Why stranded wire has 7 or 19 strands

[Analog Kid]

Someone posted something here, I think it was @TimFox but I forget exactly where, pointing out that stranded wire has 7 or 19 strands (or more for larger sizes).

Those numbers aren't arbitrary:

[SteveThackery]

I'm away from home but I think I have some 16-strand and 24-strand wire as well.

[TimFox]

When looking at wire tables and catalog pages, I found that 7 and 19 were the most common for regular stranded wire.

[jpanhalt]

INdeed they aren't.  You want close packing and somethig that is sort of round (usually).

Grok3:

https://grok.com/share/c2hhcmQtMg%3D%3D_45933a4e-5ed1-4f62-b6a1-50816df7b06f

When packing round wires into a bundle, certain numbers of wires naturally form an approximately round cross-section due to their geometric arrangement. These are often referred to as "magic numbers" in wire bundling, corresponding to highly symmetric configurations where the wires pack tightly in a hexagonal or near-hexagonal lattice. Below are the key numbers of round wires that produce an approximately round bundle:

- **1 wire**: A single wire is trivially round.
- **7 wires**: Six wires surround a central wire in a hexagonal arrangement, forming a compact, nearly circular bundle.
- **19 wires**: This adds a second layer of 12 wires around the 7-wire bundle, maintaining a roughly hexagonal and circular shape.
- **37 wires**: A third layer of 18 wires surrounds the 19-wire bundle, keeping the bundle approximately round.
- **61 wires**: A fourth layer of 24 wires is added, continuing the hexagonal packing pattern.
- **91 wires**, **127 wires**, **169 wires**, etc.: Each additional layer (30, 36, 42, etc., wires) maintains the roughly circular shape, following the formula for hexagonal packing.

The general formula for the number of wires in a hexagonal bundle with \( k \) layers around a central wire is:
\[ N = 1 + 6 \sum_{i=1}^{k} i = 1 + 3k(k+1) \]
where \( k \) is the number of outer layers. For example:
- \( k=1 \): \( N = 1 + 6 \cdot 1 = 7 \)
- \( k=2 \): \( N = 1 + 6 \cdot (1 + 2) = 19 \)
- \( k=3 \): \( N = 1 + 6 \cdot (1 + 2 + 3) = 37 \)
- \( k=4 \): \( N = 1 + 6 \cdot (1 + 2 + 3 + 4) = 61 \)

At some point (e.g., welding cable), I am not sure that sequence makes a difference.  I have some 2-0 welding cable.  You are free to come to Cleveland and count the number of strands.

Google AI

The number of strands in a very flexible 2/0 welding cable can vary depending on the specific manufacturer and type of cable (e.g., Class K or Class M).
Here's a general overview:
Class K Welding Cable:
Typically has a high strand count, which contributes to its flexibility.
Strands are usually made of 30 AWG copper wire.
Examples:
1248 strands
1254 strands
1196 strands
1330 strands
1316 strands
1235 strands
1196 strands
Class M Welding Cable:
Offers even greater flexibility than Class K.
Uses finer strands, usually 34 AWG.
Example:
3325 strands
3300 strands

[themadhippy]

but I think I have some 16-strand and 24-strand wire as well

yep both are fairly common,16/0.2 as a hook up wire and 24 strand is often flogged for speaker cables

[TimFox]

Instead of AI, go to the source:  the Belden wire catalog  https://assets.belden.com/m/1b3bf80994eb0f51/original/Cabling-Solutions-for-Industrial-Applications-Catalog-Belden-09-2020.pdf
Page 243 has wire gauges from AWG36 to AWG10 for single wires.  The vast majority are either 7 or 19 strands, but there are some with 10, 26, 37, 42, 65, or 105 strands.
If you peruse pp 108 to 227 for cables, almost all of the stranded wires in the cables are 7 or 19.
In between 227 and 243, you will find "cordage" (power cables) that typically use finer stranding.

[tooki]

Someone posted something here, I think it was @TimFox but I forget exactly where, pointing out that stranded wire has 7 or 19 strands (or more for larger sizes).

Those numbers aren't arbitrary:

(Attachment Link)

While those are certainly the most common, and for good reason, there’s a ton of alternatives.

By pure coincidence, I came across this table of AWG stranding last week and bookmarked it. I don’t think I’ve ever seen such a comprehensive one:
https://www.maeden.com/en/awg-wire-gauge-chart

(Though it appears to be missing AWG 1 and 0, oddly!)

[tooki]

INdeed they aren't.  You want close packing and somethig that is sort of round (usually).

Grok3:

https://grok.com/share/c2hhcmQtMg%3D%3D_45933a4e-5ed1-4f62-b6a1-50816df7b06f

When packing round wires into a bundle, certain numbers of wires naturally form an approximately round cross-section due to their geometric arrangement. These are often referred to as "magic numbers" in wire bundling, corresponding to highly symmetric configurations where the wires pack tightly in a hexagonal or near-hexagonal lattice. Below are the key numbers of round wires that produce an approximately round bundle:

- **1 wire**: A single wire is trivially round.
- **7 wires**: Six wires surround a central wire in a hexagonal arrangement, forming a compact, nearly circular bundle.
- **19 wires**: This adds a second layer of 12 wires around the 7-wire bundle, maintaining a roughly hexagonal and circular shape.
- **37 wires**: A third layer of 18 wires surrounds the 19-wire bundle, keeping the bundle approximately round.
- **61 wires**: A fourth layer of 24 wires is added, continuing the hexagonal packing pattern.
- **91 wires**, **127 wires**, **169 wires**, etc.: Each additional layer (30, 36, 42, etc., wires) maintains the roughly circular shape, following the formula for hexagonal packing.

The general formula for the number of wires in a hexagonal bundle with \( k \) layers around a central wire is:
\[ N = 1 + 6 \sum_{i=1}^{k} i = 1 + 3k(k+1) \]
where \( k \) is the number of outer layers. For example:
- \( k=1 \): \( N = 1 + 6 \cdot 1 = 7 \)
- \( k=2 \): \( N = 1 + 6 \cdot (1 + 2) = 19 \)
- \( k=3 \): \( N = 1 + 6 \cdot (1 + 2 + 3) = 37 \)
- \( k=4 \): \( N = 1 + 6 \cdot (1 + 2 + 3 + 4) = 61 \)

At some point (e.g., welding cable), I am not sure that sequence makes a difference.  I have some 2-0 welding cable.  You are free to come to Cleveland and count the number of strands.

The highest strand count wire I’ve ever held was a piece of Stäubli Sili-S 50 (that’s 50mm² (AWG 1) ) with 13,024 strands!
https://www.staubli.com/ch/en/electrical-connectors/products/t-m-products/cables-and-multi-strand-wires/silicone-multi-strand-wires/silistrom.html

[jpanhalt]

Instead of AI, go to the source:  the Belden wire catalog  https://assets.belden.com/m/1b3bf80994eb0f51/original/Cabling-Solutions-for-Industrial-Applications-

Isn't the real source Pythagoras, Plato, Euclid, Theaetetus, or some other Greek from over 2,000 years ago?    Close packing of circles to give a regular polyhedron is hardly a 21st century epiphany.

[TimFox]

Instead of AI, go to the source:  the Belden wire catalog  https://assets.belden.com/m/1b3bf80994eb0f51/original/Cabling-Solutions-for-Industrial-Applications-

Isn't the real source Pythagoras, Plato, Euclid, Theaetetus, or some other Greek from over 2,000 years ago?    Close packing of circles to give a regular polyhedron is hardly a 21st century epiphany.

My comment was "When looking at wire tables and catalog pages, I found that 7 and 19 were the most common for regular stranded wire."
That does not imply that other packings are mathematically impossible, just what I can buy from Belden and competitors.

[Analog Kid]

Instead of AI, go to the source:  the Belden wire catalog  https://assets.belden.com/m/1b3bf80994eb0f51/original/Cabling-Solutions-for-Industrial-Applications-

Isn't the real source Pythagoras, Plato, Euclid, Theaetetus, or some other Greek from over 2,000 years ago?    Close packing of circles to give a regular polyhedron is hardly a 21st century epiphany.

Well, it was to me.

[Analog Kid]

In @Tooki's comprehensive table, all the non-7/19, etc., strand counts are for "bunched" as opposed to "concentric" (i.e., packed) configurations.

[vk6zgo]

I'm away from home but I think I have some 16-strand and 24-strand wire as well.

I'm quite sure I can dig up some 3/029, 10/010 or 23/0076 if I look around in my junk box..

[TimFox]

I'm sure you can.
All the hook-up wire I have bought in the last few years was either 7 or 19 strands, depending on overall diameter, but I have seen finer strandings in my long life.
I once bought 1200/50 Litz wire (1200 strands of AWG50), but that was wound in several serves for practical reasons.

[tooki]

In @Tooki's comprehensive table, all the non-7/19, etc., strand counts are for "bunched" as opposed to "concentric" (i.e., packed) configurations.

You missed 37 and 61, which are also listed.

[AVGresponding]

Someone posted something here, I think it was @TimFox but I forget exactly where, pointing out that stranded wire has 7 or 19 strands (or more for larger sizes).

Those numbers aren't arbitrary:

(Attachment Link)

While those are certainly the most common, and for good reason, there’s a ton of alternatives.

By pure coincidence, I came across this table of AWG stranding last week and bookmarked it. I don’t think I’ve ever seen such a comprehensive one:
https://www.maeden.com/en/awg-wire-gauge-chart

(Though it appears to be missing AWG 1 and 0, oddly!)

Yep, and it progresses as you'd expect





Quadrant cables have a different formula, but they follow one too

[Analog Kid]

From The Art of Electronics: The x-Chapters:



Notice the penta-wedge construction, clearly visible.

[mzzj]

Notice the penta-wedge construction, clearly visible.

Wedges are supposedly slightly insulated from each other to reduce eddy current losses.
Also known as Milliken Conductor.

[coppercone2]

it looks like it milks the power company really good

[TimFox]

In a lab course at University of Chicago, I once used the actual apparatus built by Millikan for his oil-drop experiment to measure the electron’s charge, for which he won his Nobel prize.
Milliken developed this conductor about 25 years later.

[JacobPilsen]

BTW, there are DIN VDE 0295 / IEC 60228 too:
https://scankab.com/media/1964/din-vde-0295-eng.pdf

[Vtile]

Well most of the things are answered already.

The 7 (or 6+core) and 19 happens to be the "magic number" to form a _tight_ (and roundish) cross sectional pattern with identical diameter strands. This is then important for two reasons first for extrusion process where the sheating (insulation) is formed so the insulation has uniform properties (no slack wires closer to the surface etc.) and for the twisting (if used) where the wire core is given a slight helical twist to increase the bending properties ... again uniformity. Third might be the eyelet drawing if used, there a slack in the bundle would couse issues in form of eg. tension variations and possible lumbs by uneven lenght of wires etc.

The poor old wire is highly economically optimised product and also highly standardised one.

Every strand has to be laid on the wire bundle in controlled manner in the production (usually tension), this counts for how many machines you do need to the strands, the less is better (more profit).

Also the tight (or snugg) lay on the bundle will give more uniform twisting of the wire (more uniform torsion properties).

I'm not an expert, but here are some more food for thoughts.

[tggzzz]

Instead of AI, go to the source:

Yes indeed!

In times to come that concept will become a useful "touchstone question"[1] that can be used to distinguish experienced professionals from wannabe amateurs - in any field

[1] i.e. a simple easy question, the answer to which not only illuminates a wide part of the subject, but also indicates what should be done.

[tggzzz]

From The Art of Electronics: The x-Chapters:

(Attachment Link)

Notice the penta-wedge construction, clearly visible.

Understanding why it is "impossible" is illuminating.

You can't see the caption because the picture was (unfortunately) attached rather than appended. My apologies for allowing that to make the sub-thread difficult to follow.

[Analog Kid]

From The Art of Electronics: The x-Chapters:

(Attachment Link)

Notice the penta-wedge construction, clearly visible.

Understanding why it is "impossible" is illuminating.

You can't see the caption because the picture was (unfortunately) attached rather than appended. My apologies for allowing that to make the sub-thread difficult to follow.

Well, just ask and ye shall receive:



I attached it rather than "appended" it (what is that, a hyperlink?) because I scanned the pic and it exists on my hard drive, not out in "cyberspace".