Deriving Equation for Intersecting Cylinders Surface Area

Mar 2016
3
0
Virginia
I'm really struggling in trying to find an equation to describe this part it terms of surface area (material useage). Variables, as seen in the picture, are d1, d2, d3, and (a) angle. L1 is not a variable and neither is branch length, both can be calculated from the previous noted variables. Any help in figuring out an equation, or at minimum pointing me in the correct direction to get started would be much appreciated!

TVRU by MearnsQuail, on Flickr
 
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Jun 2015
915
269
England
Neither barrel length nor branch length can be calculated from the variables give.

They could indeed be given constants however.

What about the offset?
 
Mar 2016
3
0
Virginia
L1 = ( d3 * ( 1 / sin a )) + 4

Branch Length = [({( tan a * 2.5 ) + ( d3 * 0.5 )} / tan a + (( d1 * 0.5 ) / sin a ))] - ((( d1 - d2 ) / 4 ) / sin a )

Offset = L1 - (((d1 / 8 )) / tan a + (L1 / 2))

(I know these equations can be simplified down a little more, but just assume those three values to be constants)
 
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