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Physics and Folly: This is not the butterfly effect



Physics and Folly applies real world science to familiar and fantastic situations. Discover the answers no one has heard, to the questions no one ever asked.

I’m sure everyone here is familiar with the butterfly effect. Somewhere on an island nation in the Pacific, a butterfly flaps its wings. The tiny disturbance of air propagates outward, changing the surrounding atmospheric conditions by an almost indescribably small amount but just enough so a certain puff of wind catches a bit more of the warm ocean spray, becoming slightly warmer and wetter, rising and causing more air to follow suit, until a rising mass of warm, wet air forms into a storm cloud. This cycling of warm air continues, the tropical storm growing larger and larger until we’re all watching the news, secretly (and somewhat morbidly) rooting for the hurricane as some coastal town in Florida gets uprooted by the forces of Mother Nature.

Or maybe you’re a better person than me, and you don’t root for the destructive forces of nature to prevail; either way, your feelings don’t cause hurricanes. But really, neither do butterflies.

But could they?

Let’s say we have some way of coordinating a giant flock1 of butterflies, and we get them all to flap at the same time, pushing a large body of air in a circular motion. We’ll remember to align this spin with the Coriolis effect counterclockwise in the northern hemisphere, and clockwise down south. If we’re really going to try this, how big does our flock need to be?

Cyclone Tracy was a tropical cyclone that hit the small city of Darwin, Australia on Christmas Day, 1974. It absolutely devastated the city of nearly 50,000 people with wind gusts well over 200 km/h, leaving over half of the population homeless and in need of evacuation. The interesting application to our case is that Cyclone Tracy was absolutely miniscule for a powerful cyclone less than 100 km in diameter. The entire cyclone could have fit inside the eye of a large cyclone.

So then, say we fill up a Cyclone Tracy-sized volume (after all, cyclones are usually about 15 kilometres tall, and, being made of matter, occupy three dimensions) with an enormous, dense cloud of butterflies. And I know “cloud” definitely isn’t the right terminology here, but if we’re going to maximize the number of butterflies, some quick math tells us that there is space for roughly 5000 monarch butterflies in every cubic metre, so I think the word “flock,” and the even more technically correct term “swarm,” stops applying.

This is a lot of butterflies. A little over four hundred million billion, to be precise. Just for fun, let’s say we centre our cloud of butterflies over the city of Darwin. Now, if each one of those butterflies flaps its wings in a clockwise direction, the wind speed generated is a measly seven kilometres per hour. You see, after all that, a butterfly can only fly at about nine kilometres per hour. So, if there’s a stationary butterfly pushing air backwards, it’ll only push the air at a maximum of, well, nine kilometres per hour. So, unfortunately, we do not get a hurricane. However, we do get something.

The citizens of Darwin look up into the sky, which is now black all the light is blotted out by millions of billions of butterflies. They feel a gentle breeze as all of the butterflies begin to flap in unison. And then their ears pop.

You see, four hundred million billion butterflies is heavy and this dense cloud of butterflies we’ve created weighs nearly four times as much as the surrounding air. The column of butterfly-filled air descends quickly on Darwin (no amount of butterfly flapping can stop it), increasing the pressure temporarily to above six atmospheres rupturing eardrums, breaking windows, and causing a sickness previously limited to divers: nitrogen narcosis; the air actually becomes toxic due to the extreme pressures, although not severely enough to be immediately fatal.

Near the edges of the butterfly cloud, the wind speeds rise. A 360-degree jet of butterfly-filled air is shot out from under our collapsing column of butterflies, the wind speeds reaching over 500 kilometres per hour, packing an extra punch due to the high butterfly density. A wide swath of complete destruction ensues; the winds scour the land clean in a giant ring tens of kilometres wide around the city of Darwin. The city would mostly be fine, if it weren’t buried under a hundred metres of dead butterflies. The world will remember this event as one of the worst disasters in history. The cyclone in 1974 killed 65 people. But from our butterfly storm, there’d be very few survivors.

1 Actually, the search engine that determines the truth of all statements tells me that a group of butterflies is actually called a kaleidoscope; or a swarm. Also, I could probably ask anyone in the department next to mine, and they’d have told me the same thing. But I’m a physicist! Be happy I don’t refer to everything as coming in “bunches.” Flocks is a good word; I’m sticking to it.

Image: Simer Haer/The Cascade

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