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Let's assume I'm wiring a house with ethernet cables. Cables will be bundled together and each bundle will be wrapped in a sleeve to protect cables from rodents (amongst other benefits). Sleeves come in predefined inner diameters, e.g. 1/8", 1/4", 3/8" and so forth. While ethernet cables can be measured as 22 AWG to 28 AWG, external diameter may vary due to its cable jacket.

Let's assume I have a bundle consisting of 6 cables with a max diameter of 4mm. The 4mm may include a protective sleeve. My understanding is that given the diameter of a single cable, I can calculate its area.

var cableDiameter = 4;
var cableArea = ((cableDiameter * cableDiameter) * Math.PI) / 4;

To get the area of the bundle of cables, I can multiply it by the number of cables:

var cableCount = 6;
var bundleArea = cableArea * cableCount;

And then what's left if to calculate the diameter of the bundle:

var bundleDiameter = Math.Sqrt((bundleArea * 4)/ Math.PI);

I can then convert that to inches.

var inch = 25.4;
var bundleDiameterInches = Math.Round(bundleDiameter / inch, 2);

Which gives me a 9.8mm or 0.39” for the diameter of the bundle consisting of six cables with a diameter of 4mm (28 AWG), which implies I can use a sleeve with an inner diameter of 3/8” provided it can stretch to 0.39". For a bundle consisting of 6.5mm cables (24 AWG), a sleeve with an inner diameter of 5/8” or 3/4” may suffice.

But it seems my calculations may be a bit too optimistic. It doesn't include room for cables to flex when the bundle of cables are bent. I also read that other factors of the cable, such as heat and interference, may require additional spacing around each cable.

What other factors should be taken into account when calculating the diameter of a bundle of cables for wrapping them in a sleeve?

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    Where are you on this planet? This sounds like a conduit fill calculation in disguise...or are you talking about some sort of spiral wrap/sleeving, instead of a continuous tube? – ThreePhaseEel Nov 27 '19 at 1:37
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    this is the circle packing problem en.wikipedia.org/wiki/Circle_packing_in_a_circle – Jasen Nov 27 '19 at 1:39
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    I agree with three phase , this is a simple conduit fill question, from the specifics it is on the other side of the pond but on this side we use the national electric code, it has tables in chapter 9 that provide conduit or “sleeve sizes” and the number and or sizes of cables/ conductors that can be used there are both square inches and MM measurements. – Ed Beal Nov 27 '19 at 4:54
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    Is there some particular reason you want to calculate this, rather than just assembling an actual bundle of the thickest cables you expect to use, and then comparing that to actual conduit to see which it fits best in? (And I'll suggest that on the DIY site, using C# code to explain your question may impede maximum readership/comprehension) – Peter Duniho Nov 27 '19 at 6:56
  • The wires will go into the conduit without a sleeve. However, while it goes from one area of the house to another in the ceiling, it will not be in a conduit; the wires will be exposed and rodents etc. can have fun at my expense. So the areas where the wires are exposed needs to go in a sleeve that deters rodents from ruining my even bench watching disaster movies. – bloudraak Nov 28 '19 at 3:08
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I would not attempt bundling the cables before installing them in the sleeves / conduits / raceways, it will be counterproductive.

Electrical codes have guidelines for conduit fill. For example in the US, the National Electrical Code has a base rule for power wiring that you can fill 40% of the cross sectional area of a conduit or raceway. (I am oversimplifying, there's more to these rules, but not important here.)

The 40% guideline doesn't really apply as a rule to a protective sleeve for ethernet cables, but it is still a good guideline for you to use. You can cheat a little, especially if the conduit is more or less straight. It can get hard to pull more cable than this through conduit, and you should not tug very hard on ethernet cables.

Incidentally, be aware that there are limits on how many bends you can have in a conduit / raceway because as you accumulate bends it gets very hard to pull cable through. Do not cheat on this part - in fact try to have less bends than the rules permit. The NEC allows 360 degrees of total bend (for example, four 90 degree bends, eight 45 degree bends, etc.) but for communications, it's better to limit it to 270 degrees total bend.

You are using wire gauges for your cables but those are irrelevant, what matters is the outer diameter of the cable jackets.

The cross sectional fill is easy enough to calculate, but you can find lots of conduit fill charts and calculators online that will do the math for you. The code / algorithm snippets in the question are the kind of logic embedded in those calculators.

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    This is what I had in mind when I mention "bundling" ethernet cables. They are still "distinct" cables with a sleeve around them to deter rodents and keep them together when they are not in a conduit. Notice how the sleeves help in a data center. – bloudraak Nov 28 '19 at 3:59
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    @bloudraak -- I suspect such a thing may not be legal for permanently installed cables...although where are you on this planet? – ThreePhaseEel Nov 28 '19 at 6:04
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    Given there's generally no legal requirement to enclose data cabling, I don't see why a sleeve like that would be prohibited. That said, I'm also skeptical of how much it would protect against rodents. – SomeoneSomewhereSupportsMonica Nov 28 '19 at 6:19
  • @bloudraak - that braided nylon sleeving is a cable management product for keeping cables tidy. It may be of use between the sleeve / conduit and the patch panel or etc. It's not really helpful inside a conduit, it would be like wearing two pairs of underwear at the same time. I don't think adding it inside a conduit or sleeve will give you much, if any, additional rodent protection. – batsplatsterson Nov 28 '19 at 9:41
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    @SomeoneSomewhere -- because without the appropriate listings as a communications raceway, it wouldn't be subject to the correct testing for flame spread, smoke-developed, and so on... – ThreePhaseEel Nov 28 '19 at 17:14
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Dude, just search the web for "conduit fill calculator" et voila! Conduit fill limits are partially for heat, which wouldn't apply to your low-voltage wires, but also consider the ability to pull wires through it. Like batsplasterson said, mind the total bends and install appropriate access boxes as needed. Also, don't mix high and low voltage wires in the same conduit -- usually disallowed by code and would cause noise (reduced data speeds).

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