"An inch of ice on a power line can add 500 pounds of weight." Help me understand this

Factual Questions
1

During the ice storm that just ended today, the local news station and paper advised people that an inch can add 500 lbs. of weight, and this is why poles and cables sometimes fail.

The numbers don’t make sense to me, though.

Suppose the poles are spaced 40 meters apart, and to make it easier, instead of one inch we’ll say 3cm, and that the cross section of ice is 9cm, which seems extremely generous.

Excluding the additional length added by the fact that cables sag a bit between the poles, this is what I come up with:

9cm^2 (cross section) x 4000cm = 36000cm (length of cable).

Let’s be generous again and assume that ice and water weigh the same:

36 (liters of water) x 2.2 = ca. 79 lbs, much less than 500.

How do they get to 500? I know, I did assume a ideally taut cable, which would be significantly shorter, but then I left out the fact that ice has about 9/10 of the weight of water.

Are the cables much thicker and wider than I realize?

2

Ice melts and refreezes. It won’t be distributed smoothly around the cable. There will be myriad icicles, which will add considerable weight.

3

Should there be a factor of pi in there somewhere?

What are you taking as the original radius of a power line? If that radius is 1 centimeter, an inch all around will mean an area of ice pi*(3^2-1^2) or 8 pi. That gets you up to almost half of 500 lbs.

4

It seems one cubic foot of ice is 57.2 pounds so you’d need 8.74 cubic feet of ice to get 500 pounds.

I guess we need to define “power line”. Is this the poles in your neighborhood or those giant towers from the power plant? Maybe the giant towers could get that much on one line between the towers but I can’t see it coming close on a neighborhood pole.

I know the OP specified 40m between poles but do we know that is what the local news had in mind?

This:

Or this:

5

I, too, think that pi needs to figure into your calculation. Also,

Multiply times eight, if your power lines look like this.

6

Using Google maps, I measured the distance between power poles in my neighborhood. They average out to slightly more than 150’ (~46m), not 40m.

7

The OP did pull the 40m figure out of his ass. He says so, probably for ease of calculation. Not something to be criticized - close enough for back of the envelope math.

8

If they are talking ab out the power lines between high voltage towers, the distance is roughly 450-550 meters, not 40. Standard power lines are 40m apart in the city, but rurally typically more like 100m.

9

It’s also not clear what “an inch of ice” means. An inch piled onto the top surface of the line? An inch-thick sheath of ice completely surrounding the line?

Combine that with the unspecified length of line, and the figure is basically completely meaningless.

10

I could see an engineering figure misquoted during a newscast weather segment. Like maybe the 500 pounds is tension force including the extra wind loading when it whips around or is some max tolerance of the pole.

11

Yeah, that sounds plausible.

When in doubt, assume the reporter screwed up the story. You will rarely be wrong.

12
13

Am I the only one to note that there are multiple lines between the poles?

14

I’ve personally had a mature, robust, healthy tree fall down in my driveway because of less than a tenth of an inch of ice accumulation on it during an ice storm about ten years ago.

It was a good thing I parked on the street the night before.

15

Nope:

16

Lay the math out in Excel so you can understand what all the factors are, and what all the intermediate steps are. Doing this also allows you to change the input variables and see how it affects the output.

I checked the overhead lines near my house, and they’re kind of like the first picture in @Whack-a-Mole 's post upthread:

I went on Google maps and checked the distance between poles in my neighborhood. So here are my inputs:

Number of cables: 8
distance between poles: 60 meters
cable diameter: 0.02 meters
thickness of ice layer: 0.0254 meters (assume uniform thickness around circumference of each cable)
ice density: 900 kg/m^3

Result:
ice volume per line: 0.217 m^3
ice weight per line: 196 kg (430 lb)
ice weight per pole 1565 kg (3443 lb)

So by my math, an inch of ice on everything would burden each line with 430 pounds, not far from what the OP was questioning. With multiple lines, each pole sees an extra 3443 pounds of weight. Not surprising that they simply break in heavy icing conditions. At a very shallow sag angle, an extra 430 pounds of weight means a lot of extra tension in the cable.

Cross-country high-voltage transmission lines are thicker and longer. This one is 0.04 meters in diameter, and looking at Google Map again, I see span lengths of ~200 meters on the high-voltage lines down the road from me. Putting that into my Excel math, I see that each line would have 2067 pounds of ice on it. It looks like there are maybe six high-voltage lines on standoffs, and two thinner lines on top of the towers. So that’s well over 12,000 pounds of extra weight per tower.

17

In the famous ice storm of 1998 that brought chaos to Ottawa and Montreal, the ice was thick enough that a large number of the transmission towers bringing power to Montreal crumpled, leaving it with severe power supply problems and blackouts. (IIRC, they said at one point only 1 of the dozen or more high voltage lines into Montrwal was still up.) I suppose with those metal girder towers, the weight of the ice on the tower itself was an additional factor.

18

I was assuming the ice mostly sits on top, as I’ve seen it do on tree branches. An inch is ~2.5cm, so I just rounded it up to 3cm and assumed the equivalent of a square cross section, giving 9cm^2. Of course I realize it couldn’t actually be a square cross section, but I was just using that to get an area for estimation purposes.

I can see that an inch of ice all the way around the cable would be a lot more than that. This is probably the piece I was missing, plus the addition of icicles over time.

19

For a short time, I used to photograph and categorize distribution poles for the local utility. So, local power lines, not high voltage transmission lines. And while 40 meters is probably a good guess for an average in town, they can be much further apart, especially in rural areas. 150+ meters or more isn’t unheard of.

Also, they are probably thicker cables than you first thought. 1000 MCM cable is exactly 1 inch in diameter, and while that’s pretty large for distribution lines, 250 MCM is a reasonable gauge, and that’s a half inch diameter.

Finally, it’s kind of a vague statement. They may be talking about adding weight to the poles on either side, which after all are what hold up the cables. In which case you have to double or triple your numbers (or more) to account for multiple cables per span.

While “weight” generally means “subject to gravitational force,” pounds are used to measure other forces too. And the wind forces on the line will increase considerably as the ice makes their cross section grow.

20

FWIW my image of ice and power lines is not much on top or even circumferential like a spherical cow but curtains of ice hanging off.