engineering, physical experiment, physics, short, silly

Crappy Plastic Bags

Plastic grocery bags suck, and for many reasons. They’re light enough to be carried away by a particularly motivated fruit fly, which means they turn into litter very easily. And since they shred easily into tiny, tiny pieces, they’re probably an excellent source of plastic pollution, which is looking more and more like a major problem every day.

Luckily, the flimsy grocery bags I’m talking about are made of LDPE: low-density polyethylene. And while LDPE isn’t exactly the kind of thing you wanna put on a sandwich, as far as plastics go, it’s relatively mild. Chemically, it’s very similar to wax. Unlike, say PVC and polystyrene, LDPE is a lot less prone to breaking down into scary aromatic and chlorinated hydrocarbons. Plus, it’s not full of the slightly scary plasticizers found in many other plastics.

But my real issue with grocery bags is that they suck. They’re pretty shitty at the one thing they’re made for, which is holding groceries. This morning, on my way to work, I stopped to get some milk. The jug couldn’t’ve weighed more than three or four pounds, but that didn’t stop it from bursting right through the bottom and falling on the floor. I realize I’m making myself sound like a cranky old man when I say this, but I don’t remember plastic bags being quite that fragile when I was younger. And I would’ve noticed if they were, on account of the number of times I tied a grocery bag to a string and tried to fly it like a kite. They didn’t last a long time doing that, but I’d be willing to wager the modern ones would rip before you could get the kite string tied on.

But I’m going to do what crotchety old men never seem to: I’m going to back up my whining with evidence. Here is my evidence.

Crappy Plastic Bag

I’m sorry for the godawful picture, but it gets the point across. What you’re looking at is a pair of lower-mid-range digital calipers, which are pretty handy for measuring things to decent accuracy and precision. The calipers are clamped down around a flat strip of grocery-bag material which has been folded three times, giving eight layers. In the name of fairness, let’s assume that the actual thickness is 0.095 millimeters: just barely thin enough that the calipers didn’t round it up to 0.1. Divide 0.095 by eight, and you get 0.011875 millimeters, or 11.875 microns. For comparison, a human hair is usually quoted in the neighborhood of between 80 and 120 microns. The one I just pulled out of my own scalp (you’re welcome) measured 50 microns. Measuring ten sheets of printer paper and dividing by ten gave me 102 microns. A dust mite turd is apparently between 5 and 20 microns. (Wikipedia says that this book says so, and while I’ll do a lot of things for my readers, I’m not reading a thousand pages to find a passage on dust mite poop.) Human cells usually range between 10 microns and 50 microns (though some get a lot larger).

To get some more perspective, an American football field is 150 yards long and 55 1/3 yards wide. If we were to cover an entire football field with a single layer of grocery bag material, the whole damn thing would only weigh 162.9 pounds (73.9 kilograms). That’s less than me. Less than the average American football player. Hell, that’s less than my dad, and he’s built like a lean twig. Imagining the horrendous suffocation hazard that sheet will pose when it inevitably blows into the stands is making me nervous.

Now, this is only one data point, admittedly. I didn’t measure the thickness of plastic bags when I was a kid (I was too busy making kites out of them, or walking around the house with a mirror pretending I was walking on the ceiling). But that seems excruciatingly thin to me. In order for a soap bubble to be iridescent, it must undergo thin-film interference. This means that, in order to reflect violet light (the shortest wavelength visible to the eye: around 380 nanometers), the bubble can be no thicker than 71 nanometers. My grocery bag is only 167 times thicker than a damned soap bubble. No wonder my groceries fell out this morning, and no wonder every time I go to the hardware store, something pokes a hole in the bag and makes my tools fall out.

engineering, math, physics, thought experiment

The Treachery of Plumb-Lines

I’m pretty sure that’s my most pretentious article title to date, but really, the only pretentious thing about it is that it’s a Rene Magritte reference, because if you read it literally, that’s exactly what this article is about.

Imagine two skyscrapers. Both start from ordinary concrete foundations 100 meters by 100 meters, and each will be 1,000 meters high, when finished. We’ll call the first skyscraper Ruler, and the second skyscraper Plumb, for reasons I’ll explain.

Ruler is built exactly according to architectural specifications. Every corner is measured with a high-grade engineer’s square and built at precisely 90 degrees. Importantly, Ruler is constructed so that every floor is precisely 10 meters above the previous one, and every floor is 100 meters by 100 meters. This is done, of course, using a ruler. Because it’s kept so straight and square at every stage, Ruler is a very straight, square building.

Plumb, on the other hand, is kept straight and square using one of the oldest tricks in the architect’s book: the plumb-bob. True story: plumb-bobs are called that because, back in the day, they were almost always made of lead, and the Latin for lead is plumbus (or something like that; I took Latin in high school, but the teacher got deathly ill like two weeks in, so I never learned much). A well-made and well-applied plumb-bob is an excellent way to make sure something is absolutely vertical.

The builders of Plumb do use a ruler, but only to mark off the 10-meter intervals for the floors. They mark them off at the corners of the building, and they make sure the floors are perfectly horizontal using either a modified plumb-bob or a spirit level (which is largely the same instrument).

One might assume that Plumb and Ruler would turn out to be the exact same building. But anybody who’s read this blog knows that that’s the kind of sentence I use to set up a twist. Because Plumb was kept straight using plumb-bobs, and because plumb-bobs point towards the center of the Earth, and because the 100-meter difference between the east and west (or north and south walls) gives the bobs an angle difference of 0.009 degrees, Plumb is actually 11 millimeters wider at the top than at the bottom. Probably not enough to matter in architectural terms, but the difference is there.

Not only that, but Plumb’s floors aren’t flat, either, at least not geometrically flat. The Earth is a sphere, and because Plumb’s architects made its floors level with a spirit level or a plumb-bob, those floors aren’t geometrically flat: they follow the spherical gravitational equi-potential contours. Over a distance of 100 meters, the midpoint of a line across the Earth’s surface sits 0.2 millimeters above where it would were the line perfectly, geometrically straight. This difference decreases by the time you reach the 100th floor (the top floor) because the sphere in question is larger and therefore less strongly curved. But the difference only decreases by around a micron, which is going to get swamped out by even really small bumps in the concrete.

“Okay,” you might say, “so if you blindly trust a plumb-bob, your building will end up a centimeter out-of-true. What does that matter?” Well, first of all, if you came here looking for that kind of practicality, then this blog is just gonna drive you insane. Second, it doesn’t matter so much for ordinary buildings. But let’s say you’re building a 2,737-meter-long bridge (by total coincidence, the length of the Golden Gate Bridge). If you build with geometric flatness in mind, your middle pier is going to have to be 14.7 centimeters shorter than the ones at the ends. That’s almost the length of my foot, and I’ve got big feet. It’s not a big enough difference that you couldn’t, say, fill it in with concrete or something, but it’d certainly be enough that you’d have to adjust where your bolt-holes were drilled.

What’s the moral of this story? It’s an old moral that probably seems fairly ridiculous, but is nonetheless true: we live on the surface of a sphere. And, when it comes down to it, that’s just kinda fun to think about.