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An Idea About UmbrellasHere's another practical idea I discovered by accident, like the cure for hiccups.
You know how when it's windy and you're holding an umbrella, you have to fight to keep the wind from blowing it out of line? Well, if instead of holding the umbrella by the handle, you hold it by the shaft, up near the top, guess what? The force of the wind will act to keep it in line.
In the picture, you have to hold it somewhere around (or above) point B—which, conveniently, is near the center of mass, and makes the umbrella nice and wieldy.
That's the whole idea. Everything else I have to say is just some thoughts about why it works, but it's all academic, because I already know by observation that it does work.
It's pretty simple to understand, actually. If you hold the umbrella at point A, it's obvious that being in line is a stable equilibrium; and if you hold it at point D, it's obvious, or at least familiar from experience, that being in line is an unstable equilibrium. So, there must be a point in between where the behavior changes; all you have to do is hold the umbrella somewhere above that point.
I like to imagine what happens when the wind is blowing sideways. The behavior at points A and D becomes even clearer, and the behavior at point C becomes clear too. All the wind-catching surface is above point C, so the torque is all in one direction—the wrong one.
That argument sounds good, and gives more or less the right answer, but it's not actually correct. For photons hitting a black umbrella and being absorbed, the argument works just fine—the horizontally-moving photons produce a horizontal force, and the torque is all in one direction. For photons hitting a mirrored umbrella, though, already the force has a vertical component, and some of the torque is in the other direction; and for wind hitting an umbrella, well, I don't even know how to figure out the force, except to say that it's a problem of fluid dynamics.
And, it's not a trivial problem, either. For one thing, the total force doesn't even vary smoothly with angle. If you tilt the umbrella just a little too far, the wind suddenly jumps inside and grabs hold of it. For another thing, if you think about it, an umbrella is sort of like a little round airplane wing, and you have to do all kinds of numerical work to understand those.
Words Are Ideas
@ October (2003)