blackwing94
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- Jan 5, 2016
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I want to try a (big) 7 tube fin project. Am I doing this right?
I'm trying to figure out the formula for sizing tube fins. If I want 7 tube fins, what will their radius be, given a main body tube size?
I think I'm running into the problem of:
A math person can get two 1 foot boards from the 2 foot board. A carpenter can only get one 1 foot board because the saw blade took away space from the remainder of the board... real life meets math.
Forgive the graphics. I used powerpoint. Not very exact. But you get the idea. And I had to muck with the font to get π to show up.
The total length of the diameter of all the tube fins added up (left) should be
equal the arc length around the center of all the tube fins around the body tube (right).
t = Body Tube radius
r = tube fin radius (what we're solving for)
n = number of tube fins
2π(t+r) = 2 r n (solve for r)
2πt+2πr = 2rn
2πt = 2rn-2πr
2πt = r(2n-2π
r = 2πt/(2n-2π <-- the magic formula
My test case is 6 tube fins. I think, if you have 6 tube fins, they should be the same size as the body tube. But I get a slightly different answer.
For a 4 inch diameter body tube the radius would be t = 2 inches (radius is half the diameter) I kind of expect a radius of the tube fin to be 2 inches as well.
For 6 tube fins.
r = 2π2/(2*6-2π
r = 4π/(12-2π = 2.198 (close, but not 2. Is it close enough?)
Am I doing this right? Thanks for any help.
I'm trying to figure out the formula for sizing tube fins. If I want 7 tube fins, what will their radius be, given a main body tube size?
I think I'm running into the problem of:
A math person can get two 1 foot boards from the 2 foot board. A carpenter can only get one 1 foot board because the saw blade took away space from the remainder of the board... real life meets math.
Forgive the graphics. I used powerpoint. Not very exact. But you get the idea. And I had to muck with the font to get π to show up.
The total length of the diameter of all the tube fins added up (left) should be
equal the arc length around the center of all the tube fins around the body tube (right).
t = Body Tube radius
r = tube fin radius (what we're solving for)
n = number of tube fins
2π(t+r) = 2 r n (solve for r)
2πt+2πr = 2rn
2πt = 2rn-2πr
2πt = r(2n-2π
r = 2πt/(2n-2π <-- the magic formula
My test case is 6 tube fins. I think, if you have 6 tube fins, they should be the same size as the body tube. But I get a slightly different answer.
For a 4 inch diameter body tube the radius would be t = 2 inches (radius is half the diameter) I kind of expect a radius of the tube fin to be 2 inches as well.
For 6 tube fins.
r = 2π2/(2*6-2π
r = 4π/(12-2π = 2.198 (close, but not 2. Is it close enough?)
Am I doing this right? Thanks for any help.