Client wants a round base

[Zacharytanner]

Hi Guys,
I have a customer who wants a 72in round dining room table and she wants the base to be a cylinder shape made out of old 2x6 lumber. Anyone know the degrees I have to cut the 2x6 to get a pillar shape?

Thanks
Frank

 

[tjbnwi]

Depends on the number of pieces you use.

360 divided by the number of comers divided by 2 will give you the degrees of each cut.

For instance a square room

360/4=90--90/2=45

If you have the BuildCalc app for your smart phone I can explain that also. The app will give you length of sides and angles. Length depends on incised or excised.

Tom

 

[Shane Holland]

Frank,

Depends on the diameter for the cylinder. What would that be?

You should think of it as a polygon, not a circle for the calcs.

You would probably want to use an online calculator to get the number of boards needed to make the polygon based on its circumcircle. Looks like 20 boards that are 5½" wide would be needed to make a 35" cylinder.

http://keisan.casio.com/exec/system/1223430387

I think you can get the interior angles of a polygon using this formula:

180(n-2)
-----------
      n

Where "n" is the number of sides for the polygon (or in this case cylinder). Remember to half that since the angle is bisected by the two boards meeting.

Someone else may be able to give you a better/easier way.

Shane

 

[Kev]

[eek]

Does this lady know twelve Knights? Sounds like it's going to be a hefty table!

 

[tjbnwi]

Diameter of the cylinder has nothing to do with the angle of the cuts. If you had a 27' polygon with 18 sides or a 2' polygon with 18 sides the angle of the cut is the same. What changes is the length of the side.

For the above the bevels would be 10º

Inscribed the 27' poly would have 18 sides 4' 8-1/4".  Ex-scribed the length would be 4' 9-1/16"

Inscribed the 2' poly would have 18 sides    4-3/16".  Ex-scribed the length would be 4-1/4"

The formula for side length is dependent on the shape of the polygon.

The above is based on a poly with equal length sides.

You will have to create a polygon, then finish it to a circle.

Tom

 

[Holmz]

Diameter of the cylinder has nothing to do with the angle of the cuts.
...

^Nice^

While it seems trivial... like #boards =  (2*pi*r)/board-width... It can be a bit of a chin scratcher.

The boards will be at the circle's diameter only in the middle of each board, with the joins being proud of the circle's OD.
On the inside the joins will be further away from the focus, or axis, than then middle of each board.

So the boards will need to be thicker than what the 'wall thickness' of the finished cylinder, of it is going to finished into a smooth cylinder.

If the angles are 10 degrees (18 boards) then the amount that the middle falls short is (1-COS(10))* OD. Which is about 1/64 per inch of radius (OD.2).

So a 30" diameter would be 15" radius and ~7/32" off...

Or one can make the boards wider. It is easiest to use the centre of the board's diameter (or radius) to noodle out the width and then make the center what ever the end thickness is, from the inside.
So a 1" thick finished-cylinder would be cut at a 1/2" from the inside surface... But it would use a 5/4 board or perhaps even 1-1/2".

 

[Kev]

Diameter of the cylinder has nothing to do with the angle of the cuts.
...

^Nice^

While it seems trivial... like #boards =  (2*pi*r)/board-width... It can be a bit of a chin scratcher.

The boards will be at the circle's diameter only in the middle of each board, with the joins being proud of the circle's OD.
On the inside the joins will be further away from the focus, or axis, than then middle of each board.

So the boards will need to be thicker than what the 'wall thickness' of the finished cylinder, of it is going to finished into a smooth cylinder.

If the angles are 10 degrees (18 boards) then the amount that the middle falls short is (1-COS(10))* OD. Which is about 1/64 per inch of radius (OD.2).

So a 30" diameter would be 15" radius and ~7/32" off...

Or one can make the boards wider. It is easiest to use the centre of the board's diameter (or radius) to noodle out the width and then make the center what ever the end thickness is, from the inside.
So a 1" thick finished-cylinder would be cut at a 1/2" from the inside surface... But it would use a 5/4 board or perhaps even 1-1/2".

I can't believe you just went through all of that detail and didn't provide a schematic [eek] [big grin]

 

[Zacharytanner]

Thanks EVERYONE- going to start tomorrow

Frank

 

[Holmz]

[member=13058]Kev[/member] - I was trained to do that by Dr Ellison, who would be on me if he know I didn't have a diagram.

I need to find the graph paper, but all found was expensive toilet paper.

 

[tjbnwi]

Diameter of the cylinder has nothing to do with the angle of the cuts.
...

^Nice^

While it seems trivial... like #boards =  (2*pi*r)/board-width... It can be a bit of a chin scratcher.

The boards will be at the circle's diameter only in the middle of each board, with the joins being proud of the circle's OD.
On the inside the joins will be further away from the focus, or axis, than then middle of each board.

So the boards will need to be thicker than what the 'wall thickness' of the finished cylinder, of it is going to finished into a smooth cylinder.

If the angles are 10 degrees (18 boards) then the amount that the middle falls short is (1-COS(10))* OD. Which is about 1/64 per inch of radius (OD.2).

So a 30" diameter would be 15" radius and ~7/32" off...

Or one can make the boards wider. It is easiest to use the centre of the board's diameter (or radius) to noodle out the width and then make the center what ever the end thickness is, from the inside.
So a 1" thick finished-cylinder would be cut at a 1/2" from the inside surface... But it would use a 5/4 board or perhaps even 1-1/2".

That is why I posted 2 different lengths for the sides. You have to decide if you want the poly to fit inside the circle where the apexes touch the circle or outside the circle where the flats touch the circle.

In this case the op is using 2x material (he stated that in his first post). For the 18" circle I would use a width of 5-1/2", that would leave plenty of meat in the center of the board.

Here is a drawing I did to show the developer of BuildCalc the poly function was not complete enough (I beta test BuildCalc). The app did not allow for the two possible ways to calculate a poly, it does now.
https://picasaweb.google.com/tbadernwi/Octagon

Tom

 

[Holmz]

Yep Tom we are in agreement.
I can see how it could be a chin scratcher for some though.
Your pictures probably help out a great deal.
Good work!

 

[semenza]

    I was picturing that the number of sides and the angle would change based on the diameter of the column because the length of the sides is fixed at the width of a 2 x 6. But I suppose several 2 x 6s could be put together to make different length sides.

    Seth

 

[tjbnwi]

    I was picturing that the number of sides and the angle would change based on the diameter of the column because the length of the sides is fixed at the width of a 2 x 6. But I suppose several 2 x 6s could be put together to make different length sides.

    Seth

He may need more 2x6's.

Length of sides only affects diameter, number of sides affects angle.

Tom

 

[semenza]

    I was picturing that the number of sides and the angle would change based on the diameter of the column because the length of the sides is fixed at the width of a 2 x 6. But I suppose several 2 x 6s could be put together to make different length sides.

    Seth

He may need more 2x6's.

Length of sides only affects diameter, number of sides affects angle.

Tom

Right, if each side is the width of one  2 x 6 (5 1/2"), then the larger the diameter the more sides. Which will mean different angles.

So I guess the question is ....... Frank, are you going with a fixed number of sides (hexagon, etc) or a fixed width (length) of side at 5 1/2"?

Seth

 

[Zacharytanner]

Fixed width 5 1/2 Seth

 

[Zacharytanner]

I cut 8 scraps of 2x6 at 22 1/2 degrees off got this -

A ways off from a 36 in wide base I was looking for

Frank

Guess I need to use at least 2x12s

 

[Shane Holland]

Frank,

By my previous calcs, you would need to use 20 boards, not 8.

So, I think the interior angles would be 162 degrees, which would need to be bisected. So, the angle would be 81 degrees for the inside angles or 9 degrees for the outside angles.

Assuming 5½ sides, that would be a 35" polygon.

 

[tjbnwi]

21 boards at 5-9/16 will give you what you need to shape the piece to round at 36" in diameter. The bevel you need to cut is 8.571429º.

If you wanted to stay with the 8 boards they will need to be 14-1/4" wide each, bevel cut at 22.5º

Making up polygons is not as easy as it seems.

Tom

 

[SMJoinery]

Hi All.

The topic of this thread has been our (apprentice and I) lunchtime talking point for a few days.
Both of us are overwhelmed by how much maths comes into play in our profession and i feel it's one of my weaker points.
I have difficulty reviewing a complex math formula and can't seem to follow the subject or see the relation in the flow. When I read Tom's simple 360 divided by number of pieces divided by two equals degrees to cut pieces I rejoice.
Even simple roof angles, runs, degrees and pitches have me head scratching but my experience gets me to a tight fitting rafters but not straight from paper but rather from a drawn template or trial pieces.
I'm hoping that YOUTUBE content on related subject brings me the kind of Eureka moments I need.
Thanks for the education, it's why I love the FOG.

 

[Wuffles]

Hi All.

The topic of this thread has been our (apprentice and I) lunchtime talking point for a few days.
Both of us are overwhelmed by how much maths comes into play in our profession and i feel it's one of my weaker points.
I have difficulty reviewing a complex math formula and can't seem to follow the subject or see the relation in the flow. When I read Tom's simple 360 divided by number of pieces divided by two equals degrees to cut pieces I rejoice.
Even simple roof angles, runs, degrees and pitches have me head scratching but my experience gets me to a tight fitting rafters but not straight from paper but rather from a drawn template or trial pieces.
I'm hoping that YOUTUBE content on related subject brings me the kind of Eureka moments I need.
Thanks for the education, it's why I love the FOG.

That bit in bold, that's a typo right?