“Raindrops Are Not Shaped Like Raindrops” ends its physics with a promise. Drops don’t speed up the whole way down, it says: drag matches weight, so big drops fall at “nine or so metres a second”, and that is why the rain “can sting, but never cuts you deep”. It’s worth checking how close a call that is. Because without the air, rain would be lethal.
Rain clouds often float a couple of kilometres up. Something falling freely from that height, with nothing to slow it, keeps speeding up by about ten metres per second every second. Work it through and, by the time it reaches the ground, it’s doing about two hundred metres per second, around seven hundred kilometres an hour. A drop of water a few millimetres across at that speed would hurt badly. A heavy shower would be like being sandblasted. The only reason it isn’t is the air.
Here’s how the brake works. As a drop falls, it has to shove air out of its way, and the air pushes back. This push, called drag, depends very strongly on speed. For something the size of a raindrop moving quickly, drag grows roughly with the square of the speed: twice as fast means about four times the drag. So at the start of its fall, when the drop is slow, drag is tiny and gravity wins easily, and the drop speeds up. But as it speeds up, drag grows rapidly, until at some speed the upward push of the air exactly equals the downward pull of the drop’s weight. At that point the forces balance, and the drop stops speeding up. It carries on falling, but at a steady speed, called its terminal velocity. For a raindrop, this happens within the first few metres, or at most a few tens of metres, of its fall. After that, the remaining two kilometres don’t add any speed at all.
Now for the question the poem raised: why do big drops hurry while small ones creep? The answer is a matter of scaling, and it’s one of the most useful ideas in all of physics. A drop’s weight depends on how much water is in it, its volume, which grows with the cube of its width. Double the width, and the weight goes up eight times. But the drag depends on how much air the drop has to push aside, which goes with its cross-sectional area, the square of its width. Double the width, and the area goes up only four times. So a bigger drop has much more weight for each bit of area pushing against the air. To build up enough drag to balance it, it has to fall faster.
Because drag grows with the square of the speed, the terminal speed grows roughly with the square root of the drop’s size. A fine drizzle droplet, a fifth of a millimetre across, drifts down at less than a metre per second; you can barely feel it. A one-millimetre drop falls at about four metres per second. A big five-millimetre drop, near the largest size that survives, falls at about nine. And there the growth stops, because, as the poem says, drops much bigger than that are blown apart by the air into smaller drops, which fall more slowly. Nature has put a speed limit on rain.
That limit is why hail is a different story. Hailstones are solid, so they can grow far bigger without breaking up. A hailstone the size of a cricket ball has so much weight for its area that its terminal speed is well over a hundred kilometres an hour, which is why hail can smash windscreens and dent the roofs of cars, while even the heaviest monsoon downpour can only soak you.
The same scaling explains a lot of other things. It’s why a skydiver, much heavier for their area than a raindrop, reaches a terminal speed of roughly two hundred kilometres an hour, and why tucking into a head-down dive, to reduce the area, makes them much faster. It’s why a parachute works: a huge area for the same weight, and a terminal speed slow enough to land on. And it’s why an ant can fall from a tree and walk away. It’s so small that its weight is tiny compared with its area, its terminal speed is very low, and it simply drifts down.
So when the monsoon arrives and the drops sting your face, you’re feeling the result of a balance struck early in a two-kilometre fall: weight growing with the cube, drag growing with the square, and the air quietly applying the brakes on every drop at once.