how many circles can be contained within a rectangle 5

[searcher123]

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

 

[GBor]

I use CAD for this type of problem.

 

[Theophilus]

Three.



Jeff Mowry

http://www.industrialdesignhaus.com

What did you dream? It's all right--we told you what to dream.
--Pink Floyd, Welcome to the Machine

 

[Theophilus]

Seriously, I do as GBor mentioned above--draw everything to true scale and check it out.



Jeff Mowry

http://www.industrialdesignhaus.com

What did you dream? It's all right--we told you what to dream.
--Pink Floyd, Welcome to the Machine

 

[GBor]

On further thought, it seems like it would be something along the line of:

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.

 

[drawoh]

searcher123,

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

 

[KENAT]

Are all the cables the same diameter?

KENAT, probably the least qualified checker you'll ever meet...

 

[GBor]

I missed a cosine in there somewhere...sorry.

 

[MintJulep]

You need to go look at the IEC, or whatever code governs your installation.

The answer is not "as many as you can possibly jam in".

 

[vpl]

If you're talking about electrical cables in a rectangular cable tray, then you need to go ask this question in one of the electrical forums. The limitation is NOT the physical size of the cables at all. There are significant concerns dealing with heat generation and cable ampacities that come into play.



Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[CoryPad]

MathWorld is the best Internet source for math-related questions. Here is their page on circle packing:

http://mathworld.wolfram.com/CirclePacking.html

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[searcher123]

Thanks for the info. I realize that the corect anwser is not allways the largest number of cables that can be jammed in. The customer was concerned that the number of cables they wanted to fead to there equipment would not fit within the cable managment duct that was part of our design. I did end up finding my answer through soid works though. I created a rectangel and cut a hole and used the fill patern to populate the area and let solid works count the holes. I like it when I can get the software to do my thinking. It looks like I will need a bigger box.

Thanks again for the sugestions.

 

[tomwalz]

Just curious.

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.

http://www.carbideprocessors.com

 

[KiwiMace]

Easy solution: To determine the highest packing ratio possible, bid out the duct supply on a fixed price performance based contract.

 

[searcher123]

Hi Tomwalz

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.

 

[mikek10]

Take a look at

http://books.google.co.uk/books?id=...4fvg7QV&sig=o-SPMYXVW4iABSHkcBWVIiuCsgc&hl=en

 

[dvd]

Kiwimace:

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.

 

[KiwiMace]

dvd:
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.

 

[panelman]

I tend to draw it in cad and then add 50% (space not cables)

 

[zekeman]

A quick and easy approximate solution is to take the area of the rectangle and divide it by the area of the equilateral triangle formed by 3 adjacent wires and then halve that number, since the tangent (hexagonal) stacking takes up 60 deg of each wire, a total of 180 deg or 1/2 of a wire.
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.