Math

[~Alan]

XL 2000
I make lids(tops) (covers) using a jig but I would like to figure out just
how much metal I am using including scraps

take a cylinder and stand it on its end. Now looking down at the Diameter
and cutting along the Diameter you will cut the pipe in half leaving (
=PI()*Diameter/2). now placing the Diameter side against the inside of a
larger circumference pipe there is going to be a space I need to know how
to figure the size of a cover that will cover the half of the pipe and the
space that is against the Diameter side So let say I have a piece of pipe
18" and I am making a cover for it to fit into a 72" Diameter hole I cut it
in half and that leaves a half of a circumference of 28.27 and a Diameter
of 18" I still need to cover the back side noting that both sizes change
constantly
What I am doing now is squaring it out to the largest size then I lay my jig
down and cut away.
so lets say in this case I have a 18" Diameter pipe into a 72 inch hole I
will square out the 18"s
which leaves allot of scrap I now that I will always have scrap which I need
to account for.

any way is there away to do this?

 

[Guest]

Alan

I am having some problems with my excel program so the following isn't
tested BUT the formula you need goes along the following lines:

Let R=the big pipe radius
Let c=the diameter of the small pipe

The formula to calculate the small area that is enclosed by the small pipe
diameter line and the arc of the large pipe is:

A=(0.5*R^2(2*asin(c/2R)-sin(2asin(c/2R)))

Hope this is what you were after. I would suggest that in your excel
spreadsheet you have the formula read the cells where you input R & c.

 

[Leo Heuser]

Alan

Another option:

In A1 radius of the big pipe
In A2 radius of the small pipe

To get the area of the lid (half small circle+back side)

=(PI()*A2^2)/2+(A1^2)*ASIN(A2/A1)-A2*SQRT(A1^2-A2^2)

 

[~Alan]

Thank you both for you help
Question what is the end result figure in. 18" into a 24" = 711.68 ?
Since i need to charge for square inches or square feet

 

[Leo Heuser]

Thank you both for you help
Question what is the end result figure in. 18" into a 24" = 711.68 ?
Since i need to charge for square inches or square feet

You're welcome, Alan.
The result is in square inches and can be converted
to square feet by dividing by 144.

The two radii must have the same denomination, both
inches or both feet.

LeoH

 

[~Alan]

thank you again and have a good day

You're welcome, Alan.
The result is in square inches and can be converted
to square feet by dividing by 144.

The two radii must have the same denomination, both
inches or both feet.

LeoH

 

[Leo Heuser]

thank you again and have a good day

Glad to be of help.

I'm afraid, I wasn't very clear. What I meant was:
The two radii must have the same denomination, both
inches or both feet.

If both radii are in inches, the result is in square inches,
if both are in feet, the result is in square feet.

LeoH