings. It will be 4 rings and 1 base cut individually.

If you wanted to try concentric rings, you need a very thin ring thickness (0.075" thick). This is about 5/64" (1/16" after cutting with a #5). I put a concentric version on the PDF, if you want to try it.

[newfie]

thanks Ray i was reading your post there last night.by you got me confused on the one,thanks for PDF i will try them later this week.the size don't have to be exact as i put them, the little cups are for a part of a school project for my daughter i just dont want them to bulky/clumsy looking for her display thats why i went with the 1/4" thickness for the walls of the cup. i know i have them little cups somewhere maybe walmart or dollar stores,who knows if i cant them to turn out like i wants them maybe i'll find them again and buy a couple.

[EIEIO]

You probably would not have any trouble with 1/8" rather than 1/4" rings, but they would still be too thick for a concentric cutting. If I were doing it, I'd go the 2x4 route and stack 2 layers to get a 3" tall cup. If the full capacity of the cup is not needed (because it's a play or something) then the cup could be just the solid 1.5" base and one 1.5" ring, and would look pretty slick.

If you cut some, please post a photo.

[newfie]

Hey Ray thanks for all your help with the little cup pattern. But I did make a boo boo in the size I needed it was suppose to be 1-1/2" not 2-1/2". Well know worries I got it figured out after. I use a 2x4 as you said just one layer and glued a piece of 1/4" ply to the bottom of it
.it came out pretty good so heres a pic of the first one. I will post a few pics of the full project when I gets it all done.

[EIEIO]

That looks swell. The 1.5" works well with the 2x4.

Be careful if you make a bunch that they don't get stacked one inside another. With that angle they can really get stuck.