how many circles can be contained within a rectangle
how many circles can be contained within a rectangle
(OP)
Hi All
I am trying to determine how many round cables can be contained within a rectangular duct. I have found a formula for circles contained within another circle but would like to know circles within a rectangle. Can anyone help me with this
I am trying to determine how many round cables can be contained within a rectangular duct. I have found a formula for circles contained within another circle but would like to know circles within a rectangle. Can anyone help me with this





RE: how many circles can be contained within a rectangle
RE: how many circles can be contained within a rectangle
Jeff Mowry
www.industrialdesignhaus.com
What did you dream? It's all right--we told you what to dream.
--Pink Floyd, Welcome to the Machine
RE: how many circles can be contained within a rectangle
Jeff Mowry
www.industrialdesignhaus.com
What did you dream? It's all right--we told you what to dream.
--Pink Floyd, Welcome to the Machine
RE: how many circles can be contained within a rectangle
Int(A/D) * Int(B/D) - Int(2B/D)
Where A is the length of the rectangle
B is the width of the rectangle
D is the diameter of the cable
Basically, you would stagger the rows to compact them as much as possible. Because of this, you would have one of the following stacking sequences:
o o o o o o o o
o o o o o o o
Or
o o o o o o o
o o o o o o o
Either way, you lose 1/2 a cable diameter for each row.
RE: how many circles can be contained within a rectangle
Circles and cylinders pack most tightly in a hexagonal formation. Draw a hexagonal formation with required number of cables and wrap a duct around them, to scale, as noted above.
Of course, circles and cylinders do not have connectors and cable ties, and rectangles do have have flanges and embedded connectors. Reality is usually messier and more complicated than theory. Are you sure you are looking at the whole problem?
JHG
RE: how many circles can be contained within a rectangle
KENAT, probably the least qualified checker you'll ever meet...
RE: how many circles can be contained within a rectangle
RE: how many circles can be contained within a rectangle
The answer is not "as many as you can possibly jam in".
RE: how many circles can be contained within a rectangle
Patricia Lougheed
Please see FAQ731-376: Eng-Tips.com Forum Policies: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.
RE: how many circles can be contained within a rectangle
http://mathworld.wolfram.com/CirclePacking.html
Regards,
Cory
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips Fora.
RE: how many circles can be contained within a rectangle
Thanks again for the sugestions.
RE: how many circles can be contained within a rectangle
How did you account drawoh's condsiderations.
Can you slide one out and another in under the current specifications?
Tom
Thomas J. Walz
Carbide Processors, Inc.
www.carbideprocessors.com
RE: how many circles can be contained within a rectangle
RE: how many circles can be contained within a rectangle
The cableing will be installed by the customer when the rack is installed. After cable runs are finished they will be terminated. There is the possibility of future maintenance or additions but the likelihood is small. New cable can be run alongside the original bundle and old cables can be left as is or marked as dead.
RE: how many circles can be contained within a rectangle
RE: how many circles can be contained within a rectangle
That sounds like an easy solution for you: get a contractor to bid on a frivolous job without providing guidelines. I don't like that kind of thinking.
RE: how many circles can be contained within a rectangle
You caught me. Merely a jovial remark intended to portray unkindly some stereotypical contractor as one who is prepared to devise a complex mathematical maximal solution in order to improve the profitability of his project. I apologise for my slanted take on the world.
RE: how many circles can be contained within a rectangle
RE: how many circles can be contained within a rectangle
For example, say you have a duct 4" *6" and the wire size is .1 inch,then the area of each triangle is:
(d/2)^2*sqrt(3)
For d=.1 , this becomes
.00433
So 4*6/2/.00433=2771 wires approximately, but is slightly on the high side.
This compares with the rougher estimate of 4*6/.1^2=2400 wires where you do it by rows and on the low side.
RE: how many circles can be contained within a rectangle
RE: how many circles can be contained within a rectangle
RE: how many circles can be contained within a rectangle
In some industrial plants the cables are heaped in the middle of the tray like a load of gravel. But, due to inevitable crosses and tangles, the cables take more space than your calculation will indicate. Oh, and corners often take more again.
Bill
--------------------
"Why not the best?"
Jimmy Carter