Cross section cylinder calculations

[martik777]

I am not sure how to explain this so I'll give an example:

I have a 12" diameter PVC pipe, 24" in length with a wall thickness of 1/2". What is the largest diameter disc at 3/8" thick that can be cut from the pipe? ie: a hockey puck 3/8" thick.

I have done this in practise by cutting out a section of the wall then machining it flat and round. The largest disc I have been able to make is about 3" diameter. However, I'd like to be able to calculate disc sizes for various pipes diameters and thicknesses.

Thanks

 

[martik777]

The cylinder in red (hockey puck) is what I want to cut out. Obviously, it's thickness will be less than the pipe thickness due to the pipe's curvature. I need to calculate the maximum diameter of the red cylinder at a specified thickness. As I said, in practise I have been able to cut out a 3" diameter cylinder about .3" thick from a pipe with .5" wall thickness and 12" outside diameter.

 

[Ishuda]

The cylinder in red (hockey puck) is what I want to cut out. Obviously, it's thickness will be less than the pipe thickness due to the pipe's curvature. I need to calculate the maximum diameter of the red cylinder at a specified thickness. As I said, in practise I have been able to cut out a 3" diameter cylinder about .3" thick from a pipe with .5" wall thickness and 12" outside diameter.

Reorient your drawning so you are cutting the puck from the top:
Image from
http://mathworld.wolfram.com/CircularSegment.html

Look at the cord a. It would be the top of the puck. There are several formulas which give the length of the cord. One is
a = 2 R sin(\(\displaystyle \frac{\theta}{2}\))
Let the pipe thickness be T. Looking again at the image, the puck thickness would be T-h where h is the sagitta. Again, there are several formulas for that. See the link above for a few.

 

[martik777]

That's perfect. I built a spreadsheet for the formula

Thanks very much!

Here's a section of the PVC pipe and some samples of what I am making. The blanks are cut first, machined flat (to remove the curvature) then the gear teeth are slotted. The gears are used in an imperial lathe to perform approximate metric threading. The PVC is very durable, even when meshed with steel gears.