Segmented Bowl Project Part 2 – The Math

[KenH]

THE MATH, THE MATH, OH THE MATH

Sorry to be slow in responding to the math and "how to set up the table saw sled" questions. It took a little while to make sure I got the math right. In the next few hand written pictures I will show the math on how I calculated the angles for the segmented bowl and how I setup the table saw sled.

For those that have never done any segmented bowl construction before I’ll start by talking about the 12 section ring.



To calculate the cut angle for each end of the segment:

• first determine how many segments you want in each ring
• divide this number into 360
• then divide this number by 2

For example: for a12 section segment circle the cut angle = (360/12)/2 = 15 degrees
For a 10 section segment circle the cut angle = (360/10)/2 = 18 degrees


In the first drawing below are the basics for the "sin equation" and a drawing showing 50 degree angle of the bowl setup. Note: for all angle I will use a three letter notation that make up that angle.



This next drawing shows a section from the bowl and all the angles associate with it and the angles that we are looking for. I hope this is easy for you to see and understand.



The next two drawing show the math to calculate the two angles we will need to set up the table saw sled.







In setting up the table saw sled I use the angles to calculate distances instead of trying to measure these small precise angles.

For the sled tilt angle of 9.57 degrees I calculate the difference in height between the two legs of the sled. I do cut the top of the legs at a 9 degree angel for attachment to the sled.





For the Fence angle of 11.44 degrees I calculate the distance down the edge the fence that is needed for the set up.



Once you get to this point you are ready to cut segments. You may have to adjust your setup after your first set of cuts to find tune the sled to alot all the segments to line up correctly.

Good Luck

Ken

[RandyJ]

HUH???

Can I just send you some wood and have you cut the segments for me??

Thanks,

[woodArtz]

I knew I should have payed attention in Geometry class. I used to say "who will ever use this stuff anyhow?"

[ErnieM]

This next drawing shows a section from the bowl and all the angles associate with it and the angles that we are looking for. I hope this is easy for you to see and understand.

I see it fine but as for understanding it ............................

I think I'll stick to harpsichords - much simpler for a guy like me that has trouble making change for a dollar.
Ernie