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Geometry question, need outside diameter of 3 grouped objects

Geometry question, need outside diameter of 3 grouped objects

Geometry question, need outside diameter of 3 grouped objects

(OP)
If I have 3 tubes, each 1" diameter grouped together at 120° angles, what would be the diameter of a larger tube which could enclose the 3 smaller tubes?  There must be a formula, or 2, to calculate this.  Thanks.

RE: Geometry question, need outside diameter of 3 grouped objects

I don't know of a formula but why not fire up "your favorite CAD program", create your four circles and then dimension the "all encompassing" one.

RE: Geometry question, need outside diameter of 3 grouped objects

My guess at the answer is that it will be D*(1+1/Cos(30)). I don't have a CAD package to verify it though.

RE: Geometry question, need outside diameter of 3 grouped objects

(OP)
I don't have any CAD software, just pencil, paper & a calculator.

RE: Geometry question, need outside diameter of 3 grouped objects

(OP)
Kiranpatel,  would I solve for "D" in your equation?

RE: Geometry question, need outside diameter of 3 grouped objects

This is quite simple: as the tubes have equal diameters their CLs will be on a regular triangle.
Side of the triangle: d
Height of the triangle: d*cos 30°
Distance of one vertex to center of triangle: 2/3*d*cos 30°
Diameter of the enclosing circle:
D=(2*2/3*cos 30°+1)d=2.155d.

prex
motori@xcalcsREMOVE.com
http://www.xcalcs.com
Online tools for structural design

RE: Geometry question, need outside diameter of 3 grouped objects

(OP)
So "d" here is the diameter of the small tubes (1").  This looks good, at least better than the figures I was coming up with.  Thanks a lot.

RE: Geometry question, need outside diameter of 3 grouped objects

Sorry, my post was not clear enough. D is the diameter of each of the 3 tubes (1"). The term D*(1+1/Cos(30)) represents the diameter of the envelope circle. I note that the number is the same as that derived by prex.

RE: Geometry question, need outside diameter of 3 grouped objects

(OP)
I see, thanks Kiranpatel & Prex.

RE: Geometry question, need outside diameter of 3 grouped objects

(OP)
Bob, thanks for the great link, that's exactly what I was looking for.

RE: Geometry question, need outside diameter of 3 grouped objects

Being an X-tube welder I have to agree with Prex.

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