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BS: mathematicians &/or engineers a - puzzle

Mr Red 08 Dec 05 - 01:38 PM
MuddleC 08 Dec 05 - 02:10 PM
TheBigPinkLad 08 Dec 05 - 02:13 PM
MuddleC 08 Dec 05 - 02:24 PM
TheBigPinkLad 08 Dec 05 - 02:26 PM
MuddleC 08 Dec 05 - 02:32 PM
TheBigPinkLad 08 Dec 05 - 02:39 PM
Metchosin 08 Dec 05 - 02:50 PM
MuddleC 08 Dec 05 - 03:34 PM
Rapparee 08 Dec 05 - 03:56 PM
Metchosin 08 Dec 05 - 05:34 PM
Mr Red 08 Dec 05 - 06:09 PM
robomatic 08 Dec 05 - 06:48 PM
JohnInKansas 08 Dec 05 - 10:01 PM
Bobert 08 Dec 05 - 10:11 PM
JohnInKansas 09 Dec 05 - 12:05 AM
Mr Red 09 Dec 05 - 09:54 AM
GUEST 09 Dec 05 - 10:37 AM
Paco Rabanne 09 Dec 05 - 10:53 AM
TheBigPinkLad 09 Dec 05 - 02:22 PM
GUEST,Arne Langsetmo 09 Dec 05 - 04:48 PM
JohnInKansas 09 Dec 05 - 05:50 PM
GUEST,Arne Langsetmo 09 Dec 05 - 06:23 PM
JohnInKansas 09 Dec 05 - 09:59 PM
The Fooles Troupe 09 Dec 05 - 10:13 PM

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Subject: BS: mathematicians &/or engineers a - puzzle
From: Mr Red
Date: 08 Dec 05 - 01:38 PM

This is for real so lets see how many brains we get answering

Basically the question is "what is" or "where can I find" a realistic formula to calculate:

How many round wires of a given diameter can fit through a given hole size.

(Or the other way round): for a given number of wires of a given diameter - what is the minimum diameter circle that can fit round that bundle.

Inevitably the holes sizes available are fixed so the diameters will be number of discrete values. But we are trying to economize.

I am now goin' surfing for this but maybe 'Catters can get me there quicker, and better than the the formulae that we have that are meaningless.


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: MuddleC
Date: 08 Dec 05 - 02:10 PM

try this table

http://www.cabling-design.com/interaction/tips/19Apr20041.shtml


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: TheBigPinkLad
Date: 08 Dec 05 - 02:13 PM

http://www.cabling-design.com/interaction/tips/19Apr20041.shtml


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: MuddleC
Date: 08 Dec 05 - 02:24 PM

ah ha, beatcha!!!


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: TheBigPinkLad
Date: 08 Dec 05 - 02:26 PM

Just adding funtionality to your URL, muddleC ;o)


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: MuddleC
Date: 08 Dec 05 - 02:32 PM

thank you,
although the original thread didn't say how big these wires are, but some wire sizes give the cross-sectional area of the conductors themslves, not including the insulation... if any.


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: TheBigPinkLad
Date: 08 Dec 05 - 02:39 PM

It's such a long time since I used to do this stuff ... I seem to remember that the area is reduced by spiralling the wires. Bon chance.


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: Metchosin
Date: 08 Dec 05 - 02:50 PM

and don't forget the talcum powder.......


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: MuddleC
Date: 08 Dec 05 - 03:34 PM

you're talking of putting fibre optic strands into protective tubes there
with wires, I use hellerin oil.. string, a piece of locking wire and cursing!


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: Rapparee
Date: 08 Dec 05 - 03:56 PM

Stick the wires in, heat the shrink tubing, and there you are!


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: Metchosin
Date: 08 Dec 05 - 05:34 PM

my only experience was push/pulling 3/0 copper wires through a conduit with three 1/4 bends and that took talcum powder, cursing and tears. LOL...course, womens are allowed to cry.


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: Mr Red
Date: 08 Dec 05 - 06:09 PM

This is going to be glands and or Grommets so not too much force but a lot of design without the benefit of the product before us. Meanwhile I go to the URL.


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: robomatic
Date: 08 Dec 05 - 06:48 PM

If you are doing something with electric power cable in conduit, you can not legally put in as many wires as can fit. You must make allowance for the heat produced by wires in operation, as well as the possible need to pull the wire around bends. For the US you must utilize the National Electric Code.


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: JohnInKansas
Date: 08 Dec 05 - 10:01 PM

I seem to remember that the area is reduced by spiralling the wires

Spiralling doesn't change the theoretical number of wires of a given size that will fit through a hole of a given size, but to get the "maximum packing" the wires must have a specific placement relative to each other. Straight wires tend to flop about and get out of the pattern. Spiralling can be used to make them stay aligned during handling, and makes it much easier to get nearly maximum number of wires through the hole all in one bunch.

In cable manufacture, where very tight patterned spirals can be produced, with tension in the wires during the twisting, significantly smaller bundles can be produced; but if the spiral is very tight the compression "makes the wires smaller" locally, and makes the wires "not really round."

A cable with properly laid spirals also can be much more flexible when it comes to pulling the wires around a bend in a conduit - or running a cable over a pulley. An "assembled" bundle of straight wires - assuming they're glued together or encased so that they maintain alignment - gets very stiff with realtively few wires.

John


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: Bobert
Date: 08 Dec 05 - 10:11 PM

Well, yeah, there are a number of variables here:

*Lets say that the hole is 10mm and the thickness of the wire is 11mm then it is safe to assume that the answer is: zero

* But now lets take the same 10mm hole and here we have a coiled wire, much like a spring that when compressed is 11mm... At first glance you say, "No way" but when you stretch the coil (spring) with every 5mm you stretch it the diameter in decreased by 2mm... With me so far??? So if you continue to stretch the coiled (round) wire three fold over it's coiled diameter it will no pass thru the 10mm hole endlessly, or the length of the round/coiled wire...

No???

Bobert


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: JohnInKansas
Date: 09 Dec 05 - 12:05 AM

Bobert -

Good way to argue: change the question to "how many coil springs will go through a hole?"

If you take your "spring" with a coil diameter of a certain size, you're talking about something other than the wire diameter. Take two of your springs, and wind them together. (Stretch them both, and "spiral" one into the gaps of the other.) The pitch of each spring's twist will now be two times the wire diameter instead of one.

Add a third wire, and the pitch will be 3x wire diameter. When you get to six "twisted together" coils, and twist them around a straight wire of the same wire diameter you have a "close packed geometry" with seven wires of the same diameter in it. This bundle of seven wires (not necessarily springs) will go through a hole that is three times the diameter of an individual wire. It doesn't really make much difference whether the "layer" of six wires that fit up against the one in the middle are coiled, twisted, or just run straight through the hole. Seven wires will go through a hole three times the diameter of each individual wire. If you add another wire, the hole must get bigger. If you remove a wire, the hole isn't as full as it could be.

Since the cross section of the 7-wire strand is essentially circular, you could add one more wire by increasing the hole size by one wire-diameter. If you increase the hole size by approximately 2x the wire diameter, you can add another "layer" of wires. You can add 12 wires in the second layer, giving a total of 19 wires in the bundle that will fit through a hole 5 times the diameter of an individual wire. The "fill" in this last layer is a little less than theoretically perfect, but the result for a 19-wire layup of properly aligned individual wires is a "nearly perfect" round cross section.

Attempting to add an additional layer around the 19-wire layup doesn't "come out even" so you get a "lumpy" cable. Since the 19-wire layup is the largest conveniently sized cross section that's essentially circular, larger cables are typically made by using seven "circular strands" of 19-wire bundles. If each "strand" is considered as a wire, seven strands fit through a hole that's three times the strand diameter. The strand diameter is five times the wire diameter, so a hole fifteen times the diameter of an individual wire will pass an assembled cable containing 7 x 19 = 105 wires.

You could of course make a layup of seven seven-wire strands to fit 49 wires through a hole 3 x 3 = 9 wire diameters.

The 7x19 construction (that's also the technical name for it) is the most common construction used for aircraft control cables, and in the rare instances where that many wires was needed would be the common layup for manufactured electrical cables.

For any bundle with other than one, seven, and (loosely speaking) nineteen wires, there will always be "lost space," in a circular hole, and it's nearly impossible to control an actual geometry for the positions of the individual wires, so a "perfect fit" is very difficult to produce.

For a practical application with "loose" wires, the proper procedure is to a) take *short pieces of the number of wires that need to go through the hole, b)put a ty-wrap around them, c) "scrunch" the bundle until it's pretty nearly round, and d) measure the bundle or find a grommet that will fit on it.

* You can pull out a length of wire, and zig-zag it to make a trial bundle without cutting the wires off your spool.

If one or more wires in your bundle is a different size than all the others, the last method is preferred.

John


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: Mr Red
Date: 09 Dec 05 - 09:54 AM

We found a sheet from a company called Vactite

it lists the ratio of wire to hole diameters for a given number wires.

The ratio varies from 2 at 2 (obvious) to 9 for 61 wires and looks to gently increase almost linearly thereafter but no data listed.

so the our spreadsheet is now complete. But we figured the easiest way to find out is to throw a handfull of ball bearings into rings of given diameter and shake. Pick off the proudest and count.

Now the big one - how many banjo players can you fit on the point of a pin.......................


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: GUEST
Date: 09 Dec 05 - 10:37 AM

you guys are awesome. I cannot believe something so off-topic got so many useful answers. wow.


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: Paco Rabanne
Date: 09 Dec 05 - 10:53 AM

Don't forget about the co efficient of linear expansion!


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: TheBigPinkLad
Date: 09 Dec 05 - 02:22 PM

Don't forget about the co efficient of linear expansion!

That's how you freeze the balls off a brass monkey!


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: GUEST,Arne Langsetmo
Date: 09 Dec 05 - 04:48 PM

Hmmmm. IIRC, the "close packing" problem is actually a somewhat non-trivial problem in mathematics. For two dimensions, it's been proved for a while that hexagonal close packing is optimal for identical diameter circles, but for three dimensions (and spheres), the proof of the Kepler Conjecture hasn't even been established with certainty (there is a proof that's been offered, but it's still under evalutation by other mathematicians, AFAIK...).

When circles or spheres of different diameters are involved, the problem of minimum area or volume for packing gets far more complicated.

Cheers,


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: JohnInKansas
Date: 09 Dec 05 - 05:50 PM

The question as originally asked does imply a two dimensional situation, although one can easily imagine ways to make things more complicated.

For any "real world" wiring problem, the questions of whether the wires (or their insulation) well melt when you put too many through a tight hole, and whether the crosstalk between wires kills your circuit function are likely to be of about as much significance as whether the hole is the "minimum geometrically possible" size.

John


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: GUEST,Arne Langsetmo
Date: 09 Dec 05 - 06:23 PM

John in Kansas:

Yes, but the original question did ask for mathematicians....   ;-)

Cheers,


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: JohnInKansas
Date: 09 Dec 05 - 09:59 PM

Arne -

If the origional questor had been an engineer, he'd a known better...

But isn't there a song about "Thanks for the Algorithms"?

John


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Subject: RE: BS: mathematicians &/or engineers a - puzzle
From: The Fooles Troupe
Date: 09 Dec 05 - 10:13 PM

"Now the big one - how many banjo players can you fit on the point of a pin....................... "

That's dead easy - the same answer as the answer to the original medieval question about angels on the head of a pin...

As many as can!


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