Segmenting for a peppermill

[triw51]

I have some 1" square blanks I would like to segment into a pepper mill. The wood is iron wood with little to no figure in it. I would like to use 5 pieces with thin maple strips seperating the iron wood.
My question is do I divide 360 degrees by 5 and cut my iron wood to that angle (which is 72 degrees) or do I subtract 72 from 90 and cut at 18 degrees?
I have not done this before and not sure how to figure the angle of that cut. Thanks in advance for any help

 

[Greg Phillips]

72 divided by 2 =36.

 

[airborne_r6]

I'm not sure how well this will work. Some math tells me that starting with 1" square blocks the diameter of your finished blank will be less than 1.5 inches. It will get slightly larger with the addition of the maple strips, but probably not much.

five segments = 72deg per segment
72/2 = 36deg cut on each side of blank

length of side = X = 1

rad = (X/2)/tan36
= 0.5/tan36
= 0.7265 inches

diameter = rad x 2
= 0.7265in x 2
= 1.45in

 

[triw51]

This is what I am looking to accomplish. (I copied the pictures from exotic blanks) If I use 5 blanks will I get a blank 2 1/2" OD?

 

[D.Oliver]

Greg nailed it. 36 degrees is the angle you want on each side of of the iron wood pieces. Once you glue the two piece of iron wood togather with each having a 36 degree bevel their resulting angle will be 72 degrees. 36 + 36 = 72.

 

[D.Oliver]

According to my math you would need at the very least nine segments if they cannot exceed 1 inch. Possibly with addition of maple strips you might make 8 work. With nine segments you would have 20 degree angles.

 

[airborne_r6]

This is what I am looking to accomplish. (I copied the pictures from exotic blanks) If I use 5 blanks will I get a blank 2 1/2" OD?

No, if you use five 1" blanks you will get an OD of 1.45".

 

[triw51]

what formula do you use to to detirmine the OD of a segmented blank? Thank you guys I now know hoe to detirmine the angle of cut I want for segmenting like this.

 

[airborne_r6]

My previous formulas were good but when I entered the numbers I was using a different calculator than normal and so my numbers are wrong. For a five sided blank with 1" segments the radius should be 0.6881in (~11/16") and the diameter should be 1.376in (~1 3/8").

The formula to calculate the outside diameter of a longitudinally segmented round piece is:
OD=X/tan(180/Y)
Where X is outside length of the segment after cutting the angles and Y is the number of segments.

One caveat, I have never actually done any segmenting, I just derived this mathematically and the formula may not work in all circumstances, although the only one where I can see that it won't work would be if you have to cut the inner part of the segment (the point of the triangle) off to get them to fit together.

 

[D.Oliver]

My math skills aren't as good as airborne's so I just guessimated it this way. You want a piece that is 2.5" OD. That piece would have a circumference of 7.85 inches. You are using 1" pieces so 7.85/1 would come to about 8 pieces. Howerer, I used 1" as the lenth of your piece, but it will be a little more because with a round piece you are measuring an arc and not a straight line. That is why I suggested 9 pieces, but also siad that with the addition of maple strips you could possibly make 8 work.

 

[BlackPearl]

This is what I am looking to accomplish. (I copied the pictures from exotic blanks) If I use 5 blanks will I get a blank 2 1/2" OD?

Is there a good spread sheet for figuring blanks like this? I would call it a staved vessel or blank.

I have been told that the calculus needed to figure out the formula for this was not invented when I went to school.

The only RAD I ever dealt with was a wave, and I got a TAN just by paddling out for the next one.

 

[Haynie]

This is what I am looking to accomplish. (I copied the pictures from exotic blanks) If I use 5 blanks will I get a blank 2 1/2" OD?

Is there a good spread sheet for figuring blanks like this? I would call it a staved vessel or blank.

I have been told that the calculus needed to figure out the formula for this was not invented when I went to school.

The only RAD I ever dealt with was a wave, and I got a TAN just by paddling out for the next one.

That just sounds dirty

 

[airborne_r6]

This is what I am looking to accomplish. (I copied the pictures from exotic blanks) If I use 5 blanks will I get a blank 2 1/2" OD?

Is there a good spread sheet for figuring blanks like this? I would call it a staved vessel or blank.

I have been told that the calculus needed to figure out the formula for this was not invented when I went to school.

The only RAD I ever dealt with was a wave, and I got a TAN just by paddling out for the next one.

As long as I am doing my math right, the table that I attached should do exactly what you are looking for. I even included the angles to cut the segments.

 

[airborne_r6]

I was curious how well the table I made worked so I drew the one with 10 segments of 4" width and it was almost exact. Any error would definitely come from my drawing.

 

[Mason Kuettel]

too simple?

Can someone explain why this diagram would not work? I have not done this type of segmenting before (and not a whole lot of segmenting, period), but this thread caught my interest. So while my geometry students were testing I constructed this very simple drawing that is based on an 18 degree cut coming off of one corner of a 1 inch blank. The final product would have a diameter of 2 inches.

 

[D.Oliver]

Mason your math is correct. Your way could also work and actually gets you a little more OD than our method. I've never tried it your way, but as they say there's more ways than one to do something. However, Triw51 was looking for a OD of 2.5" so even if he aligns the peices like you've shown he will still need more than 5 staves.

 

[bobleibo]

If anyone can use this chart feel free. Makes it pretty simple. The segment length is the length of the outside edge of the segment. You can work the formula in either direction to obtain the segment length or the overall diameter of whatever you are building.

 

[airborne_r6]

Can someone explain why this diagram would not work? I have not done this type of segmenting before (and not a whole lot of segmenting, period), but this thread caught my interest. So while my geometry students were testing I constructed this very simple drawing that is based on an 18 degree cut coming off of one corner of a 1 inch blank. The final product would have a diameter of 2 inches.

I never even considered cutting the blank that way. That would work good. It still won't get the desired diameter in this situation but is a great way to extend the wood at hand and make less cuts. Good thinking!!