### Author Topic: 15 miles of wire: guess the volume  (Read 15603 times)

#### Chew

• Jupiter
• Posts: 545
##### 15 miles of wire: guess the volume
« on: May 09, 2012, 04:13:01 PM »
What is your gut intuitive guess for the volume occupied by 15 miles of wire? Assume 26 AWG (.405 mm diameter) and the insulation is as thick as the wire itself; e.g. the total diameter is 1.215 mm.

I guessed before I calculated it and I was way off.

#### DataCable

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• Posts: 138
##### Re: 15 miles of wire: guess the volume
« Reply #1 on: May 09, 2012, 04:39:29 PM »
210 cubic feet.
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#### Valis

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##### Re: 15 miles of wire: guess the volume
« Reply #2 on: May 09, 2012, 05:26:28 PM »
I didn't get any intuitive grasp of the volume, so I did an order of magnitude calculation in my head. The process is something like this:

15 miles is roughly 24 km (10*1.6=16, add half of that and it's 24).
The area of a cross-section for the wire is about 3*0.6^2, or 3*0.36, or about 1 mm^2, which is 10^-6 m^2.
Finally, the volume is 24*10^3*10^-6 = 0.024 (m^3), or 24 liters. That's the lower estimate, so my guesstimate would be less than 30 l, which would be a bit over one cubic feet.

#### Echnaton

• Saturn
• Posts: 1490
##### Re: 15 miles of wire: guess the volume
« Reply #3 on: May 09, 2012, 05:40:03 PM »
My top of the head estimations came out this way 15 miles X 1.6 gives about 24 KM of wire.  If wire was say 1 mm in diameter then 1000 strands could be laid side to side within 1 meter. If it were in 1 m long cuts, then 1 km of wire would be 1000 pieces or 1/1000 of a m3.  So the whole thing would be 24/1000 of a m3.

So with wire at 1.2 mm my guess is it would be about 1.2^2 * 24 or about 36/1000 cubic meters  A web site tells me that is about 1.25 cubic feet.

« Last Edit: May 09, 2012, 05:52:08 PM by Echnaton »
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#### Ranb

• Earth
• Posts: 210
##### Re: 15 miles of wire: guess the volume
« Reply #4 on: May 09, 2012, 05:48:12 PM »
I got .99 cubic feet using the volume of a cylinder 0.0478 inches wide by 15 miles high.  I wasn't going to guess this one; I used a calulator.

Ranb

#### Echnaton

• Saturn
• Posts: 1490
##### Re: 15 miles of wire: guess the volume
« Reply #5 on: May 09, 2012, 06:05:11 PM »
I guessed before I calculated it and I was way off.

I didn't guess but was surprised at the results of my volume estimation was so small.  I could never have done this in imperial units, it is so much easier to work in metric
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#### Bob B.

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##### Re: 15 miles of wire: guess the volume
« Reply #6 on: May 09, 2012, 07:09:01 PM »
I didn't get a chance to post my guess, but I was going to say about two cubic [feet] at the most.

Edited to add the word "feet".
« Last Edit: May 12, 2012, 06:07:33 PM by Bob B. »

#### gillianren

• Uranus
• Posts: 1963
##### Re: 15 miles of wire: guess the volume
« Reply #7 on: May 09, 2012, 07:37:38 PM »
I so have no guess for that.
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#### ka9q

• Neptune
• Posts: 3010
##### Re: 15 miles of wire: guess the volume
« Reply #8 on: May 09, 2012, 07:55:53 PM »
There are of course many different wire sizes. AWG 18 wire has a diameter of about 1 mm. I think most of the signal wiring was smaller than that precisely to save weight, but the power wiring would undoubtedly have been much heavier. Apollo's primary power supply was 28V DC, a low voltage that requires fairly heavy conductors to carry a lot of power. Some of it was also distributed as 3-phase 115V 400 Hz AC, but it was mainly for devices that need AC (like induction motors) rather than to lighten the wiring. In those days, AC inverters were one of the heavier and less reliable subsystems on a spacecraft.

Copper is a dense element, almost 9x as dense as water. A liter of the stuff would have a mass of almost 9 kg; one cubic foot (28.3 L) would be 253 kg! Of course, part of each wire is the much less dense insulation, probably Teflon.

Modern electronics allows spacecraft wiring to be vastly reduced in weight, bulk and complexity, also simplifying connectors. That's important because they're still among the most unreliable of all electrical components.

One advantage of modern electronics is lower power consumption, allowing lighter power wiring. Power semiconductors now make DC-DC conversion easy and efficient, so it's easier to use higher voltages for more efficient transmission over greater distances. The ISS, for example, operates its solar arrays at about 160V DC, and utility power is 124.5V DC. (Of course, the ISS is much larger than Apollo.)

But the real breakthrough in wiring has come from digital electronics. Every spacecraft has zillions of sensors and control devices all over the place, and in Apollo each required its own dedicated wiring and connector pins.

The wiring harnesses were massive, hard to make and easy to damage (remember Apollo 1). Redundancy was hard to provide. Analog signals often had to go significant distances, creating noise problems. Quite a bit of wiring passed between the CM and SM, or between the two stages of the LM, requiring large explosively-driven "guillotine" cutters for separation. That in turn required "deadfacing" relays and switches to disconnect each line and prevent a short circuit when it was cut.

Now you make a high speed digital bus with just a few wires, route it all over the spacecraft and attach it through bus interface electronics to each sensor or control. Being digital and usually differential (a balanced twisted pair), the bus is inherently much less susceptible to noise. Analog sensor signals are converted locally to digital before going on the bus. The reduction in wiring complexity is so great that it becomes easy to add another bus for full redundancy.
« Last Edit: May 09, 2012, 08:26:32 PM by ka9q »

#### Not Myself

• Earth
• Posts: 217
• Unwanted Irritant
##### Re: 15 miles of wire: guess the volume
« Reply #9 on: May 12, 2012, 01:36:02 PM »
I didn't get a chance to post my guess, but I was going to say about two cubic at the most.

Hard to be wrong, if you don't specify the units

My guess was much too high.
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#### Bob B.

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##### Re: 15 miles of wire: guess the volume
« Reply #10 on: May 12, 2012, 06:06:39 PM »
I didn't get a chance to post my guess, but I was going to say about two cubic at the most.

Hard to be wrong, if you don't specify the units

Oops.  That should have been two cubic feet.

#### Not Myself

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##### Re: 15 miles of wire: guess the volume
« Reply #11 on: May 12, 2012, 06:13:58 PM »
I didn't get a chance to post my guess, but I was going to say about two cubic at the most.

Hard to be wrong, if you don't specify the units

Oops.  That should have been two cubic feet.

Then that's actually a pretty good guess.  Substantially better than mine
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#### Chew

• Jupiter
• Posts: 545
##### Re: 15 miles of wire: guess the volume
« Reply #12 on: May 12, 2012, 06:26:07 PM »
Then that's actually a pretty good guess.  Substantially better than mine

Was it worse than 10 cubic feet? That was my guess.

#### Not Myself

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##### Re: 15 miles of wire: guess the volume
« Reply #13 on: May 12, 2012, 06:36:33 PM »
Was it worse than 10 cubic feet? That was my guess.

I went with a cubic metre
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#### Chew

• Jupiter
• Posts: 545
##### Re: 15 miles of wire: guess the volume
« Reply #14 on: May 12, 2012, 09:13:09 PM »
Well, now I don't feel so bad.